Международная конференция студентов, аспирантов и молодых ...
09.04.2014 • Views
Share Embed Flag

Международная конференция студентов, аспирантов и молодых ...

Международная конференция студентов, аспирантов и молодых ...

Международная конференция студентов, аспирантов и молодых ...

SHOW MORE
SHOW LESS
ePAPER READ
DOWNLOAD ePAPER
phys.msu.ru

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

START NOW

F_`^mgZjh^gZydhgn_j_gpbyklm^_glh\ZkibjZglh\bfheh^uomq_guo<br />

ihnmg^Zf_glZevgufgZmdZf©Ehfhghkh\-2005»<br />

K_dpby©NbabdZª<br />

K[hjgbdl_abkh\<br />

Zij_ey]Nbabq_kdbcnZdmevl_l<br />

Fhkdh\kdbc]hkm^Zjkl\_ggucmgb\_jkbl_lbfF

^\_gZ^pZluc jZa \ Fhkdh\kdhf ]hkm^Zjkl\_gghf mgb\_jkbl_l_ ijh\h^beZkv<br />

F_`^mgZjh^gZy dhgn_j_gpby klm^_glh\ ZkibjZglh\ b fheh^uo mq_guo ih<br />

nmg^Zf_glZevgufgZmdZf©Ehfhghkh\ªHkh[mxlhj`_kl\_gghklv_cijb^Zehlhqlh<br />

hgZkhklhyeZkv\i_jbh^ijZa^gh\Zgbye_lg_]hx[be_yF=MGm`ghhlf_lblvqlh<br />

ba]h^Z\]h^jZkl_lqbkehmqZklgbdh\wlh]hnhjmfZgZmqghcfheh^_`b\wlhf]h^mbo<br />

[uehq_eh\_dijbq_fkfh]ebijb_oZlvb\uklmiblvklm^_glh\bZkibjZglh\ba<br />

^jm]bo ]hjh^h\ Jhkkbb b [eb`g_]h aZjm[_`vy H[s__ qbkeh ijbkeZgguo l_abkh\<br />

^hdeZ^h\ gZ k_dpbb khklZ\beh Ke_^m_l lZd`_ hlf_lblv dZd \ukhdbc mjh\_gv<br />

kh^_j`Zgby kZfbo ^hdeZ^h\ lZd b ij_djZkgh_ hnhjfe_gb_ [hevrbgkl\Z ba gbo Ih<br />

wlbf ihdZaZl_eyf dhgn_j_gpby ©Ehfhghkh\-ª gb \ q_f g_ mklmiZeZ fgh]bf<br />

©\ajhkeufªZgZeh]bqguff_jhijbylbyf<br />

Klm^_glu klZjrbo dmjkh\ ZkibjZglu b fheh^u_ khljm^gbdb bf_eb \hafh`ghklv<br />

\uklmiblvk^hdeZ^Zfbihkh[kl\_ggufj_amevlZlZfgZih^k_dpbyoho\Zlu\Zxsbo<br />

ijZdlbq_kdb \k_ Zki_dlu nbabq_kdhc gZmdb GZ dZ`^hc ih^k_dpbb<br />

ij_^k_^Zl_evkl\mxsbf kh\f_klgh k ijbkmlkl\mxsbfb khljm^gbdZfb nbabq_kdh]h<br />

nZdmevl_lZ [ueb \u^_e_gu emqrb_ khh[s_gby Z\lhju dhlhjuo gZ]jZ`^_gu<br />

]jZfhlZfbF=MGb`_ijb\_^_gubf_gZwlbofheh^uolZeZgleb\uomq_guo<br />

Rm]Zjh\:K–klm^dmjkZdZnwdki_jbf_glZevghcZkljhghfbb<br />

=juaeh\Z?

Ih^k_dpbyjZ^bhnbabdb 5<br />

J:>BHNBABD:<br />

Ij_^k_^Zl_evih^k_dpbb<br />

ijhn^n-fgEh]]bgh\:e_dkZg^jK_j]__\bq<br />

M>D<br />

>BNJ:DPBHGGU?IHL?JB

6<br />

EHFHGHKH@<br />

Bkihevamy]jZgbqgu_mkeh\by^eygZijy`zgghkl_cwe_dljbq_kdh]hbfZ]gblgh]h<br />

ihe_c>@kljhblkyj_r_gb_gZ\g_rg_cih\_joghklbm]hedh\h]hhljZ`Zl_ey<br />

4. Ijbf_gyybgl_]jZevgmxl_hj_fmDbjo]hnZ-=_evf]hevpZ>@\uqbkey_lky<br />

ihe_\^Zevg_c^bnjZdpbhgghcahg_bfhsghklvwg_j]bbbaemq_gby<br />

Bkke_^mxlky ^\Z gZijZ\e_gby iheyjbaZpbb iZ^Zxs_c \hegu iZjZee_evgh_ b<br />

i_ji_g^bdmeyjgh_ j_[jm m]hedh\h]h hljZ`Zl_ey < i_j\hf kemqZ_ hp_gdZ ^bnjZdpbhg<br />

guo ihl_jv khklZ\ey_l W baemq /W iZ^Zxs § λ/a Z \h \lhjhf kemqZ_ – W baemq /W iZ^Zxs §<br />

3.82*λ/aA^_kvW baemq –fhsghklv^bnjZdpbhgguoihl_jvW iZ^Zxs –fhsghklviZ^Zxs_c<br />

gZm]hedh\uchljZ`Zl_ev\heguλ –^ebgZhilbq_kdhc\hegu\\Zdmmf_a –oZjZdl_jguc<br />

jZaf_jk\_lh\h]himqdZIhdZaZghqlhmqzlk^\b]Z=mkZ-Owgo_gZm\_ebqb\Z_lqbkeh\hc<br />

dhwnnbpb_gl\–jZaZ<br />

Ebl_jZlmjZ<br />

1. V.B. Braginsky, S.P. Vyatchanin, Phys. Lett. A 324, 345 (2004),<br />

2. K. Artmann, Ann. Physik 2, 87 (1948),<br />

3. H.K.V. Lotsch, JOSA 58, 551 (1968),<br />

4. H.M. Lai, F.C. Cheng, W.K. Tang, JOSA A 3, 550 (1986),<br />

5. E>EZg^Zm?FEbnrbpWe_dljh^bgZfbdZkiehrguokj_^NbafZleblFh<br />

kd\Z<br />

6. K: :ofZgh\ KX Gbdblbg Nbabq_kdZy HilbdZ Ba^-\h Fhkdh\kdh]h Mgb<br />

\_jkbl_lZ<br />

M>D-537.52<br />

?CKLH<<br />

KHK

Ih^k_dpbyjZ^bhnbabdb 7<br />

\ha^mrghckf_kbh^gZdh\hijhkhklZ[bebaZpbbj_`bfh\]hj_gby^hkboihjhklZ_lky<br />

hldjuluf ihwlhfm gZklhysZy jZ[hlZ y\ey_lky ijh^he`_gb_f pbdeZ wdki_jbf_glZev<br />

guojZ[hlijh\h^bfuo\wlhfgZijZ\e_gbb<br />

8<br />

EHFHGHKHHDKG?J:>B:EVGHKLBIHLHDH

Ih^k_dpbyjZ^bhnbabdb 9<br />

kfhljygZlhqlhba\_klgu_nZdlhjulZdb_dZdg_h^ghjh^ghklvkj_^ubZgbahljhiby<br />

dhlhju_fh]ml\uau\Zlvbkdjb\e_gbyemq_ca^_kviheghklvxhlkmlkl\mxlGZ^hhlf_<br />

lblvqlh^ZggZyaZ^ZqZj_rZeZkvgZfbdZdqZklv[he__h[s_cZbf_ggh–ijh[e_fu<br />

jZkijhkljZg_gby wg_j]bb mijm]bo Zdmklbq_kdbo \heg hl lhq_qgh]h \_dlhjgh]h bklhq<br />

gbdZ\ZgbahljhiguodjbklZeeZokkbevgufiv_ahwnn_dlhfl_agZqbl_evgh©ijh^Z\<br />

eb\Zxs_fª ih\_joghklv f_^e_gghklb < hlebqb_ hl lZdh]h hlghkbl_evgh keh`gh]h<br />

kemqZy\q_flhkoh`_]hih-\b^bfhfmbknhghgghcnhdmkbjh\dhcfuh`b^Zebih<br />

emqblvjZ^bZevgu_ihlhdb wg_j]bb\jZkkfZljb\Z_fhfbahljhighfh^ghjh^ghfl\_j<br />

^hfl_e_H^gZdhj_amevlZlu\uqbke_gbcij_\ahreb\k_gZrbh`b^Zgby<br />

JZkq_luihlhdh\wg_j]bb\gZklhys_cjZ[hl_ijh\h^bebkvkbkihevah\Zgb_fke_<br />

^mxs_cba\_klghcnmgdpbb=jbgZ^eylhq_qgh]h\_dlhjgh]hbklhqgbdZ>@<br />

⎛<br />

ikT r 2 ik<br />

⎛ Lr<br />

ikT<br />

r<br />

1<br />

⎞⎞<br />

⎜<br />

2 e ∂ e e<br />

G =<br />

− ⎜ ⎟⎟<br />

ij δ k<br />

ij T<br />

−<br />

]^_ k<br />

2<br />

L , k T –\hegh\u_ qbkeZ<br />

4πρω<br />

⎝<br />

r ∂xi∂x<br />

j ⎝ r r ⎠⎠<br />

^eyijh^hevghcbihi_j_qguo\hegω –boqZklhlZ r , x i –-jZkklhygb_hlbklhqgbdZb<br />

dhhj^bgZlgZykbkl_fZkqblZ_fqlhgZr\_dlhjgucbklhqgbdjZkiheh`_g\^hevhkbz\<br />

gZqZe_ dhhj^bgZl >Ze__ [ueb ijh\_^_gu \uqbke_gby ihlhdZ wg_j]bb ih nhjfme_<br />

1 *<br />

Ρi<br />

= − Tijv<br />

j ]^_ Ρ i –kh[kl\_gghihlhdwg_j]bb\_dlhjMfh\Z-Ihcglbg]ZT ij –l_gahj<br />

2<br />

^_nhjfZpbcZ v –dhe_[Zl_evgZykdhjhklvDZdihdZaZebgZrbjZkq_luihlhdwg_j]bb<br />

j<br />

( Ai)<br />

n<br />

Pi<br />

∑ ]^_ ( A i ) n<br />

fh`gh ij_^klZ\blv \ ke_^mxs_f kljmdlmjghf \b^_ = 7 \hh[s_<br />

n<br />

n=<br />

2 r<br />

]h\hjy aZ\bkyl hl gZijZ\e_gby gZ[ex^_gby eywlh]hkem

10<br />

EHFHGHKH_ckl\bl_evgZy`_qZklvihlhdZwg_j]bbhl\_dlhjgh]hlhq_qgh<br />

]hbklhqgbdZ\`b^dhklbij_^klZ\ey_lkh[hcjZ^bZevgu_ebgbbbkoh^ysb_hlbklhq<br />

gbdZ<br />

Jbk^Z_lij_^klZ\e_gb_hjZkij_^_e_gbb^_ckl\bl_evghcqZklbihlhdZwg_j]bb<br />

\^Zevg_fihe_gZr_]hbklhqgbdZFh`ghhlf_lblvke_^mxsmxhkh[_gghklvemqbdZd<br />

[u hkpbeebjmxl hdheh jZ^bZevguo gZijZ\e_gbc < ^Zevg_f ihe_ lZdb_ hkpbeeypbb<br />

dZd \b^gh ba ZgZeblbq_kdh]h j_r_gby k\yaZgu k bgl_jn_j_gpbhggufb keZ]Z_fufb<br />

oZjZdl_jbamxsbfb \aZbfh^_ckl\b_ ijh^hevguo b ihi_j_qguo \heg LZdbf h[jZahf<br />

fh`gh k^_eZlv \u\h^ h lhf qlh m]eh\u_ ihlhdb wg_j]bb y\eyxlky ke_^kl\b_f h^gh<br />

\j_f_ggh]h\ha[m`^_gby^\molbih\\heg<br />

Ebl_jZlmjZ<br />

1. :G;ZjoZlh\G

Ih^k_dpbyjZ^bhnbabdb 11<br />

emq_gZ ebg_cgZy aZ\bkbfhklv f_`^m jZkij_^_e_gb_f ih ]em[bg_ hklZlhqguo gZijy`_<br />

gbc<br />

σ (x)<br />

bdhwnnbpb_glhfhljZ`_gbygZaZ^Zdmklbq_kdh]hbfimevkZ<br />

R(x)<br />

^eyfZeh]h<br />

baf_g_gbyZdmklbq_kdh]hbfi_^ZgkZa<br />

σ ( x ) = K × R(<br />

x)<br />

,<br />

]^_dhwnnbpb_gl . hij_^_ey_lkymijm]bfbk\hckl\Zfbkj_^u<br />

>eyijh\_jdbijZ\bevghklb\u[hjZfh^_ebijh\_^_ghfh^_ebjh\Zgb_jZkijhkljZ<br />

g_gbyZdmklbq_kdh]hbfimevkZ\kehbklhckj_^_kbaf_gyxsbfkyhlkehydkehxZdmklbq_<br />

kdbf bfi_^Zgkhf ih\lhjyxsbf jZkij_^_e_gb_ hklZlhqguo gZijy`_gbc < j_amevlZl_<br />

fh^_ebjh\Zgby ihemq_gh qlh dhwnnbpb_gl hljZ`_gby Zdmklbq_kdh]h kb]gZeZ R(x)<br />

ih<br />

nhjf_ ih\lhjy_l jZkij_^_e_gb_<br />

hklZlhqguogZijy`_gbcih]em[bg_<br />

GZ jbkmgd_ ij_^klZ\e_gZ<br />

ijbgpbibZevgZy ko_fZ f_lh^Z Q_j_a<br />

hilh\hehdgh eZa_jguc bfimevk hkgh\ghc<br />

]Zjfhgbdb Nd:YAG eZa_jZ<br />

^el_evghklv bfimevkZ τ<br />

L<br />

= 7 gk wg-<br />

_j]by E ≈1 f>` ihiZ^Z_l gZ ih-<br />

\_joghklv bkke_^m_fh]h h[jZapZ ]^_<br />

Hilbdh-Zdmklbq_kdbc<br />

ij_h[jZah\Zl_ev<br />

σ [ <br />

HljZ`_gguc<br />

kb]gZe<br />

:dmklbq_kdbckb]gZe<br />

\ha[m`^Z_lky hilbdhZdmklbq_kdbc<br />

kb]gZe HljZ`_gguc hl g_h^ghjh^ghkl_c<br />

Zdmklbq_kdbc kb]gZe j_<br />

[<br />

]bkljbjm_lky rbjhdhihehkguf iv_-<br />

ahwe_dljbq_kdbfij_h[jZah\Zl_e_f<br />

Ijbijh\_^_gbbwdki_jbf_glZbkihevah\Zebkvh[jZapubagbd_e_\uoblblZgh<br />

\uokieZ\h\khklZlhqgufbgZijy`_gbyfbjZkij_^_e_ggufbih]em[bg_^hfdf<br />

WlbgZijy`_gby[uebihemq_gu\j_amevlZl_mijhqg_gbyrebnh\Zgbyihebjh\Zgby<br />

l_jfbq_kdhcblhdZjghcqbklh\hch[jZ[hlhd>eyj_]bkljZpbbhljZ`_gguomevljZa\m<br />

dh\uo bfimevkh\ [ue ki_pbZevgh kdhgkljmbjh\Zg rbjhdhihehkguc hilbdh-<br />

Zdmklbq_kdbcij_h[jZah\Zl_evkdhk\_gghcj_]bkljZpb_cZdmklbq_kdbobfimevkh\JZa<br />

j_r_gb_ih]em[bg_h]jZgbqb\Z_lkyijhkljZgkl\_gghcijhly`_gghklvxnjhglZahg^b<br />

jmxs_]hZdmklbq_kdh]hbfimevkZ x p ≈ 25 fdf<br />

J_amevlZluijh\_^_gguowdki_jbf_glh\ih\hkklZgh\e_gbxhklZlhqguogZijy<br />

`_gbcgZoh^ylky\ohjhr_cdhjj_eypbbkdhgljhevgufb^Zggufbij_^hklZ\e_ggufb<br />

N=MIFFII©KZexlªWlhih^l\_j`^Z_lkijZ\_^eb\hklv\u[jZgghcfh^_ebbiha\h<br />

ey_l \ ^Zevg_cr_f bkihevah\Zlv ^Zgguc f_lh^ ^ey g_jZajmrZxs_]h dhgljhey hklZ<br />

lhqguogZijy`_gbc\f_lZeeZo<br />

Ebl_jZlmjZ<br />

1. =mk_\

12<br />

EHFHGHKHD2<br />

WNN?DLUBIJHY

Ih^k_dpbyjZ^bhnbabdb 13<br />

kl\eyekyij_h[jZah\Zl_eyfbH:

14<br />

EHFHGHKHD<br />

:>:ILB

Ih^k_dpbyjZ^bhnbabdb 15<br />

ihegbl_evgZyihf_oZK^jm]hcklhjhgu^_iheyjbah\Zggu_dhfihg_gluihf_o\h[_bo<br />

ih^j_r_ldZo lZd`_ hdZau\Zxlky g_dhjj_ebjh\Zggufb Z wlh fh`_l kms_kl\_ggh ih<br />

\ebylvgZwnn_dlb\ghklvjZ[hlukbkl_fuhkgh\gufmkeh\b_fnmgdpbhgbjh\Zgbydh<br />

lhjhc y\ey_lky keZ[Zy dhjj_eypby ihe_agh]h kb]gZeZ b ihf_o b kbevgZy dhjj_eypby<br />

dhfihg_glihf_of_`^mkh[hc<br />

GZjbkihdZaZgubgl_]jZevgu_nmgdpbbjZkij_^_e_gbywnn_dlb\ghklbjZ[h<br />

lu::J-\ub]jur\HKIR µ -ijbijb_f_qZklbqghiheyjbah\Zgguoihe_agh]hkb]<br />

gZeZb^\moihf_oijbkj_^g_ckl_i_gbijhkZqb\Zgby

16<br />

EHFHGHKHD<br />

FBDJHPMG:FBG:D:IE?<br />

Ih^k_dpbyjZ^bhnbabdb 17<br />

>ey bgl_jij_lZpbb nhjfu dZieb gZ[ex^Z_fhc ijb \ha^_ckl\bb \klj_qguo<br />

I:@Ihwlhfm ijh<br />

nbevdZiebihdZaZggucgZjbk \fh`ghjZkkfZljb\ZlvdZdfh^bnbpbjh\Zgguckh<br />

eblhgklhyqbo\heggZih\_joghklb`b^dhklb\ha[m`^_gguc\mkeh\byo[he__keh`<br />

guo q_f \ kemqZ_ dhe_[Zgbc dx\_lu dZd p_eh]h ?keb lZdZy bgl_jij_lZpby y\ey_lky<br />

ijZ\bevghclhgZ[ex^Z_fucijhnbev^he`_g[ulvj_amevlZlhf\bamZevgh]hmkj_^g_<br />

gby\ukhdhqZklhlguodhe_[ZgbcdZieb\ua\Zggh]hbg_jpbhgghklvxajbl_evgh]h\hk<br />

ijbylbyLh]^Zk]eZ`_ggucibd\ijhnbe_dZieblhevdhdZ`_lkyd\ZabklZpbhgZjgufZ<br />

gZkZfhf^_e_hgy\ey_lkyebrv\g_rgbfdhglmjhfh]b[Zxs_c\ukhdhqZklhlguodh<br />

e_[Zgbcih\_joghklbdZieb<br />

Z[\<br />

Jbk WkdbauijhnbeydZiebZdZiey\hlkmlkl\b_^bgZfbq_kdbo\ha^_ckl\bc[dZiey^\b`msZy<br />

kyihklmiZl_evghijb\ha^_ckl\bbI:@Ihwlhfm ^jm]Zy \ha<br />

fh`gZybgl_jij_lZpbykhklhbl\lhfqlh\ha\ur_gb_gZih\_joghklbdZieb^_ckl\b<br />

l_evghy\ey_lkyd\ZabklZpbhgZjgufh[t_dlhf\hagbdZxsbf\ke_^kl\b_h[jZam_fuo\<br />

dZie_Zdmklbq_kdbol_q_gbc >eyjZa\blby wlhc bgl_jij_lZpbb[ueZjZkkfhlj_gZmi<br />

jhs_ggZy \kihfh]Zl_evgZy aZ^ZqZ h \hagbdgh\_gbb Zdmklbq_kdbo l_q_gbc \ `b^dhf<br />

ihemijhkljZgkl\_]jZgbqZs_fkmijm]bfl\_j^ufihemijhkljZgkl\hf\dhlhjhfgZ<br />

\klj_qm ^jm] ^jm]m jZkijhkljZgyxlky ^\_ \ul_dZxsb_ \hegu Jwe_y JZkq_l ihdZaZe<br />

qlhkmffZjgZykbeZjZ^bZpbhggh]h^Z\e_gbygZijZ\e_gZkljh]h\\_jolhevdhlZf]^_<br />

\klj_qgu_\ul_dZxsb_\hegubf_xlh^bgZdh\mxZfieblm^mHldehg_gby\klhjhgmhl<br />

wlh]hf_klZijb\h^yldgZdehgm\_dlhjZkmffZjghckbeu\klhjhgmijhlb\hiheh`gmx<br />

hldehg_gbx Wlh k\hckl\h gZ\h^bl gZ fukev h \hafh`ghklb nhjfbjh\Zgby `b^dh]h<br />

klhe[Zkp_gljhf\h[eZklbjZ\_gkl\ZZfieblm^\klj_qguojwe__\kdbo\heg>eywlh]h<br />

lj_[m_lkyqlh[uZfieblm^u\klj_qguo\hegkjZ\gb\Zebkv^jm]k^jm]hf\h[eZklbih^<br />

dZie_c<br />

Bf_xlkyb^jm]b_f_oZgbafunhjfbjh\Zgby\ha\ur_gbygZdZie_

18<br />

EHFHGHKHB:=GHKLBD:HKL:LHQGUOG:IJY@?GBC<br />

Ih^k_dpbyjZ^bhnbabdb 19<br />

imevk ih\lhjyxsbc nhjfm h]b[Zxs_c bgl_gkb\ghklb eZa_jgh]h bfimevkZ < jZ[hl_<br />

bkihevah\ZekyNd-YAGeZa_jk^bh^ghcgZdZqdhc^ebl_evghklvbfimevkZgkwg_j]by<br />

fd>`J_]bkljZpbybfimevkh\ijhba\h^beZkvijbihfhsbrbjhdhihehkgh]hiv_ah<br />

ijb_fgbdZgZhkgh\_djbklZeeZgbh[ZlZeblbyihehkZ-F=pqlhiha\heyehihem<br />

qblvjZaj_r_gb_ih\j_f_gbihjy^dZgk<br />

eydZ`^h]hbah[<br />

jZaph\[uehihemq_ghijhkljZgkl<br />

\_ggh_ jZkij_^_e_gb_ hlghkbl_ev<br />

gh]hbaf_g_gbykdhjhklba\mdZGZ<br />

jbk ijb\_^_gh ihemq_ggh_ jZk<br />

ij_^_e_gb_ ^ey ieZklbgu lhesb<br />

ghcff Dhhj^bgZlZ Y hlkqblu<br />

\Z_lky \ gZijZ\e_gbb i_ji_g^bdm<br />

eyjghf r\m p_glj r\Z khhl\_lkl<br />

\m_lY HkvXgZijZ\e_gZ\^hev<br />

r\Z<br />

GZ jbkihdZaZghjZkij_<br />

^_e_gb_ hlghkbl_evgh]h baf_g_gby<br />

kdhjhklb \^hev gZijZ\<br />

e_gby i_ji_g^bdmeyjgh]h r\m <<br />

h[eZklb \[ebab r\Z gZ[ex^Z_lky<br />

aZf_lgh_ baf_g_gb_ kdhjhklb<br />

ijbqbgZ dhlhjh]h aZdexqZ_lky \<br />

baf_g_gbb kljmdlmju f_lZeeZ \<br />

ijhp_kk_i_j_ieZ\db<br />

Ihemq_ggu_jZkij_^_e_gby<br />

ihe_c hklZlhqguo ih nhjf_ kh\<br />

iZ^Zxl k jZkij_^_e_gb_fgZijy<br />

`_gbc \ k\Zjguo r\Zo ihemq_g<br />

guojZajmrZxsbfbf_lh^Zfb<br />

bkIjhkljZgkl\_ggh_ jZkij_^_e_gb_ hlghkbl_evgh]h<br />

baf_g_gbykdhjhklb\ieZklbg_lhesb<br />

Jbk JZkij_^_e_gb_ hklZlhqguo gZijy`_gbc \^hev<br />

gZijZ\e_gbyi_ji_g^bdmeyjgh]hr\m<br />

Ebl_jZlmjZ<br />

1. =mav:GFZohjlN==msZHBmf<br />

dZDb_\- 1977. – 150 c<br />

2. Guz A.N. Elastic waves in bodies with initial (residual) stresses. Int. Appl. Mechanics,<br />

2002, 38, 1, pp.23-59<br />

3. =mk_\

20<br />

EHFHGHKHD<br />

J:KIJ?>?E?GB?WE?DLJBQ?KDBOA:JY>H<<br />

G:IJH;GUOF:KK:OBAIE:

Ih^k_dpbyjZ^bhnbabdb 21<br />

ijhkljZgkl\_ggh]h jZkij_^_e_gby aZjy^Z Ohly aZ\bkbfhklv Zfieblm^u kb]gZeZ hl<br />

\j_f_gb hlebqZeZkv hl wdkihg_gpbZevghc ^ey hibkZgby ijhp_kkZ \\h^behkv oZjZd<br />

l_jgh_\j_fykiZ^ZZfieblm^u<br />

GZi_j\hfwlZi_baf_j_gbyijh\h^bebkvgZ\ha^mo_ijb\eZ`ghklbf_g__<br />

J_amevlZlu wdki_jbf_glh\ ihdZaZeb kms_kl\_ggh_ \ebygb_ kihkh[Z ijb]hlh\e_gby<br />

h[jZapZ gZ ihke_^mxsb_ \ZjbZpbb jZkij_^_e_gby aZjy^Z Fb]jZpby we_dljbq_kdbo<br />

aZjy^h\fh`_l[ulvh[mkeh\e_gZg_kdhevdbfbijhp_kkZfbih\_joghklghcbh[t_f<br />

ghcijh\h^bfhklvxg_cljZebaZpb_caZjy^h\bhgZfb\ha^moZ>@IjbjZaebqguof_<br />

lh^Zoijb]hlh\e_gbyh[jZapZfh]mlhlebqZlvkydZdk\hckl\Zih\_joghklblZdb\gml<br />

j_ggb_ k\hckl\Z Ih\_joghklgZy ijh\h^bfhklv kms_kl-\_ggh aZ\bkbl gZijbf_j hl<br />

dhebq_kl\ZZ^khj[-bjh\Zgghc\h^uLZdkjZamihke_ijh]j_\Zh[jZapZ\ieZf_gbdb<br />

kehjh^ghc]hj_edb\j_fyj_eZdkZpbbjZkij_^_e_gbyaZjy^ZgZg_k_ggh]hgZh[jZa_p<br />

khklZ\eyeh ihjy^dZ fbgmlu Z ihke_ ijh]j_\Z \ i_qb ijb l_fi_jZlmj_ ƒ& –<br />

5,5 qZkh\<br />

GZih\_^_gb_jZkij_^_e_gbyaZjy^Z\eby_lg_lhevdhkihkh[ijb]hlh\e_gbygh<br />

b ij_^uklhjby h[jZapZ < h^ghf ba wdki_jbf_glh\ knhjfbjh\Zeky g_h[uqguc ^b<br />

ihevgucibdijhkljZgkl\_ggh]hjZkij_^_e_gbyaZjy^Zjbk nhjfZdhlhjh]hijZd<br />

lbq_kdbg_f_gyeZkvZZfieblm^ZkiZ^ZeZkoZjZdl_jguf\j_f_g_fhdheh qZkh\<br />

ohly\wlhc`_k_jbbmaZjy^h\gZg_k_gguof_lh^hfdhglZdlghcwe_dljbaZpbb\j_fy<br />

j_eZdkZpbb[uehihjy^dZ qZkh\<br />

Bkke_^h\Zehkv lZd`_ \ebygb_ hdjm`_gby h[jZapZ gZ jZkij_^_e_gb_ aZjy^h\<br />

GZwe_dljbq_kdb_aZjy^ugZoh^ysb_kygZh[jZap_^_ckl\mxlkbeubah[jZ`_gbykh<br />

klhjhgu f_lZeebq_kdbo ^_lZe_c jZ[hq_c dZf_ju ?keb ahg^ hklZ\eyeky ih^ g_ih^<br />

\b`guf h[jZaphf lh q_j_a g_dhlhjh_ \j_fy gZ ih\_joghklb h[jZapZ \[ebab ahg^Z<br />

nhjfbjh\Zeky ibd gZ djb\hc ijhkljZgkl\_ggh]h jZkij_^_e_gby aZjy^Z >Z`_ _keb<br />

kbff_ljbah\Zlvhdjm`_gb_bhl\_klbahg^\gmljbjZ[hq_]hh[t_fZhklZ_lkykeZ[h_<br />

we_dljbq_kdh_ihe_kha^Z\Z_fh_ba-aZjZaghcjZ[hlu\uoh^Zf_lZeebq_kdbowe_f_g<br />

lh\K\h[h^gu_aZjy^u\d\Zjp_i_j_jZkij_^_eyxlkylZdbfh[jZahfqlh[ukdhfi_g<br />

kbjh\Zlvwe_dljbq_kdh_ihe_\gmljbh[jZapZH[mkeh\e_ggh_wlbfwnn_dlhfjZkij_<br />

^_e_gb_aZjy^h\fh`ghgZ[ex^Zlv_kebgZqZlvbaf_j_gb_jZkij_^_e_gbyaZjy^h\ih<br />

ke_lh]hdZdh[jZa_p^he]h_\j_fygZoh^beky\ihdh_<br />

;ueh ijh\_^_gh bkke_^h\Zgb_\ebygbykihkh[Zbaf_j_gbcgZw\hexpbxjZk<br />

ij_^_e_gbyaZjy^h\

22<br />

EHFHGHKHD<br />

<br />

G:HKGH

Ih^k_dpbyjZ^bhnbabdb 23<br />

dhgljhebjh\ZeZkvojhf_ev-dhi_e_\hcl_jfhiZjhc >_khj[pby]Zah\badZlh^Zdhgljh<br />

ebjh\ZeZkvkihfhsvxfhghihevgh]hfZkk-ki_dljhf_ljZ

24<br />

EHFHGHKH

Ih^k_dpbyjZ^bhnbabdb 25<br />

JZkq_lm]eh\;jw]]Z^eykj_aZ α =10°<br />

\ iZjZl_eemjbl_ihdZaZeqlhlhqd_^\mdjZl<br />

gh]h jZkk_ygby ijb λ = 633 gf khhl\_lkl\m_l<br />

*<br />

qZklhlZ mevljZa\mdZ f theor<br />

= 185. 6 F=p Ih j_<br />

amevlZlZf wdki_jbf_glZevgh]h bkke_^h\Zgby<br />

m]ehqZklhlguo oZjZdl_jbklbd ^ey ^Zgghc<br />

Zdmklhhilbq_kdhcyq_cdbqZklhlZ^\mdjZlgh<br />

]h jZkk_ygby khklZ\beZ \_ebqbgm<br />

f * = 188. 4 F=p .<br />

DZd \b^gh ba jbk 1 ^ey gZ[ex^_gby<br />

^\mdjZlgh]h jZkk_ygby \ ^Zgghc ]_hf_ljbb<br />

\aZbfh^_ckl\by gZ Zdmklhhilbq_kdmx yq_cdm<br />

g_h[oh^bfhih^Z\Zlvk\_lg_h[udgh\_gghcih<br />

eyjbaZpbbih^m]ehf;jw]]Zkhhl\_lkl\mxsbf<br />

( e)<br />

gZijZ\e_gbyf \hegh\uo \_dlhjh\ k &<br />

1<br />

eb[h<br />

( e)<br />

k &<br />

Jbk

26<br />

EHFHGHKH

Ih^k_dpbyjZ^bhnbabdb 27<br />

(−)<br />

(+)<br />

A^_kv Φ - Zfieblm^Z baemqZ_fhc imqdhf \klj_qghc \hegu Φ -Zfieblm^u \hegu<br />

h[jZlghck\yab x b τ -[_ajZaf_jgu_dhhj^bgZlZb\j_fy χ<br />

1, 2<br />

-dhwnnbpb_gluhljZ<br />

`_gbyαb<br />

b Θ -iZjZf_ljuijhihjpbhgZevgu_iehlghklbimqdZbd\Z^jZlmZfieblm^u<br />

\hegu gZdZqdb vg<br />

b v<br />

b<br />

-[_ajZaf_jgu_]jmiih\Zykdhjhklv baemq_gbybkdhjhklv bg<br />

`_dpbbwe_dljhgh\imqdZ X = 2πN<br />

λ<br />

-[_ajZaf_jgZy^ebgZZ N<br />

λ<br />

-qbkeh^ebg\heggZ<br />

^ebg_ijhkljZgkl\Z\aZbfh^_ckl\by<br />

Gb`_ij_^klZ\e_guj_amevlZluihemq_ggu_ijbqbke_gghfj_r_gbbmjZ\g_gbc<br />

^ey ke_^mxsbo agZq_gbc iZjZf_ljh\ 0.0005,<br />

0.05, b<br />

vg<br />

vb<br />

= 1, 2<br />

0 Ijb<br />

χ = 0 2<br />

(+)<br />

l_evgmxkihkh[ghklvihwlhfm\hegZ Φ baemqZ_lkyiheghklvxbmjZ\g_gb_^eyg__<br />

g_lj_[m_lkyGZJbkij_^klZ\e_gZaZ\bkbfhklv[_ajZaf_jgh]h\j_f_gbg_ebg_cgh]h<br />

gZkus_gbyg_mklhcqb\hklb τ<br />

gZk.<br />

hl[_ajZaf_jghc^ebgu Nλ<br />

ZgZJbkbah[jZ`_gZ\<br />

aZ\bkbfhklb hl Nλ<br />

fZdkbfZevgZy<br />

[_ajZaf_jgZy Zfieblm^Z<br />

\hafms_gby \hegu iehlghklb τ gZk<br />

imqdZ | R | = | R(<br />

X 2, τ<br />

gZk.<br />

) | IhkdhevdmiZjZf_lj<br />

Nλ<br />

ijbgbfZ-<br />

<br />

_l lhevdh p_eu_ agZq_gby m<br />

djb\uo gZ jbkmgdZo bf_xl<br />

<br />

kfuke lhevdh \u^_e_ggu_ lhqdb<br />

10 ,<br />

qlhkh\iZ^Z_lkihjh]h\hc^ebghc<br />

<br />

\uqbke_gghc ih ZgZeblb-<br />

q_kdhc nhjfme_ ebg_cghc<br />

<br />

1 λ<br />

l_hjbb >@ AZ\bkbfhklv hl<br />

<br />

^ebgu agZqbl_evgZ lhevdh \<br />

^bZiZahg_ hl ihjh]Z - N<br />

λ<br />

= 10<br />

Jbk<br />

^h Nλ<br />

= 20 ÷ 25 >Zevg_cr__<br />

m\_ebq_gb_ ^ebgu g_ kdZau\Z-<br />

_lky gZ \j_f_gb g_ebg_cgh]h<br />

gZkus_gby g_mklhcqb\hklb b<br />

mjh\g_ __ g_ebg_cghc klZ[bebaZpbbJbkWlh–kms_kl\_gguc<br />

j_amevlZl bf_xsbc \Z`gh_agZq_gb_ijbijZdlbq_kdhc<br />

jZajZ[hld_bklhqgbdh\we_dljh-<br />

fZ]gblgh]hbaemq_gbygZ\klj_-<br />

qguo \hegZo bf__lky g_dhlhjZy<br />

<br />

<br />

<br />

<br />

_5 _<br />

^ebgZ kbkl_fu ij_\ur_-<br />

1. Dma_e_\ F< JmoZ^a_<br />

::We_dljh^bgZfbdZiehlguo<br />

gb_dhlhjhcg_p_e_khh[jZagh<br />

<br />

Ebl_jZlmjZ<br />

<br />

<br />

1 λ<br />

<br />

we_dljhgguo imqdh\ \ ieZaf_<br />

FGZmdZk<br />

Jbk

28<br />

EHFHGHKHD<br />

DG?EBG?CGHCG?KL:PBHG:JGHCL?HJBB<br />

?GGH=HBAEMQ?GBYJWI<br />

G<br />

F=MbfF

Ih^k_dpbyjZ^bhnbabdb 29<br />

(( ˆ ) )<br />

e ⎡( ( 0<br />

ˆ ) )<br />

1 e 2 2 * *<br />

− ( ) ⎡ ik<br />

2<br />

0 +∂ ∂ z + ( v c ∂ ∂ t ( A0A+ + A0A−)exp( iy) + DK⎤−<br />

2γ<br />

mc ⎢⎣<br />

⎥⎦<br />

1 2 2 *<br />

− ( ) 2 ik +∂ ∂ z + ( v c ∂ ∂ t ( A A )exp(2 iy) DK <br />

2<br />

+ − + ⎤<br />

2γ<br />

mc ⎢⎣<br />

⎥⎦<br />

dy<br />

= k v ρ= −iy dy ρ = γ −iy dy ρ = γ − iy dy<br />

dt<br />

2π 2π 2π<br />

1 1 −1 1 −1<br />

0ˆ, exp( ) 0, ˆ1 exp( ) 0, ˆ2 exp( 2 ) 0<br />

π<br />

∫<br />

π<br />

∫<br />

π<br />

∫<br />

0 0 0<br />

2<br />

2 2 2 −1<br />

A^_kv ω±<br />

= ( k0<br />

± χ)<br />

c + ωb<br />

〈 γ 〉 Ijb\u\h^_mjZ\g_gbcij_^iheZ]Zehkvqlh<br />

nmgdpbb ~ϕ , A gZ^ebg_ ±<br />

λ baf_gyxlkykeZ[hWlhiha\hey_lihgbablvihjy^hd^bn<br />

0<br />

n_j_gpbjh\Zgby\i_j\uo^\momjZ\g_gbyokbkl_ful_i_j_clbdf_^e_ggufZf<br />

ieblm^ZfIhemq_ggu_ihke_wlh]hmjZ\g_gbyy\eyxlkyhkgh\gufb\g_ebg_cghcg_<br />

klZpbhgZjghcl_hjbb\ugm`^_ggh]hbaemq_gbyJWI\ihe_\b]e_jZbl_hjbbEKWhk<br />

gh\ZgguogZlZdhfbaemq_gbb<br />

Ωb<br />

bgdj_f_gl^Z_lky<br />

1 3<br />

2<br />

2<br />

2<br />

i 3 ⎡Ω<br />

| | ⎛ ⎞⎤<br />

bω<br />

+ x<br />

4<br />

Ω<br />

b<br />

⎢<br />

⎜1<br />

⎟<br />

2<br />

2 | |<br />

⎥<br />

2<br />

⎢ 4 1 | |<br />

+ γ . (6)<br />

γ + x ω<br />

| |<br />

+ ⎥<br />

⎣<br />

Nhjfmeu^eybgdj_f_glh\iha\heyxlihba\_klghcf_lh^bd_gZclbmkeh\bykZ<br />

fh\ha[m`^_gby \hagbdgh\_gby ]_g_jZpbb \ we_dljh^bgZfbq_kdhc kbkl_f_ EKW<br />

bf_xs_c^ebgm L LZdgZijbf_j^eydhee_dlb\gh]hj_`bfZklZjlh\h_mkeh\b_\ha<br />

gbdgh\_gby]_g_jZpbbbf__l\b^<br />

−1<br />

| δω | ⎧arch<br />

| κ | ,<br />

(7)<br />

L > ⎨<br />

uc ⎩π<br />

2.<br />

I_j\ZynhjfmeZkijZ\_^eb\Zijbg_mklhcqb\hklbgZihimlghc\heg_\lhjZy–<br />

gZ\klj_qghcZκ -dhwnnbpb_glhljZ`_gbyhlbaemqZl_eyEKW<br />

Ebl_jZlmjZ<br />

1. Dma_e_\F

30<br />

EHFHGHKHD<br />

RBJHDHIHEHKGH?>?L?DLBJH

Ih^k_dpbyjZ^bhnbabdb 31<br />

kdjulu_aZdhghf_jghklbijbZgZeba_wlbojy^h\bkihevamyjZaebqgu_f_lh^uj_]mey<br />

jbaZpbb\j_f_gguojy^h\bboihke_^mxs_]hZgZebaZ<br />

?

32<br />

EHFHGHKH@<br />

D wlhfm `_ deZkkm y\e_gbc hlghkblky baf_j_gb_©[_a \aZbfh^_ckl\byª >-8].<br />

Wlhl qbklh d\Zglh\uc wnn_dl iha\hey_l j_]bkljbjh\Zlv gZebqb_ ih]ehsZxs_]h k\_l<br />

h[t_dlZ\^Zgghch[eZklbijhkljZgkl\Zg_ihkueZygZg_]hgbh^gh]hd\ZglZbkhhl<br />

\_lkl\_gghkhklj_fys_ckydgmex\_jhylghklvxih]ehs_gbynhlhgZh[t_dlhf<br />

LZdhcd\Zglh\ucwnn_dlfh`ghbkihevah\Zlv\p_eyoi_j_^Zqbrbnjh\Zgghcbg<br />

nhjfZpbb@^Zggucf_lh^iha\hey_lijZdlbq_kdbk_^bgbqghc\_jhylghklvx^_l_dlbjh\Zlv<br />

ih^kemrb\Zgb_ ihkdhevdm ex[hc ih^kemrb\Zxsbc Z]_gl [m^_l g_ba[_`gh \hafmsZlv<br />

nZamj_]bkljbjm_fuobfnhlhgh\bl_fkZfufjZajmrZlvd\Zglh\mxbgl_jn_j_gpbx<br />

< jZ[hl_ ijhZgZebabjh\Zg lZdhc dZgZe i_j_^Zqb b ijhba\_^_gZ hp_gdZ fZdkb<br />

fZevghckdhjhklbi_j_^Zqb^eyg_]hIhemq_ggu_jZkq_luihdZau\Zxlqlhdkh`Ze_<br />

gbxkdhjhklvi_j_^Zqby\ey_lky^h\hevghgbadhcbiZ^Z_lkm\_ebq_gb_fjZkklhygby<br />

Ebl_jZlmjZ<br />

1. Deutsch D. Proc. R. Soc. London Ser. A, 400, 97, 1985.<br />

2. B:I:AHG:G:HKGH

Ih^k_dpbyjZ^bhnbabdb 33<br />

hilbq_kdbf nhghgZf j_r_ldb Hkgh\u\Zykv gZ j_amevlZlZo bkke_^h\Zgby we_dljhgnhghggh]h\aZbfh^_ckl\by\$O*D$V*D$V]_l_jhkljmdlmjZo>@Z\lhju>@ihdZaZ<br />

ebqlhihehkZij_h[jZah\Zgby$O*D$V*D$Vkf_kbl_eyjZ[hlZxs_]hijbl_fi_jZlmj_<br />

7 .khklZ\bla==pijbnhghgghfdZgZe_hoeZ`^_gby]hjyqbowe_dljhgh\L_hj_<br />

lbq_kdZyhp_gdZrmfh\hcl_fi_jZlmjuijb_fgbdZgZhkgh\_$O*D$V*D$Vkf_kbl_ey<br />

^ZeZagZq_gby71a-DgZqZklhl_]_l_jh^bgZL=p>@kjZ\gbfu_kemqrbfb<br />

oZjZdl_jbklbdZfbk\_joijh\h^gbdh\uokf_kbl_e_c>@Hp_gdZhilbfZevghcfhsghklb<br />

]_l_jh^bgZ 3/2 ^ey $O*D$V*D$V kf_kbl_ey ijh\_^_ggZy Z\lhjZfb>@iha\hebeZ<br />

gZclb agZq_gb_3/2aP:ijb km[fbdjhgguo jZaf_jZo kf_kbl_ey qlh ^_eZ_l \ha<br />

fh`gufkha^Zgb_gZbohkgh\_fZljbqguoijb_fguok_dpbc<br />

Kljmdlmju [ueb ba]hlh\e_gu gZ hkgh\_ h^bghqgh]h ]_l_jhi_j_oh^Z<br />

Al x Ga x–1 $V*D$V\ujZs_ggh]hf_lh^hffhe_dmeyjgh-emq_\hcwiblZdkbb>eymemqr_<br />

gbyhfbq_kdh]hdhglZdlZd']Zam[uebkihevah\Zgkbevghe_]bjh\Zgguckehc*D$V<br />

dhgp_gljZpbye_]bjmxs_cijbf_kb[kf -3 lhesbghcgfLbibqgu_dhglZdl<br />

gu_khijhlb\e_gbykljmdlmjkhklZ\beb-Hfkf 2 Ih^\b`ghklvµbih\_joghklgZy<br />

dhgp_gljZpbywe_dljhgh\Q s [uebgZc^_gubabaf_j_gbchkpbeeypbcRm[gbdh\Z-^_-<br />

=ZZaZbi_j_kqblZgu^eyl_fi_jZlmjuL DIhemq_ggu_agZq_gbyµbQ s ZlZd`_<br />

^ebgZbrbjbgZkljmdlmjuO:ij_^klZ\e_gu\lZ[ebp_<br />

# µ 77 kf 2 @<br />

2<br />

P<br />

IF<br />

( f ) PIF<br />

(0) = 1(1+<br />

( f / f<br />

3dB)<br />

) IhehkZ ijh<br />

f_`mlhqguoqZklhlbaf_j_ggZygZfbijbD<br />

^ey kf_kbl_ey $O*D$V*D$V k dhgp_gljZ<br />

pb_c ^\mf_jguo we_dljhgh\Q s kf -2 b<br />

ih^\b`ghklvx— kf 2

34<br />

EHFHGHKH

Ih^k_dpbyjZ^bhnbabdb 35<br />

Kh\j_f_ggh_ jZa\blb_ bgnhjfZpbhggh-baf_jbl_evguo kbkl_f b jZkrbj_gb_<br />

^bZiZahgh\mkeh\bcijbf_g_gbyba^_ebcij_^ty\ey_ldk_gkhjgufwe_f_glZfhkh[u_<br />

lj_[h\Zgby ih ihf_ohmklhcqb\hklb d we_dljhfZ]gblguf ihf_oZf [ukljh^_ckl\bx<br />

gZ^_`ghklbbgnhjfZlb\ghklbfbgbZlxjghklb\hafh`ghklb\kljZb\Zgby\dhgkljmd<br />

pbx Ijbf_g_gb_ f_oZghexfbg_kp_glguo k\_lh]_g_jZpbhgguo k_gkhjh\ ^Z\e_gby<br />

FEK>kqm\kl\bl_evgufbwe_f_glZfbkhkj_^hlhq_ggh]hbjZkij_^_e_ggh]hlbiZih<br />

a\heyxlj_rblvwlbijh[e_fuBkihevah\Zgb_k\_lh\uokb]gZeh\b\hehdhgghchilbdb<br />

j_rZ_l aZ^Zqm khijy`_gby k_gkhjh\ k \hehdhggufb ebgbyfb b ih\ur_gby ihf_oh<br />

mklhcqb\hklbdwe_dljhfZ]gblgufihf_oZfhlkmlkl\b_^\b`msbokyqZkl_cbl\_j^h<br />

l_evghklv k_gkhjZ h[_ki_qb\Zxl gZ^_`ghklv Z bkihevah\Zgb_ ihfbfh Zfieblm^gh-<br />

\j_f_gguo iZjZf_ljh\ hilbq_kdh]h kb]gZeZ _]h ijhkljZgkl\_gghc fh^meypbb b kh<br />

klhygbyiheyjbaZpbbih\urZ_lbgnhjfZlb\ghklv<br />

F_oZghexfbg_kp_gpbyFE dZd nbabq_kdh_ y\e_gb_ h[mkeh\e_gZ kihkh[gh<br />

klvxk\_lysboky\_s_kl\f_oZghexfbghnhjh\ljZgknhjfbjh\Zlvf_oZgbq_kdbc\b^<br />

wg_j]bb \ k\_lh\h_ baemq_gb_ Bkihevah\Zgb_ ^Zggh]h y\e_gby \ ij_h[jZah\Zl_evghc<br />

l_ogbd_hldju\Z_l\hafh`ghklvkha^Zgbyk_gkhjh\ijbgpbibZevghgh\h]hlbiZ<br />

F_oZghexfbg_kp_glgu_k_gkhju^Z\e_gbyFEK>bkihevamxly\e_gb_exfb<br />

g_kp_glgh]hbaemq_gbykh_^bg_gbcdeZkkZ:IIy\<br />

eyxlky wg_j]hg_aZ\bkbfhklv lZdlbevghklv \hafh`ghklv kha^Zgby lhgdhie_ghqguo<br />

qm\kl\bl_evguo we_f_glh\ ijZdlbq_kdb ex[hc iehsZ^b k jZkij_^_e_gghc qm\kl\b<br />

l_evghklvxbijhklhlZdhgkljmdpbb<br />

M>D<br />

HKHA>:GBBGH@ gh gZ hkgh\_ hj]Zgbq_kdbo ihem<br />

ijh\h^gbdh\eykha^Zgbygh\h]hnmgdpbhgZevgh]hijb[hjZ\h^gucjZkl\hjhj]Zgbq_kdh]h<br />

ihemijh\h^gbdZS-lbiZaZeb\Zeb\\ZggmgZ^g_dhlhjhcjZkiheZ]Zekyf_^gucwe_dljh^<br />

iehsZ^vxffJZaf_j\Zggu×2,5×2,5 ffAZl_fih\_jowlh]hjZkl\hjZkha^Z\Zeb<br />

lhgdmxihjy^dZfdfie_gdmbaihemijh\h^gbdZQ-lbiZ

36<br />

EHFHGHKH

Ih^k_dpbyjZ^bhnbabdb 37<br />

^mebjh\Zgguf ih bgl_gkb\ghklb wg_j]_lbq_kdbf imqdhf \ g_f \ha[m`^Zxlky l_ieh<br />

\u_\hegukhijh\h`^Zxsb_ky\ke_^kl\b_l_ieh\h]hjZkrbj_gbymijm]bfb^_nhjfZ<br />

pbyfb>@:fieblm^ZbnZaZ]_g_jbjm_fh]hnhlhZdmklbq_kdh]hkb]gZeZaZ\bkblhll_<br />

ieh\uobmijm]boiZjZf_ljh\h[jZapZqlhiha\hey_lijhba\h^blvbobaf_j_gb_<br />

P_evxjZ[hlu[uehkha^Zgb_Z\lhfZlbabjh\Zgghcwdki_jbf_glZevghcmklZgh\<br />

dbiha\heyxs_chij_^_eylvl_fi_jZlmjhijh\h^ghklvl\_j^uol_ebabaf_j_gguoaZ<br />

\bkbfhkl_cnZah\h]hk^\b]ZN:kb]gZeZhlqZklhlufh^meypbbbklhqgbdZbaemq_gby<br />

;ehd-ko_fZjZajZ[hlZgghcwdki_jbf_glZevghcmklZgh\dbijb\_^_gZgZjbk<br />

Z<br />

Z[<br />

1 2 3 4 5 6<br />

Jbk;ehd-ko_fZwdki_jbf_glZevghcmklZgh\db<br />

>ey hk\_s_gby h[jZapZ Z bkihevah\Zeky ihemijh\h^gbdh\uc eZa_j k<br />

^ebgghc\hegu gfK\_li_j_^Z\ZekyhlbaemqZl_eydh[jZapmjZaf_s_gghfm<br />

\baf_jbl_evghcyq_cd_q_j_ahilbq_kdbc\hegh\h^>eyj_]bkljZpbbnhlhZdm<br />

klbq_kdh]h kb]gZeZ bkihevah\Zebkv iv_ahwe_dljbq_kdbc ij_h[jZah\Zl_ev[ \uihe<br />

g_gguc ba iv_ahd_jZfbdb PLK- Kb]gZe k h[deZ^db iv_ah^ZlqbdZih^Z\Zeky gZ<br />

\oh^ kbgojhggh]h mkbebl_ey kh \kljh_ggufb -jZajy^gufb ZgZeh]h\h-pbnjh\ufb<br />

ij_h[jZah\Zl_eyfblock-in amplifier SR-nbjfuStanfordHkh[_gghklvx^Zggh<br />

]hijb[hjZy\ey_lkygZebqb_\uoh^gh]hfh^mebjmxs_]hkb]gZeZkj_]mebjm_fhcZf<br />

ieblm^hcZijb]h^gh]h^eymijZ\e_gbyeZa_jhfqlhiha\hey_lmkljZgblvf_oZgbq_<br />

kdmxfh^meypbxeZa_jgh]hemqZWlhlkb]gZelZd`_y\ey_lkyhihjgufijbZgZeba_N:<br />

kb]gZeZkiv_ah^ZlqbdZKbgojhgguc^_l_dlhjiha\hey_lihemqblvqZklhlgmxaZ\bkb<br />

fhklvZfieblm^ubnZauN:kb]gZeZbi_j_^Zlvwlb^Zggu_q_j_abgl_jn_ckHP IEEE-<br />

\dhfivxl_j>ey\uiheg_gbybgl_jn_ckguonmgdpbcbmijZ\e_gbyoh^hfwdk<br />

i_jbf_glZ[ueZgZibkZgZki_pbZevgZyijh]jZffZgZyaud_K<br />

Ijbiv_ahwe_dljbq_kdhcj_]bkljZpbb^ey^\mokehcghckbkl_fuh[jZa_p-iv_ah<br />

ij_h[jZah\Zl_ev iehkdh]h l_ieh\h]h bklhqgbdZ b h[jZapZ lhesbgZ dhlhjh]h fgh]h<br />

[hevr_ ^ebgu l_ieh\hc ^bnnmabb qZklhlgZy aZ\bkbfhklv nZah\h]h k^\b]Z 3 f_`^m<br />

F<br />

nhlhZdmklbq_kdbfbhihjgufkb]gZeZfbbf__l\b^>@ tg ϕ = 1- , ]^_)–[_ajZa<br />

n<br />

f_jgZyqZklhlZZQ–iZjZf_ljaZ\bkysbchllhesbguh[jZapZK 1 bij_h[jZah\Zl_ey<br />

(h 2 boijb\_^_gguofh^me_cXg]Z (<br />

a<br />

b (<br />

a<br />

<br />

khhl\_lkl\_ggh<br />

3<br />

3<br />

Z - Zu<br />

2 1+<br />

( −1)H1<br />

1 1+<br />

( −1)H1<br />

<br />

n = , Zp<br />

= , Z<br />

2 u<br />

= ]^_ =<br />

2Z ( Z − Z p<br />

) 3 1+<br />

( −1)H<br />

2 1+<br />

( −1)H<br />

( a(a ,<br />

u<br />

1<br />

1

38<br />

EHFHGHKH@G_dhlhjh_jZkoh`^_gb_wdki_jbf_glZevguobebl_jZlmjguo^Zgguo<br />

fh`_l[ulvk\yaZghkgZebqb_fkde_cdbdhlhjZyg_mqblu\Z_lky\^\mokehcghcfh^_eb<br />

>@bkdhg_qgufbjZaf_jZfbeZa_jgh]himqdZjZkkqblZggZy\>@fh^_evh^ghf_jgZy<br />

Ijbbkke_^h\Zgbbl_fi_jZlmjguoaZ\bkbfhkl_c\Z`gufby\eyxlkyg_lhevdhZ[<br />

khexlgu_agZq_gbyiZjZf_ljh\ghbbohlghkbl_evgu_baf_g_gbyIhwlhfm^Zggucf_<br />

lh^fh`_l[ulvbkihevah\Zgijbbkke_^h\ZgbbnZah\uoi_j_oh^h\Djhf_lh]hZfieb<br />

lm^ZN:kb]gZeZijyfhijhihjpbhgZevgZl_ieh\hfmjZkrbj_gbxh[jZapZ>@J_]bkl<br />

jbjmyiv_ahij_h[jZah\Zl_eyfbkkhhl\_lkl\mxs_ciheyjbaZpb_cijh^hevgmxb^\_ih<br />

i_j_qgu_ dhfihg_glu N: kb]gZeZjbk fh`gh ihemqblv khhl\_lkl\mxsb_ dhfih<br />

g_glu l_gahjZ l_ieh\h]h jZkrbj_gby Wlh iha\hebl bkke_^h\Zlv N: f_lh^hfhlghkb<br />

l_evgh_ baf_g_gb_ dhwnnbpb_glh\ l_ieh\h]h jZkrbj_gby qlh fh`_l [ulv ihe_aguf<br />

ijbbkke_^h\ZgbbZgbahljhiguol\_j^uol_e<br />

êøò÷ÿýûñ<br />

Ü òôû÷òýíùõ÷í<br />

JZ[hlZ[ueZ\uiheg_gZijbih^^_j`<br />

d_ ]jZglh\ Ij_ab^_glZ JN ih^^_j`db \_^m<br />

sbo gZmqguo rdhe GR- b<br />

JNNB<br />

Ebl_jZlmjZ<br />

1. =mk_\ : Dmq_jh\ B Y<br />

@LNl\uiklj-5.<br />

3. Nbabq_kdb_ \_ebqbgu KijZ\hqgbd<br />

Ih^j_^BK=jb]hjv_\Z?AF_ceboh\Z<br />

FWg_j]hZlhfba^Zlk

Ih^k_dpbyjZ^bhnbabdb 39

Ih^k_dpbyk\_joijh\h^ysbobwe_dljhgguok\hckl\l\_j^uol_e 39<br />

K

40<br />

EHFHGHKHD<br />

KLJMDLMJGU?KDMLL?J:>BLHH:FBYDJYFJ<br />

Hohlgbdh\DK<br />

F=MbfFey/D)H 4 Sb 12 b&D)H 4 Sb 12 \oh^_ijh\_^_gguobkke_^h\Zgbc<br />

[uehh[gZjm`_ghjZks_ie_gb_ebgbbYDJki_dljZkmjvfudjhf_hkgh\ghcebgbbgZ<br />

[ex^Zxlky kZl_eeblh\ b ^\_ ebgbb La gZ YFJ ki_dlj_ ^ey /D)H 4 Sb 12 >ey<br />

NaFe 4 Sb 12 gbq_]hih^h[gh]hg_gZ[ex^Zehkv>eyh[tykg_gbyf_oZgbafZjZks_ie_gby<br />

ebgbc [ueb ijh\_^_gu jZkq_lu f_lh^hf ebg_Zjbah\Zgguo ijbkh_^bg_gguo iehkdbo<br />

\hegLAPW k ihfhsvx ijh]jZffu Wien2k KjZ\gb\Zebkv j_amevlZlu ihemq_ggu_<br />

f_lh^hfjZkq_lZkYDJki_dljhfkmjvfuGZb[he__\_jhylgufh[tykg_gb_fhkh[_ggh<br />

kl_c ki_dljh\ y\ey_lky \hafh`ghklv kf_s_gby qZklb ]hkl_\uoLa, Ca Zlhfh\ \^hev<br />

gZijZ\e_gby^`gZaA.<br />

JZkq_luihdZaZebke_^mxs__LIjbkf_s_gbbLabap_gljZevghcihabpbbgZ<br />

0.1 A\kyd\Z^jmihevgZykljmdlmjZLamdeZ^u\Z_lky\ihehkmd=pqlh^_eZ_lg_\ha<br />

fh`guf_z^_l_dlbjh\Zgb_LLWg_j]bydjbklZeebq_kdhcj_r_ldbijbkf_s_gbbLaih<br />

gZijZ\e_gbxbaf_gy_lkykeZ[h\hlebqbbhl^\b`_gbyih^jm]bfgZijZ\e_gb<br />

yfLLLQbkehkZl_eeblh\gZYDJki_dlj_kh\iZ^Z_lkqbkehfg_wd\b\Ze_glguoZlhfh\<br />

kmjvfu \ djbklZeebq_kdhc ]jmii_ Imm LY Ih khihklZ\e_gbx ^Zgguo jZkq_lh\ b<br />

YDJ \uqbke_gk^\b]LakhklZ\eyxsbca Aqlhkh]eZkm_lkykj_gl]_gh\kdbf^Zg<br />

gufb[hevrhcdhwnnbpb_gll_ieh\h]hjZafulby^ey/D<br />

Ijbf_g_gb_fbdjhkdhibq_kdbof_lh^h\YFJbYDJkh\f_klghkDE-LQLWLRd\Zg<br />

lh\ufb jZkq_lZfb \i_j\u_ ihdZaZeh \hafh`ghklv klZlbq_kdh]h kf_s_gby ]hkl_\h]h<br />

ZlhfZbap_gljZevghcihabpbb\^hevdm[bq_kdhchkb^`\aZiheg_gghfkdmll_jZ<br />

^bl_LaFe 4 Sb 12 .<br />

M>D<br />

HKH;?GGHKLBWE?DLJHGGH=HLJ:GKIHJL:<br />

F=MbfF

Ih^k_dpbyk\_joijh\h^ysbobwe_dljhgguok\hckl\l\_j^uol_e 41<br />

_f ^ey hp_gdb \hafh`ghkl_c bo ijbf_g_gby \ fbdjhwe_dljhgbd_ \ dZq_kl\_ fZkdb<br />

jmxs_]hbih^aZl\hjgh]h^bwe_dljbdZ<br />

Djhf_lh]hie_gdbZfhjngh]hm]e_jh^Zfh]mlkem`blvm^h[gufbfh^_evgufb<br />

h[t_dlZfb^eybamq_gbyf_oZgbafh\we_dljhggh]hi_j_ghkZ\kbevghg_mihjy^hq_gguo<br />

kj_^Zo\_ebqbghc[_kihjy^dZklZlbq_kdh]hihl_gpbZeZ\dhlhjuofh`ghwnn_dlb\gh<br />

mijZ\eylvbaf_g_gb_fmkeh\bchkZ`^_gby–wg_j]bbbl_fi_jZlmjuih^eh`db\ahg_<br />

jhklZie_gdb<br />

JZ[hlZihk\ys_gZbkke_^h\Zgbxw\hexpbbf_oZgbafh\we_dljhggh]hi_j_ghkZ\<br />

rbjhdhf^bZiZahg_l_fi_jZlmjbwe_dljbq_kdboihe_c\ie_gdZoZfhjngh]hm]e_jh^Z<br />

kh^_j`Zsbodj_fgbcbdbkehjh^ijbbaf_g_gbbwg_j]bbhkZ`^_gby<br />

=b^jh]_gbabjh\Zggu_ Zfhjngu_ m]e_jh^gu_ ie_gdb kh^_j`Zsb_ dj_fgbc b<br />

dbkehjh^\ujZsb\Zebkvf_lh^hfjZaeh`_gbyiZjh\keh`gh]hdj_fgbc-hj]Zgbq_kdh]h<br />

kh_^bg_gby – ihebf_lben_gbekbehdkZgZ >KG 3 ) 3 Si(CH 3 C 6 H 5 SiO) 3 Si(CH 3 ) 3 @ \ ieZaf_<br />

klbfmebjh\Zggh]hjZajy^Zihklhyggh]hlhdZlhdieZafu–4 :gZijy`_gb_

42<br />

EHFHGHKH

Ih^k_dpbyk\_joijh\h^ysbobwe_dljhgguok\hckl\l\_j^uol_e 43<br />

gbb\b^h\nZagZbah[jZ`_gbbiehlghklb\boj_cihemq_gghfijbfZl_fZlbq_kdhffh<br />

^_ebjh\Zgbb D<br />

BKKE?>H

44<br />

EHFHGHKHbnnmaby<br />

d\ZabqZklbp b jhkl<br />

]hjyq_]h iylgZ<br />

J_abklb\gZy<br />

h[eZklv<br />

i_j_dju\Z_l<br />

\kz k_q_gb_<br />

ie_gdb<br />

Jbk Fh^_ev f_oZgbafZ jZ[hlu h^ghnh<br />

lhggh]hk\_joijh\h^gbdh\h]h^_l_dlhjZ<br />

gZi_j_oh^_\j_abklb\gh_khklhygb_ihehkdb<br />

gbljb^Z gbh[by gZoh^ys_cky \ k\_joijh-<br />

\h^ys_fkhklhygbbbkf_s_gghclhdhf[eba<br />

dbf ih \_ebqbg_ d djblbq_kdhfm lhdm jZkiZjb\Zgby=bga[mj]Z-EZg^ZmD\Zglk\_lZih<br />

]ehszgguc k\_joijh\h^gbdhf ijb\h^bl d<br />

jZajmr_gbx dmi_jh\kdbo iZj b h[jZah\Zgbx<br />

eZ\bgu d\ZabqZklbp qbkeh dhlhjuo hij_^_-<br />

ey_lkywg_j]b_cih]ehs_ggh]hd\ZglZLhh[<br />

jZam_lky h[eZklv ]^_ k\_joijh\h^bfhklv<br />

ih^Z\e_gZ beb jZajmr_gZ lZd gZau\Z_fh_<br />

©]hjyq__ iylghª >@ Ba-aZ ^bnnmabb d\ZabqZklbp<br />

iehsZ^v ©]hjyq_]h iylgZª m\_ebqb\Z_lky<br />

h^gh\j_f_ggh ijhbkoh^bl i_j_jZkij_^_e_gb_<br />

k\_joijh\h^ys_]h lhdZ ih k_q_-<br />

gbxk\_joijh\h^gbdZb^ey^hklZlhqghmadhc<br />

ie_gdb \_ebqbgZ iehlghklb lhdZ gZqbgZ_l<br />

ij_\urZlvdjblbq_kdmxjbkQZklvihehkdbi_j_oh^bl\ghjfZevgh_khklhygb_qlh<br />

ijb\h^bld\hagbdgh\_gbxwe_dljbq_kdh]hkhijhlb\e_gbyIhke_^mxsZy^bnnmabyd\Z<br />

abqZklbp\ih^eh`dmbboj_eZdkZpbyijb\h^bldmf_gvr_gbx]hjyq_]hiylgZbq_j_a<br />

g_dhlhjh_ \j_fy hgh bkq_aZ_l k\_joijh\h^bfhklv\hkklZgZ\eb\Z_lky b ^_l_dlhj \gh\v<br />

]hlh\dj_]bkljZpbbhq_j_^gh]hnhlhgZBfimevkgZijy`_gbygZ^_l_dlhj_ihihjy^dm<br />

\_ebqbgu khklZ\ey_lf< >ebl_evghklv bfimevkZ gZijy`_gby hij_^_ey_lky ]eZ\guf<br />

h[jZahf\j_f_g_fhklu\Zgby]hjyq_]hiylgZbkhklZ\ey_lhdhehik>@<br />

ey^hklb`_gbyl_fi_jZlmjuDbadjbhklZlZijhba\h^beZkvhldZqdZiZjh\]_eby<br />

D\Zglh\Zy wnn_dlb\ghklvQE hij_^_ey_lky dZd hlghr_gb_ qbkeZ kjZ[Zlu\Z<br />

gbc^_l_dlhjZdqbkemiZ^ZxsbogZg_]hnhlhgh\aZlhl`_bgl_j\Ze\j_f_gb<br />

N<br />

j_] .<br />

QE = , (1)<br />

N<br />

iZ^.<br />

N iZ^ hij_^_eyehkv ih \_ebqbg_ fhsghklb iZ^Zxs_]h baemq_gby baf_j_ggh]h ijb[h<br />

jhfNewFocus Inc.<br />

Kdhjhklv l_fgh\h]h kq_lZ hij_^_ey_lky dZd qbkeh kjZ[Zlu\Zgbc ^_l_dlhjZ \<br />

_^bgbpm\j_f_gb\hlkmlkl\bbbaemq_gby<br />

J_amevlZluwdki_jbf_glZihhij_^_e_gbxaZ\bkbfhklbQEgZ^ebg_\hegu<br />

fdfbkdhjhklbl_fgh\h]hkq_lZhllhdZkf_s_gbyijbjZaebqguojZ[hqbol_fi_jZlm<br />

jZoij_^klZ\e_gugZjbkBkke_^m_fu_^_l_dlhjuh[gZjm`b\Zxl\ukhdmxQE\BD<br />

^bZiZahg_ Ihgb`_gb_ l_fi_jZlmju ijb\h^bl d agZqbl_evghfm ih\ur_gbx QE LZd<br />

ijb L D d\Zglh\Zy wnn_dlb\ghklv ^hklb]Z_l Z ijb L D QE§ Ijb ijb<br />

[eb`_gbbddjblbq_kdhfmlhdmaZ\bkbfhklvd\Zglh\hcwnn_dlb\ghklbhllhdZkf_s_

Ih^k_dpbyk\_joijh\h^ysbobwe_dljhgguok\hckl\l\_j^uol_e 45<br />

QE,%<br />

11 12 13 14 15 16 17 18 19 20 21 22 23 24<br />

10 2 10 7<br />

QE,% 4.2K<br />

QE,% 3.2K<br />

10 1 QE,% 2.0K<br />

10 6<br />

l_fgh\u_ ijb .<br />

10 0<br />

10 -1<br />

10 -2<br />

10 -3<br />

10 -4<br />

10 -5<br />

l_fgh\u_ ijb D<br />

l_fgh\u_ ijb .<br />

10 0<br />

11 12 13 14 15 16 17 18 19 20 21 22 23 24<br />

I b<br />

, µA<br />

Jbk AZ\bkbfhklv d\Zglh\hc wnn_dlb\ghklb<br />

hldjulu_ kbf\heu b kdhjhklb l_fgh\h]h kq_lZ<br />

aZdjulu_ kbf\heu hl lhdZ kf_s_gby ijb<br />

l_fi_jZlmjZoDDbD<br />

10 5<br />

10 4<br />

10 3<br />

10 2<br />

10 1<br />

Kdhjhklvkq_lZk <br />

gby \uoh^bl gZ gZkus_gb_ qlh<br />

k\b^_l_evkl\m_l h lhf qlh ijb<br />

L D QE h]jZgbq_gZ dhwnnbpb_g<br />

lhf ih]ehs_gby l_ \gmlj_ggyy<br />

d\Zglh\Zy wnn_dlb\ghklv [ebadZ d<br />

AZ\bkbfhklv kdhjhklb l_f<br />

gh\h]h kq_lZ hl lhdZ kf_s_gby y\<br />

ey_lkywdkihg_gpbZevghc<br />

R = a ⋅ exp( b ⋅ I I ) (2)<br />

dk<br />

]^_ab b –dhwnnbpb_gluhij_^_<br />

ey_fu_ ba l_hjbb Ihkdhevdm ijb<br />

jh^Z l_fgh\uo bfimevkh\ g_ ykgZ<br />

khhl\_lkl\mxsZyl_hjby_s_g_ih<br />

kljh_gZ<br />

K\_joijh\h^gbdh\u_ h^ghnh<br />

lhggu_^_l_dlhjugZwnn_dl_we_d<br />

ljhggh]hjZah]j_\Z\lhgdbok\_jo<br />

ijh\h^gbdh\uoie_gdZofh]ml[ulvijbf_g_gu\hfgh]boh[eZklyolj_[mxsbo^_l_d<br />

lbjh\Zgbybaemq_gbyk\_jogbadhcbgl_gkb\ghklbk\ukhdbf\j_f_ggufjZaj_r_gb_f<br />

lZdbodZd^bZ]ghklbdZbl_klbjh\Zgb_K;BK\we_dljhgbd_ki_dljhkdhibyh^bghqguo<br />

fhe_dme ZgZeba baemq_gby d\Zglh\uo lhq_d \ ihemijh\h^gbdh\uo gZghkljmdlmjZo Z<br />

lZd`_^eyj_]bkljZpbbk\_jokeZ[uokb]gZeh\\Zkljhghfbb<br />

Ebl_jZlmjZ<br />

1. Gol’tsman G.N., et al., IEEE Trans. on Appl. Supercond., Vol. 13, No. 2, June 2003, pp.<br />

192-195<br />

2. Goltsman G. et al., Appl. Phys. Lett. 79, 705 (2001);<br />

3. Sobolewski R., et al., Proc. SPIE vol. 5123, pp. 2-12 (2003).<br />

b<br />

c<br />

M>D 535.232.61<br />

KI?DLJ:EVG:YQM

46<br />

EHFHGHKH_l_dlhjij_^klZ\ey_lkh[hcmadmxgfihehkdmlhgdhcgfk\_joijh\h<br />

^ys_cie_gdbNbN\uiheg_gghc\nhjf_f_Zg^jZ×10 beb×20 fdfK\_joijh<br />

\h^ysZyie_gdZNbNijbf_gy_fZy^eyba]hlh\e_gby^_l_dlhjZgZghkblkygZkZinbjh<br />

\mxih^eh`dmf_lh^hfj_Zdlb\gh]hfZ]g_ljhggh]hjZkiue_gby\]Zah\hckf_kbZj]hgZb<br />

ZahlZeyhilbfZevghcjZ[hlu^_<br />

l_dlhjZkms_kl\_gghqlh[uihehkdZk\_joijh\h^gbdZ[ueZh^ghjh^ghc<br />

Ijbgpbi^_ckl\by^_l_dlhjZhkgh\ZggZwnn_dl_we_dljhggh]hjZah]j_\Z\mevl<br />

jZlhgdbo iezgdZo k\_joijh\h^gbdh\ b h[jZah\Zgbb ghjfZevghc h[eZklb]hjyq_]hiyl<br />

gZijbih]ehs_gbbnhlhgZ>@>_l_dlhjgZoh^blkyijbl_fi_jZlmj_]hjZa^hgb`_djb<br />

lbq_kdhc b kf_sZ_lky ihklhygguf lhdhf [ebadbf d lhdm jZkiZjb\Zgby =bga[mj]Z -<br />

EZg^ZmIh]ehs_gb_hilbq_kdh]hd\ZglZh[eZ^Zxs_]h^hklZlhqghcwg_j]b_cijb\h^bl<br />

djZkiZjb\Zgbxdmi_jh\kdboiZjbh[jZah\ZgbxeZ\bgud\ZabqZklbp-aZjh`^Z_lky]hjy<br />

q__iylghaZkq_l^bnnmabbd\ZabqZklbpijhbkoh^bli_j_jZkij_^_e_gb_wg_j]bb\we_d<br />

ljhgghc ih^kbkl_f_ =hjyq__ iylgh jZkl_l qlh \uau\Z_l m\_ebq_gb_ iehlghklb ljZgk<br />

ihjlgh]hk\_joijh\h^ys_]hlhdZ\k_q_gbbie_gdbDh]^ZagZq_gb_iehlghklblhdZij_<br />

\urZ_ldjblbq_kdh_j c = 6÷7Â 6 :kf 2 ijbDk\_joijh\h^bfhklv\k_q_gbblhgdhc<br />

ie_gdb jZajmrZ_lky - \hagbdZ_l bfimevk gZijy`_gbyf< dhlhjuc j_]bkljbjm_lky<br />

ko_fhckt_fZkb]gZeZ<br />

OZjZdl_jbklbdhcqm\kl\bl_evghklb^_l_dlhjZy\ey_lkyd\Zglh\Zywnn_dlb\ghklv<br />

(QEjZ\gZyhlghr_gbxqbkeZnhlhgh\aZj_]bkljbjh\ZgguoaZ\j_fy2dqbkemnhlh<br />

gh\iZ^ZxsbogZ^_l_dlhjaZlh`_\j_fyJZg__ijh\_^_ggu_bkke_^h\Zgbyki_dljZev<br />

ghcaZ\bkbfhklbQE^_l_dlhjZihdZaZeb>@qlh\^hklmighf^eybaf_j_gbc^bZiZahg_<br />

^ebg\heg-fdfqm\kl\bl_evghklv^_l_dlhjZwdkihg_gpbZevghiZ^Z_lkm\_ebq_gb<br />

_f^ebgu\heguiZ^Zxs_]hbaemq_gby>ZggZyaZ\bkbfhklvfh`_l[ulvij_^klZ\e_gZ<br />

\ujZ`_gb_fQE=A· exp(-b  ijbnbdkbjh\ZgghfagZq_gbbjZ[hq_cl_fi_jZlmju<br />

blhdZkf_s_gby]^_b-qbke_ggucdhwnnbpb_glhij_^_ey_fucbaki_dljZevguobaf_<br />

j_gbcZA-dhwnnbpb_glaZ\bkysbchlZ[khexlghcfhsghklbbklhqgbdZbaemq_gby<br />

>eyhij_^_e_gbybg_h[oh^bfhihemqblvaZ\bkbfhklvqm\kl\bl_evghklb^_l_dlh<br />

jZhl^ebgu\hegubaemq_gbyBklhqgbdhffhghojhfZlbq_kdh]hbaemq_gbyy\eyekybg<br />

njZdjZkgucki_dljhf_ljBDK-^bZiZahg^ebg\heg-fdfBkke_^m_fuch[jZa_p<br />

gZoh^beky\djbhklZl_ijbl_fi_jZlmj_`b^dh]h]_ebyDbkf_sZekyihihklhyggh<br />

fmlhdmkihfhsvxbklhqgbdZKb]gZekh[jZapZih\ukhdhqZklhlghfmljZdlmih^Z\Zeky<br />

gZkbkl_fmKey wdjZgbjh\db iZjZabl<br />

gh]hdhfgZlgh]hbaemq_gbyijbf_gyebkvkZinbjh\h_\^bZiZahg_-3 fdfbebdj_f<br />

gb_\h_-5.6 fdf\oh^gu_hdgZdjbhklZlZZlZd`_oheh^gu_kZinbjh\ucbebdj_f<br />

gb_\ucnbevlju\gmljbdjbhklZlZ H^ghnhlhggucj_`bf^_l_dlbjh\ZgbygZ[ex^Zeky\<br />

^bZiZahg_^ebg\heghl fdf^h fdf<br />

>ey hij_^_e_gby dhwnnbpb_glZ : g_h[oh^bfh agZlv fhsghklv bklhqgbdZ baem<br />

q_gby:[khexlghq_jghl_eh:QLy\ey_lkybklhqgbdhfkba\_klgufagZq_gb_fiehl<br />

ghklbbaemq_gbylZdbfh[jZahfj_amevlZlubaf_j_gbyQEkbkihevah\Zgb_f:QL\dZ<br />

q_kl\_bklhqgbdZiha\heyxlhij_^_eblvfgh`bl_ev:bke_^h\Zl_evghZ[khexlgh_agZ<br />

q_gb_d\Zglh\hcwnn_dlb\ghklb^_l_dlhjZ<br />

Ijb bkihevah\Zgbb :QL \ dZq_kl\_ bklhqgbdZ h[jZa_p ihf_sZeky \ ljZgk<br />

ihjlguckhkm^>vxZjZbbaemq_gb_ih^\h^behkvdh[jZapmihljm[_kih]ehsZxsbfb

Ih^k_dpbyk\_joijh\h^ysbobwe_dljhgguok\hckl\l\_j^uol_e 47<br />

kdhjhklvkq_lZ^_l_dlhjZk <br />

600<br />

550<br />

500<br />

450<br />

400<br />

350<br />

300<br />

250<br />

200<br />

150<br />

100<br />

50<br />

0<br />

Ib/Ic=0.978<br />

Ib/Ic=0.976<br />

Ib/Ic=0.94<br />

Ib/Ic=0.914<br />

Ib/Ic=0.88<br />

510 515 520 525 530 535 540 545 550 555 560 565 570 575<br />

kl_gdZfb^eykgb`_gbyihl_jvijbhljZ`_gbb<br />

>bZiZahgl_fi_jZlmj:QL\Zjvbjh\Zekyhl<br />

^hDfZdkbfZevgZyiehlghklvki_dljZevgh<br />

]hjZkij_^_e_gbywg_j]bb\wlhfkemqZ_ijboh<br />

^beZkvgZbgl_j\Ze^ebg\heghl^hfdf<br />

Dhwnnbpb_gl:hij_^_eyekybakjZ\g_gbywdk<br />

i_jbf_glZevghc b l_hj_lbq_kdhc djb\uo aZ\b<br />

kbfhklb qm\kl\bl_evghklb ^_l_dlhjZ hl l_fi_<br />

jZlmju :QL Baf_j_gb_ hldebdh\ ^_l_dlhjZ \<br />

T(K)<br />

JbkAZ\bkbfhklvqbkeZhlkq_lh\^_l_dlhjZ<br />

hl l_fi_jZlmju :QL ijb jZaebqguo lhdZo<br />

kf_s_gby^_l_dlhjZ,EagZq_gb_djblbq_kdh<br />

]hlhdZ,F fd:<br />

0.1<br />

0.01<br />

^Zgghf ^bZiZahg_ ^ebg \heg ijh\h^b<br />

ehkv \i_j\u_ jbk Bkihevamy ihem<br />

q_ggu_agZq_gbyd\Zglh\hcwnn_dlb\gh<br />

klb ^_l_dlhjZ fh`gh ijh\_klb dZeb[<br />

jh\dm agZq_gbc d\Zglh\hc wnn_dlb\gh<br />

klbihemq_ggu_ijbbkihevah\Zgbb^jm<br />

]bobklhqgbdh\baemq_gbyjbk<br />

Ijh\_^_gb_ ^Zggh]h bkke_^h\Z<br />

gbyy\ey_lkyZdlmZevgufihkdhevdmih<br />

a\hey_l ihemqblv Z[khexlgu_ agZq_gby<br />

d\Zglh\hc wnn_dlb\ghklb ^_l_dlhjZ ^ey<br />

hij_^_e_gghc \hegu baemq_gby hij_^_<br />

eblv ihjh]h\uc fbgbfmf wg_j]bb d\Zg<br />

1.0 1.5 2.0 2.5 3.0<br />

lZbaemq_gbydhlhjuc_s_fh`_l[ulvaZj_]bkljbjh\Zgqlhiha\hebeh[umlhqgblvnb<br />

abq_kdb_ijbgpbiujZ[hlu^_l_dlhjZbjZkrbjblvh[eZklv_]hijbf_g_gby<br />

Ebl_jZlmjZ<br />

1. Semenov A. et al., Supercond. Sci.Technol., 15, R1 (2002);<br />

2. Verevkin A. et al.,Journal of Modern Optics, vol. 51, No 9-10, 1447-14458 (2004)<br />

3. Korneev A. et al., Appl.Phys.Lett., vol. 84, No 26 (2004)<br />

QE,%<br />

1E-3<br />

1E-4<br />

1E-5<br />

λfdf<br />

JbkAZ\bkbfhklvqm\kl\bl_evghklb^_l_dlhjZ4(<br />

hl ^ebgu \hegu AgZq_gby ihemq_ggu_ k ihfhsvx<br />

BDKq_jgu_kbf\heudZeb[jh\Zggu_gZagZq_gby<br />

ihemq_ggu_kihfhsvx:QLijyfZyebgby<br />

M>D 538.945<br />

BAF?G?GB?KL?I?GBEHD:EBA:PBBA:JH>UR:<br />

K

48<br />

EHFHGHKHeybkke_^h\Zgby[ueb\ayluh[jZapufgh]hkehcghckljmdlmjuNb/Pddhebq_<br />

kl\h[bkeh_\jZ\gyehkv;uebbaf_j_gum]eh\u_aZ\bkbfhklbH c2 (Θ\l_fi_jZlmj<br />

ghf^bZiZahg_hl D^hL]^_L* -l_fi_jZlmjZjZaf_jgh]hdjhkkh\_jZ<br />

Ihemq_ghqlhijbbaf_g_gbbΘhl^hg_dh_]hΘaZjh^urk\_joijh\h^ys_c<br />

nZauehdZebah\Zg\h^ghfi_jbh^_fgh]hkehcghcS/NkljmdlmjuH[jZa_pfh`ghjZk<br />

kfZljb\Zlv dZd ^\mf_jguc Ijb Θ > Θ i_ji_g^bdmeyjgZy khklZ\eyxsZy fZ]gblgh]h<br />

iheyhdZau\Z_l\ebygb_gZkl_i_gvehdZebaZpbbiZjZf_ljZihjy^dZjZafu\Zy_]hih<br />

g_kdhevdbfi_jbh^Zffgh]hkehcghckljmdlmjuD<br />

KI?DLJ:EVGUCKHKL:

Ih^k_dpbyk\_joijh\h^ysbobwe_dljhgguok\hckl\l\_j^uol_e 49<br />

fZevgufbihl_jyfblZdbkms_kl\_ggmxaZ\bkbfhklv^bwe_dljbq_kdhcijhgbpZ_fhklb<br />

k_]g_lhwe_dljbdZhlijbeh`_ggh]h\g_rg_]hwe_dljbq_kdh]hihey<br />

Bkke_^h\Zgby ie_ghd Y-Ba-Cu-O ijh\h^bebkv \ _fdhklghf \ukhdhqZklhlghf<br />

50<br />

EHFHGHKHey hibkZgby lZdbo \boj_c bo ^\b`_gby \ ^`ha_nkhgh\kdbo<br />

dhglZdlZob\aZbfh^_ckl\by\boj_ckieZgZjgufb^_n_dlZfb[uebihemq_gumjZ\g_<br />

gby g_ehdZevghc we_dljh^bgZfbdb Ijb wlhf jZkkfZljb\Zebkv ieZgZjgu_ ^_n_dlu<br />

f_`^m bahljhigufb k\_joijh\h^gbdZfb F_`^m l_f D<br />

KLJMDLMJ:B>BWE?DLJBQ?KDB?K

Ih^k_dpbyk\_joijh\h^ysbobwe_dljhgguok\hckl\l\_j^uol_e 51<br />

GZhkgh\_^Zgguoihjhrdh\hcj_gl]_gh\kdhc^bnjZdpbbhij_^_e_gguiZjZ<br />

f_ljubkbg]hgbywe_f_glZjguoyq__dihemq_gguokh_^bg_gbcWe_f_glZjgu_yq_c<br />

dbh[hbokh_^bg_gbcbf_xlhjlhjhf[bq_kdmxkbg]hgbxbijhkljZgkl\_ggmx]jmiim<br />

Cmm2 –D 11 2vIZjZf_ljuwe_f_glZjguoyq__dbf_xlagZq_gbya= 5.4434(1) Å; b=<br />

5.4506(1) Å; c= 45.527(2) Å^ey%L 4 Pb 1.5 Ti 4.5 O 16.5 bD Å; b= 5.4185(8) Å; c=<br />

45.267(5) Å ^eyBi 5 Ca 0.5 GaTi 3.5 O 16.5 .<br />

AZ\bkbfhklb^bwe_dljbq_kdhcijhgbpZ_fhklbhll_fi_jZlmjuT\qZklhl<br />

ghfbgl_j\Ze_-d=pij_^klZ\e_gugZjbkmgd_LZdhc\b^LoZjZdl_j_g^eyN:<br />

kihemp_eufmgZijbf_j^eyCaBi 8 Ti 7 O 27 (m >@bBi 7 Ti 4 NbO 21 (m >@>ey<br />

kh_^bg_gby%L 5 Ca 0.5 GaTi 3.5 O 16.5 rbjhdbc gbadhl_fi_jZlmjgucgZieu\ehdZebah\Zg\<br />

h[eZklbL 1 =730-DZ\ukhdhl_fi_jZlmjgucfZdkbfmfbf__lagZq_gb_-L 2 Db<br />

^ey%L 4 Pb 1.5 Ti 4.5 O 16.5 L 1 =670-DbL 2 Dkhhl\_lkl\_gghBkke_^h\Zgbyijbdhf<br />

gZlghcl_fi_jZlmj_iheyjbaZpbbPhl\_ebqbguijbeh`_ggh]hiheyEihdZaZebgZeb<br />

qb_i_l_ev]bkl_j_abkZP(Eqlh\f_kl_k\ukhdbfbagZq_gbyfbmdZau\Z_lgZk_]<br />

g_lhwe_dljbq_kdh_khklhygb_wlbokh_^bg_gbc<br />

Jbk AZ\bkbfhklv ^bwe_dljbq_kdhc ijhgbpZ_fhklb hl l_fi_jZlmju ^ey kh_^bg_gbc<br />

Bi 4 Pb 1.5 Ti 4.5 O 16.5 bBi 5 Ca 0.5 GaTi 3.5 O 16.5<br />

AgZq_gbyL 2 lZdbfh[jZahfkhhl\_lkl\mxll_fi_jZlmjZfDxjbL K \wlbokh<br />

_^bg_gbyo l_ l_fi_jZlmjZf kljmdlmjgh]h nZah\h]h i_j_oh^Z k_]g_lhwe_dljbdiZjZwe_dljbdIjhbkoh`^_gb_gbadhl_fi_jZlmjguohkh[_gghkl_cgZLfh`_l[ulv<br />

h[mkeh\e_ghnZah\ufi_j_oh^Zfk_]g_lhwe_dljbdI-k_]g_lhwe_dljbdII [2].<br />

Ebl_jZlmjZ<br />

1. Rm\Z_\:L

52<br />

EHFHGHKH

Ih^k_dpbyk\_joijh\h^ysbobwe_dljhgguok\hckl\l\_j^uol_e 53<br />

aZa_fe_gghc f_lZeebq_kdhc pbebg^jbq_kdhc dZf_jhc kem`Zs_c \lhjuf we_dljh^hf<br />

Ijb lZdhc Zkbff_ljbb we_dljh^h\ jZajy^ \hagbdZe ebrv m

54<br />

EHFHGHKH

Ih^k_dpbyk\_joijh\h^ysbobwe_dljhgguok\hckl\l\_j^uol_e 55<br />

@HA?NKHG:–WDKI?JBF?GL:EVGH?<br />

K?L?EVKL

56<br />

EHFHGHKH

Ih^k_dpbyk\_joijh\h^ysbobwe_dljhgguok\hckl\l\_j^uol_e 57<br />

\bkfmlh\uo dmijZlh\ KhklZ\eyxsb_ kljmdlmjm j_ahgZgku gZ[ex^Zxlky ijb kf_s_<br />

gbyoVm^h\e_l\hjyxsbomkeh\bxeV = «& nhg MhilbfZevgh^hibjh\Zgguoh[jZa<br />

ph\kljmdlmjZgZ[ex^Z_lky\^bZiZahg_wg_j]bc”eV ≤fw

58<br />

EHFHGHKH@[uehykghqlhfgh]hahgghklvk\_joijh\h^ysbos_e_c<br />

^he`gZ bkq_aZlv \³]jyaghf´ ij_^_e_ M^b\bl_evguf k\hckl\hf fgh]hahgghc k\_jo<br />

ijh\h^bfhklb\kbkl_f_0J% 2 y\ey_lkylhh[klhyl_evkl\hqlhhgZg_bkq_aZ_ldZdwlh<br />

ihdZaZgh\^ZgghcjZ[hl_ijbm\_ebq_gbbhklZlhqgh]hkhijhlb\e_gbygZ^\Zihjy^dZb<br />

[he__ Ijbqbghc klZ[bevghklbfgh]hahgghck\_joijh\h^bfhklb\0JB 2 y\ey_lkyfZ<br />

ehklvihl_gpbZeh\jZkk_ygbyf_`^mσbπ-ahgZfb>@<br />

GZfb[uebbamq_guihebdjbklZeebq_kdb_h[jZapuMg 1-x Al x B 2 kdhgp_gljZpby<br />

fb”x ”bkhhl\_lkl\_gghcdjblbq_kdbfbl_fi_jZlmjZfbK •T c •<br />

K < dZq_kl\_ wdki_jbf_glZevguo f_lh^h\ bkihevah\Zgu fbdjhdhglZdlgZyZg^j__\<br />

kdZyblmgg_evgZyki_dljhkdhibbH[Zwlbof_lh^Zj_Zebah\ZgukihfhsvxdhglZdlh\<br />

gZfbdjhlj_sbg_break junction) [5].<br />

Ke_^m_l hlf_lblv qlh baf_j_gb_ l_fi_jZlmjguo aZ\bkbfhkl_c s_e_c ∆ σ (T b<br />

∆ π (T [he__ ij_^ihqlbl_evgh k ihfhsvx Zg^j__\kdhc ki_dljhkdhibb lZd dZd ^hklZ<br />

lhqghj_adZykm[]Zjfhgbq_kdZys_e_\ZykljmdlmjZgZ[ex^Z_lkyijZdlbq_kdb\iehlv^h<br />

djblbq_kdhc l_fi_jZlmju T c Ihke_^g__ iha\hey_l hp_gblv ehdZevgmx djblbq_kdmx<br />

l_fi_jZlmjmT c \h[eZklbfbdjhdhglZdlZ<br />

GZfbmklZgh\e_ghqlhl_fi_jZlmjgu_aZ\bkbfhklbs_e_c∆ σ (Tb∆ π (Tmkbk<br />

l_fuMg 1-x Al x B 2 hlebqZxlkydZq_kl\_ggufh[jZahfL_fi_jZlmjgu_aZ\bkbfhklb∆ σ (T)<br />

[ebadbd;DR-lbim

Ih^k_dpbyl\_j^hl_evghcgZghwe_dljhgbdb 59<br />

L

60<br />

EHFHGHKH

Ih^k_dpbyl\_j^hl_evghcgZghwe_dljhgbdb 61<br />

M>D<br />

BKKE?>H:<br />

HFWIJ<br />

∗∗ >zfbg@dhlhjucZdlb\ghbkihevam_lky\f_^bpbg_<br />

\ nhlhl_jZi_\lbq_kdbo wnn_dlZo ijb e_q_gbb `_elmob gh\hjh`^_gguo dh`guo [h<br />

e_ag_c Z lZd`_ jZdh\uo aZ[he_\Zgbc Ba\_klgh qlh hkgh\gh_ khklhygb_ fhe_dme db<br />

kehjh^Z y\ey_lky ljbie_lguf h^gZdh ijb ih]ehs_gbb wg_j]bb fhe_dmeu dbkehjh^Z<br />

i_j_oh^yl \ \ha[m`^_ggh_ kbg]e_lgh_ khklhygb_ >ey hkms_kl\e_gby wlh]h ijhp_kkZ<br />

dZdijZ\behbkihevah\ZebkvdjZkbl_eb\uklmiZxsb_\jhebnhlhk_gkb[bebaZlhjh\b<br />

h[_ki_qb\Zxsb_i_j_^Zqmwg_j]bbljbie_lghfmdbkehjh^mhgZklhys_]h\j_f_gbwnn_dl]_g_jZpbb 1 H 2 gZ<br />

ih\_joghklb gZghdjbklZeeh\ por-Si gZ[ex^Zeky dZq_kl\_ggh ih ki_dljZf nhlhexfb<br />

g_kp_gpbb

62<br />

EHFHGHKH

Ih^k_dpbyl\_j^hl_evghcgZghwe_dljhgbdb 63<br />

Ki_dljuWIJ^eyf_ah- por-Siihemq_ggu_gZ\ha^mo_\hlkmlkl\b_bijbhk\_<br />

s_gbbiheghklvxkh\iZebqlhmdZau\Z_lgZhlkmlkl\b_]_g_jZpbb 1 H 2 \wlhffZl_jbZ<br />

e_Wlhih^l\_j`^Z_lwdkblhggucf_oZgbafi_j_^Zqbwg_j]bbdbkehjh^mlZddZd\f_<br />

ah- por-SikjZaf_jhfgZghdjbklZeeh\[he__gfwdkblhguijbdhfgZlghcl_fi_jZlmj_<br />

l_jfbq_kdb^bkkhpbbjmxl\ke_^kl\b_fZeuowg_j]bck\yab>@<br />

Ebl_jZlmjZ<br />

1. 7KHL:6XUIDFH6FLHQV5HSRUWV3<br />

2. Kovalev D., Gross E., Künzner N. et al. // Phys. Rev. Lett. 2002. 89. P. 137401-1.<br />

3. ImeQL_ogbdZWIJ-ki_dljhkdhibb³Fbj´K<br />

4. EbkZq_gdhF=Lbfhr_gdhHFWE?DLJHFB=J:PBB<br />

Dmlmjh\:GFZke_ggbdh\ZggZyjZ[hlZihk\ys_gZj_r_gbxi_j\hcbawlboaZ^ZqGZb[he__i_jki_dlb\<br />

gufb^eykha^ZgbyaZahjh\g_h[oh^bfhcfZehcrbjbguij_^klZ\eyxlkyf_lh^ukbk<br />

ihevah\Zgb_f dhf[bgZpbc gZgheblh]jZnbq_kdbo f_lh^h\ b f_lh^h\ we_dljhobfbb<br />

we_dljhobfbq_kdh_gZg_k_gb_ljZ\e_gb_>@b^jm]bownn_dlh\ijhbkoh^ysbo\lhg<br />

dboie_gdZowe_dljhfb]jZpbyZlhfh\f_lZeeZ\lhgdboie_gdZo>@ZggZyi_j_fuqdZkhklhyeZba^\mokeh_\ojhfZgfbahehlZgfOjhf[ue<br />

g_h[oh^bf^eymemqr_gbyZ^]_abbahehlZ Lheklu_we_dljh^uhdZgqb\ZebkvdhglZdl<br />

gufb iehsZ^dZfbjZaf_jhfo ff d dhlhjuf ih^\_^_gu mijm]b_ b]hevqZlu_<br />

eZidb LZdh_ \dexq_gb_ h[_ki_qb\Zeh ih^dexq_gb_ ba]hlh\e_gguo h[jZaph\ d we_d

64<br />

EHFHGHKH:<br />

KIHFHSVXIHJBKLH=HDJ?FGBY<br />

;_eh]hjhoh\B:Jy[qbdh\X<<br />

F=MbfF

Ih^k_dpbyl\_j^hl_evghcgZghwe_dljhgbdb 65<br />

exfbg_kp_gpbyNE\IDh[mkeh\e_gZbaemqZl_evghcZggb]beypb_cwdkblhgh\\ha<br />

fh`ghklv kms_kl\h\Zgby dhlhjuo ijb dhfgZlghc l_fi_jZlmj_ ih^l\_j`^Z_lky dZd<br />

wdki_jbf_glZevgufbnZdlZfblZdbl_hj_lbq_kdbfbjZkq_lZfbH^gZdhwdkblhgufh<br />

]mlZggb]bebjh\Zlv[_auaemqZl_evghi_j_^Z\Zywg_j]bxfhe_dme_dbkehjh^Z\ke_^kl<br />

\b_q_]hhgZi_j_oh^bl\\ha[m`^_ggh_kbg]e_lgh_khklhygb_>@<br />

IhjhrhdIDihemqZekyklZg<br />

^Zjlguf we_dljhobfbq_kdbf ljZ\<br />

e_gb_f ieZklbg fhghdjbklZeebq_<br />

kdh]h dj_fgby p-lbiZ k m^_evguf<br />

khijhlb\e_gb_f! Hf kf\we_d<br />

ljhebl_ gZ hkgh\_ ieZ\bdh\hc db<br />

kehlu b wlbeh\h]h kibjlZ \ayluo \<br />

ijhihjpbb Iehlghklv lhdZ<br />

ljZ\e_gby\Zjvbjh\ZeZkvhl^h<br />

f:kf 2 NEgZghdjbklZeeh\ID\ha<br />

[m`^ZeZkv baemq_gb_f Zahlgh]h eZ<br />

a_jZ k ^ebghc \hegu gf b<br />

^ebl_evghklvx bfimevkZ gk J_<br />

]bkljZpbyki_dljh\NEijh\h^beZkv<br />

ijbdhfgZlghcl_fi_jZlmj_kihfh<br />

svx NWM Hamamatsu >ey j_]bkl<br />

jZpbb dbg_lbd NE bkihevah\Zeky<br />

pbnjh\hc aZihfbgZxsbc hkpbeeh<br />

]jZnAgilent.<br />

Ki_dlju NE ihjhrdZ ID<br />

ihemq_ggu_ gZ \ha^mo_ b \ \Zdmmf_<br />

(0.01 Lhjj ij_^klZ\e_gu gZ jbk 1.<br />

A^_kv ohjhrh aZf_lgh m\_ebq_gb_<br />

bgl_gkb\ghklbNEIDijb\Zdmmfb<br />

jh\Zgbb h[jZapZ qlh fh`gh h[tyk<br />

gblv kgb`_gb_f \ \Zdmmf_ dhgp_g<br />

ljZpbb dbkehjh^Z ke_^h\Zl_evgh<br />

[hevr__ dhebq_kl\h \ha[m`^_gguo<br />

wdkblhgh\ Zggb]bebjm_l baemqZ<br />

l_evgh<br />

IjbwlhfgZb[he__bgl_gkb\<br />

guci_j_ghkwg_j]bbijhbkoh^blgZ<br />

^ebg_ \hegu gf khhl\_lkl\mx<br />

s_c wg_j]bb w< >Zgghc \_eb<br />

Bgl_gkb\ghklvhlg_^<br />

0,0<br />

600 800 1000<br />

>ebgZ\hegugf<br />

qbghcy\ey_lkyjZagbpZwg_j]bcf_`^mhkgh\gufb\ha[m`^_ggufkhklhygbyfbfhe_<br />

dmedbkehjh^Z>@GZ\klZ\d_djbkij_^klZ\e_gZaZ\bkbfhklv]Zr_gbyNEhl^ebgu<br />

\hegudhlhjZyjZkkqblu\ZeZkvdZdhlghr_gb_ki_dljh\NEIDgZoh^ys_]hkyih^\Z<br />

dmmfhfbgZhldjulhf\ha^mo_

66<br />

EHFHGHKH

Ih^k_dpbyl\_j^hl_evghcgZghwe_dljhgbdb 67<br />

dZfb>eyihemq_gby[he__lhgdh]hjbkmgdZkZfbowe_dljh^h\h[jZa_pih^\_j]Z_lkyaZ<br />

k\_ld_gZwe_dljhgghffbdjhkdhi_Ihke_q_]hijh\h^blkyj_Zdlb\gh_bhggh_ljZ\e_<br />

gb_ ]_jfZgby b we_dljhggh]h j_abklZ ih wlhfm jbkmgdm. < j_amevlZl_ gZ dj_fgb_\hc<br />

ih^eh`d_ihemqZ_lky`_kldZyih^\_r_ggZyfZkdZq_j_adhlhjmxaZl_fgZiueyxlkh[<br />

kl\_gghwe_dljh^u<br />

D<br />

IEHLGHKLVWE?DLJHGGUOKHKLHYGBCZgbebg::<br />

F=MbfFbhdkb^ lblZgZ – rbjhdhahgguc ihemijh\h^gbd ijbf_gy_fuc dZd \ obfbb<br />

nhlhdZlZebahqbkldZ\h^ubl^lZd\ihke_^gb_]h^ub\nbabd_kheg_qgu_we_<br />

f_glunhlh^_l_dlhju]Zah\u_k_gkhju

68<br />

EHFHGHKH@d\Zglh\uolhqdZo>@bihjbkluoihemijh\h^gbdZo>@

Ih^k_dpbyl\_j^hl_evghcgZghwe_dljhgbdb 69<br />

guol_fi_jZlmjZo\bgl_j\Ze_l_fi_jZlmjhlºK^hºKkrZ]hf\ºKGZjbkZ<br />

ij_^klZ\e_gu\hevlZfh]jZffu^eyh[jZapZkjZaf_jZfbgZghdjbklZeeblh\\gf<br />

>Ze__ [ue ijh\_^_g ^_lZevguc ZgZeba ihemq_gguo \hevlZfh]jZffb\uqbke_<br />

gb_ihgbfnmgdpbbiehlghkl_cwe_dljhgguokhklhygbc\gZghihjbklhfTiO 2 jbk[)<br />

kmq_lhfl_fi_jZlmjgh]hjZafulbynmgdpbbjZkij_^_e_gbyD<br />

J?E:DK:PBYWG?J=BBWE?DLJHGGH=H?GBY<br />

@beb fhe_dmeyjgh]h<br />

dbkehjh^Z>3, 4].<br />

>ey hibkZgby ijhp_kkZ ^hghjgh-Zdp_ilhjgh]h i_j_ghkZ wg_j]bb \ k\yaZgguo<br />

kbkl_fZo[ueZij_^eh`_gZke_^mxsZykbkl_fZg_ebg_cguo^bnn_j_gpbZevguomjZ\<br />

g_gbc<br />

⎧<br />

I<br />

exc<br />

N<br />

⎪N<br />

<br />

1<br />

= N0<br />

⋅σ<br />

⋅ −<br />

Eexc<br />

τ<br />

⎨<br />

⎪<br />

ne<br />

n<br />

e<br />

= β ⋅ N1<br />

⋅ng<br />

− ,<br />

⎪⎩<br />

τ<br />

A<br />

1<br />

D<br />

− β ⋅ N<br />

1<br />

⋅n<br />

g

70<br />

EHFHGHKHeyZgZ<br />

ebaZijb\_^_gghcfh^_eb\Zjvbjh\ZebkvlZdb_\_ebqbgudZd β , τ<br />

D<br />

, σ , I<br />

exc<br />

Ih^k_dpbyl\_j^hl_evghcgZghwe_dljhgbdb 71<br />

AZ\bkbfhklv N 1 ( I exc<br />

) ^eykbkl_f[_aijbf_k_c β = 0 km[ebg_cgZWlhk\yaZgh<br />

N<br />

kgZkus_gb_fqbkeZ\ha[m`^_gguogZghdjbklZeeh\<br />

>ey kbkl_f k ijbf_kvx ≠0<br />

I exc klZgh\blky<br />

N<br />

k\_joebg_cghckfjbkWlhy\e_gb_fh`ghh[tykgblvke_^mxsbfh[jZahfGZgZ<br />

qZevghfwlZi_ijbfZeuo\ha[m`^_gbyohkgh\gmxjhev\ijhp_kk_j_eZdkZpbbwg_j<br />

]bbb]jZ_lijhp_kkj_dhf[bgZpbbwdkblhgh\kbaemq_gb_fd\ZglZk\_lZIhwlhfmaZ\b<br />

N 1<br />

I exc<br />

kbfhklv ( )<br />

N 1<br />

β k jhklhf β aZ\bkbfhklv ( )<br />

bf__llhl`_oZjZdl_jdZdb\kemqZ_g_e_]bjh\Zgguokbkl_fIjb<br />

N<br />

hij_^_e_gghf agZq_gbb \ha[m`^_gby dhebq_kl\h gZghdjbklZeeh\ kh^_j`Zsbo wdkb<br />

lhgklZgh\blkyagZqbl_evgufHkgh\gmxjhev\ijhp_kk_j_eZdkZpbbwg_j]bbgZqbgZ<br />

_lb]jZlvi_j_^ZqZwg_j]bbwdkblhgh\Zdp_ilhjZfDhebq_kl\hgZghdjbklZeeh\g_kh<br />

^_j`Zsbowdkblhgm\_ebqb\Z_lkyqlh\_^_ldihy\e_gbx^hihegbl_evghc\hafh`gh<br />

klbh[jZah\Zgbywdkblhgh\

72<br />

EHFHGHKHD 546.26:620.187<br />

IH>

Ih^k_dpbyl\_j^hl_evghcgZghwe_dljhgbdb 73<br />

ke_^mxs_c hqbkld_ gZghljm[hd K ihfhsvx ijhk\_qb\Zxs_c b jZkljh\hc we_dljhg<br />

ghcfbdjhkdhibbbkke_^h\Zgh\ebygb_iZjZf_ljh\jhklZ^Z\e_gb_j_Zdpbhggh]h]ZaZ<br />

l_fi_jZlmjZdhebq_kl\hkhklZ\bkihkh[gZg_k_gbydZlZebaZlhjZb[mn_jgh]hkehygZ<br />

dhebq_kl\hbiZjZf_ljuihemqZ_fuogZghljm[hd<br />

H[gZjm`_ghqlh^eymki_rgh]hjhklZgZghljm[hdi_j_^gZg_k_gb_fgZih^eh`dm<br />

kehy dZlZebaZlhjZ g_h[oh^bfh hkZ^blv gZ g__ [mn_jguc kehc$OFu \hkihevah\Zebkv<br />

wlbfk\hckl\hf^eylh]hqlh[u\ujZklblvgZghljm[dbgZaZ^ZgguomqZkldZoih^eh`dbK<br />

ihfhsvx we_dljhggh-emq_\hc eblh]jZnbb [ueb ba]hlh\e_gu Zexfbgb_\u_ iehsZ^db<br />

jZaf_jhf^hgf 2 bihehkdblhesbghcgfAZl_fgZ\_kvh[jZa_p[uegZg_k_g<br />

kehc)HL_fg_f_g__gZghljm[dbjhke_lhevdhgZiehsZ^dZoihdjuluo$OJhklr_edZd<br />

gZ$OiehsZ^dZo\dexqZykZfu_g_[hevrb_lZdbgZ$OihehkdZojbk<br />

10 5 300 K<br />

dV/dI (Ω)<br />

10 4<br />

10 3<br />

4.2 K<br />

15 K<br />

16.5 K<br />

10 2<br />

-0,3 -0,2 -0,1 0,0 0,1 0,2 0,3<br />

V (B)<br />

Jbk JWF bah[jZ`_gb_ gZghljm[hd<br />

\ujZs_gguogZ$OiehsZ^dZo<br />

Jbk AZ\bkbfhklv ^bnn_j_gpb<br />

Zevgh]hkhijhlb\e_gbyhlgZijy`_<br />

gby ijb jZaguo l_fi_jZlmjZo ^ey<br />

h[jZapZ kh^_j`Zs_]h hdheh <br />

gZghljm[hd\s_ebf_`^mf_lZeeb<br />

q_kdbfbdhglZdlZfb<br />

Bkke_^h\Zg jhkl gZghljm[hd gZ ijh\h^ysbo kehyo hkZ`^_gguo gZ6L 3 N 4 f_f<br />

[jZgmH[gZjm`_ghqlhhilbfZevgu_mkeh\by^eykbgl_aZgZghljm[hdkha^Zxlkyijb<br />

bkihevah\Zgbb´kwg^\bqZ´khklhys_]hbakeh_\gf7Lgf3Ggf$Ogf<br />

)H´Kwg^\bq´hklZ\Zekyijh\h^ysbfihke_&9'-jhklZgZghljm[hd\kemqZ__kebbk<br />

ihevah\Zebkvhlghkbl_evghgbadb_l_fi_jZlmjZkbgl_aZ o &b^Z\e_gb_Zp_lbe_gZ<br />

IZ ;ueb ba]hlh\e_gu h[jZapu k gZghljm[dZfb i_j_dbgmlufb q_j_a kd\hagmx<br />

s_evbhibjZxsbfbkygZf_lZeebq_kdb_iehsZ^dbbamdZaZgguokeh_\f_lZeeh\^ey<br />

ijh\_^_gbyljZgkihjlguobaf_j_gbcKhijhlb\e_gb_h[jZapZkh^_j`Zs_]hhdheh<br />

gZghljm[hd ijb dhfgZlghc l_fi_jZlmj_ khklZ\eyeh ihjy^dZ Hf ke_^h\Zl_evgh<br />

khijhlb\e_gb_\i_j_kq_l_gZh^gmgZghljm[dmjZ\ghijbf_jghdHfWlZ\_ebqbgZ<br />

\k_]h\^\ZjZaZ[hevr_fbgbfZevgh\hafh`ghc\_ebqbgukhijhlb\e_gbygZghljm[db<br />

dHfqlhiha\heyehij_^iheh`blvqlhgZghljm[dZgZoh^blky\ohjhr_fdhglZdl_<br />

kf_lZeehfL_fg_f_g__baf_j_gbyijbgbadbol_fi_jZlmjZojbkihdZaZebqlh<br />

ijh\h^bfhklvkbevghaZ\bkblhll_fi_jZlmjubhlijbeh`_ggh]hgZijy`_gby

74<br />

EHFHGHKHD<br />

>BG:FBD:NHJFBJH

Ih^k_dpbyl\_j^hl_evghcgZghwe_dljhgbdb 75<br />

GZg_k_gb_ihjbklh]hdj_fgbygZl_dklmjbjh\Zghcih\_joghklbhkms_kl\eyehkv<br />

obfbq_kdbff_lh^hf>@\\h^guojZkl\hjZoHF, HNO 3 ijb_kl_kl\_gghfhk\_s_gbbb<br />

dhfgZlghcl_fi_jZlmj_Bkihevamyf_lh^jZkljh\hcwe_dljhgghcfbdjhkdhibbJ?F<br />

\jZ[hl_bamq_gZ^bgZfbdZnhjfbjh\ZgbyIDgZl_dklmjbjh\Zgghffbdjhj_ev_n_\aZ<br />

\bkbfhklbhlj_`bfh\ljZ\e_gbyIhdZaZghqlhehdZevgh_\hagbdgh\_gb_IDgZl_d<br />

klmjbjh\Zgghcih\_joghklbgZ[ex^Z_lkyq_j_a-fbgijbwlhfkehcIDnhjfbjm_l<br />

kylhevdh\^hevhkgh\ZgbcibjZfb^bkhklhblbaihj-fdf<br />

M\_ebq_gb_\j_f_gbnhjfbjh\ZgbyIDijb\h^bldm\_ebq_gbxiehsZ^bIDaZ<br />

kq_lkljZ\eb\Zgby[hdh\uo]jZg_cibjZfb^\hae_bohkgh\Zgbcbm\_ebq_gbxjZaf_jh\<br />

ihjjbk [ Ihegh_ ihdjulb_ ID \k_c ih\_joghklb ieZklbgu ijhbkoh^bl aZ-30<br />

fbg\aZ\bkbfhklb hl dhgp_gljZpbb ljZ\bl_ey Ijb wlhf bkoh^guc l_dklmjbjh\Zg<br />

gucfbdjhj_ev_niheghklvxkljZ\eb\Z_lkyZgZih\_joghklbgZ[ex^Z_lkyh^ghjh^gZy<br />

k_ldZihjkjZaf_jZfbihjafdfHkh[_gghklblZdh]hba[bjZl_evgh]hnhjfbjh\Zgby<br />

ID gZ l_dklmjbjh\Zgghc ih\_joghklb h[tykgyxlky jZaghc kdhjhklvx ljZ\e_gby jZa<br />

ebqguodjbklZeeh]jZnbq_kdboiehkdhkl_cibjZfb^qlhboh[jZah\u\Zxl<br />

Bamq_gunhlhexfbg_kp_glgu_bZglbhljZ`Zxs__k\hckl\ZIDgZl_dklmjbjh<br />

\Zgghcih\_joghklbIhdZaZghqlhgZg_k_gb_lhgdh]hkehyIDijb\h^bldmemqr_gbx<br />

ZglbhljZ`Zxsbok\hckl\l_dklmjbjh\Zgghcih\_joghklb<br />

Ebl_jZlmjZ<br />

1. =hj[ZqLYDhlh\ZG

76<br />

EHFHGHKHh[jhllhbEZg]Zijh\_^_gh^_lZevgh_<br />

bamq_gb_ ihe_c gZijy`_gbc gZjmr_ggh]h kehy ih\_joghklb b ^_n_dlh\djbklZeebq_<br />

kdhckljmdlmjuIhdZaZghgZebqb_gZijy`_ggh-^_nhjfbjh\Zggh]hkhklhygbyih\k_fm<br />

fbdjhj_ev_nmih\_joghklbjbk>_lZevgh_KLFbkke_^h\Zgb_lhih]jZnbbih\_jo<br />

ghklbknhjfbjh\Zgguoie_ghdgZghdjbklZeebq_kdh]hdj_fgbyihdZaZehqlhbkoh^gZy<br />

ih\_joghklvih^eh`_dfh^bnbpbjm_lkybgZ[ex^Zxlkywe_f_glukljmdlmjujZaf_jZ<br />

fbhl^hgfjbkgZdhlhjuonhjfbjm_lkymihjy^hq_ggucgZghj_ev_nijh<br />

y\eyxsbcky\\b^_\ha\ur_gbcgZ^ih\_joghklvxgZghf_ljh\uojZaf_jh\qlhkhhl<br />

\_lkl\m_l\_jrbgZfdj_fgb_\uodjbklZeeblh\Zm]em[e_gbyf_`^mgbfb–\uoh^mgZ<br />

ih\_joghklv madbo gZghf_ljh\uo ihj :gZeba KLF bah[jZ`_gbc ihi_j_qguo kj_ah\<br />

mdZau\Z_lqlh\ukhlZgZghj_ev_nZg_ij_\urZ_lgf<br />

M>D<br />

HIJ?>?E?GB?DHGP?GLJ:PBBEHD:EBAH:D?EV@Ko_fmbaf_j_gbyih\_joghklgh]hihl_gpbZeZ\^Zgghff_<br />

lh^_fh`ghij_^klZ\blvdZdkbkl_fmFHIjbk]^_Z –jZkklhygb_f_`^mkbkl_fhc<br />

ahg^h[jZa_p U i –iZ^_gb_ihl_gpbZeZgZ^bwe_dljbq_kdhfkeh_3 s –ih\_joghklguc

Ih^k_dpbyl\_j^hl_evghcgZghwe_dljhgbdb 77<br />

ihl_gpbZeQ sc –iehlghklvh[t_fgh]haZjy^Z\D-Si:H; Q ss –iehlghklvaZjy^Zih\_jogh<br />

klguokhklhygbcD-Si:H.<br />

Ijbbaf_g_gbbijbeh`_ggh]hdkljmdlmj_gZijy`_gbykf_s_gby\j_amevlZl_<br />

ba]b[Zahgijhbkoh^blZdlb\ZpbyehdZebah\ZgguokhklhygbcWlhijb\h^bldbaf_g_<br />

gbxjZkij_^_e_gbyaZjy^Z\ijbih\_joghklghch[eZklbZfhjngh]hihemijh\h^gbdZ<br />

AZjy^gZih\_joghklbZ-6L+fh`ghhi<br />

j_^_eblvdZd<br />

Q =−C ⋅ U − U . (1)<br />

ss<br />

i<br />

( BV s )<br />

Bkihevamy aZdhg =ZmkkZ b j_rZy mjZ\<br />

g_gb_ImZkkhgZ ihemqbf\ujZ`_gb_^eydhg<br />

p_gljZpbb bhgbabjh\Zgguo ehdZebah\Zgguo<br />

khklhygbc\s_ebih^\b`ghklbZfhjngh]hih<br />

emijh\h^gbdZ N IE \ aZ\bkbfhklb hl ih\_jogh<br />

klgh]hihl_gpbZeZU s :<br />

2<br />

εε<br />

0 i UBV<br />

−Us<br />

N ( U ) = ⋅<br />

(2)<br />

IE<br />

s<br />

q⋅ε<br />

s<br />

Z<br />

2<br />

.<br />

]^_ ε i , ε s –^bwe_dljbq_kdb_ ijhgbpZ_fhklb<br />

\ha^mrghckj_^ubD-Si:H;<br />

JZ[hlZ\uihegy_lkyijbnbgZgkh\hcih^^_j`d_Fbgbkl_jkl\ZH[jZah\ZgbyJN<br />

Ebl_jZlmjZ<br />

JbkWg_j]_lbq_kdZy^bZ]jZffZ<br />

dhglZdlZf_lZee^bwe_dljbdD6L+ijb<br />

1. Vatel O., Tanimoto M. Kelvin probe force microscope for potential distribution measurement<br />

of semiconductors devices// J. Appl. Phys. 77(6). 2358-2362 (1995)<br />

M>D<br />

KJ:

78<br />

EHFHGHKHD<br />

WE?DLJHIE:KLBQ?KDBCWNN?DL<br />

Ih^k_dpbyl\_j^hl_evghcgZghwe_dljhgbdb 79<br />

lhevdh\ahg_ehdZevgh]h\ha^_ckl\bybfimevkZlhdZZ\^Zebhlg_]hgZ\k_c[hdh\hc<br />

ih\_joghklbGDhlkmlkl\mxlGZ[ex^Z_lky]jZ^b_gliehlghklbyfhdljZ\e_gbyhli_<br />

jbn_jbbdp_gljm^_n_dlZZlZd`_\^hevjZ^bmkZGDFZdkbfZevgZyiehlghklv\k_]^Z<br />

gZ[ex^Z_lkymih\_joghklbGDbm[u\Z_lihf_j_m^Ze_gbyhlg__Wlhk\b^_l_evkl\m<br />

_lhlhfqlhijb\ha^_ckl\bbbfimevkZlhdZ\GDdjhf_ih\_joghklguo^_n_dlh\jh`<br />

^Z_lkylZd`_kdhie_gb_^bkehdZpbcehdZebah\Zgguo\dhgmkhh[jZaghffbdjhh[t_f_\<br />

10 2 -10 5 jZa f_gvr_f h[t_fZ GD Bkke_^h\Zgu jZaf_ju nhjfZ b ijbjh^Z kdhie_gby<br />

^bkehdZpbc_]h\ebygb_gZf_oZgbq_kdb_k\hckl\ZGDK^_eZg\u\h^hlhfqlhkdhi<br />

e_gb_^bkehdZpbcihjh`^_ghbehdZebah\Zgh\fbdjhh[t_f_dZgZeZijhl_dZgbylhdZ<br />

Bkke_^h\Zgb_f_lh^hfj_gl]_gh]jZnbbihdZau\Z_lqlh\ehdZevghcahg_lhdh<br />

\h]h\ha^_ckl\byijhl_dZgbybfimevkZlhdZdjbklZeebq_kdZykljmdlmjZkbevgh^_nhj<br />

fbjh\ZgZZ\^Zebhlwlhcahgu-^_nhjfZpbyhlkmlkl\m_lHl`b]ijbD\l_q_gb_<br />

q ijb\h^bl d qZklbqghfm \hkklZgh\e_gbx bkoh^ghc djbklZeebq_kdhc kljmdlmju Z<br />

^Zevg_crbchl`b]ijbD\l_q_gb_q-dijZdlbq_kdbiheghfm__\ha\jZlmWlhl<br />

wdki_jbf_glZevguc nZdl ih^l\_j`^Z_l h[gZjm`_ggh_ f_lh^hf ljZ\e_gby kdhie_gb_<br />

^bkehdZpbc b iha\hey_l k^_eZlv \u\h^ h lhf qlh ^bkehdZpbb \ kdhie_gbb y\eyxlky<br />

ih^\b`gufb >hihegbl_evgu_ ^Zggu_ h k\hckl\Zo kha^Zggh]h ehdZevgh]h kdhie_gby<br />

^bkehdZpbcihemq_gu\ukhdhqm\kl\bl_evgufbdkljmdlmjgufg_kh\_jr_gkl\Zff_lh<br />

^Zfb jhlZpbhgghc iheamq_klb b \gmlj_gg_]h lj_gby < bkoh^gh [_a^bkehdZpbhgguo<br />

GDgZ[ex^Z_lkyfZeZy\_ebqbgZjhlZpbhgghciheamq_klbbaZ^_j`dZ__gZqZeZhihegbl_evgu_ ^Zggu_ \ ihevam h[gZjm`_gguo wnn_dlh\ ihemq_gu \ wdki_<br />

jbf_glZoih\ha^_ckl\bxk_jbyfbbfimevkh\lhdZgZbkoh^gh[_a^bkehdZpbhggu_h^<br />

ghhkgh jZklygmlu_ GD ijb dhfgZlghc l_fi_jZlmj_

80<br />

EHFHGHKH:M=E?JH>:<br />

A:DEXQ?GGH=HZ]_klZgkdh]hgZmqgh]hp_gljZJ:G<br />

Bkke_^h\Zgb_fZl_jbZeh\kgZghjZaf_jgufbkljmdlmjZfbh[eZ^Zxsbfbjy^hf<br />

mgbdZevguok\hckl\y\ey_lkyZdlmZevguf^eyihgbfZgbyijbjh^ubf_oZgbafZfhe_<br />

dmeyjguo\aZbfh^_ckl\bcbnZah\uoij_\jZs_gbc<br />

Wlhc aZ^Zq_ hl\_qZ_l wdki_jbf_glZevgh_ bkke_^h\Zgb_ l_iehijh\h^ghklb <br />

fbdjhihjbklh]hkl_deZgZkus_ggh]h^bhdkb^hfm]e_jh^ZKH 2 ).<br />

JZ[hlZ [ueZ ijh\_^_gZ k p_evx bamq_gby ih\_^_gby KH 2 \ fbdjhihjbklhf<br />

kl_de_\qZklghklb\djblbq_kdhch[eZklb

Ih^k_dpbyl\_j^hl_evghcgZghwe_dljhgbdb 81<br />

djblbq_kdmxh[eZklv>bhdkb^m]e_jh^ZklZ[be_gbf__lgbadb_djblbq_kdb_iZjZf_l<br />

jubg_jZaeZ]Z_lky\bkke_^h\Zgghch[eZklbl_fi_jZlmjb^Z\e_gbc<br />

Bkke_^h\Zgby wnn_dlb\ghc l_iehijh\h^ghklb wnn fbdjhihjbklh]h kl_deZ<br />

gZkus_ggh]hKH 2 ijh\_^_guijbihfhsb\ukhdhlhqgh]hmkljhckl\Zih]j_rghklvdh<br />

lhjh]hg_ij_\urZ_l<br />

Ijb\h^ylkyj_amevlZluwdki_jbf_glZevgh]hbkke_^h\Zgby wnn fbdjhihjbklh]h<br />

kl_deZkhkj_^gbfjZaf_jhfihj –6 fgZkus_ggh]hKH 2 , \bgl_j\Ze_l_fi_jZlmj<br />

290-Db^Z\e_gbbFIZ<br />

J_amevlZlubkke_^h\Zgbyke_^mxsb_\i_j\u_bkke_^h\ZgZ wnn fbdjhihjbklh<br />

]hkl_deZgZkus_ggZyKH 2 , ihdjblbq_kdhcbah[Zj_\i_j\u_h[gZjm`_gj_adh\ujZ<br />

`_ggucfZdkbfmfl_iehijh\h^ghklb fZdk fbdjhihjbklh]hkl_deZgZkus_ggh]hKH 2<br />

\djblbq_kdhch[eZklb<br />

< j_amevlZl_ wdki_jbf_glZ ih l_iehijh\h^ghklb \ djblbq_kdhc h[eZklb h[gZ<br />

jm`_gh mf_gvr_gb_ Zfieblm^u fZdk kf_s_gb_ l_fi_jZlmju fZdkbfmfZ \ klhjhgm<br />

gbadbo l_fi_jZlmj ijhy\e_gb_ fZdkbfmfZ \ [he__ rbjhdhf bgl_j\Ze_ l_fi_jZlmj<br />

q_f^eyqbklh]hKH 2 .<br />

H[gZjm`_ggu_ wnn_dlu h[tykgyxlky h[jZah\Zgb_f ^\monZaguo ZfhjnghdjbklZeebq_kdbo<br />

kljmdlmj – gZghkljmdlmj \ KH 2 klhesbghc kehy \- gf \<br />

ijbe_]Zxs_cdkl_demih\_joghklb<br />

KBGOJHLJHGGU?BKKE?>H

82<br />

EHFHGHKH<<br />

Gh\hkb[bjkdbc]hkm^Zjkl\_ggucmgb\_jkbl_l<br />

;hevrhcbgl_j_kdf_lh^Zfihemq_gbygZghqZklbp\hagbdrbc\ihke_^gb_]h<br />

^u h[mkeh\e_g g_h[oh^bfhklvx ihemq_gby h[t_dlh\ k aZ^Zggufb k\hckl\Zfb ^ey<br />

kha^ZgbyjZaebqguodeZkkh\gZghijb[hjh\Wlbk\hckl\Zfh]mlbaf_gylvky\rbjhdhf<br />

^bZiZahg_bhij_^_eyxlkyf_lh^Zfbihemq_gbyiZjZf_ljZfbijbdhlhjuoijhbkoh^bl<br />

kbgl_a k\hckl\Zfb b jZaf_jZfb dZlZebaZlhjZ H^gbf ba i_jki_dlb\guo gZijZ\e_gbc<br />

y\ey_lkybkke_^h\Zgb_gh\uoZeehljhiguonhjfm]e_jh^Z\qZklghklbgZghljm[hdGZ<br />

gZklhysbcfhf_glgZb[he__rbjhdh_jZkijhkljZg_gb_^eykbgl_aZm]e_jh^guogZghl<br />

jm[ ihemqbeb f_lh^u l_jfbq_kdh]h dZlZeblbq_kdh]h jZaeh`_gby m]e_\h^hjh^h\<br />

(TCVD b l_jfbq_kdh]h dZlZeblbq_kdh]h jZaeh`_gby m]e_\h^hjh^h\ \ ijbkmlkl\bb<br />

ieZafuPCVD

Ih^k_dpbyl\_j^hl_evghcgZghwe_dljhgbdb 83<br />

gu_ nmee_j_gh-ih^h[gu_ qZklbpu bf_xsb_ emdh\bqgmx kljmdlmjm JZaf_ju deZkl_<br />

jh\f_lZeeZ\Zjvbjmxlky\ij_^_eZohl-gf<br />

H[gZjm`_ghkms_kl\_ggh_\ebygb_we_dljhnhj_aZgZghljm[hdgZdZq_kl\_ggmx<br />

kljmdlmjmm]e_jh^gh]hfZl_jbZeZIjbjZ[hl_\j_`bf_[_ajZajy^ZfZl_jbZeknbevl<br />

jZkhklhyebaZfhjngh]hm]e_jh^ZbgdZikmebjh\ZgguodeZkl_jh\`_e_aZ\m]e_jh^guo<br />

gZghqZklbpZobgZghljm[hdIjb\dexq_gbbjZajy^ZgZghljm[unbevljZg_^hklb]Zeb,<br />

ghhgb[uebgZc^_gu\fZl_jbZe_kh[jZgghfkZgh^ZjZkiheh`_ggh]h^h\oh^Z\]h<br />

jyqmxahgm]^_l_fi_jZlmjZbkhklhygb_dZlZebaZlhjZg_khhl\_lkl\mxlmkeh\byfjhk<br />

lZ gZghljm[hd ;ueb ijh\_^_gu wdki_jbf_glu k gbadbf we_dljbq_kdbf ihe_fgb`_<br />

ijh[hcgh]h \ dhlhjuo gZ nbevlj_ [ueZ h[gZjm`_gZ g_[hevrZy dhgp_gljZpby h^gh<br />

kl_ghqguodhjhldbo gZghljm[hdbwdki_jbf_glukh[jZlghciheyjghklvx \dhlhjuo<br />

gZghljm[u gZ nbevlj_ g_ h[gZjm`_gu gh h[gZjm`_gu gZ pbebg^jbq_kdhf Zgh^_ <<br />

gbadhl_fi_jZlmjghcieZaf_gZdjmiguoqZklbpZogZdZieb\Z_lkyhljbpZl_evgucaZjy^<br />

aZkq_ljZaghklbihlhdZwe_dljhgh\bbhgh\IjbwlhfaZjy^qZklbpuaZ\bkblhlwe_d<br />

ljhgghcl_fi_jZlmjubjZaf_jZqZklbpuGZebqb_aZjy^Zijb\h^bldihy\e_gbxwe_d<br />

ljhklZlbq_kdbokbe^_ckl\mxsboijhlb\\yadbokbeihlhdZijbhibkZgghc\ur_dhg<br />

kljmdpbb jZajy^gh]h ijhf_`mldZ Ijb ^hklb`_gbb g_dhlhjh]h djblbq_kdh]h aZjy^Z<br />

bebjZaf_jZaZ\bkys_]hhlijbeh`_gguo\g_rgboihe_cgZghljm[ZgZqbgZ_l^\b]Zlv<br />

kyijhlb\ihlhdZihgZijZ\e_gbxdZgh^m

84<br />

EHFHGHKH

Ih^k_dpbyl\_j^hl_evghcgZghwe_dljhgbdb 85<br />

Bkke_^h\Zgb_ihebdjbklZeebq_kdbolj_okehcguoie_ghdCo/Cu/Coijbbahl_j<br />

fbq_kdhfhl`b]_ihdZaZeh<br />

— \_ebqbgu [bebg_cghc b [bd\Z^jZlbqghc dhfihg_gl dhk\_gghc h[f_gghc<br />

k\yabbaf_gyxlkykm\_ebq_gb_flhesbguf_^ghcijhkehcdb<br />

—\ie_gdZoklhesbghcijhkehcdbKukhhl\_lkl\mxs_c-fmb-fmZglbn_j<br />

jhfZ]gblguffZdkbfmfZf[bd\Z^jZlbqgZydhfihg_glZdhk\_gghch[f_gghck\yabbk<br />

q_aZ_lijbl_fi_jZlmj_hl`b]Z h Kb h Kkhhl\_lkl\_ggh<br />

—ih\_^_gb_fZ]gblhj_abklb\gh]hhlghr_gbyh[mkeh\e_ghbaf_g_gb_f^ebgu<br />

k\h[h^gh]hijh[_]Zwe_dljhgh\baf_g_gb_fdhk\_gghch[f_gghck\yabf_`^mkehyfb<br />

Kh ba-aZ baf_g_gby kljmdlmju ie_ghd b ]jZgbp jZa^_eZ b g_fZ]gblghc ijhkehcdb<br />

jZaf_jZ a_j_g i_jbh^Z b Zfieblm^u r_jhoh\Zlhklb f_`nZaguo ]jZgbp m\_ebq_gby<br />

fZ]gblguofhklbdh\\g_fZ]gblghcijhkehcd_<br />

Ebl_jZlmjZ<br />

1. Levy P.M. Giant magnetoresistance in magnetic layered and granular materials // Solid<br />

6WDWH3K\VLFV‹P. 367-462.<br />

2. Parkin S.S.P. Giant magnetoresistance and oscillatory interlayer coupling in polycrystalline<br />

transition metal multilayers // In book of Eds. B. Heinrich and J.A.C. Bland Ultrathin<br />

Magnetic Structures II. Springer-Verlag Berlin Heidelberg. 1994. P.148 - 194.<br />

3. %UXQR37KHRU\RILQWHUOD\HUPDJQHWLFFRXSOLQJ3K\V5HY%‹3-439.<br />

M>D<br />

>

86<br />

EHFHGHKH

Ih^k_dpbyl\_j^hl_evghcgZghwe_dljhgbdb 87<br />

ke_\ha^_ckl\byBFIhlf_q_ghh[jZah\Zgb_gZih\_joghklbGe^\molbih\gZghkljmd<br />

lmjd\Zabi_jbh^bq_kdbojbkbbahljhiguonjZdlZevguo<br />

jbkFZ]gblhbg^mpbjh\ZggZygZghkljmdlmjZgZih\_joghklbGe<br />

JZkij_^_e_gb_ gZghdeZkl_jh\ \ i_jbh^bq_kdbo p_ihqdZo hibku\Z_lky \ ijb<br />

[eb`_gbb ghjfZevgh]h jZkij_^_e_gby F_lh^Zfb k_lhd b Nmjv_-ZgZebaZ hp_g_gZ<br />

njZdlZevgZyjZaf_jghklvdeZkl_jh\-djZl_jh\njZdlZevguokljmdlmjdhlhjZykhklZ\beZ<br />

1,76.<br />

Baf_g_gb_lhiheh]bbih\_joghklbGekl_q_gb_f\j_f_gbdhjj_ebjm_lkbaf_<br />

g_gb_f fbdjhl\_j^hklb b l_jfh^bgZfbq_kdbo iZjZf_ljh\ ieZ\e_gby GZ[ex^Z_fu_<br />

fZ]gblhbg^mpbjh\Zggu_gZghf_ljbq_kdb_mihjy^hq_ggu_kljmdlmju\Geh[km`^Zxl<br />

kykihabpbbkZfhhj]ZgbaZpbbfZ]gblhbg^mpbjh\Zgguo^_n_dlh\

88<br />

EHFHGHKHBG:FBQ?KD:Y L?HJBY DHKLB<br />

GbdheZ_\ZHI<br />

F=MbfF< Ehfhghkh\Znbabq_kdbcnZdmevl_l<br />

H^ghcbahkgh\guoijh[e_fkh\j_f_gghcklZlbklbq_kdhcnbabdby\ey_lkyih<br />

kljh_gb_l_hjbb`b^dhklbBf__lky[hevrhcwdki_jbf_glZevgucfZl_jbZeihl_jfh<br />

^bgZfbq_kdbf k\hckl\Zf jZaebqguo `b^dhkl_c HibkZgb_ wlbo ^Zgguo k\yaZgh k p_<br />

eufjy^hfkeh`ghkl_c<br />

Ih^k_dpbyl_hj_lbq_kdhcnbabdb 89<br />

kljZgkl\_

90<br />

EHFHGHKH

Ih^k_dpbyl_hj_lbq_kdhcnbabdb 91<br />

g_gme_\hc fZkkhc m π (r) GZjy^m k fZkkh\uf qe_ghf b qe_ghf hibku\Zxsbf d\Zjdibhggh_\aZbfh^_ckl\b_\eZ]jZg`bZgπ-f_ahggh]hihey\wlhch[eZklbkg_ba[_`gh<br />

klvxijboh^blky\\h^blv blZdgZau\Z_fuckdbjfh\kdbcqe_gibhggh]hkZfh^_ckl\by<br />

hkgh\gZyjhevdhlhjh]hkhklhbl\ij_^hl\jZs_gbbdheeZikZf_rdZ<br />

R\dhlhjhcn_jfbhggh_ihe_ijbh[j_lZ_l[_kdhg_qgh<br />

[hevrmxfZkkmM 0 →∞, \ke_^kl\b_q_]hhgh ^bgZfbq_kdbaZgmey_lky\wlhch[eZklbkf<br />

gZijbf_j>@Zibhggh_ihe_bf__lfZkkmm π, jZ\gmxj_ZevghcfZkk_π-f_ahgZ<br />

Ijb ihkljh_gbb kZfhkh]eZkh\Zggh]h j_r_gby mjZ\g_gbc ^\b`_gby bf__lky jy^<br />

ijbgpbibZevguohlebqbchlDkemqZy>@ Ij_`^_\k_]h^eyijb^Zgbykheblhggh]h<br />

oZjZdl_jZj_r_gbxhibku\Zxs_fmih\_^_gb_ibhggh]hihey\h\g_rg_ch[eZklbf_rdZ<br />

l_i_jv g_ lj_[m_lky \\h^blv ^hihegbl_evgh_ kZfh^_ckl\b_ f_ahgh\ \ wlhc h[eZklb ih<br />

kdhevdm lj_[m_fuc lhiheh]bq_kdbc oZjZdl_j j_r_gby Z\lhfZlbq_kdb h[_ki_qb\Z_lky aZ<br />

kq_l kdbjfbhgghchedgehog-dhgnb]mjZpbbibhggh]hihey ;he__lh]h\DhdZau\Z_l<br />

kyijbgpbibZevghg_\hafh`gufbkdexqblvbajZkkfhlj_gbygme_\mxn_jfbhggmxfh^m<br />

ih^h[ghlhfmdZdwlh^_eZehkv\DWlhh[klhyl_evkl\hbmkeh\b_kms_kl\h\ZgbykZ<br />

fhkh]eZkh\Zggh]hj_r_gby^eydbjZevgh]hm]eZ\h[eZklbkhklZ\eyxsbod\Zjdh\ ijb\h<br />

^yld^hihegbl_evghfmkhhlghr_gbxk\yau\Zxs_fmn_jfbhggmxM(r)bibhggmxm π (r)<br />

fZkkh\u_nmgdpbb\ijhf_`mlhqghch[eZklbf_rdZIjbgZeh`_gbb_kl_kl\_ggh]hlj_[h<br />

\ZgbyM(r→R)→ ∞ [uehihemq_ghg_ljb\bZevgh_bgl_]jZevgh_mkeh\b_gZm π (r)

92<br />

EHFHGHKH 1 qlh ijhy\ey_lky\hlkmlkl\bb klZpbhgZj<br />

guokhklhygbck^_ckl\bl_evgufbEbnbabq_kdbkhhl\_lkl\m_liZ^_gbxgZp_glj<<br />

j_Zevghklb h^gZdh bklhqgbd k Z > 137 bf__l keh`gmx \gmlj_ggxx kljmdlmjm ih<br />

13<br />

wlhfmgZij_^_evghfZeuojZkklhygbyo< 10 − kfmjZ\g_gb_gm`^Z_lky\mlhqg_<br />

gbbkmq_lhfwlh]hh[klhyl_evkl\Zqlh\jy^_kemqZ_\iha\hey_l\hkklZgh\blvkZfhkh<br />

ijy`_gghklv aZ^Zqb < qZklghklb jZkkfZljb\Zehkv h[j_aZgb_ dmehgh\kdhc kbg]meyj<br />

ghklbki_j_oh^hf ihl_gpbZeZ\dhgklZglmijbg_dhlhjhf r > 0<br />

0 kf>@bijb\_^_g<br />

gu_lZfkkuedbbebg_i_jlmj[Zlb\gucmq_lijyfh]hfZ]gblgh]h^bihev-^bihevgh]h<br />

\aZbfh^_ckl\by>@<br />

@b\^ZgghfkemqZ_bf_xl\b^<br />

( i n+<br />

I) ψ = 0<br />

−<br />

r=a<br />

γ , (2)<br />

]^_ n –\g_rgyyghjfZevdih\_joghklbkn_jujZ^bmkZaGZmjh\g_\hegh\uonmgdpbc<br />

wlhhagZqZ_lqlh\j_r_gbbl_i_jv[m^mlmqZkl\h\ZlvkeZ]Z_fu_kbg]meyjgu_\gme_<br />

J_r_gb_mjZ\g_gbyk]jZgbqgufmkeh\b_fijb\h^bldke_^mxs_fmmjZ\<br />

g_gbx^eymjh\g_ck\yaZgguokhklhygbck E < m iheguffhf_glhfjbhij_^_e_gghc<br />

q_lghklvxl<br />

= j ±1 2<br />

( 2λa)<br />

2<br />

( + + − )<br />

( m+ E + m−E)<br />

q−s<br />

λ ( )<br />

m E m E<br />

s<br />

= γ<br />

⋅<br />

Fq ( −s,1− 2 s,2 a) + m+ E− m−E Fq ( − s+ 1,1−2 s,2 λa)<br />

p−k<br />

⋅<br />

q+<br />

s<br />

Fq ( + s,1+ 2 s,2 λa) + ( m+ E− m− E)<br />

Fq ( + s+ 1,1+<br />

2 s,2 λa)<br />

p−k<br />

]^_ k = ±( j +1 2)<br />

^ey = j ±1 2<br />

2 2 2<br />

s = k − Zα<br />

, λ = m − E , F ( a,<br />

b,<br />

z)<br />

–nmgdpby<br />

Dmff_jZ\ujh`^_ggZy]bi_j]_hf_ljbq_kdZynmgdpby<br />

Zαm ZαE Γ(<br />

q − s)<br />

Γ(1<br />

+ 2s)<br />

p = , q = − , γ =<br />

.<br />

λ λ Γ(<br />

q + s)<br />

Γ(1<br />

− 2s)<br />

l , ( ) 2<br />

IhdZ Zα<br />

< 1iZjZf_ljs –^_ckl\bl_evgucbmjZ\g_gb_\_s_kl\_gghIj_^_e<br />

a → 0 khhl\_lkl\m_lh[jZs_gbx\gmev γ qlh^Z_l q + s = −n<br />

, n = 0,1...<br />

bijb\h^bld<br />

klZg^Zjlghfmhl\_lm^eymjh\g_c^bjZdh\kdhcqZklbpu\dmehgh\kdhfihe_<br />

Ijb Zα<br />

> 1iZjZf_ljs –qbklhfgbfuc s = iε<br />

bmjZ\g_gb_klZgh\blkynZ<br />

ah\uf<br />

2ε ln 2λa + 2πn<br />

= nZa_ijZ\hcqZklb (4)<br />

(3)

Ih^k_dpbyl_hj_lbq_kdhcnbabdb 93<br />

]^_n –p_eh_qbkeh − ∞ ≤ n ≤ ∞ Bag_ihkj_^kl\_gghke_^m_lqlhijb^hklZlhqghfZ<br />

euoZdh]^Z]bi_j]_hf_ljbq_kdb_nmgdpbb\fh`ghkqblZlvjZ\gufb_^bgbp_aZ\b<br />

kbfhklvmjh\g_cwg_j]bbhl ln a [m^_l[ebadZdi_jbh^bq_kdhcki_jbh^hfπ<br />

ε ihkdhevdm<br />

\uoh^ ln a aZwlhagZq_gb_dhfi_gkbjm_lkyi_j_oh^hfdke_^mxs_fmagZq_gbxnWlh^h<br />

dZau\Z_lZghgkbjh\Zggh_\ur_ml\_j`^_gb_h[hlebqbb^Zggh]hf_lh^Zhlj_]meyjbaZpbb<br />

q_j_ah[j_aZgb_dmehgh\kdhckbg]meyjghklb—\^ZgghfkemqZ_mjh\gbwg_j]bb[m^mli_<br />

jbh^bq_kdbfb^_ckl\bl_evgufbnmgdpbyfbjZ^bmkZZ\iehlv^hkZfuofZeuoagZq_gbcZ.<br />

;he__^_lZevgh_ZgZeblbq_kdh_bkke_^h\Zgb_mjZ\g_gbyij_^klZ\ey_lagZqb<br />

l_evgu_ljm^ghklbihwlhfmdjZ_\ZyaZ^ZqZbkke_^h\ZeZkvqbke_ggh<br />

Ihemq_guagZq_gbygZb[he__gbadhe_`Zsbos-mjh\g_c^eyjZaebqguoZb^bZiZah<br />

gZbaf_g_gbcZhl -7 ^h -4 [hjh\kdh]hjZ^bmkZ

94<br />

EHFHGHKH

Ih^k_dpbyl_hj_lbq_kdhcnbabdb 95<br />

ihevah\Zlv f_lh^ ^ey jZkq_lZ ki_dljh\ ih]ehs_gby baemq_gby b dhf[bgZpbhggh]h<br />

jZkk_ygby fgh]hZlhfguofhe_dmebai_j\uoijbgpbih\<br />

Ebl_jZlmjZ<br />

1. AZkeZ\kdbc=FKlhoZklbqghklv^bgZfbq_kdbokbkl_f,³GZmdZ´Fhkd\Z<br />

2. Mki_ob kh\j_f_gghc we_dljhgbdb lhf ihk\yszg ijh[e_fZf ^bgZfb<br />

q_kdh]hoZhkZ<br />

3. Namiot V.A., Chernavskii D.S. 3K\V/HWW$Y‹S-4 (2003) (22dec.)<br />

4. Audretsch J., Mensky M.B., Namiot V.A. Phys. Let. A. v.203 p.209-214 (1995)<br />

5. 0HQVN\0%&KDRV6ROLWRQV )UDFWDOVY‹S-1387 (1995)<br />

6. GZfbhl -gZqZevgh_bdhg_qgh_khklhygb_g_ij_h[jZah\Zgghckbkl_fuaZibr_f<br />

mkeh\b_ bg\ZjbZglghklb kbkl_fu hlghkbl_evgh hi_jZpbb ijhkljZgkl\_ggh]h hljZ`_<br />

gby\\b^_<br />

_<br />

6<br />

I<br />

<br />

S S<br />

_ _ 6LI<br />

<br />

= _ beb _ ><br />

L<br />

<br />

<br />

< I _ 6 _ L > _ = _ < S<br />

I<br />

_ 6 _ SL<br />

_ ,<br />

]^_S – hi_jZlhj\aZbfh^_ckl\byihkj_^kl\hfdhlhjh]hkbkl_fZi_j_oh^blbagZqZev<br />

gh]hkhklhygby\dhg_qgh_<br />

Mkeh\b_bg\ZjbZglghklbhlghkbl_evghijhkljZgkl\_ggh]hhljZ`_gbyg_ihkj_^<br />

kl\_gghke_^m_lbamkeh\bydhffmlZpbb\b^Z> 63@<br />

= bebbkoh^yba\b^Zhi_jZlhjZS<br />

\ij_^klZ\e_gbb\aZbfh^_ckl\by<br />

Q=<br />

<br />

∞<br />

−∞<br />

∞<br />

∞ Q<br />

−L<br />

6 = ∑ ∫G[<br />

∫G[<br />

Q7<br />

+<br />

LQW<br />

[<br />

+<br />

LQW<br />

[<br />

Q<br />

,<br />

Q<br />

−∞<br />

+<br />

<br />

bamkeh\bydhffmlZpbb\nhjf_ 3+<br />

LQW<br />

[<br />

3<br />

= +<br />

LQW<br />

[<br />

<br />

]^_ [ = 3[ = [<br />

−[<br />

.<br />

:gZeh]bqgu_khhlghr_gbyfh`ghihemqblvlZd`_^eyhi_jZpbcaZjy^h\h]hkh<br />

ijy`_gbybh[jZs_gby\j_f_gbG_h[oh^bfhhkh[hih^q_jdgmlvqlhmkeh\b_dhffm<br />

lZpbby\ey_lkyimklvb^hklZlhqgufgh\h\k_g_g_h[oh^bfufmkeh\b_f^eykhojZg_<br />

&

96<br />

EHFHGHKH

Ih^k_dpbyl_hj_lbq_kdhcnbabdb 97<br />

Ebl_jZlmjZ<br />

1. I_kdbgFRj_^_j>`>>j_eeK>J_eylb\bklkdZyd\Zglh\Zyl_hjbyBHGNFB000.<br />

3. BpbdkhgDAx[_j@;D\Zglh\Zyl_hjbyiheyFhkd\ZFbj<br />

4. Lee T.D.: A theory of spontaneous T-violation. // Phys.Rev., 1973. V.DS. 1226-1229.<br />

5. Kobayashi M., Maskawa T.: CP violation in the renormalizable theory of weak interaction.<br />

// Prog. Theor. Phys., 1973. V. 49.<br />

6. Liu J., Wolfenstein L.: Spontaneous CP violation in the SU(2)xU(1) model with two<br />

Higgs doublets. // Nucl. Phys., 1987. V.B.289.<br />

7. G_ebiZ GN NbabdZ we_f_glZjguo qZklbp DZeb[jh\hqgu_ ihey Fhkd\Z<br />

he]hiheh\ F< >m[bgbg FG ;hahgu Ob]]kZ \<br />

^\mo^m[e_lghcfh^_ebkgZjmr_gb_fKJ-bg\ZjbZglghklb<br />

M>D<br />

KMFFBJHB:=J:FFN?CGF:G:< N=1<br />

KMI?JKBFF?LJBQGHC D

98<br />

EHFHGHKH@<br />

ZckhgZblh<br />

`^_kl\Mhj^Zfh`ghhlkmffbjh\Zlv[hevrmxqZklv^bZ]jZffN_cgfZgZ>eyl_o^bZ<br />

]jZffdhlhju_g_m^Zehkvkmffbjh\ZlvlZdbfh[jZahf[ueh\ukdZaZghij_^iheh`_gb_<br />

hkljmdlmj_bo\deZ^h\\^\molhq_qgmxnmgdpbx=jbgZdZeb[jh\hqgh]hihey

Ih^k_dpbyl_hj_lbq_kdhcnbabdb 99<br />

hdeZ^hlf_q_g`xjbdZdh^bgbaemqrbogZih^k_dpbb

100<br />

EHFHGHKH b kh\j_f_ggu_ qbke_g<br />

gu_ jZkq_lu dhglbgmZevguo bgl_]jZeh\ hij_^_eyxsbo wlb \Zdmmfgu_ kj_^gb_ ih<br />

a\heyxl \ lhf qbke_ bkke_^h\Zlv g_i_jlmj[Zlb\gu_ \deZ^u \ wlb ijhiZ]Zlhju Wlb<br />

\deZ^u gZb[he__ gZ]ey^gh ij_^klZ\e_gu \ \bevkhgh\kdhf jZaeh`_gbb hi_jZlhjh\<br />

a b<br />

a b<br />

TAµ ( x) Aν ( y)<br />

b Tc ( x) c ( y)<br />

\dhlhjhfhgbijhy\eyxlky\\b^_kl_i_gguoihijZ\hdd<br />

2<br />

\_^ms_fm qe_gm ihjy^dZ O(( x−<br />

y) − ) khhl\_lkl\mxs_]h \ jZaeh`_gbb _^bgbqghfm<br />

hi_jZlhjm Ke_^mxsb_ hi_jZlhju ^Zxsb_ \deZ^ \ wlh jZaeh`_gb_ _klv hi_jZlhju<br />

fZkkh\hcjZaf_jghklb<br />

2 a a<br />

Aµ ( x)<br />

b c ( x) c ( x ).<br />

Hlf_lbf h^gh g_fZeh\Z`gh_ ijbgpbibZevgh_ jZaebqb_ f_`^m ijhiZ]ZlhjZfb<br />

dZeb[jh\hqguoihe_c\Z[_e_\hcbg_Z[_e_\hcl_hjbyoIjbf_qZl_evgufy\ey_lkylhl<br />

nZdlqlh\Z[_e_\hc U (1) -l_hjbb\ihegucijhiZ]Zlhjnhlhggh]hiheydZeb[jh\hqguc<br />

iZjZf_ljα \oh^blebrvq_j_aljb\bZevgmxijh^hevgmxqZklv<br />

1 pµ pν p<br />

2 µ<br />

pν<br />

Gµν ( p) = ( η ) G( p )<br />

2 µν<br />

− − α , (1)<br />

2 4<br />

p p p<br />

2<br />

]^_ G( p ) g_ aZ\bkbl hl α \g_Z[_e_\hc l_hjbb wlh ml\_j`^_gb_ m`_ g_\_jgh qlh<br />

fh`ghihdZaZlvijh\_^y\uqbke_gby\gbarboihjy^dZol_hjbb\hafms_gbc>hdZaZ<br />

l_evkl\hwlh]hml\_j`^_gbyfh`ghgZclbgZijbf_j\>@WlhgZ[ex^_gb_iha\hey_l<br />

gZfihkljhblvke_^mxsmxdZeb[jh\hqgh-bg\ZjbZglgmx\_ebqbgm<br />

< T( A ( x) A µ<br />

µ<br />

( y) + αc( x) c( y))<br />

><br />

0<br />

.<br />

Hkh[ucbgl_j_kij_^klZ\ey_lh^gZdhkemqZcg_Z[_e_\hcl_hjbb@ijb<br />

ihfhsb f_lh^h\ g_dhffmlZlb\ghc l_hjbb ihey ihdZaZgh qlh dZeb[jh\hqghbg\ZjbZglgufy\ey_lkydhg^_gkZl<br />

∫ h^gZdh^Zggh_ml\_j`^_gb_gm`^Z_lky<br />

2 4<br />

< Aµ<br />

( x)<br />

d x><br />

\g_dhlhjhfihykg_gbbldgZijbf_jba\b^ghqlh\qZklghfkemqZ_Z[_e_\hcl_hjbb<br />

d 2<br />

Aµ<br />

( x) 0<br />

Dc(0)<br />

dα < > =−<br />

ikz 4<br />

e d k<br />

a^_kv Dc<br />

( z)<br />

≡∫ bwlZ\_ebqbgZjZ\gZgmexebrvijb D<br />

2<br />

c(0) = 0 qlhkijZ\_^<br />

k + iε<br />

eb\hgZijbf_j\jZaf_jghcj_]meyjbaZpbb<br />

0 α= 0<br />

= 0,<br />

l_hlkmlkl\b_dhg^_gkZpbb^moh\\ehj_gp_\hcdZeb[jh\d_<br />

LZdbfh[jZahf\^ZgghcjZ[hl_ihemq_guke_^mxsb_j_amevlZlu\h-i_j\uo\<br />

U (1) -l_hjbb ihdZaZgZ dZeb[jh\hqgZy bg\ZjbZglghklv \Zdmmfgh]h kj_^g_]h<br />

µ<br />

< T( A ( x) A ( y) + c( x) c( y))<br />

> bihkljh_gy\guc\b^\bevkhgh\kdh]hjZaeh`_gbywlh<br />

µ<br />

α<br />

0

Ih^k_dpbyl_hj_lbq_kdhcnbabdb 101<br />

d 2<br />

]h hi_jZlhjZ Ij_^eh`_g f_lh^ ijh\_jdb jZ\_gkl\Z Aµ<br />

( x) 0<br />

0<br />

dα < > = \g_Z[_e_\hc<br />

l_hjbbiml_fbamq_gbyk\hckl\^moh\h]hdhg^_gkZlZIhdZaZghqlh\g_dhffmlZlb\ghc<br />

l_hjbbihey\bevkhgh\kdh_jZaeh`_gb_ijhba\_^_gbyhi_jZlhjh\g_kijZ\_^eb\hbih<br />

2<br />

wlhfm ba dZeb[jh\hqghc bg\ZjbZglghklb dhg^_gkZlZ < A µ<br />

>g_evay k^_eZlv \u\h^ h<br />

ijbkmlkl\bbkhhl\_lkl\mxs_]hhi_jZlhjZ\\bevkhgh\kdhfjZaeh`_gbbdZeb[jh\hqgh<br />

bg\ZjbZglgh]hijhba\_^_gbyhi_jZlhjh\\dhffmlZlb\ghcl_hjbb<br />

:\lhj[eZ]h^Zj_g:: KeZ\gh\maZihklZgh\dmaZ^Zqb<br />

Ebl_jZlmjZ<br />

1. Gubarev F.V., Stodolsky L., Zakharov V.I. Phys.Rev.Lett 86 (2001) 2220<br />

2. Gubarev F.V., Zakharov V.I. Phys.Lett.B 501 (2001) 28<br />

3. Arriola E.R., Bowman P.O., Broniowski Q. Landau-gauge condensates from the quark<br />

propagator on the lattice, hep-ph/0408309<br />

4. Slavnov A.A., hep-th/0407194<br />

5. Slavnov A.A. Noncommutative gauge theories and gauge invariance of dimension two<br />

condensate in Yang-Mills theory, Phys. Lett. B 608 (2005) 171-176<br />

M>D 530.12; 539.12<br />

KD:EJBAF

102<br />

EHFHGHKH@ Ba-f_jguo mjZ\g_gbc Wcgrl_cgZ dhlhju_<br />

ihklmebjmxlky\\b^_<br />

5 1 5<br />

RAB − GAB R= æ<br />

QAB<br />

2<br />

]^_ Q<br />

AB<br />

– 5-f_jgucl_gahjwg_j]bb-bfimevkZihemqZxlkyh[uqgu_mjZ\g_gbyWcg<br />

rl_cgZkhklZg^Zjlgufl_gahjhfwg_j]bb-bfimevkZwe_dljhfZ]gblgh]hihey\ijZ\hc<br />

qZklb \lhjZy iZjZ mjZ\g_gbc FZdk\_eeZ b g_dhlhjh_ kdZeyjgh_ mjZ\g_gb_ Baf_jguomjZ\g_gbc]_h^_abq_kdboihemqZ_lky\_dlhjgh_mjZ\g_gb_khhl\_lkl\mxs__<br />

mjZ\g_gbx^\b`_gbyaZjy`_gghcqZklbpukhklZg^ZjlghckbehcEhj_gpZbkdZeyj<br />

gh_mjZ\g_gb_^Zxs__ihklhygkl\hhlghr_gbywe_dljbq_kdh]haZjy^Zijh[ghcqZk<br />

lbpud__fZkk_ GZdhg_p^himklbfu_\l_hjbbij_h[jZah\Zgbydhhj^bgZlkhhl\_lkl<br />

\mxl ba\_klguf dZeb[jh\hqguf ij_h[jZah\Zgbyf \_dlhjgh]h ihl_gpbZeZ we_dljh<br />

fZ]gblgh]hihey<br />

Ljm^ghklvx l_hjbb DZempu y\eyehkv kdZeyjgh_ mjZ\g_gb_ \ul_dZxs__ ba<br />

mjZ\g_gbcWcgrl_cgZdhlhjh_ijb\h^behd`_kldhck\yabf_`^mkdZeyjghcdjb\ba<br />

ghcbwe_dljhfZ]gblgufkdZeyjhf F F µν<br />

µν<br />

H^gZdhwlmijh[e_fmm^ZehkvjZaj_rblv<br />

\jZfdZoeZ]jZg`_\h]hih^oh^Zihklmebjmymkeh\b_ G<br />

55<br />

=−1gZmjh\g_eZ]jZg`bZ<br />

gZ

Ih^k_dpbyl_hj_lbq_kdhcnbabdb 103<br />

1 ∂ ⎛ 1 ⎞ 8<br />

ϕ 2 ∂x ⎜<br />

ϕ<br />

⎟<br />

⎝ ⎠ 3c ds<br />

µν 2 µ<br />

µ g<br />

Gm0<br />

d u<br />

Φ =− =−<br />

2 ν 2 2<br />

LZdbfh[jZahfijboh^bfd\u\h^mqlhkdZeyjgh_ihe_\l_hjbbDZempufh<br />

`_lhl\_qZlvaZbaemq_gb_aZjy`_gghcqZklbp_cwe_dljhfZ]gblgh]hiheyDlZdhc`_<br />

bgl_jij_lZpbbijb\h^blZgZebakdZeyjgh]hmjZ\g_gby]_h^_abq_kdboHlghr_gb_aZ<br />

jy^Z qZklbpu d __ fZkk_ l_i_jv g_ y\ey_lky ihklhygghc \_ebqbghc qlh oZjZdl_jgh<br />

^eybaemqZxs_cqZklbpu<br />

Ebl_jZlmjZ<br />

1. DZempZ LD D ijh[e_f_ _^bgkl\Z nbabdb K[ :ev[_jl Wcgrl_cg b l_hjby<br />

]jZ\blZpbbFFbjk– 534.<br />

2. Ebnrbp?FL_hjbyiheyFGZmdZ<br />

.<br />

M>D<br />

BKKE?>HIHEVGHC>B:=J:FFU<br />

< L?HJBBIHEYKMI?JKLJMG<br />

Juqdh\><<br />

F=MbfF

104<br />

EHFHGHKHD<br />

K:FH>?CKL

Ih^k_dpbyl_hj_lbq_kdhcnbabdb 105<br />

Ihiuldb\uqbke_gbyo\hklh\h]hqe_gZij_^ijbgbfZebkv\keZ[hfklZlbq_kdhf<br />

ihe_ijbg_j_eylb\bklkdbokdhjhklyo[2] b\qZklguokemqZyoba\_klguof_ljbd<br />

=jZ\blbjmxsZyfZkkZ<br />

Ih^kq_l \k_o qe_gh\ \ mjZ\g_gbyo ^\b`_gby \ i_j\hf ijb[eb`_gbb ijhba\h<br />

^beky^eyijhkljZgkl\jbqqb-iehkdhcnhgh\hcf_ljbdb[3]ghhklZ\Zebkvg_\uykg_g<br />

gufb ihy\e_gb_ jZaebqguo fZkkh\uo iZjZf_ljh\ohly fZkkZ g_ \oh^bl \ mjZ\g_gb_<br />

]_h^_abq_kdhcb\hafh`ghklvh[h[s_gbyaZ^ZqbgZkemqZcijhba\hevghbkdjb\e_ggh<br />

]hijhkljZgkl\Z<br />

Ijh[e_fZk\yaZgZkdh\ZjbZglgufkhojZg_gb_fl_gahjZwg_j]bb-bfimevkZqZk<br />

λ<br />

λρ<br />

lbpu ^eydhlhjh]hlj_[m_lky\uiheg_gb_mkeh\by* µ<br />

K λ<br />

− * Kλρµ<br />

= \g___fbjh\hc<br />

ebgbbG – l_gahjWcgrl_cgZ h – kh[kl\_ggh_]jZ\blZpbhggh_ihe_qZklbpumkeh\b_<br />

λ<br />

gZibkZgh \ dZeb[jh\d_ Ehj_gpZ K<br />

µ<br />

= Kλµ<br />

>ey kemqZ_\ dh]^Z hgh Z\lhfZlbq_kdb<br />

m^h\e_l\hjy_lkygZijbf_j ijhkljZgkl\Z k dhkfheh]bq_kdhc ihklhygghc g_dhlhju_<br />

\b^udhgnhjfgh-iehkdbonhgh\uof_ljbdfh`ghgZibkZlvhl\_l<br />

µ µν µ ν ⎛ λ WDLO ⎞<br />

] = Pκ<br />

( J + ] ] ) ⎜−<br />

5λν<br />

] + Iν<br />

⎟,<br />

⎝ <br />

⎠<br />

µ<br />

]^_ hl[jhr_gu \k_ qe_gu ij_\urZxsb_ bkoh^gmx kl_i_gv ijb[eb`_gby]<br />

\u<br />

iheg_gZi_j_ghjfbjh\dZiZjZf_ljZ<br />

<br />

H<br />

<br />

<br />

κ<br />

−<br />

ε<br />

<br />

= , ε = + ,<br />

H<br />

bihke_i_j_ghjfbjh\db\u[jZggZlmjZevguciZjZf_ljP = HO\hklh\hcqe_gbf__l<br />

lhl`_\b^qlhb\[3]. LZdbfh[jZahfijhbkoh^blhldehg_gb_ljZ_dlhjbbfZkkb\ghc<br />

qZklbpuhl]_h^_abq_kdhc<br />

QZklgufbkemqZyfbdh]^Zwg_j]bykhojZgy_lky\g_aZ\bkbfhklbhl\_ebqbgh,<br />

y\eyxlkyijhkljZgkl\Zkdhkfheh]bq_kdhcihklhygghcdhgnhjfgh-iehkdb_ijhkljZg<br />

kl\Z b g_dhlhju_ ^jm]b_ [5] < kemqZ_ dhkfheh]bq_kdhc ihklhygghc b dhgnhjfghiehkdboijhkljZgkl\jbqqb-qe_gmjZ\g_gby^\b`_gbyaZgmey_lkybmjZ\g_gb_^\b`_<br />

gbybf__llhl`_\b^qlhb\[3]gh^ey[he__rbjhdh]hdeZkkZnhgh\uof_ljbdeyf_ljbdh[s_]h\b^Z\h<br />

ijhkhklZ_lkyhldjuluf<br />

LZdbf h[jZahf \\_^_gb_ fhgZ^u e iha\hey_l \uihegblv deZkkbq_kdmx i_j_<br />

ghjfbjh\dm\mjZ\g_gbb^\b`_gbykkZfh^_ckl\b_f g_\oh^y\ijhlb\hj_qb_kijbg<br />

pbihfwd\b\Ze_glghklb<br />

Ebl_jZlmjZ<br />

1. Dirac P.A.M. Classical Theory Of Radiating Electrons, Proc. Roy. Soc. Lond. A167<br />

(1938) 148.<br />

2. WittB.S.De and Brehme R.W. Radiation Damping In A Gravitational Field, Annals Phys.<br />

9 (1960) 220; B.S.DeWitt and C.M.DeWitt, «Falling charges» Physics 1 (1964) 3.<br />

3. Mino Y., Sasaki M. and Tanaka T. Gravitational radiation reaction to a particle motion<br />

Phys.Rev. D55 (1997) 3457 [arXiv:gr-qc/9606018].<br />

4. Gal'tsov D.V. and Spirin P. Radiation reaction reexamined: Bound momentum and Schott<br />

term, arXiv:hep-th/0405121.<br />

5. Staub S. On radiation reaction in gravitation theory. Diploma project, Ecole polytechnique<br />

federale de Lausanne 2005.

106<br />

EHFHGHKHD<br />

I?J?K?D:XSB?KYS-;J:GUB:GBAHLJHIGU? FH>?EB<br />

L?FGHCWG?J=BB<br />

∗∗ Hjeh\>=<br />

F=MbfF

Ih^k_dpbyl_hj_lbq_kdhcnbabdb 107<br />

— ^eykn_jbq_kdh]h-nZaZjZkrbj_gbykf_gy_lkynZahck`Zlbybebbf__lf_klh[_k<br />

dhg_qgh_jZkrbj_gb_\aZ\bkbfhklbhliZjZf_ljh\kbkl_fu<br />

— ^eyiehkdh]hijhkljZgkl\ZnZaZjZkrbj_gbykf_gy_lkynZahck`Zlby<br />

< ]bi_j[hebq_kdhf kemqZ_ gZ \j_f_gghc [_kdhg_qghklb ihemqZ_f bahljhigh_<br />

ijhkljZgkl\h>eyhklZevguo\g_rgboijhkljZgkl\gZ[ex^Z_lkyi_j_oh^hlhkh[_ggh<br />

klblbiZ[ebgZdlbimkb]ZjubebgZh[hjhl,\aZ\bkbfhklbhlagZdh\iZjZf_ljh\<br />

BgneypbhggZynZaZnZaZmkdhj_ggh]hjZkrbj_gby ihemq_gZ^ey\k_okemqZ_\<br />

\g_rgboijhkljZgkl\__m^h[ghhoZjZdl_jbah\Zlvkl_i_gvx_-nhe^bg]Z:<br />

a( τ2)<br />

ef=<br />

ln ,<br />

a( τ1)<br />

eh]Zjbnfhfhlghr_gbyfZkrlZ[gh]hnZdlhjZ\dhg_qgucfhf_glbgneypbhgghcklZ<br />

^bbdfZkrlZ[ghfmnZdlhjm\gZqZevgucfhf_gl<br />

GZebqb_ iehkdhc khklZ\eyxs_c \h \g_rg_f ijhkljZgkl\_ mf_gvrZ_l kl_i_gv<br />

bgneypbhgghcnZaubijb[hevrboagZq_gbyojZaf_jghklbq-k\g_rg_]hijhkljZgkl<br />

\ZbgneypbhggZynZaZhlkmlkl\m_l@<br />

Ebl_jZlmjZ<br />

1. Chiang-Mei Chen, Gal'tsov D.V., Gutperle M. S-brane Solutions in Supergravity Theories,<br />

Phys.Rev. D66 (2002) 024043, hep-th/0204071.<br />

2. Quevedo F. Lectures on string/brane cosmology, Class.Quant.Grav. 19 (2002) 5721,<br />

arXiv:hep-th/0210292.<br />

3. Gutperle M., Kallosh R., Linde A. M/String Theory, S-branes and Accelerating Universe,<br />

JCAP 0307 (2003), 001, arXiv:hep-th/0304225.<br />

M>D<br />

IHKLJH?GB?>BHGUO=BI?J;J:GF?LH>HFP?IHQ?DLH>U<br />

Hjeh\>=<br />

F=MbfF< Ehfhghkh\Znbabq_kdbcnZdmevl_l<br />

DeZkkbq_kdb_ j_r_gby l_hjbb kmi_jkljmgF-l_hjbb>@hibku\Zxsb_ ijhly<br />

`_ggu_h[t_dlu–]bi_j[jZgu–bf_xl\Z`gh_agZq_gb_^eyihbkdZgh\uoke_^kl\bc<br />

wlhcl_hjbb^hklmiguowdki_jbf_glZevghcijh\_jd_gZmkdhjbl_eyogh\h]hihdhe_gby<br />

bkihfhsvxZkljhnbabq_kdbobaf_j_gbc-4].<br />

JZkkfhljbf^_ckl\b_kh^_j`Zs__ihe_f_ljbq_kdh]hl_gahjZihe_Zglbkbff_l<br />

jbqgh]hl_gahjZjZg]Zqbihe_ ^beZlhgZdhlhjh_\oh^bl\[hahgguck_dlhjjZaebqguo

108<br />

EHFHGHKH

Ih^k_dpbyl_hj_lbq_kdhcnbabdb 109<br />

Ijb wlhf agZq_gbb gZc^_gh gh\h_ j_r_gb_ dhlhjh_ m^h\e_l\hjy_lihklZ\e_g<br />

gufmkeh\byfZkkbflhlbq_kdbiehkdh_kj_]meyjguf]hjbahglhfboZjZdl_jbam_lky<br />

q_lujvfyk\h[h^gufbiZjZf_ljZfb<br />

Ebl_jZlmjZ<br />

1. Duff M.J., Lu H., Pope K1 The Black Branes of M-theory, Phys.Lett. B382 (1996) 73,<br />

hep-th/9604052<br />

2. Lu H., Pope C.N., Xu W. Liouville and Toda Solutions in M-theory, hep-th/9604058<br />

3. Gavrilov V.R., Ivashchuk V.D., Melnikiv V.N., Multidimensional cosmology with multicomponent<br />

perfect fluid and Toda lattice, gr-qc/9407019<br />

4. Olshanetsky M.A., Perelomov A.M. Explicit Solutions of Classical Generalized Toda<br />

Models, Invent. Math. 54 (1979) 261<br />

M>D 524.8<br />

LHQGHBGL?=JBJM?F:YFH>?EV;:EEBKLBQ?KDHC<br />

:=J?=:PBB< PBEBG>JBQ?KDHCB KN?JBQ?KDHCKBFF?LJBB<br />

:g^jb_\kdbc::<br />

F=MbfF< Ehfhghkh\Znbabq_kdbcnZdmevl_l<br />

>ZggZy jZ[hlZ ihk\ys_gZ fh^_ebjh\Zgbx \hagbdgh\_gby djmighfZkrlZ[ghc<br />

kljmdlmju jZkij_^_e_gby\_s_kl\Z \h @<br />

JZkkfZljb\Z_lky iehkdZy 5] mqblu\Zlvqlh]jZ\blZpbhggu_kbeuijb<br />

[eb`_ggh dhfi_gkbjmxl©oZ[[eh\kdh_ aZf_^e_gb_ª \ua\Zggh_ g_ij_ju\guf m\_eb<br />

q_gb_f ijhkljZgkl\_ggh]h fZkrlZ[Z LZdbf h[jZahf w\hexpby ehdZevguo \hafms_<br />

gbcfh`_l[ulvhibkZgZmjZ\g_gbyfb<br />

&<br />

⎧ρt<br />

+ div(<br />

ρu)<br />

= 0<br />

⎨ & & & ,<br />

⎩(<br />

ρu)<br />

t<br />

+ div(<br />

ρu<br />

⊗ u)<br />

= 0<br />

\ujZ`ZxsbfbaZdhgukhojZg_gbyfZkkubbfimevkZ A^_kv ρ -ihe_iehlghklb u & -<br />

ihe_kdhjhklb<br />

Ijb i_j_k_q_gbb ljZ_dlhjbc qZklbp iue_\b^gh]h \_s_kl\Z gZjmrZ_lky h^gh<br />

agZqghklviheykdhjhklb\h^ghclhqd_ijhkljZgkl\Z\hagbdZxlg_kdhevdhihlhdh\ DZd<br />

ihdZau\Zxl^Zggu_qbke_ggh]hfh^_ebjh\Zgby]jZ\blZpbhggh_\aZbfh^_ckl\b_f_`^m<br />

ihlhdZfbijb\h^bldm^_j`Zgbx\_s_kl\Z\h[eZklbhlghkbl_evghfZeh]hjZaf_jZ Wlh<br />

gZ[ex^_gb_biha\hebehij_^eh`blvlZdgZau\Z_fmx©fh^_evijbebiZgbyª>@\dhlh<br />

jhc]jZ\blZpbhggucaZo\Zlfh^_ebjm_lkyg_mijm]bfkebiZgb_fqZklbp©iuebª<br />

110<br />

EHFHGHKHU<br />

IJB?CKL

Ih^k_dpbyl_hj_lbq_kdhcnbabdb 111<br />

^_ckl\by\hafms_gbyagZqbl_evghf_gvr_oZjZdl_jguoi_jbh^h\\j_f_gbZlhfZkms_kl<br />

\m_l\hafh`ghklvj_rZlvaZ^Zqmg_h]jZgbqb\Zy\_ebqbgm\hafms_gbyb\uihegblvjZk<br />

qzluZgZeblbq_kdbIjbf_jZfbih^h[guoijhp_kkh\kem`Zl\aZbfh^_ckl\b_Zlhfhfbbh<br />

gh\kmevljZdhjhldbfbbfimevkZfbwe_dljhfZ]gblgh]hiheydhlhju_fh]ml[ulvlZd`_b<br />

iheyfb [ukljuo ly`zeuo aZjy`_gguo qZklbp < wlhc jZ[hl_ jZa\blh j_eylb\bklkdh_<br />

h[h[s_gb_ ijb[eb`_gby \g_aZiguo \hafms_gbc ^ey mjZ\g_gby>bjZdZbgZ_]hhkgh\_<br />

jZkkfhlj_guwe_dljhggu_i_j_oh^ubjh`^_gb_we_dljhg-ihabljhgguoiZjijb\aZbfh<br />

^_ckl\bbly`zeh]hZlhfZkmevljZdhjhldbfbfimevkhfwe_dljhfZ]gblgh]hihey<br />

Ih\_^_gb_ we_dljhgZ \ \h^hjh^hih^h[ghf Zlhf_ hibku\Z_lky mjZ\g_gb_f >b<br />

jZdZlhfgu__^bgbpubkihevamxlky<br />

L F S<br />

<br />

F $<br />

]^_ qe_gu F S = D<br />

U F khklZ\eyxl ]ZfbevlhgbZg + bahebjh\Zggh]h ZlhfZ Z<br />

\aZbfh^_ckl\b_k\g_rgbfihe_f_klv 8 U W $ ; S –hi_jZlhjbfimevkZ b<br />

–fZljbpu>bjZdZc –kdhjhklvk\_lZKqblZ_fqlhaZ\bkbfhklv\_dlhjgh]hihl_g<br />

pbZeZhldhhj^bgZlrb\j_f_gbtk\h^blkyd $ ]^_ W N U –nZaZwe_dljh<br />

fZ]gblghc\hegu\hegh\hc\_dlhj ,<br />

k 0 ω 0 c ω –djm]h\ZyqZklhlZKgZqZeZ\_dlhj<br />

0<br />

guc bkdZeyjguc ihl_gpbZeuihey\u[bjZxlkylZdqlh<br />

0 Ihke_dZeb[jh<br />

\hqgh]h ij_h[jZah\Zgby>@ $ $ I, I F Wk I $Ub\u[hjZ hkb X<br />

\^hev N \aZbfh^_ckl\b_k\g_rgbfihe_f 8 UW <br />

[<br />

.<br />

Ijb[eb`_gb_ \g_aZiguo \hafms_gbc iha\hey_l ij_^klZ\blv ihl_gpbZe<br />

8 UW \\b^_ 8 U W <br />

[ ]^_<br />

<br />

FW [ <br />

<br />

GW<br />

Ijb \aZbfh^_ckl\bb k bfimevkhf we_dljhfZ]gblgh]h ihey ]Zmkkh\hc nhjfu<br />

<br />

wnn_dlb\ghc ^ebl_evghklvx ~ ), ( U W ( <br />

H[S<br />

<br />

W N <br />

U<br />

<br />

FRV W N U ,<br />

ihemqZ_f T( U W b FTU ]^_<br />

= D<br />

U<br />

F <br />

T ( U W ( <br />

H[S<br />

@lhqgh_\ujZ`_gb_^eyZfieblm^ui_j_oh^Zbakhklhygby<br />

| j !kwg_j]b_c ( M \khklhygb__ f !kwg_j]b_c ( I bf__l\b^kj [2]):<br />

D I M<br />

I [H L ( I ( M [ F H L F M<br />

b\_jhylghklvi_j_oh^Z<br />

D I M<br />

<br />

T <br />

T <br />

4 4 ) <br />

* [<br />

<br />

<br />

<br />

, (1)<br />

]^_\\_^zg\_dlhj 4 4 [<br />

4 \<br />

4 ]<br />

T<br />

I MF , I M ( I ( MbhkvZgZijZ\e_gZ\^hev<br />

QZj\bgZ^eyg_ij_ju\gh]hki_d<br />

ljZ>@qlhiha\hebehihemqblvZgZeblbq_kdb_\ujZ`_gby^eynhjfnZdlhjh\<br />

JZ[hlZ\uiheg_gZijbnbgZgkh\hcih^^_j`d_Jhkkbckdh]hnhg^Znmg^Zf_glZevguobkke_^h\Zgbc<br />

]jZgl‹ 04-02-ZbINTAS]jZgl‹ 03-54-4294).

112<br />

EHFHGHKH

Ih^k_dpbyl_hj_lbq_kdhcnbabdb 113<br />

N:A:;?JJBMJ:@iheh`beZgZqZehkbkl_fZlb<br />

q_kdbfbkke_^h\Zgbyf]_hf_ljbq_kdhcnZau\jZaebqguoaZ^ZqZod\Zglh\hcf_oZgbdb<br />

=_hf_ljbq_kdZynZaZba\_klgZb\^jm]boh[eZklyonbabdbkfgZijbf_j>@L_hjby<br />

lhiheh]bq_kdbonZajZa\b\ZeZkv]eZ\gufh[jZahf^eyebg_cguokbkl_f@<br />

MjZ\g_gb_lbiZOZjljbfh`_l[ulvbkihevah\Zgh^eyhibkZgby[ha_-wcgrl_cgh\kdh]h<br />

dhg^_gkZlZ ]^_ wlh mjZ\g_gb_ ijbgylh gZau\Zlv g_ehdZevguf mjZ\g_gb_f =jhkkZ-<br />

IblZ_\kdh]h<br />

P_evx^ZgghcjZ[hluy\ey_lkygZoh`^_gb_nZau;_jjb^eyg_ebg_cgh]hmjZ\<br />

g_gbylbiZOZjljb<br />

{ − i! ∂ + H Ö ( R(<br />

t),<br />

Ψ(<br />

t))<br />

} Ψ =<br />

t χ<br />

0,<br />

(1)<br />

HÖ<br />

Ö Ö<br />

χ<br />

( R(<br />

t),<br />

Ψ(<br />

t))<br />

= H ( R(<br />

t))<br />

+ χV<br />

( R(<br />

t),<br />

Ψ(<br />

t))<br />

2<br />

( ) ( )<br />

2<br />

Ö µ ( t)<br />

pÖ<br />

ρ(<br />

t)<br />

xpÖ<br />

+ px Ö σ t x<br />

H ( R(<br />

t))<br />

= +<br />

+<br />

2 2 2<br />

+ ∞ 2<br />

2<br />

Ö<br />

a(<br />

t)<br />

x<br />

c(<br />

t)<br />

y<br />

V<br />

] ( , )<br />

2<br />

( R(<br />

t),<br />

Ψ ( t))<br />

= ∫ dy[<br />

+ b(<br />

t)<br />

xy + Ψ y t<br />

− ∞<br />

2<br />

2<br />

A^_kv µ (t)<br />

, ρ (t)<br />

, σ (t)<br />

, a (t)<br />

, b (t)<br />

, c(t)<br />

-iZjZf_ljuihl_gpbZeZ χ -iZjZf_ljg_ebg_cgh<br />

klb<br />

@ihemq_guj_r_gbyaZ^ZqbDhrb\Z^bZ<br />

[Zlbq_kdhf ijb[eb`_gbb \ deZkk_ ljZ_dlhjgh-khkj_^hlhq_gguo nmgdpbc ^ey mjZ\g_<br />

gbykgZqZevgufbmkeh\byfb\\b^_kh[kl\_gguonmgdpbcf]gh\_ggh]h]Zfbevlh<br />

gbZgZ<br />

HÖ<br />

( R(<br />

t ), Ψ ( t )) Ψ = E Ψ .<br />

χ<br />

0 n 0 n n n<br />

GZ hkgh\_ ihemq_ggh]h j_r_gby ih^l\_j`^Zxlky \u\h^u Z^bZ[Zlbq_kdhc l_h<br />

j_fu^eyebg_cguokbkl_fbhij_^_ey_lky\b^nZau;_jjb<br />

⎛ 1 ⎞ ⎡ χc<br />

µ ⎤ 1 ⎛ ρ ⎞<br />

γ = ⎜n<br />

+ ⎟ 1<br />

⎜ ρ − µ ⎟,<br />

2<br />

∫ ⎢ −<br />

2 2 ⎥ d d<br />

⎝ ⎠ ⎣ Ω ⎦ 2Ω<br />

⎝ µ ⎠<br />

n = [ σ+χ ] µ−ρ ,<br />

C<br />

2<br />

Ω a (2)<br />

]^_ C g_dhlhjucdhglmj\ijhkljZgkl\_iZjZf_ljh\@<br />

:\lhjqZklbqghih^^_j`Zgklbi_g^b_cg_dhff_jq_kdh]hnhg^Z©>bgZklbyª<br />

Ebl_jZlmjZ<br />

1. Berry M.V. Quantum Phase Factors Accompanying Algebraic Changes // Proc. Roy. Soc.<br />

London. — 1984. — Vol. A392, No~1802. — P. 45-58.

114<br />

EHFHGHKH

Ih^k_dpbyl_hj_lbq_kdhcnbabdb 115<br />

3. Feranchuk I.D., Ivanov A.A. Operator method for nonperturbative calculation of the<br />

thermodynamic values in quantum statistics: diatomic molecular gas // J. Phys. A: Math.<br />

Gen., 2004, Vol. ‹P. 9841-9860.<br />

M>D 537.8 (075.8)<br />

HKH;?GGHKLBJ?R?GBYBGL?=JH->BNN?J?GPB:EVGUO<br />

MJ:<br />

Eukh\J@^b<br />

njZdpbhggu_aZ^Zqbbamq_gu]hjZa^hkeZ[__Hkgh\gZyijh[e_fZaZdexqZ_lky\[hevrbo<br />

fZl_fZlbq_kdbo keh`ghklyo k\yaZgguo k j_r_gb_f mjZ\g_gbc FZdk\_eeZ \ kj_^Zo ]^_<br />

]jZgbpujZa^_eZf_`^mkj_^Zfbkmlvg_iZjZee_evgu_iehkdhklbMkeh\byg_ij_ju\ghklb<br />

]^_<br />

±<br />

I<br />

β<br />

,<br />

∞<br />

m<br />

+<br />

−<br />

+ β<br />

− β<br />

τ<br />

∫[ (<br />

β+<br />

Rβ) ⋅H<br />

y+<br />

( Iβ+<br />

Rβ)<br />

⋅H1y] ⋅dβ=<br />

T⋅H2y+<br />

∫<br />

0<br />

β<br />

I T ⋅ ⋅dβ<br />

(1)<br />

1 β<br />

H2y<br />

0<br />

±<br />

R<br />

β, T β —Zfieblm^uiZ^Zxs_cbhljZ`_gghc\hegT –Zfieblm^Zih\_joghkl<br />

ghc\heguβ —ihi_j_qgh_\hegh\h_qbkeh<br />

Hilbq_kdb_\hegh\h^uI_jkZg]eIh^j_^R_\q_gdh

116<br />

EHFHGHKHbnjZdpbywe_dljhfZ]gblguo\heggZ^bwe_dljbq_kdbokljmdlmjZo<br />

FGZmdZ<br />

IJBF?G?GB?NHJF:EBAF:GVXF?G:-I?GJHMA:D<br />

A:>:Q:FG?EBG?CGHCWE?DLJH>BG:FBDB

Ih^k_dpbynZah\uoi_j_oh^h\\l\_j^uol_eZo 117<br />

N:AHU

118<br />

EHFHGHKHD<br />

HKH;?GGHKLBBG>MPBJH

Ih^k_dpbynZah\uoi_j_oh^h\\l\_j^uol_eZo 119<br />

ghjh^gh_ b g_h^ghjh^gh_ fZ]gblhwe_dljbq_kdh_ GZoh`^_gb_ jZ\gh\_kgh]h khklhygby<br />

ijb nbdkbjh\Zgguo iheyo ijhba\h^behkv iml_f fbgbfbaZpbb l_jfh^bgZfbq_kdh]h ih<br />

l_gpbZeZkbkl_fuJ_r_gb_fy\ey_lkykibgh\Zypbdehb^ZD<br />

BAMQ?GB?IJBJH>UKIBGH

120<br />

EHFHGHKH@ey ihemq_gby g_e_]bjh\Zgguo<br />

h[jZaph\ bkihevah\Zeky jZkl\hj bahijh<br />

ibeZlZ Ti (IV \ bahijhibeh\hf kibjl_<br />

>ey nhjfbjh\Zgby e_]bjh\Zgguo Zahlhf<br />

kljmdlmjmdZaZgguc\ur_jZkl\hjkf_rb<br />

\Zeky k \h^guf jZkl\hjhf NH 4 Cl Ihem<br />

q_ggu_ lZdbf h[jZahf kf_kb \u^_j`b\Z<br />

ebkv gZ \ha^mo_ \ l_q_gb_ qZkh\ ijb<br />

dhfgZlghc l_fi_jZlmj_ b aZl_f \ukmrb<br />

\ZebkvijbK\l_q_gb_qZkh\>Ze__<br />

h[jZapuhl`b]ZebkvgZ\ha^mo_ijbD<br />

\ l_q_gb_ g_kdhevdbo qZkh\ Ihemq_ggu_<br />

h[jZapu TiO 2 khklhyeb ba dhg]ehf_jZlh\<br />

jZaf_jhfihjy^dZfdfdhlhju_\k\hx<br />

hq_j_^v khklhyeb ba gZghdjbklZeeh\ ^bZ<br />

f_ljhf-gf<br />

Ki_dlj WIJ g_e_]bjh\Zgguo h[jZaph\<br />

TiO 2 ij_^klZ\e_ggZjbk 1NhjfZkb]gZeZ<br />

WIJ b \_ebqbgZ g-nZdlhjZ k\b^_<br />

l_evkl\mxlhlhfqlh^Zgguckb]gZeWIJ<br />

h[mkeh\e_g we_dljhgZfb aZo\Zq_ggufb<br />

gZ fhe_dmeu dbkehjh^Z>@Ijb hk\_s_<br />

gbbki_dljWIJg_f_gyeky<br />

GZ jbk ij_^klZ\e_gu ki_dlju<br />

WIJ hdkb^Z lblZgZ e_]bjh\Zggh]h Zahlhf<br />

(N- TiO 2 NhjfZ ki_dljZ b \_ebqbgu g-<br />

nZdlhjh\g 1 =2.001, g 2 =1.998, g 3 k\b<br />

^_l_evkl\m_lhlhfqlh\^Zgguoh[jZapZo<br />

ijbkmlkl\mxl fhe_dmeyjgu_ ]jmiiu NO,<br />

aZo\Zq_ggu_\djbklZee_TiO 2 >@Ijbhk\_s_gbbbgl_gkb\ghklvp_gljZevghcebgbbki_d<br />

ljZbgl_]jZevghjZklzlbijbwlhfmdZaZggZyebgbyjZkiZ^Z_lkygZ^\_dhfihg_glu<br />

LZdbfh[jZahf\^ZgghcjZ[hl_nhlhdZlZeblbq_kdZyZdlb\ghklvN-TiO 2 fh`_l<br />

[ulvh[tykg_gZh[jZah\Zgb_f\_]hdjbklZeebq_kdhcj_rzldbNOfhe_dmeyjguo]jmii<br />

>Zggh_bkke_^h\Zgb_ij_^klZ\ey_lbgl_j_kdZd\nmg^Zf_glZevghcnbabd_bamq_gb_<br />

ijbjh^ukibgh\uop_gljh\\hdkb^_lblZgZlZdb\ijbdeZ^ghch[eZklbnhlhdZlZebaZ<br />

Ih^k_dpbynZah\uoi_j_oh^h\\l\_j^uol_eZo 121<br />

2. Serwicka E., Schlierkamp M.W., Naturforsch Z. 36 a, 226-232 (1981).<br />

3. Primet M., Che M., Naccache C, Mathieu M.V. and Imelik B. J. Chin Phys, 1970, 67,<br />

1629.<br />

M>D<br />

KMI?JBHGGU?DBKEHJH>HIJHYSB?IJHGBDB<br />

122<br />

EHFHGHKHD<br />

BKKE?>H

Ih^k_dpbynZah\uoi_j_oh^h\\l\_j^uol_eZo 123<br />

M>D7<br />

KLJMDLMJ:BDJBKL:EEH-KLJMDLMJGU?O:J:DL?JBKLBDB<br />

N:A:

124<br />

EHFHGHKH

Ih^k_dpbynZah\uoi_j_oh^h\\l\_j^uol_eZo 125<br />

kdb_ijhp_kku\\_s_kl\_\h\j_fykbkl_aZy\eyxlkyihk\h_ckmlbg_q_fbgufdZd<br />

keh`guf ih\_^_gb_f l_ kZfhhj]ZgbaZpb_c>@Hgb oZjZdl_jbamxlky ke_^mxsbfb<br />

hkgh\gufbijbagZdZfbkZfhhj]Zgbamxsbokykbkl_fl_jfh^bgZfbq_kdZyhldjulhklv<br />

kbevgZyg_jZ\gh\_kghklvgZjmr_gb_kbff_ljbbkdZqdhh[jZagucoZjZdl_jbaf_g_gby<br />

nbabq_kdbooZjZdl_jbklbd<br />

H^gbfba\hafh`guoZevl_jgZlb\guoih^oh^h\gZgZr\a]ey^fh`_lklZlvbk<br />

ihevah\Zgb_ f_lh^h\ l_hjbb kZfhhj]ZgbaZpbb Kbkl_fZ gZau\Z_lky kZfhhj]Zgbamx<br />

s_cky_kebhgZ[_aki_pbnbq_kdh]h\ha^_ckl\byba\g_h[j_lZ_ldZdmx-lhijhkljZgkl<br />

\_ggmx\j_f_ggmxbebnmgdpbhgZevgmxkljmdlmjmijbh[j_lZ_lgh\u_dhee_dlb\gu_<br />

k\hckl\ZdhlhjufbbagZqZevghg_h[eZ^Zxl__we_f_gluWlbk\hckl\Zijhy\eyxlky\<br />

\b^_ dhjj_eypbc l_ kha^Zxlky b ih^^_j`b\Zxlky \hkijhba\h^bfu_ \aZbfhhlghr_<br />

gbyf_`^mm^Ze_ggufbqZklyfbkbkl_fu

126<br />

EHFHGHKHbwe_dljbq_kdb_ bkke_^h\Zgby PCW h[gZjm`bebhkljuc ibd\aZ\bkbfhklb0L ijb<br />

395 h KbjZafulucfZdkbfmfijb360 h KIjbL! h Kijb[eb`_ggh\uihegy_lkyaZ<br />

dhgDxjb-D<br />

KL:LBKLBQ?KD:YL?JFH>BG:FBD:B>BNNMABHGG:Y<br />

DBG?LBD:LUOJ:KL

Ih^k_dpbynZah\uoi_j_oh^h\\l\_j^uol_eZo 127<br />

eyKms_kl\_gghchkh[_gghklvx^ZgghcjZ[hluy\ey_lkymq_l\hafh`ghcobfbq_kdhc<br />

k\yab\kbkl_f_ijb\h^ys_cdh[jZah\Zgbx\jZkl\hj_obfbq_kdbodhfie_dkh\Zkkh<br />

pbZlh\lbiZ:.

128<br />

EHFHGHKHD<br />

IJHP?KKUI?J?IHEYJBA:PBBDH;:EVLKH>?J@:SBO<br />

DJBKL:EEH@<br />

GZh[jZapukjZaebqghcdhgp_gljZpb_cijbf_kbKh 2+ hl<br />

k -5 \i ^h k -3 \i ih^Z\Zebkv fZeu_ ihey<br />

?

Ih^k_dpbynZah\uoi_j_oh^h\\l\_j^uol_eZo 129<br />

2. Jm^ydD<br />

IJHP?KKUI?J?DEXQ?GBYK b<br />

ijhp_kkh\__i_j_kljhcdbih^\ha^_ckl\b_fwe_dljbq_kdh]hihey\djbklZeeZo@<br />

MklZgh\e_ghqlhbkoh^gZy^hf_ggZykljmdlmjZgbh[bckh^_j`ZsbodjbklZeeh\<br />

ij_bfms_kl\_gghkhklhblbaf_edboZ-^hf_gh\

130<br />

EHFHGHKH

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 131<br />

NBABD:F:=GBLGUOYD<br />

F:=GBLHHILBQ?KDB?WNN?DLU<br />

GHF?JGUONHLHGGUODJBKL:EE:O<br />

DZebr:G;_ehl_eh\ey hibkZgby b fh^_ebjh\Zgby k\hckl\ h^ghf_jguo nhlhgguo djbklZeeh\ \<br />

jZ[hl_bkihevah\Zgf_lh^fZljbpi_j_oh^Z>@dhlhjuchkgh\ZggZlhfqlh\dZ`^hf<br />

keh_ g_aZ\bkbfh ^jm] hl ^jm]Z jZkijhkljZgyxlkylbiZ ghjfZevguo \heg h[eZ^Zx<br />

sbohij_^_e_gghciheyjbaZpb_cbgZijZ\e_gb_fjZkijhkljZg_gbybihegh_we_dljh<br />

Jbk

132<br />

EHFHGHKHeyghjfbjh\Zgguo\he<br />

gh\uo\_dlhjh\\kemqZ_iZ^_gbyk\_lZih^m]ehfθkijZ\_^eb\ukhhlghr_gby<br />

n = sinθ , n<br />

y<br />

2<br />

4<br />

2<br />

2<br />

n<br />

2<br />

± ±<br />

2 y<br />

g<br />

z<br />

g +<br />

−<br />

2<br />

4<br />

ε<br />

0<br />

2<br />

⎛ ε ⎞ n<br />

= − ⎜ +<br />

1 y<br />

ε<br />

⎟<br />

1<br />

1<br />

⎝ ε<br />

0 ⎠ 2<br />

2<br />

⎛ n<br />

y<br />

⎜1<br />

−<br />

⎝ 2ε<br />

0<br />

⎞<br />

⎟<br />

⎠<br />

⎪<br />

⎧⎛ ε ⎞<br />

⎨<br />

⎜ −<br />

1<br />

1<br />

⎟<br />

⎪⎩ ⎝ ε<br />

0 ⎠<br />

,<br />

]^_ ε , ε , 1 0<br />

g —dhfihg_glul_gahjZ^bwe_dljbq_kdhcijhgbpZ_fhklbijbgZebqbbgZ<br />

fZ]gbq_gghklbA^_kvhkvzgZijZ\e_gZi_ji_g^bdmeyjghd]jZgbpZfkeh_\Ziehkdh<br />

klvxiZ^_gbyy\ey_lkyiehkdhklvyz>eykhklZ\eyxsbo\_dlhjZgZijy`_gghklbwe_d<br />

ljbq_kdh]hihey^eyghjfZevguofh^kijZ\_^eb\ukhhlghr_gby<br />

ig<br />

n<br />

ynz<br />

Ex<br />

= −<br />

E<br />

y<br />

, Ez<br />

= E<br />

2 2<br />

2<br />

y<br />

nz<br />

+ n<br />

y<br />

− ε1<br />

n<br />

y<br />

− ε<br />

0<br />

.<br />

K\yavZfieblm^ghjfZevguofh^gZ\oh^_b\uoh^_nhlhggh]hdjbklZeeZ^Z_lky<br />

\fZljbqghcnhjf_<br />

A<br />

−1<br />

−1<br />

−1<br />

−1<br />

0<br />

= D0<br />

D1P1<br />

DN<br />

PN<br />

DN<br />

DN<br />

+ 1AN<br />

+ 1<br />

,<br />

]^_A n —klhe[_pkhklZ\e_ggucbaZfieblm^ghjfZevguo\heg\n-fkeh_ P<br />

n<br />

—fZl<br />

jbpZ-ijhiZ]Zlhjhibku\ZxsZyjZkijhkljZg_gb_ghjfZevguo\heg\n-fkeh_Z D<br />

n<br />

—<br />

^bgZfbq_kdZy fZljbpZ k\yau\ZxsZy Zfieblm^u ghjfZevguo \heg b lZg]_gpbZevgu_<br />

dhfihg_glugZijy`_gghkl_cwe_dljbq_kdh]hbfZ]gblgh]hihe_chgZgm`gZ^eymq_lZ<br />

]jZgbqguo mkeh\bc gZ ]jZgbpZo keh_\ Ihemq_ggu_ khhlghr_gby iha\heyxl \uqbk<br />

eylvoZjZdl_jbklbdbhljZ`_ggh]hbijhr_^r_]hk\_lZ<br />

IjhkljZgkl\_ggZy ^bki_jkby \ fZ]gblguo ND ijb\h^bl d \hafh`ghklb kha^Z<br />

gbygZbohkgh\_i_j_kljZb\Z_fuo^_fmevlbie_dkhjh\K\_lh\u_emqbjZaebqghc^eb<br />

ghc\heguijbhljZ`_gbbhlih\_joghklbNDhdZau\ZxlkyijhkljZgkl\_gghjZa^_e_g<br />

gufb–wnn_dl^_fmevlbie_dkbjh\Zgby>@Ih^[bjZyjZaebqgu_iZjZf_ljuNDfh`<br />

gh^h[blvkykblmZpbbdh]^ZmdZaZggucijhkljZgkl\_gguck^\b]ebg__gih^ebg_\he<br />

guD-537.632<br />

HILBQ?KDB?BF:=GBLHHILBQ?KDB?KI?DLJU<br />

FGH=HKEHCGUOF:=GBLGUOKLJMDLMJ^COFEZR(X)-ASI(Y)} N<br />

∗∗ ;Zluj_\:K

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 133<br />

fh]ml jZkkfZljb\Zlvky dZd fZ]gblgu_ nhlhggu_ djbklZeeu dh]^Z lhesbgu keh_\<br />

kjZ\gbfu k ^ebghc \hegu iZ^Zxs_]h k\_lZ beb dZd ]b[jb^gu_ fmevlbkehb dh]^Z<br />

lhesbgu keh_\ g_ ij_\urZxl g_kdhevdbo gZghf_ljh\>@DZd ^ey h^gh]h lZd b ^ey<br />

^jm]h]h deZkkZ fmevlbkeh_\ gZ[ex^Z_lky j_ahgZgkgh_ mkbe_gb_ fZ]gblhhilbq_kdh]h<br />

hldebdZdhlhjh_ihdZg_m^Z_lkyiheghklvxhibkZlvl_hj_lbq_kdb>@>ey\uykg_<br />

gbyijbjh^ugZ[ex^Z_fuownn_dlh\\]b[jb^guofmevlbkehyog_h[oh^bfu^Zevg_c<br />

rb_wdki_jbf_glZevgu_bl_hj_lbq_kdb_bkke_^h\Zgby<br />

Zggu_h[jZapu[uebihemq_gu\eykbkl_fuk<br />

gZb[he__lheklufbkehyfbo∼gfbn dZd^eygZghdhfihablh\>@gZ[ex^Z_lky<br />

g_fhghlhggZyaZ\bkbfhklv\_ebqbguWWDhlh[t_fgh]hkh^_j`Zgbyf) CoFeZrbmkb<br />

e_gb_FHhldebdZ\[eb`g_cBDh[eZklbki_dljZ>eykbkl_fkf_gvrbfblhesbgZfb<br />

fZ]gblgh]hkehyo∼1-gffugZ[ex^Zebm\_ebq_gb_wnn_dlZ\\b^bfhcbMNh[<br />

eZklb ki_dljZ ijb fZeuo lhesbgZo kehy dj_fgby b iZ^_gb_ \_ebqbgu wnn_dlZ k _]h<br />

jhklhfI jbk IhdZaZgh qlh \ fmevlbkehyo kms_kl\_ggh baf_gyxlky agZq_gby dZd<br />

^bZ]hgZevguo lZd b g_^bZ]hgZevguo khklZ\eyxsbo L>I :gZebaihe_\uoaZ\bkbfh<br />

kl_cWWDihdZaZeqlhfmevlbkehbko∼gfgZkusZxlky\iheyoihjy^dZH_qlh

134<br />

EHFHGHKHCoFeZr(x)Si(y)] n<br />

>eyh[tykg_gbyihemq_gguoj_amevlZlh\ijh\h^behkvfh^_ebjh\Zgb_fZ]gblh<br />

hilbq_kdbo ki_dljh\ \ ijb[eb`_gbb wnn_dlb\ghc kj_^u b gZ hkgh\_ fZdjhkdhibq_<br />

kdhcNj_g_e_\kdhcfZ]gblhhilbdb^eymevljZlhgdbokeh_\<br />

JZ[hlZ \uiheg_gZ ijb ih^^_j`d_ Jhkkbckdh]h nhg^Z nmg^Zf_glZevguo bkke_^h\Zgbc ]jZglu<br />

‹-02-b-02-bijh]jZffuMgb\_jkbl_luJhkkbb<br />

Ebl_jZlmjZ<br />

1. Dieny B. at al. J.Magn.Magn.Mater.185(1998)283<br />

2. Gan’shina E. at al. Physica B(2001)260<br />

3. =ZgvrbgZ ?: b ^j K[hjgbd ljm^h\ O,O F_`^mgZjh^ghc dhgn_j_gpbb GFFF<br />

Fhkd\Zk<br />

M>D3; 538.975<br />

F:=GBLGU?BF:=GBLHHILBQ?KDB?K

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 135<br />

bkke_^h\Zl_e_cqlhh[mkeh\e_ghh[gZjm`_gb_f\gbojy^Zgh\uonbabq_kdboy\e_gbc<br />

\lhfqbke_gZ[ex^_gb_fhkpbeeypbhggh]hih\_^_gbyg_dhlhjuonbabq_kdbooZjZdl_<br />

jbklbdijbbaf_g_gbblhesbgufZ]gblguobg_fZ]gblguokeh_\. P_evx^ZgghcjZ[h<br />

lu y\ey_lky bkke_^h\Zgb_ fZ]gblguo b fZ]gblhhilbq_kdbo k\hckl\ &R0R&R lj_o<br />

kehcguokbkl_f<br />

BamqZ_fu_ &R0R&Rh[jZapu[uebihemq_gukihfhsvx fZ]g_ljhggh]hjZkiu<br />

e_gbyijb[Zah\hf^Z\e_gbb\\ZdmmfghcdZf_j_f_gvr_10 -8 Lhjjb^Z\e_gbbjZ[hq_]h<br />

]ZaZZj]hgZ1x10 -3 Lhjj. LhesbgZ Khkeh_\W Co \bamqZ_fuolj_okehcguokbkl_fZo[u<br />

eZh^bgZdh\hc;uebihemq_gu^\_k_jbbh[jZaph\kW Co bgfijbwlhflhesbgZ<br />

fheb[^_gh\h]hkehyW FR baf_gyeZkvhl ^h gf. Qlh[uba[_`Zlvhdbke_gbyh[jZapu<br />

[uebihdjulu 10-gfkeh_fm]e_jh^ZBkke_^h\Zgb_fbdjhkljmdlmjubamqZ_fuoh[jZa<br />

ph\ [ueb \uiheg_gu k ihfhsvx j_gl]_gh\kdh]h ^bnjZdpbhggh]h ZgZebaZlhjZ ;5'<br />

GZebqb_ i_jbh^bq_kdbo kljmdlmjq_ldh \ujZ`_gguo ]jZgbp jZa^_eZ \ bkke_^m_fuo<br />

h[jZapZo[uehih^l\_j`^_gh^ZggufbfZehm]eh\h]hj_gl]_gh\kdh]hjZkk_ygby Baf_j_<br />

gb_ i_l_ev ]bkl_j_abkZ b djb\uo gZfZ]gbqb\Zgby [ueh \uiheg_gh gZ fZ]gblhhilbq_<br />

kdhffZ]g_lhf_lj_kihfhsvxwd\ZlhjbZevgh]hwnn_dlZD_jjZWWD/A^_kv/ ,–<br />

I 0 )/I 0 ]^_,b, 0 bgl_gkb\ghklvk\_lZhljZ`_ggh]hhlgZfZ]gbq_ggh]hbg_gZfZ]gbq_ggh<br />

]hh[jZapZkhhl\_lkl\_ggh

136<br />

EHFHGHKH

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 137<br />

jbeeby\[ebabnZah\h]hi_j_oh^Zk\_joijh\h^gbd-baheylhjh[eZ^Zxlihhlghr_gbxd<br />

iehkdhklb ie_gdb g_[u\Zehc Zgbahljhib_c fZ]gblhkhijhlb\e_gby>@^hklb]Zxs_c<br />

10 7 \fZ]gblguoiheyo^hLebbf_xs_cqbklhhj[blZevgmxijbjh^m<br />

Ihemq_gb_ fZ]gblguo k\_joj_r_lhd )H%H ijh\h^behkvgZmgbdZevghfh[hjm<br />

^h\Zgbb^eyjZkiue_gby\jZajy^_khkpbeebjmxsbfbwe_dljhgZfb\Zlfhkn_j_djbi<br />

lhgZih^jmdh\h^kl\hf^lg=

138<br />

EHFHGHKH)HÅ)/Be(20Å)] 150 wlbagZq_gby^hklb<br />

]Zxl 100 =k 200 =kb 500 =kkhhl\_lkl\_ggh<br />

>eyk_jbcFKJ)H%Hki_j_f_gghclhesbghckeh_\%HagZq_gbyhkgh\guoiZ<br />

jZf_ljh\ kihglZgghc gZfZ]gbq_gghklb dhwjpblb\ghc kbeu h[f_ggh]h kf_s_gby b<br />

wnn_dlb\gh]hiheyfZ]gblghcZgbahljhibbbgl_jn_ckh\bkiulu\Zxl]em[hdb_hkpbe<br />

eypbbki_jbh^hf–8Å \aZ\bkbfhklbhllhesbgukeh_\%HHkpbeeypbbkihglZgghc<br />

gZfZ]gbq_gghklb \ ^Zgghf kemqZ_ ih-\b^bfhfm h[mkeh\e_gu baf_g_gbyfb bgl_]jZ<br />

eh\dhk\_ggh]hh[f_ggh]h\aZbfh^_ckl\byf_`^mn_jjhfZ]gblgufbkehyfb)Hdhlh<br />

ju_bkiulu\Zxlhkpbeeypbbkjhklhflhesbg%H:^_d\Zlghcl_hj_lbq_kdhcfh^_evx<br />

^eyZgZebaZih\_^_gbykihglZgghcgZfZ]gbq_gghklby\ey_lkyh[h[s_ggh_ijb[eb`_<br />

gb_JDDB<br />

:gZeh]bqgu_ aZ\bkbfhklb fZ]gblguo iZjZf_ljh\ ^ey k_jbb Fe(t Fe )/Be(8Å) g_<br />

^_fhgkljbjmxl y\gh hkpbeeypbhgghc aZ\bkbfhklb \ ij_^klZ\e_gghf ^bZiZahg_ lhe<br />

sbg Z [hevrbgkl\h h[jZaph\ h[eZ^Zxl gZfZ]gbq_gghklvx ij_\urZxs_c =k<br />

A^_kvih-\b^bfhfm[hevrmxjhevb]jZxlf_`kehcgu_h[f_ggu_\aZbfh^_ckl\byZg<br />

lbn_jjhfZ]gblgh]h oZjZdl_jZ qlh ijhy\ey_lky \ f_gvrbo \_ebqbgZo kihglZgghc gZ<br />

fZ]gbq_gghklb ih kjZ\g_gbx k k_jb_c jZkkfhlj_gghc \ur_ b gZebqbb h[f_ggh]h<br />

kf_s_gby<br />

Ebl_jZlmjZ<br />

1. Parkin S.S.P., More N., and Roche K.P., Phys. Rev. Lett., 1989. 64(19): p. 2304–2307.<br />

2. Freeman A.J., and Fu C.L., Journal of Applied Physics, 1987. 61(8): p. 3356.<br />

3. Bielejec E., Ruan J., and Wenhao Wu, Phys. Rev. B, 2001. 63: p. 100502.<br />

M>D2; 538.975<br />

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 139<br />

hlh``_guijbl_fi_jZlmj_L ann b h K\l_q_gb_h^gh]hqZkZ\\Zdmmf_<br />

Bkke_^h\Zgb_fbdjhkljmdlmjubamqZ_fuoh[jZaph\[ueb\uiheg_gukihfhsvxj_gl<br />

]_gh\kdh]h^bnjZdpbhggh]hZgZebaZlhjZXRDH[t_fgu_fZ]gblgu_oZjZdl_jbklbdb<br />

gbd_e_\uoie_ghd[uebbaf_j_gugZ\b[jZpbhgghffZ]g_lhf_lj_BgnhjfZpbyhijb<br />

ih\_joghklguo fZ]gblguo oZjZdl_jbklbdZo h[jZaph\ [ueZihemq_gZkihfhsvxfZ]<br />

gblhhilbq_kdh]hfZ]g_lhf_ljZBaf_j_gb_ijbih\_joghklguoi_l_ev]bkl_j_abkZ[ueh<br />

\uiheg_ghkihfhsvxwd\ZlhjbZevgh]hwnn_dlZD_jjZWWD/A^_kv/ I – I 0 )/I 0 ]^_<br />

IbI 0 bgl_gkb\ghklvk\_lZhljZ`_ggh]hhlgZfZ]gbq_ggh]hbg_gZfZ]gbq_ggh]hh[jZa<br />

pZkhhl\_lkl\_ggh<br />

F R Vol /M S Ba\_klgh>@qlhlZdh_ khhlghr_gb_ijbih\_joghklguobh[t_fguoagZq_<br />

gbcG K bF R /M S oZjZdl_jgh^eyfZ]gblguoie_ghdlhesbghc–gfIhZgZeh]bbk<br />

kms_kl\mxsbfb ^Zggufb>@wlhl nZdl fh`_l [ulv h[tykg_g jZaebqghc ^hf_gghc<br />

kljmdlmjhcijbih\_joghklgh]hkehyb\gmlj_gg_]hh[t_fZie_gdb<br />

Ki_dljZevgu_aZ\bkbfhklbWWDhlwg_j]bbd\Zglh\iZ^Zxs_]hk\_lZ «&ihem<br />

q_ggu_^eybamqZ_fuoie_ghdgbd_eyihdZaZebqlh^ey\k_obamqZ_fuoie_ghdnhjfZ<br />

ki_dljh\WWD/«&y\ey_lkyijZdlbq_kdbh^bgZdh\hc>eyie_ghdh^ghck_jbb\_eb<br />

qbgZWWDg_aZ\bkblhllhesbguh[jZapZqlhh[mkeh\e_ghl_fqlhlhesbgZbamqZ_<br />

fuo ie_ghd t Ni [hevr_ ]em[bgu ijhgbdgh\_gby k\_lZ \ kj_^m t pen jZ\ghc ^ey n_jjh<br />

fZ]gblguof_lZeeh\–gf\h[eZklbwg_j]bbd\Zglh\iZ^Zxs_]hk\_lZ«&

140<br />

EHFHGHKH

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 141<br />

ijhgbpZ_fhklbZke_^h\Zl_evghb\k_ohilbq_kdboiZjZf_ljh\fZ]gblgh]hfZl_jbZeZ<br />

>@ey ^hklb`_gby fZdkbfZevghc<br />

^h[jhlghklb ^Zggh]h j_ahgZlhjZ kgZqZeZ<br />

\Zjvbjh\Zebkv lhesbgu ^bwe_dljbq_kdbo<br />

a_jdZe Z aZl_f bkihevamy wdki_jbf_g<br />

lZevgu_^Zggu_hlghkbl_evghhilbq_kdbo<br />

iZjZf_ljh\ b fZ]gblhkhijhlb\e_gby gZ<br />

ghdhfihablZ &R-(Al-2 >@ hij_^_eyeky<br />

FJW ijb mf_gvr_gbb lhesbgu fZ]gbl<br />

ghc ie_gdb hl ^h gf J_amevlZlu<br />

\uqbke_gbc^eyFNDk^_n_dlhfjZaghc<br />

lhesbguij_^klZ\e_gugZjbkmgd_

142<br />

EHFHGHKHbgZklbybFPNNF<br />

Ebl_jZlmjZ<br />

1. Lyubchansky I.L. at al. J.Phys. D: Appl. Phys. 36 (2003) R277-R287<br />

2. Inoue M. at al. J.Appl.Phys. 85 (1999) 5988<br />

3. =jZgh\kdbc:;b^j@WLNlhf\uiklj-1265<br />

4. KlZjhkl_gdh KG JhaZgh\ DG K[hjgbd l_abkh\ -hc _`_]h^ghc gZmqghc dhg<br />

n_j_gpbbBLIWHBD<br />

HKH;?GGHKLBF:=GBLGUOK

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 143<br />

GZfZ]gbq_gghklv gZkus_gby jZkkqblu\ZeZkv ih jZafZ]gbqb\Zxs_fm nZdlhjm<br />

lhgdhciezgdbkmqzlhf\_ebqbguiheygZkusZxs_]hh[jZa_p\gZijZ\e_gbbi_ji_g<br />

^bdmeyjghfiehkdhklb<br />

Ihke_hl`b]Zbkoh^gh]hh[jZapZijhbkoh^blj_adh_mf_gvr_gb__]hdhwjpblb\<br />

ghckbeuhl^hWH^gZdhihke_hl`b]ZijbKkghjfZevgufbmkeh\byfb<br />

hoeZ`^_gbydhwjpblb\gZykbeZbihe_kfudZgbykbevghjZklml–^hWbWkh<br />

hl\_lkl\_gghlh]^ZdZdm\lhjh]hh[jZapZhlh``zggh]hijbKhlh``zgijbK<br />

hoeZ`^zgbhlh``zgijbKdhwjpblb\gZykbeZbihe_kfudZgbyaZf_lghg_hleb<br />

qZxlkyhl^jm]bohlh``zgguoh[jZaph\

144<br />

EHFHGHKHey e_glu hlh``_gghc ijb T ann =<br />

650 h K gZ[ex^Zehkv j_adh_ m\_ebq_gb_ agZq_gby H C vol qlh h[mkeh\e_gh iheghc djb<br />

klZeebaZpb_ch[jZapZ<br />

;uehh[gZjm`_ghqlhijbih\_joghklgu_fZ]gblgu_k\hckl\Zkms_kl\_gghhl<br />

ebqZxlkyhlh[t_fguo@GZeb<br />

qb_jZaebqZxsbokyhklZlhqguogZijy`_gbckha^Z\Z_fuogZdhglZdlghcbk\h[h^ghc<br />

klhjhgZoe_gl\ijhp_kk_boba]hlh\e_gbyZlZd`_jZaebqgZyfhjnheh]byklhjhgfh]ml<br />

[ulvlZd`_ijbqbgZfbhibkZggh]h\ur_jZaebqby

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 145<br />

Hkh[h]h \gbfZgby aZkem`b\ZeZ g_h[uqgZy nhjfZ ijbih\_joghklguo i_l_ev<br />

]bkl_j_abkZ;uehh[gZjm`_ghqlh\hlh``_gguoh[jZapZoijbg_dhlhjuohjb_glZpb<br />

yo´iehkdhklgh]hfZ]gblgh]hiheyijyfZybh[jZlgZy\_l\bijbih\_joghklguoi_l_ev<br />

]bkl_j_abkZf_gyxlkyf_klZfb_<br />

lZevgh_ bamq_gb_ fZ]gblguo k\hckl\ dZd nmgdpbb m]eZ ´ ihdZaZeh qlh kms_kl\m_l<br />

bgl_j\Ze m]eh\´ ijbdhlhjuo gZ[ex^ZxlkyiheghklvxbebqZklbqghbg\_jlbjh\Zg<br />

gu_ i_leb ]bkl_j_abkZ Ihemq_ggu_ wdki_jbf_glZevgu_ ^Zggu_ fh`gh dZq_kl\_ggh<br />

h[tykgblv \ jZfdZo ^\monZaghc fh^_eb k ^\mfy g_b^_glbqgufb nZaZfb oZjZdl_jb<br />

amxsbfbky h^ghhkghc fZ]gblghc Zgbahljhib_c b Zglbn_jjhfZ]gblguf h[f_gguf<br />

\aZbfh^_ckl\b_ff_`^mgbfb<br />

Ebl_jZlmjZ<br />

1. Yoshizawa Y., Oguma S., Yamauchi K. // J. Appl. Phys. 1988. V.64. P. 6044-6046.<br />

2. Suzuki K., Makino A., Inoue A., Masumoto T. // J. Appl. Phys. 1993. V. 74. P. 3316-<br />

3322.<br />

3. Makino A., Hatanai T., Inoue A., Masumoto T. // Mater. Sci. Eng. 1997. V. A 226-228. P.<br />

594-602.<br />

4. Hernando A., Vasques M., Kulik T., Prados C. // Phys. Rev. B. 1995. V. 51. P. 3581-<br />

3586.<br />

5. RZeu]bgZ??FhehdZgh\HDJB

146<br />

EHFHGHKHeydZ`^h]hh[jZapZbai_leb]bkl_j_abkZjZkq_l<br />

gufiml_f[ueZihemq_gZnmgdpbyjZkij_^_e_gbyqZklbpihjZaf_jmFh`ghk^_eZlv<br />

ij_^iheh`_gb_ qlh\b^ l_fi_jZlmjghcaZ\bkbfhklbfZ]gblghc\hkijbbfqb\hklbg_<br />

ihkj_^kl\_gghk\yaZgkoZjZdl_jhfjZkij_^_e_gbyqZklbpihjZaf_jm<br />

eyh[jZapZdhlhjuchlebqZ_lkyhlwlh]hebrvdhgp_gljZpb_cdh[ZevlZ\_kih<br />

emq_gZ^jm]ZyjZaf_jgZyaZ\bkbfhklv–ijbkmlkl\m_ln_jjhfZ]gblgZynjZdpbyijbq_f<br />

jZkij_^_e_gb_n_jjhfZ]gblguoqZklbpihjZaf_jm^hklb]Z_lfZdkbfmfZijbÅ,<br />

kmi_jiZjZfZ]gblguo–ijbÅ. Mh[jZapZgZhkgh\_gbljZlZdh[ZevlZn_jjhfZ]gbl<br />

guo qZklbp [hevr_ NZah\u_ i_j_oh^u hlkmlkl\mxl oh^ l_fi_jZlmjghc djb\hc fZ]<br />

gblghc \hkijbbfqb\hklb kbevgh hlebqZ_lky JZkij_^_e_gb_ n_jjhfZ]gblguo qZklbp<br />

ih jZaf_jm ^hklb]Z_l fZdkbfmfZ ijb Å, kmi_jiZjZfZ]gblguo – ijb,68 Å. M<br />

h[jZapZgZhkgh\_Zp_lZlZdh[ZevlZdhgp_gljZpbydhlhjh]h^hklb]Z_l\_k\u^_ey<br />

_lky kmi_jiZjZfZ]gblgZy njZdpby jZkij_^_e_gb_ ^hklb]Z_l fZdkbfmfZ ijb Å),<br />

n_jjhfZ]gblgu_qZklbpulZd`_ijbkmlkl\mxlfZdkbfmfijbÅ).<br />

>ey \k_o h[jZaph\ h[gZjm`_gu g_h[jZlbfu_ baf_g_gby fZ]gblguo k\hckl\ \<br />

l_fi_jZlmjghfoh^_djb\hcfZ]gblghc\hkijbbfqb\hklb<br />

< aZ\bkbfhklb hl kheb dhlhjZy bkihevam_lky ^ey \hkklZgh\e_gby dh[ZevlZ b<br />

dhgp_gljZpbbdh[ZevlZfh`ghf_gylvkhhlghr_gb_kmi_jiZjZfZ]gblguobn_jjhfZ]<br />

gblguoqZklbpD<br />

BKKE?>H

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 147<br />

bahebjh\Zgguokehyokq_j_^h\Zgb_fR-Si-Mn 2 -Si-RBaf_j_gbygZfZ]gbq_gghklbkh<br />

_^bg_gbcGd x La 1-x MnSiijh\_^_gu\jZ[hl_>@L_fi_jZlmjgu_bihe_\u_aZ\bkbfhklb<br />

gZfZ]gbq_gghklb kh_^bg_gby GdMnSi mdZau\Zxl gZ n_jjhfZ]gblguc lbi mihjy^hq_<br />

gby\j_^dha_f_evghcih^j_rzld_\lh\j_fydZd\\_^_gb_eZglZgZijb\h^bldihy\e_<br />

gbx Zglbn_jjhfZ]gblgh]h mihjy^hq_gby \ kh_^bg_gbyo k x ≤ 0. 6 < ^Zgghc jZ[hl_<br />

ijh\_^_gubaf_j_gbyfZ]gblhdZehjbq_kdh]hwnn_dlZ^\mokhklZ\h\GdMnSimdhlhjh<br />

]h bf__l f_klh h^bg nZah\uc i_j_oh^-]h jh^Z ba n_jjhfZ]gblghc nZau \ iZjZfZ]<br />

gblgmxkT C<br />

= 314K<br />

; Gd 0,5 La 0,5 MnSimdhlhjh]hijbl_fi_jZlmjZogb`_T t<br />

= 103K<br />

\ha<br />

gbdZ_lZglbn_jjhfZ]gblgh_mihjy^hq_gb_bbf_xlf_klh^\ZnZah\uoi_j_oh^Z-]h<br />

jh^Z ba Zglbn_jjhfZ]gblghc nZau \ n_jjhfZ]gblgmx ijb T t<br />

= 103K<br />

b-]h jh^Z ba<br />

n_jjhfZ]gblghcnZau\iZjZfZ]gblgmxijbT C<br />

= 185K<br />

.<br />

L_fi_jZlmjgZyaZ\bkbfhklvFDW\ihe_ H ≈ 7. 4dW<br />

kh_^bg_gbyGd 0,5 La 0,5 MnSi<br />

ij_^klZ\e_gZgZjbkIhe_\u_aZ\bkbfhklbFDW\h[eZklbnZah\h]hi_j_oh^ZbaZg<br />

lbn_jjhfZ]gblghcnZau\n_jjhfZ]gblgmxijb T ≈ Tt<br />

ij_^klZ\e_gugZ\klZ\d_djb<br />

kmgdm

148<br />

EHFHGHKH

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 149<br />

bgl_j_kdihbkdmfZl_jbZeh\dhlhju_fh]eb[ukem`blv\dZq_kl\_jZ[hq_]hl_eZlZdbo<br />

mklZgh\hd Ih^jh[guc h[ahj [hevrh]h dhebq_kl\Z jZ[hl ihy\b\rboky \ ihke_^g__<br />

\j_fy^Zg\dgb]_>@@H^gZdhbamq_gb_fZ]gblhdZehjbq_kdh]hwnn_dlZ\hdj_kl<br />

ghklyonZah\h]hi_j_oh^Zi_j\h]hjh^Zkhijy`_ghkjy^hfljm^ghkl_cIjyfu_baf_<br />

j_gby \_ebqbgu Z^bZ[Zlbq_kdh]h baf_g_gby l_fi_jZlmju ljm^h_fdb b ijh\h^ylky<br />

ebrv\g_[hevrhfdhebq_kl\_eZ[hjZlhjbcBaf_j_gby\_ebqbgubahl_jfbq_kdh]hba<br />

f_g_gbywgljhibbg_\hafh`guihwlhfmhgZjZkkqblu\Z_lkygZhkgh\_baf_j_gby^jm<br />

]boiZjZf_ljh\fZl_jbZeZIjhs_\k_]hihemqblvbaf_g_gb_wgljhibbbgl_]jbjmyba<br />

\_klgh_khhlghr_gb_FZdk\_eeZ<br />

⎛∂M<br />

⎞<br />

∆ S = ∫ ⎜ ⎟<br />

⎝ ∂T<br />

⎠<br />

Gh\hdj_klghklbnZah\h]hi_j_oh^Zi_j\h]hjh^Zwlh\ujZ`_gb_g_\uihegy_l<br />

kyihwlhfmZdlmZevghcy\ey_lkyaZ^ZqZ\uqbke_gbykdZqdZwgljhibbk\yaZggh]hk\u<br />

^_e_gb_fkdjulhcl_iehlui_j_oh^ZLZdb_jZkq_lufh`ghijh\_klb^eyf_lZfZ]gbl<br />

gh]h i_j_oh^Z \ Zglbn_jjhfZ]g_lbd_ – y\e_gby khklhys_]h \ hijhdb^u\Zgbb ih^j_<br />

r_lhdfZ]gblgufihe_f<br />

Ba\_klgh qlh hkgh\gu_ hkh[_gghklb ih\_^_gby Zglbn_jjhfZ]g_lbdZ fh`gh<br />

hibkZlvbkihevamyl_jfh^bgZfbq_kdbcihl_gpbZe\b^Z>@<br />

F = E A + E H = − K U cos 2 Θ − (½)χ H 2 = − K U cos 2 Θ − (½)(χ || cos 2 Θ + χ ⊥ sin 2 Θ) H 2<br />

=^_K U –dhgklZglZZgbahljhibbχ || bχ ⊥ –ijh^hevgZybihi_j_qgZy\hkijbbfqb\hklb<br />

khhl\_lkl\_ggh Fbgbfmfm wg_j]bb khhl\_lkl\m_l hjb_glZpby ih^j_r_lhd \^hev beb<br />

ihi_j_dgZijZ\e_gby\_dlhjZgZijy`_gghklbfZ]gblgh]hiheyDjblbq_kdh_ihe_ijb<br />

dhlhjhfijhbkoh^bljZa\hjhlih^j_r_lhdjZ\gy_lky<br />

Hcr<br />

=<br />

H<br />

dH<br />

2 KU<br />

χ⊥ − χ ||<br />

Wgljhibyh[jZapZhij_^_ey_lky\ujZ`_gb_fS = −(∂F/∂TLh]^ZkdZq_dwgljh<br />

ibbijbi_j_oh^_[m^_ljZ\_gjZaghklbwgljhibb^\monZa<br />

⎛∂χ k<br />

S ⊥ ⎞ ⎛∂χ<br />

⎞ ∂<br />

∆ = ⎜ ⎟H − ⎜ ⎟H<br />

−<br />

⎝ ∂T ⎠ ⎝ ∂T ⎠ ∂T<br />

2 || 2 u<br />

1/2<br />

CR<br />

1/2<br />

CR<br />

Bkihevamy\b^aZ\bkbfhklbdjblbq_kdh]hiheybgZfZ]gbq_gghklbe_]dhihdZ<br />

aZlvqlh<br />

⎛∂χ<br />

χ<br />

⊥ ⎞ ⎛∂<br />

2 || ⎞ ∂k<br />

1/2 1/2 2 u<br />

⎜ ⎟HCR<br />

− HCR<br />

S T<br />

⎜<br />

T<br />

⎟ −<br />

∆ ⎝ ∂ ⎠ ∂ ∂T ∂HCR<br />

=<br />

⎝ ⎠<br />

=−<br />

∆I χ H −χ<br />

H ∂T<br />

⊥<br />

CR<br />

LZdbf h[jZahf \u[jZggZy fh^_ev hdZau\Z_lky kh]eZkh\Zgghc k mjZ\g_gb_f<br />

DeZci_jhgZ–DeZmabmkZ<br />

JZ[hlZih^^_j`ZgZ]jZglhfJNNB04-02-16709-Z.<br />

Ebl_jZlmjZ<br />

1. Gschneidner K.A. Jr, Pecharsky V.K. Journ. Appl. Phys. 85 (1999), 5365.<br />

||<br />

CR

150<br />

EHFHGHKHD<br />

H;G:JM@?GB?_fbgJ<<br />

F=MbfFhgZklhys_cjZ[hlubgl_j_kdfZg]ZgblZf[uek\yaZgkdhehkkZevguffZ]gb<br />

lhkhijhlb\e_gb_fDFKdhlhjh_gZ[ex^Zehkv\g_dhlhjuokhklZ\ZoijbdhfgZlghc<br />

l_fi_jZlmj_

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 151<br />

1<br />

0<br />

0<br />

ω·10 4<br />

-1<br />

-2<br />

-3<br />

+ dW<br />

<br />

<br />

a<br />

ω ·10 4<br />

-1<br />

-2<br />

-3<br />

a<br />

330 K<br />

325<br />

320<br />

315<br />

∆ρ/ρ, %<br />

-4<br />

0<br />

-4<br />

-8<br />

-12<br />

-16<br />

-20<br />

-24<br />

100 150 200 250 300 350 400<br />

T, K<br />

b<br />

∆ρ/ρ, %<br />

-4<br />

0<br />

-4<br />

-8<br />

-12<br />

-16<br />

-20<br />

-24<br />

b<br />

305<br />

350<br />

330<br />

325<br />

300<br />

315<br />

0 2 4 6 8 10<br />

+dW<br />

JbkL_fi_jZlmjgZyaZ\bkbfhklvh[t_f<br />

ghc fZ]gblhkljbdpbb ω (a b fZ]gblhkh<br />

ijhlb\e_gby∆ρ/ρ (b)<br />

JbkBahl_jfuh[t_fghcfZ]gblhkl<br />

jbdpbb ω (a b fZ]gblhkhijhlb\e_gby<br />

∆ρ/ρ (b\jZchg_lhqdbDxjb<br />

KhklZ\u La 1-x : x MnH 3 (A = Sr, Ba ij_^klZ\eyxl kh[hc Zglbn_jjhfZ]g_lbd<br />

LaMnH 3 e_]bjh\ZggucbhgZfb: 2+ dhlhju_y\eyxlkyZdp_ilhjZfbBa-aZ\ub]jurZ\<br />

wg_j]bbs-d)/(d-dh[f_gZghkbl_ebaZjy^ZjZkiheZ]Zxlky\n_jjhfZ]gblghcNFqZk<br />

lbh[jZapZbhlkmlkl\mxl\:NF@DFKfZg]Zgblh\h[tykgy_lkyijbkmlkl<br />

\b_f\gbomdZaZggh]hfZ]gblgh-^\monZagh]hkhklhygbyF>NK@ihdZaZghqlh\NFqZklbh[jZapZgZoh^ys_]hky\F>NKihklhyggu_j_r_ldb<br />

mf_gvr_guHlkx^Zke_^m_lqlhijbL ≥ L K ^he`ghgZ[ex^Zlvkybaebrg__ihkjZ\<br />

g_gbxkebg_cgufihLl_ieh\h_jZkrbj_gb_\ua\Zggh_jZajmr_gb_fF>NKdhlh<br />

jh_ b gZ[ex^Zehkv \ ^Zgghc jZ[hl_ \h \k_o bkke_^h\Zgguo h[jZapZo GZeh`_gb_<br />

\g_rg_]hfZ]gblgh]hihey\wlhcL-h[eZklb^he`ghm\_ebqb\Zlvkl_i_gvNFihjy^dZ<br />

\hdj_klghklbijbf_k_ckbevg__q_f\kj_^g_fihdjbklZeemlZddZd_]h^_ckl\b_mkb<br />

eb\Z_lky s-d h[f_ghf >jm]bfb keh\Zfb fZ]gblgh_ ihe_ [m^_l \hkklZgZ\eb\Zlv<br />

F>NKjZajmr_ggh_gZ]j_\Zgb_fbijbkms___fmk`Zlb_j_r_ldbWlhb_klv]b]Zgl<br />

kdZy h[t_fgZy fZ]gblhkljbdpby H^gZdh mdZaZgguc \ur_ ijhp_kk \hkklZgh\e_gby<br />

F>NKfZ]gblgufihe_fbf__lf_klh\h]jZgbq_gghfL-bgl_j\Ze_g_fgh]h\ur_L K .<br />

Ihwlhfmdjb\u__ω|(Lbf_xlfZdkbfmf\[ebabL K b[ukljhkiZ^Zxlijb^Zevg_cr_f<br />

ih\ur_gbbL.<br />

WlZjZ[hlZ[ueZ\uiheg_gZijbih^^_j`d_JNNBijh_dluN 03-02-b-02-17810).<br />

Ebl_jZlmjZ<br />

1. GZ]Z_\WEMNG66 (1996) 833; Phys. Rep., 346 (2001) 387.<br />

2. Yanase A., Kasuya T. J. Phys. Soc. Japan, 25 (1968) 1025.

152<br />

EHFHGHKHD<br />

MKBE?GB?WNN?DL:N:J:>?YG:DJ:XNHLHGGHC<br />

A:IJ?S?GGHCAHGU

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 153<br />

ZfZ]gblgZy^ebgZ l 2D<br />

2D<br />

a<br />

f_gvr_q_f_]h[hjh\kdbcjZ^bmk<br />

ex<br />

( l < aex<br />

)<br />

\hlkml\bbfZ]gbl<br />

gh]hihey<br />

Hkgh\guf \hijhkhf y\ey_lky \ebygb_ \ha[m`^_guo mjh\g_c EZg^Zm

154<br />

EHFHGHKHJHG-F\Cu-K.baemq_gbbJZkq_ldjbklZeebq_kdhckljmdlmju\uiheg_gkbkihev<br />

ah\Zgb_f ijh]jZffu FullProf FZ]gblgu_ baf_j_gby \uiheg_gu gZ dhff_jq_kdhf<br />

\b[jZpbhgghffZ]gblhf_lj_OI-ZlZd`_kihfhsvxKDfZ]gblhf_ljZfZjdb<br />

FJFS-5 (Quantum Design).<br />

H[jZapuihemq_ggu_ijbl_fi_jZlmj_ DgZ\ha^mo_[uebmki_rghjZkkqb<br />

lZgudZddjbklZeehkljmdlmjgh-h^ghnZagu_ijhkljZgkl\_ggZy]jmiiZR 3 k_kebo”<br />

khklhysb_ ba kf_kb jhf[hw^jbq_kdhc b hjlhjhf[bq_kdhcijhklj ]jmiiZ - Pnma nZa<br />

ijb”o”bh^ghnZagu_hjlhjhf[bq_kdb__kebo•ijhklj]jmiiZPnmaIh\u<br />

r_gb_l_fi_jZlmjukbgl_aZ^h Dijb\_ehdj_adhfmmf_gvr_gbxdjbklZeehkljmd<br />

lmjghcg_h^ghjh^ghklbIjb]hlh\e_ggu_ijbwlhcl_fi_jZlmj_h[jZapu[uebmki_rgh<br />

jZkkqblZgudZdjhf[hw^jbq_kdb__kebx”bhjlhjhf[bq_kdb_x•<br />

2,0<br />

1,5<br />

6K<br />

300K<br />

1,0<br />

0,20<br />

M (emu/g)<br />

0,5<br />

0,0<br />

-0,5<br />

M (emu/g)<br />

0,15<br />

0,10<br />

0,05<br />

H = 100 Oe<br />

-1,0<br />

-1,5<br />

-2,0<br />

-60 -40 -20 0 20 40 60<br />

H (kOe)<br />

T = 5 K<br />

FC<br />

ZFC<br />

Intensity<br />

2x10 4<br />

3x10 4 10 20 30 40<br />

1x10 4<br />

0<br />

Yobs<br />

Ycalc<br />

Yobs-Ycalc<br />

Bragg_position<br />

0,00<br />

0 100 200 300 400<br />

T (K)<br />

20 40 60 80 100 120 140<br />

2Θ<br />

Jbk. 1 Jbk. 2<br />

ayehrbgkdh]h-Fhjbykl_fi_jZlmjhcG__ey D

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 155<br />

>@ ayehrbgkdh]h-FhjbyKihfhsvxijh\_^_g<br />

guo g_cljhgh]jZnbq_kdbo bkke_^h\Zgbc m^Zehkv \uykgblv qlh ^Zgguc khklZ\ bkiu<br />

lu\Z_ldjbklZeehkljmdlmjguci_j_oh^jhf[hw^j–hjlhjhf[ijbihgb`_gbbl_fi_jZ<br />

lmjuLZdbfh[jZahfj_amevlZluijh\_^_gguogZfbbkke_^h\Zgbciha\heyxlkms_kl<br />

\_ggh jZkrbjblv bf_xsb_ky k\_^_gby h fZ]gblghc b djbklZeebq_kdhc kljmdlmj_<br />

LaCo 0.5 Fe 0.5 O 3 .<br />

Ebl_jZlmjZ<br />

1. Raccah P.M., Goodenough J.B. // J. Appl. Phys. 1968, 39, p.1209-1210.<br />

2. Itoh M., Natori I., Kubota S. et al. // J. Phys. Soc. Jpn. 1994, 63, p.1486-1493.<br />

3. Asai K., Yokokura O., Nishimori N. et al. // Phys. Rev. B 1994, 50, p.3025-3032.<br />

4. Bedel L., Roger A.C., Estournes C. et al. // Catalysis Today 2003, 85 p.207-218<br />

5. Cambley R. E., Stamps R.L. // J. Phys.: Condens. Matter. 1993, 5, p.3727-3786<br />

6. Koehler W.C., Wollan E.O., Wilkinson M.K. // Phys. Rev. 1960, 118, p. 58-70.<br />

M>D<br />

FH>?EBJH

156<br />

EHFHGHKH

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 157<br />

L?FI?J:LMJG:YA:

158<br />

EHFHGHKH@ Wnn_dl FL lZd`_ dZd b<br />

DFKgZ[ex^Z_lkyijbi_j_oh^_f_lZee-baheylhjb^hklb]Z_lfZdkbfZevguoagZq_gbc<br />

\g_kdhevdh^_kyldh\ijhp_glh\\rbjhdhfBD-^bZiZahg_hl^hfdf\iheyo^h<br />

LWnn_dlFLgZ[ex^Z_lkydZd\fhghdjbklZeeZolZdb\lhgdboie_gdZofZg]Zgb<br />

lh\Hlf_lbfqlhwdki_jbf_glZevgu_jZ[hluihbkke_^h\ZgbxfZ]gblhijhimkdZgby\<br />

fZg]ZgblZokDFKijh\h^blkylhevdhZ\lhjZfb^hdeZ^Z<br />

< lhgdbo ie_gdZo fZg]Zgblh\ k DFK \_ebqbgZ fZ]gblhijhimkdZgby hilbq_<br />

kdb_ fZ]gblhhilbq_kdb_ b we_dljbq_kdb_ k\hckl\Z aZ\bkyl hl kl_obhf_ljbb lbiZ b<br />

mjh\gy e_]bjh\Zgby gZijy`_gbc \ ie_gd_ b \b^Z ih^eh`db Bkke_^h\Zgb_ wlbo<br />

k\hckl\ \ ie_gdZo kbkl_fu/D 1-x Pr x ) 0.7 Ca 0.3 MnO 3 [ ihdZaZeh qlh bah\Ze_glgh_<br />

aZf_s_gb_LabhgZfbPr^ho ijZdlbq_kdbg_f_gy_l\_ebqbgmFLqlhk\yaZghkh<br />

keZ[ufbaf_g_gb_fhlghr_gbybhgh\Mn 3+ /Mn 4+ @G_bah\Ze_glgh_aZ<br />

f_s_gb_La 3+ bhgZfbCa +2 ,Sr +2 ,Na +1 ,Ag +1 ijb\h^bldm\_ebq_gbxL K^hl_fi_jZlmj\u<br />

r_dhfgZlghcbd[hevrbfihagZq_gbxwnn_dlZfDFK∼bFL∼>@GZeb<br />

qb_ \ ie_gd_ La 0.82 Na 0.18 MnO 3 FL∼ijbL Diha\hebehgZfba]hlh\blv hjb]b<br />

gZevguc fZd_l fh^meylhjZ BD-baemq_gby jZ[hlZxsbc ijb dhfgZlghc l_fi_jZlmj_<br />

>@@KjZ\gbl_evguc<br />

ZgZeba ^Zgguo fZ]gblhkhijhlb\e_gby b fZ]gblhijhimkdZgby BD-baemq_gby ie_gdhc<br />

La 0.8 Ag 0.1 MnO 3+δ iha\hebejZa^_eblv\deZ^u\fZ]gblhkhijhlb\e_gb_k\yaZggu_kdh<br />

ehkkZevgufblmgg_evguffZ]gblhkhijhlb\e_gb_fZlZd`_mklZgh\blvnmgdpbxl_f<br />

i_jZlmjghc aZ\bkbfhklb lmgg_evgh]h fZ]gblhkhijhlb\e_gby ∆ρ/ρ~(a+b/√T) b hij_^_<br />

eblv\_ebqbgmkibg-iheyjbaZpbbghkbl_e_caZjy^ZJa<br />

Dhfie_dkgh_ bkke_^h\Zgb_ hilbq_kdbo fZ]gblhhilbq_kdbo b we_dljbq_kdbo<br />

k\hckl\ie_ghdfZg]Zgblh\ihdZaZehqlh\_ebqbguFKFLbbaf_g_gbyijhimkdZgby<br />

\[ebabL K l_f[hevr_q_ff_gvr_kj_^gbcjZ^bmke_]bjmxs_]hdZlbhgZGZb[hevrbc<br />

wnn_dlFL^hklb]Z_lky\fZg]ZgblZohilbfZevgh]hkhklZ\ZkfZdkbfZevgufh[t_fhf<br />

h^ghk\yaghcn_jjhfZ]gblghc\ukhdhijh\h^ys_cnZauk[hevrhc\_ebqbghcbaf_g_<br />

gby ijhimkdZgby \[ebab L K b k ihemijh\h^gbdh\uf oh^hf we_dljhkhijhlb\e_gby b<br />

ijhimkdZgbyBD-baemq_gby\iZjZfZ]gblghch[eZklbJ_amevlZlubkke_^h\ZgbcfZg]Z<br />

gblh\fh]mlkem`blvhkgh\hc^eykha^Zgbyhilhwe_dljhgguomkljhckl\ BD-^bZiZahgZ<br />

gZwnn_dl_FLbl_fi_jZlmjgh]hbaf_g_gbyijhimkdZgbyk\_lZGZijbf_jlZdbodZd<br />

hilbq_kdbc aZl\hj hkeZ[bl_ev BD-baemq_gby ^bklZgpbhgguc ^Zlqbd l_fi_jZlmju<br />

bbebfZ]gblgh]hiheyfh^meylhjBD-baemq_gby<br />

JZ[hlZ \uiheg_gZ ijbih^^_j`d_Ijh]jZffuHNGJ:G©Gh\u_ fZl_jbZeub<br />

kljmdlmjuªNPGLI=D‹JNNB=jZgl‹-02-16630).<br />

Ebl_jZlmjZ<br />

1. Kmohjmdh\ XI EhrdZj_\Z GG =ZgvrbgZ ?: DZmev :J =hj[_gdh HX<br />

NZl__\ZD:IbkvfZ\@LNl1K<br />

2. Kmohjmdh\ XI EhrdZj_\Z GG =ZgvrbgZ ?: DZmev :J =hj[_gdh HX<br />

Fhklh\sbdh\Z?

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 159<br />

5. Kmohjmdh\ XI L_e_]bg :< =ZgvrbgZ ?: EhrdZj_\Z GG DZmev :J<br />

=hj[_gdhHXFhklh\sbdh\Z?@Zgghfmdjbl_jbxm^h\e_l\hjyxllhevdhkbkl_fuwnn_dlb\guc]Zfbevlh<br />

gbZgdhlhjuo\[ebabdjblbq_kdhclhqdbih^h[_gfh^_ebBabg]Z<br />

hihegbl_evgh^eydhgp_gljZpbcp gZfbihemq_gul_fi_jZlmjgu_<br />

aZ\bkbfhklbl_jfh^bgZfbq_kdboiZjZf_ljh\ lZdbo dZdgZfZ]gbq_gghklvml_ieh_f<br />

dhklvC,\hkijbbfqb\hklvχbhij_^_e_ggu^eygbokhhl\_lkl\mxsb_bg^_dkugZhk<br />

gh\_l_hjbbdhg_qgh-jZaf_jgh]hkd_cebg]Z<br />

JZ[hlZ ih^^_j`ZgZ ]jZglhf JNNBijh_dl ‹-02- gZmqghc rdheuGR-2253.2003.2),<br />

NPI³Bgl_]jZpby´‹Bb]jZglhfNhg^Zkh^_ckl\byhl_q_kl\_gghcgZmd_:DFmjlZaZ_\<br />

Ebl_jZlmjZ<br />

1. NhevdJ=heh\ZqXY\hjkdbcLDjblbq_kdb_ihdZaZl_eblj_of_jghckeZ[hjZa<br />

[Z\e_gghcaZfhjh`_gghcfh^_ebBabg]ZMNG‹K-200.<br />

2. >hp_gdh

160<br />

EHFHGHKH

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 161<br />

M>D<br />

eyijh\_^_gbywdki_jbf_glZevguobkke_^h\ZgbcjZajZ[hlZghiulguch[jZa_p<br />

fZ]gblh-bfimevkghcmklZgh\dbey l_hj_lbq_kdhc hp_gdb \hafh`ghkl_c f_lh^Z fZ]gblhbfimevkgh]h<br />

f_lZgby jZajZ[hlZgZ fZl_fZlbq_kdZy fh^_ev hkgh\hc dhlhjhc y\ey_lky<br />

mjZ\g_gb_^\b`_gbyijh\h^ys_]hl_eZih^^_ckl\b_fwe_dljhfZ]gblguokbe>@:gZ<br />

eba ihemq_gghc fZl_fZlbq_kdhc fh^_eb iha\hey_l hij_^_eblv \k_ iZjZf_lju ^\b`_<br />

gbyijh\h^gbdZbke_^h\Zl_evghhilbfZevgucimlvjZa]hgZbfZkkmijh\h^gbdZijb<br />

aZ^ZgguoiZjZf_ljZomklZgh\db>eyZgZebaZfZl_fZlbq_kdhcfh^_ebjZajZ[hlZgZijh<br />

]jZffZZ^Zilbjh\ZggZyih^ihevah\Zl_ey-dhgkljmdlhjZ<br />

Ebl_jZlmjZ<br />

1. NbabdZ\ukhdboiehlghkl_cwg_j]bbIh^j_^IDZev^bjheub=Dghin_eyi_j<br />

kZg]eHGDjhobgZ–F–k–187.<br />

2. ;hg^Ze_lh\D4<br />

H;MF?GVR?GBB

162<br />

EHFHGHKH@P_evjZ[hlu–ihbkdijbqbgg_klZ<br />

[bevghklbiheyklZjlZbbamq_gb_hkh[_gghkl_cjZg__h[gZjm`_gguo^\mof_oZgbafh\<br />

i_j_dexq_gby-j_eZdkZpbhggh]hbZdk_e_jZpbhggh]h>@<br />

H[jZapu:FKHbakieZ\Zkh^_j`Zs_]hFe, 9,3 % Mn, 1,8 % B, 6 % Si,<br />

1,3 %Ck\g_rgbf^bZf_ljhffdfb^bZf_ljhff_lZeebq_kdhc`beufdfjZa<br />

ebqghc^ebguBamqZehkv\ebygb_jZaf_jh\h[jZaph\bnhjfubolhjp_\JZg__[ueh<br />

h[gZjm`_ghqlhnhjfZlhjpZhdZau\Z_lkms_kl\_ggh_\ebygb_gZijhp_kki_j_dexq_<br />

gbyihwlhfmhkgh\gh_\gbfZgb_m^_eyehkvbkke_^h\Zgbxlhjph\H[jZapuh[jZ[Zlu<br />

\Zebkvnlhjh\h^hjh^ghcdbkehlhcZahlghcdbkehlhcbojhfibdhf<br />

J_amevlZluIjbkljZ\eb\Zgbblhjph\ihe_klZjlZbnemdlmZpbbmf_gvrbebkv\<br />

b[he__jZaZkljZ\eb\Zgb_kl_deygghch[hehqdb\p_gljZevghch[eZklbh[jZapZijb<br />

\_ehdi_j_oh^mba-klZ[bevgh]hkhklhygby\-klZ[bevgh_BG:FBDBIH

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 163<br />

gb_dhlhjh]h \i_j\mxhq_j_^vh[mkeh\e_ghg_h^ghjh^gufh[f_gguf\aZbfh^_ckl<br />

\b_f>@@<br />

H^gZdh^hkboihjg_jZkkfZljb\ZeZkvih\_joghklgZyiheyjblhggZy^bgZfbdZe_]<br />

dhhkgh]h:NF\h\g_rg_fihklhygghfwe_dljbq_kdhfihe_@<br />

< k\yab k wlbf p_ev ^Zgghc jZ[hlu khklhbl \ ZgZeba_ \ebygby d\Z^jZlbqgh]h<br />

fZ]gblhhilbq_kdh]h \aZbfh^_ckl\by gZ mkeh\by nhjfbjh\Zgby ih\_joghklguo fZ]<br />

gblguoiheyjblhgh\\ihem[_kdhg_qghfZglbn_jjhfZ]g_lbd_\ijbkmlkl\bbihklhyg<br />

gh]hwe_dljbq_kdh]hiheyghjfZevgh]hd]jZgbp_jZa^_eZkj_^<br />

Ijh\_^_gguc\gZklhys_cjZ[hl_ZgZebaiheyjblhggh]hki_dljZihemh]jZgbq_ggh]h<br />

e_]dhhkgh]h :NF gZoh^ys_]hky \h \g_rg_f we_dljbq_kdhf ihe_ iZjZee_evghf e_]dhc<br />

hkb\qZklghklbihdZaZeqlhmq_ld\Z^jZlbqgh]hfZ]gblhhilbq_kdh]h\aZbfh^_ckl\byijb<br />

\h^bldp_ehfmjy^mjZg__g_ba\_klguoZghfZebc\^bki_jkbhgguok\hckl\Zobmkeh\byo<br />

ehdZebaZpbbiheyjblhgghc\hegu[_]ms_c\^hevih\_joghklbZglbn_jjhfZ]g_lbdZ<br />

gZ]jZgbp_:NF-b^_Zevgucf_lZee\hafh`ghnhjfbjh\Zgb_h^ghiZjpb<br />

Zevgh]hih\_joghklgh]hfZ]gblgh]h70- iheyjblhgZmkeh\bykms_kl\h\Zgbydhlhjh]h<br />

aZ\bkylg_lhevdhhl\_ebqbgughbhlagZdZijh_dpbb\g_rg_]hwe_dljbq_kdh]hihey<br />

EgZgZijZ\e_gb_ghjfZebnd]jZgbp_jZa^_eZkj_^ijbwlhfki_dlj^Zggh]hlbiZih<br />

\_joghklghc iheyjblhgghc70-\hegu g_ bf__l dhjhldh\hegh\hc lhqdb hdhgqZgby<br />

ih\_joghklguciheyjblhgi_j\h]hlbiZ<br />

\kemqZ_]jZgbpujZa^_eZ:NF-\Zdmmf^bki_jkbhggZydjb\Zyih\_jogh<br />

klgh]hfZ]gblgh]h70-iheyjblhgZh[eZ^Z_ldhjhldh\hegh\hclhqdhchdhgqZgbyih<br />

eyjblhg\lhjh]hlbiZZmkeh\by_zehdZebaZpbb\[ebabih\_joghklbfZ]g_lbdZlZd`_<br />

kms_kl\_gghaZ\bkylhlhlghkbl_evghchjb_glZpbb\_dlhjh\Ebn;<br />

Ebl_jZlmjZ<br />

1. Ih\_joghklgu_ iheyjblhguih^ j_^ :]jZgh\bqZ < F GZmdZ<br />

k<br />

2. $EUDKD.7LOOH\'56XUI6FL5HS9‹3−222.<br />

3. ;mq_evgbdh\RZ\jh\H

164<br />

EHFHGHKH

Ih^k_dpbynbabdbfZ]gblguoy\e_gbc 165<br />

Ebl_jZlmjZ<br />

1. @mjZ\e_\

166<br />

EHFHGHKHD- 532<br />

WG?J=?LBQ?KDBCKI?DLJ>

Ih^k_dpbynbabdbihebf_jh\ 167<br />

NBABD:IHEBF?JH<<br />

Ij_^k_^Zl_evih^k_dpbb<br />

^n-fgFZoZ_\Z?e_gZ?\]_gv_\gZ<br />

M>D, 539.19<br />

=EH;MEU:FNBNBEVGUOF:DJHFHE?DME<br />

∗∗ MrZdh\Z:K<br />

F=MbfF

168<br />

EHFHGHKH

Ih^k_dpbynbabdbihebf_jh\ 169<br />

J_amevlZlubkke_^h\Zgbyk\h[h^ghcwg_j]bbij_^klZ\e_gugZ^bZ]jZff_]eh[m<br />

eyjguokhklhygbcjbk\aZ\bkbfhklbhl`_kldhklbfZdjhfhe_dmeugbhlwg_j]bb<br />

ijbly`_gby iheyjguo ]jmii d jZkl\hjbl_ex ε Ps Kn_jbq_kdZy nhjfZ khhl\_lkl\m_l<br />

]eh[me_kiheh`bl_evgufih\_joghklgufgZly`_gb_fKm\_ebq_gb_fwg_j]bbε Ps ih<br />

\_joghklgh_ gZly`_gb_ klZgh\blky hljbpZl_evguf b fZdjhfhe_dmeZ ijbgbfZ_l dhg<br />

nhjfZpbx©h`_j_ev_ªIjb^Zevg_cr_fm\_ebq_gbbwg_j]bbε Ps ]b[dZyfZdjhfhe_dmeZ<br />

ijbgbfZ_lnhjfm^bkdZZ`_kldZy–nhjfmlhjZ<br />

JZ[hlZ\uiheg_gZijbih^^_j`d_JNNBijh_dl-03-bINTAS.<br />

M>D-544.03<br />

KLJMDLMJ:BK

170<br />

EHFHGHKH

Ih^k_dpbynbabdbihebf_jh\ 171<br />

e_gbc\^hevfbp_eeyjguop_i_clj_[mxs_]hg_[hevrhcaZljZluwg_j]bb\j_amevlZ<br />

l_q_]h\yadhklvkbkl_fumf_gvrZ_lky<br />

172<br />

EHFHGHKHD<br />

DHFIE?DKHH;J:AH

Ih^k_dpbynbabdbihebf_jh\ 173<br />

aZibkZgZk\h[h^gZywg_j]bykbkl_fugZc^_gZdjblbq_kdZydhgp_gljZpbyfbp_eehh[jZ<br />

ah\Zgbyb_zaZ\bkbfhklvhldhgp_gljZpbcdhfihg_glh\jZkl\hjZZlZd`_bokljmdlmj<br />

guoiZjZf_ljh\Ijhke_`_gZw\hexpbyjZkij_^_e_gbyijbihke_^h\Zl_evghfm\_ebq_<br />

gbbdhgp_gljZpbbebg_cguop_i_cIhdZaZghqlhfbp_eeu\jZkl\hj_khkms_kl\mxlk<br />

hl^_evgufbihebwe_dljheblgufbdhfie_dkZfbLZd`_^eyjZaebqguodhgp_gljZpbcb<br />

^ebgebg_cguop_i_c[ehd-bhghf_jZjZkkqblZgukj_^gbcaZjy^fbp_eeubkj_^gb_Z]<br />

j_]Zpbhggu_qbkeZbihdZaZghqlhhgbkbevghaZ\bkylhlkhhlghr_gbyf_`^m^ebgZ<br />

fb ebg_cguo p_i_c b aZjy`_gguo [ehdh\ b keZ[h aZ\bkyl hl dhgp_gljZpbb [ehdbhghf_jZ<br />

H[gZjm`_gh qlh _keb h[jZah\Zgb_ kl_obhf_ljbq_kdbo ihebwe_dljheblguo<br />

dhfie_dkh\g_\hafh`ghlhijbba[uld_ebg_cguop_i_c\jZkl\hj_ijhbkoh^bli_j_<br />

aZjy^dZfbp_eeey^Zggh]hijb[eb`_gbygZc^_guaZ\bkbfhklbjZ\gh<br />

\_kghch[t_fghc^hebihebf_jZh[t_fghc^hebgbadhfhe_dmeyjguobhgh\\gmljby^jZ<br />

bdhwnnbpb_glZih\_joghklgh]hgZly`_gbyhldhebq_kl\Z^h[Z\e_gghckhebIhkljh_gZ<br />

^bZ]jZffZhij_^_eyxsZyh[eZklvkms_kl\h\Zgbyy^jZfbp_eeu\aZ\bkbfhklbhldheb<br />

q_kl\Z ^h[Z\e_gghc kheb LZd`_ jZkkqblZgZ aZ\bkbfhklv jZ\gh\_kguo iZjZf_ljh\ fb<br />

p_eeu\aZ\bkbfhklbhlkl_i_gbaZjy`_gghklbihebf_jguop_i_c<br />

M>D.7<br />

DDE:KKBNBD:PBBN:AHB:=J:FF<br />

:KKHPBBJMXSBOKBKL?FKG?KDHEVDBFBLBI:FB<br />

L?JFHH;J:LBFUOOBFBQ?KDBOK@]^_[uehihdZaZghqlhlhiheh]bynZah\uo^bZ]jZffwlbokbkl_fkm<br />

s_kl\_ggh aZ\bkbl hl qbke_gguo agZq_gbc wgljhibb b wg_j]bb h[jZah\Zgby k\yab <<br />

gZklhys_c jZ[hl_ j_amevlZlu jZ[hl>@h[h[sZxlky gZ kemqZc ke_^mxs_c [he__<br />

keh`ghcZkkhpbbjmxs_ckbkl_fu<br />

JZkkfZljb\Z_lkykbkl_fZkh^_j`ZsZy^\ZkhjlZa\_gv_\A m bB n dZ`^h_badh<br />

lhjuokh^_j`blihm (nlZdgZau\Z_fuonmgdpbhgZevguo]jmii:

174<br />

EHFHGHKH

Ih^k_dpbynbabdbihebf_jh\ 175<br />

4. :jghev^ ?EBJH

176<br />

EHFHGHKHD541.64:532.73<br />

K

Ih^k_dpbynbabdbihebf_jh\ 177<br />

p_ib kihkh[gu ijbgbfZlv jZaebqgu_ iheh`_gby hlghkbl_evgh hkgh\ghc p_ib K\h<br />

[h^gZywg_j]bygZ_^bgbpm^ebgufZdjhfhe_dmeuij_^klZ\bfZ\\b^_kmffumijm]hc<br />

wg_j]bb jZkly`_gby [hdh\uo p_i_c b wg_j]bb dhglZdlh\ [hdh\uo p_i_c jZaebqgh]h<br />

khjlZ^jm]k^jm]hf<br />

Hkgh\gu_ j_amevlZlu gZrbo bkke_^h\Zgbc ij_^klZ\e_gu gZ jbkmgd_A^_kv<br />

∆ f = − -jZaghklv k\h[h^guo wg_j]bc ^\mo khklhygbc < h^ghf ba gbo [hdh\u_<br />

f 2<br />

f 1<br />

p_ib iheghklvx k_]j_]bjh\Zggu hlghkbl_evgh hkgh\ghc p_ib l_ \k_ p_ib khjlZ :<br />

jZkiheZ]Zxlkyihh^gmklhjhgmhlhkgh\ghcp_ibZkhjlZ< –ih^jm]mx f 1<br />

178<br />

EHFHGHKHD<br />

DHFIVXL?JGH?FH>?EBJH

Ih^k_dpbynbabdbihebf_jh\ 179<br />

M>D<br />

HILBQ?KDB?F?LH>UBKKE?>H

180<br />

EHFHGHKHD<br />

KBGL?AIHEB?GH

Ih^k_dpbynbabdbl\_j^h]hl_eZ 181<br />

NBABD:L

182<br />

EHFHGHKH

Ih^k_dpbynbabdbl\_j^h]hl_eZ 183<br />

LZdbf h[jZahf k^_eZgZ ihiuldZ n_ghf_gheh]bq_kdb ijhykgblv ijbqbgm \ha<br />

gbdgh\_gby l_jfhbg^mpbjh\Zgguo©aZij_s_gguoª j_ne_dkh\ \ hdkb^_ pbgdZ ijh\_<br />

^_ghqbke_ggh_fh^_ebjh\Zgb_bkhihklZ\e_gb__]hj_amevlZlh\kwdki_jbf_glZevgu<br />

fb^Zggufbfbljb_gdh

184<br />

EHFHGHKH@b)H&- 4 [7]<br />

>Zggu_\ZjbZpbbiZjZf_ljh\kj_^u χxx<br />

\j_ahgZgkghch[eZklbdZdbgZebqb_<br />

χ<br />

fZ]gblghcZgbahljhighc^h[Z\db<br />

xy<br />

ijb\h^yldkms_kl\_ggufke_^kl\byf\l_hjbb<br />

hljZ`_gbyLZdijbbkke_^h\Zgbb[jw]]h\kdh]hhljZ`_gbyhli_jbh^bq_kdbokljmdlmj<br />

hdZau\Z_lkyqlhiheh`_gb_rbjbgZbbgl_]jZevgZybgl_gkb\ghklv[jw]]h\kdh]hfZd<br />

kbfmfZkms_kl\_ggh\Zjvbjmxlky\j_ahgZgkghch[eZklbdZdaZkq_lbaf_g_gby^ebgu<br />

\hegulZdbaZkq_lij_ehfe_gbybih]ehs_gbyaZqlhhl\_qZxl^bZ]hgZevgu_dhfih<br />

g_glu χxx<br />

ijbq_fgZ[ex^Z_fu_baf_g_gbyfh]mlbkihevah\Zlvky^eyg_ihkj_^kl\_g<br />

gh]hhij_^_e_gbyj_ahgZgkguoiZjZf_ljh\<br />

BeexkljZpb_c^Zgguo\hafh`ghkl_cy\eyxlkyijh\_^_ggu_fh^_evgu_jZkq_<br />

lu m]eh\uo b ki_dljZevguo aZ\bkbfhkl_c [jw]]h\kdh]h hljZ`_gby ^ey Fljmdlmju<br />

>)H&R@ki_jbh^hfgfbbkihevah\Zgb_fdhfihg_gl<br />

χxx<br />

χ<br />

,<br />

xy<br />

^ey)Hba>@<br />

GZjbkijb\_^_gZki_dljZevgZyaZ\bkbfhklvkf_s_gbylhqgh]h[jw]]h\kdh]h<br />

4π<br />

fZdkbfmfZbeb\_dlhjZjZkk_ygby = sin θ ihemq_ggZybajZkkqblZgguo[_a<br />

Q<br />

λ<br />

Bragg<br />

mq_lZfZ]gblghc^h[Z\db χxy<br />

^bnjZdpbhgguodjb\uoZgZjbk\hkklZgh\e_ggZyba<br />

wlhc©ik_\^h-wdki_jbf_glZevghcªaZ\bkbfhklbnmgdpby Re χxx<br />

kihfhsvxdbg_fZlb<br />

q_kdhc nhjfmeu b ^bgZfbq_kdh]h \ujZ`_gby ^eyihijZ\dbgZij_ehfe_gb_^eym]eZ<br />

;jw]]Z>@<br />

0,584<br />

0,583<br />

Re χ<br />

XX<br />

, 10 -6<br />

10000<br />

Q, A -1 700 710 720 730<br />

5000<br />

In itial Re χ XX<br />

Result from:<br />

kinematical<br />

dynamical [8]<br />

expressions<br />

0,021<br />

0,020<br />

∆ θ B<br />

, r a d<br />

0,582<br />

700 710 720 730<br />

0<br />

-5000<br />

0,019<br />

700 710 720 730<br />

Jbk Jbk Jbk

Ih^k_dpbynbabdbl\_j^h]hl_eZ 185<br />

IhkdhevdmjZkkfZljb\Z_fZyfh^_evy\ey_lkyijhf_`mlhqghcf_`^m^bgZfbq_<br />

kdbfbdbg_fZlbq_kdbfjZkk_ygb_ffh`ghkqblZlvqlh^ZggucZe]hjblf\hkklZgh\<br />

e_gby nmgdpbb Re χxx<br />

^hklZlhqgh ohjhrh jZ[hlZ_l Imχxx<br />

fh`_l [ulv hij_^_e_gZ k<br />

ihfhsvxij_h[jZah\ZgbyDjZf_jkZ–Djhgbg]Zbeb\hkklZgh\e_gZbaki_dljZevghcaZ<br />

\bkbfhklbi_j\h]h[jw]]h\kdh]hfZdkbfmfZkfjbkdZd[uehk^_eZgh\>@<br />

Ijbi_j_oh^_dkehbklh-Zgbahljhigufkj_^Zfdkh`Ze_gbxijhkl_crb_khhl<br />

ghr_gby^eyk^\b]Z[jw]]h\kdh]hfZdkbfmfZi_j_klZxljZ[hlZlv\ke_^kl\b_kf_rb\Z<br />

gbykh[kl\_gguoiheyjbaZpbcBdZdihdZaZebfh^_evgu_jZkq_luih^h[gucf_lh^g_<br />

fh`_l[ulvbkihevah\Zg^eyhij_^_e_gbyfZ]gblguodhfihg_gl χxy<br />

\]_hf_ljbbf_<br />

jb^bhgZevgh]hwnn_dlZD_jjZ<br />

1<br />

52.4<br />

0<br />

1<br />

53.4<br />

0<br />

1<br />

54.9<br />

µ<br />

in F e<br />

0<br />

1<br />

55.9<br />

0 , 0 1 , 1 2 , 2<br />

0 , 0 1 , 1 2 , 2<br />

0<br />

700 720<br />

700 720<br />

JbkGhjfbjh\Zggu_ki_dlju[jw]]h\kdh]hhljZ`_gby^eyijZ\hcebgbbb<br />

e_\hckbf\heudjm]h\hciheyjbaZpbbAgZq_gbym]eh\ijb\_^_gu\]jZ^mkZo<br />

H^gZdh nhjfZ ebgbb j_ahgZgkgh]h ki_dljZ hljZ`_gby b _]h Zkbff_ljbyijb<br />

baf_g_gbb gZijZ\e_gby ihey hklZxlky gZb[he__ qm\kl\bl_evgufb d gZebqbx fZ]<br />

gblgh]hmihjy^hq_gbyb_]hjZkij_^_e_gbxih]em[bg_GZjbkijb\_^_guki_dlju<br />

hljZ`_gby jZkkqblZggu_ \ ]_hf_ljbb f_jb^bhgZevgh]h wnn_dlZ D_jjZ k mq_lhf<br />

©fZ]gblghcª ^h[Z\db χxy<br />

\[ebab [jw]]h\kdh]h hljZ`_gby JZaebqb_ jZkkqblZgguo<br />

ki_dljh\^ey^\moijhkl_crbofh^_e_cjZkij_^_e_gbyfZ]gblguofhf_glh\^_fhg<br />

kljbjm_l\hafh`ghklbj_ahgZgkgh]hfZ]gblgh]hjZkk_ygbyj_gl]_gh\kdboemq_c\bk<br />

ke_^h\Zgbb ijhnbe_c fZ]gblgh]h mihjy^hq_gby j_ahgZgkguo Zlhfh\ ih i_jbh^m<br />

fgh]hkehcghckljmdlmju<br />

Ebl_jZlmjZ<br />

1. :aaZfJ;ZrZjZGWeebikhf_ljbybiheyjbah\Zgguck\_lFFbj<br />

2. ;Zjdh\kdbc EF ;hja^h\ =G N_^hjh\ NB

186<br />

EHFHGHKHD 669.788:669.017.3<br />

IJHP?KKUα ↔ β IJ?V-HJH><br />

Afb_gdh>K<br />

F=MbfF-@dhlhju_dlhfm`_fh]mlkms_kl\_ggh<br />

mf_gvrblvklhbfhklvfZl_jbZeZIhwlhfm\dZq_kl\_h[t_dlZbkke_^h\Zgby[ue\aylh[jZ<br />

a_pkieZ\Z3G-Zl&Xhkgh\ghchkh[_gghklvxdhlhjh]hy\ey_lkylhqlhihke__]h]b^<br />

jbjh\Zgbyh[jZam_lky-nZaZkh^_j`Zgb_\h^hjh^Z\dhlhjhcfh`_l^hklb]Zlv>-8].<br />

;ueb ijh\_^_gu j_gl]_gh]jZnbq_kdb_ bkke_^h\Zgby kljmdlmjguo oZjZdl_jb<br />

klbdh[jZapZkieZ\Zbbobaf_g_gb_ihke_gZkus_gby\h^hjh^hfbihke_^mxs_cj_<br />

eZdkZpbbBaf_j_gbyijh\h^bebkvgZmkh\_jr_gkl\h\ZgghfZ\lhfZlbabjh\Zgghfdhf<br />

ie_dk_>JHG-MF-kbkihevah\Zgb_ffhghojhfZlbq_kdh]hCu–Kα 1 baemq_gbyGZku<br />

s_gb_\h^hjh^hfijh\h^behkvwe_dljheblbq_kdb<br />

;uehmklZgh\e_ghqlh\bkoh^ghfkhklhygbb\h[jZap_ihke__]hijb]hlh\e_gby<br />

\hagbdZxlmijm]b_gZijy`_gbyσk`ZlbygZijZ\e_ggu_\^hevih\_joghklbh[jZapZ\_<br />

2<br />

ebqbgZdhlhjuo<br />

σ =−60d] ff<br />

Ihke_we_dljheblbq_kdh]hgZkus_gbyh[jZapZ\h^hjh<br />

^hfijbiehlghklblhdZf:kf\l_q_gb_fbg[h]ZlZy\h^hjh^hf-nZaZg_h[jZam<br />

_lkyohlykh]eZkghebl_jZlmjguf^Zgguf^he`gZkms_kl\h\Zlvkf_kvα-bβ-nZa>-4].<br />

-@Ih^h[gucj_amevlZlfh`ghh[tykgblvl_f<br />

qlh_s_^hgZkus_gbykieZ\Z\h^hjh^hf\g_fbf__lky[hevrh_qbkeh^_n_dlh\hq_f<br />

k\b^_l_evkl\m_lkbevgh_jZafulb_^bnjZdpbhgguofZdkbfmfh\Ihwlhfmih\lhjgh_gZ<br />

kus_gb_ijh\h^behkvijb\^\h_m\_ebq_gghciehlghklblhdZLZdh_]b^jbjh\Zgb_ijb\_<br />

ehdh[jZah\Zgbx-b.-nZaJZkq_luihdZaZebqlhdhebq_kl\h-nZau\h[eZklyojZaghc<br />

djbklZeeh]jZnbq_kdhchjb_glbjh\dbhdZaZehkvjZagufbh[s__kh^_j`Zgb_\h^hjh^Z\nZa_<br />

n 0.44<br />

H<br />

n<br />

Pd<br />

=<br />

Ijbj_eZdkZpbbh[jZapZ\ghjfZevguomkeh\byogZ[ex^Zekyijhp_kk<br />

β →α<br />

ij_\jZs_gbydhlhjucb^_lk\hajZklZxs_ckdhjhklvxQ_j_aqj_eZdkZpbbgZ<br />

ebqb_-nZau\h[jZap_g_gZ[ex^Zeb;uehmklZgh\e_ghqlhmijm]b_gZijy`_gbyk`Zlby<br />

2<br />

\α-nZa_ljZgknhjfbjh\Zebkv\mijm]b_gZijy`_gbyjZkly`_gby<br />

σ = 45d] ff<br />

lh]^Z<br />

2<br />

dZd\-nZa_hgbkhojZgbebkvghboZ[khexlgZy\_ebqbgZ\hajhkeZ<br />

σ =−25d] ff<br />

).<br />

IhdZaZghqlhb\kemqZ_h[jZah\Zgby-nZau\α-nZa_b^_lfgh]hnZah\ucjZk<br />

iZ^Ih^h[gucj_amevlZl[ueihemq_g\i_j\u_<br />

JZ[hlZih^^_j`ZgZ]jZglZfbJNNB‹-02-16533

Ih^k_dpbynbabdbl\_j^h]hl_eZ 187<br />

Ebl_jZlmjZ<br />

1. :\^xobgZjZ]hp_ggu_fZl_jbZeub^jZ]hp_ggu_dZfgb<br />

k-166 (2004)<br />

2. :\^xobgZ bZ]ghklbdZ fZl_jbZeh\ l ‹ k-34,<br />

2003<br />

3.

188<br />

EHFHGHKHey\k_okbkl_f<br />

\uqbkeyeZkvwg_j]byjZkl\hjbfhklbZlhfZm]e_jh^Z\ihabpbyo\g_^j_gbyJ_amevlZlu<br />

jZkq_lh\ ihdZaZeb qlh jZkl\hjbfhklv \ HPD-`_e_a_wg_j]by jZk\hjbfhklb w<<br />

\ur_q_f\=PD-gbd_e_wH:

Ih^k_dpbynbabdbl\_j^h]hl_eZ 189<br />

j_oh^guof_lZeeh\bkieZ\h\beb\dZq_kl\_f_lZeebq_kdbo]b^jb^h\jZkkfZljb\Z_lky<br />

dZdh^bgbai_jki_dlb\guoiml_ckha^Zgbygh\uolhieb\guowe_f_glh\^ey\h^hjh^<br />

ghc wg_j]_lbdb>-@ < ^Zgghc jZ[hl_ ijh\h^behkv l_hj_lbq_kdh_ bkke_^h\Zgb_ Z[<br />

khj[pbb\h^hjh^Z\h[t_f_kieZ\h\Pd 3 MegZhkgh\_iZeeZ^bykd-, 4d-i_j_oh^gufb<br />

f_lZeeZfbMe= 3d (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn), 4d (Zr, Nb, Mo, Tc, Ru, Rh, Pd,<br />

Ag, Cdkp_evxbamq_gbyk\hckl\\h^hjh^ghckhj[pbb\aZ\bkbfhklbhle_]bjmxs_c<br />

ijbf_kbBkke_^h\Zgb_ijh\h^behkvkihfhsvxi_j\hijbgpbiguojZkq_lh\hibjZx<br />

sbokygZl_hjbxnmgdpbhgZeZiehlghklbLNIkbkihevah\Zgb_ff_lh^Zihegh]hih<br />

l_gpbZeZ \ [Zabk_ ebg_cgh ijbkh_^bg_gguo iehkdbo \hegEII< b \ ijb[eb`_gbb<br />

ehdZevghc iehlghklbIEI >@ DjbklZeebq_kdZy kljmdlmjZ kieZ\h\ kljhbeZkv k bk<br />

ihevah\Zgb_f]jZg_p_gljbjh\Zgghcdm[bq_kdhcj_r_ldbiZeeZ^by\p_glj_]jZg_cdh<br />

lhjhc gZoh^bebkv Zlhfu iZeeZ^by Z \ m]eZo – Zlhfu ijbf_kb :gZeba ZlhfghdjbklZeebq_kdhckljmdlmjuihdZaZeqlh\h^hjh^fh`_laZgbfZlv^\ZjZaebqguohdlZ<br />

w^jbq_kdbo iheh`_gby < i_j\hf hdlhmae_ Zlhf \h^hjh^Z hdjm`_g r_klvx ZlhfZfb<br />

iZeeZ^by\i_j\hcdhhj^bgZpbhgghckn_j_lh]^ZdZd\h\lhjhfhdlhmae_\h^hjh^hd<br />

jm`Zxlq_luj_ZlhfZiZeeZ^byb^\ZZlhfZijbf_kgh]hwe_f_glZIjb\g_^j_gbb\h^h<br />

jh^ hdZau\Z_l ^Z\e_gb_ gZ kieZ\ ba-aZ dhlhjh]h gZ[ex^Zehkv m\_ebq_gb_ iZjZf_ljZ<br />

j_r_ldb kieZ\ZIh j_amevlZlZf i_j\hijbgpbiguo jZkq_lh\ k\hckl\ Zlhfguo b we_d<br />

ljhgguokljmdlmjkieZ\h\[ueZ\uy\e_gZke_^mxsZyaZdhghf_jghklvwg_j]byZ[khj[<br />

pbb \h^hjh^Z m[u\Z_l ih f_j_ aZiheg_gby d-h[hehqdb i_j_oh^gh]h f_lZeeZ ijf_kb<br />

:gZebawe_dljhgghckljmdlmjukieZ\ZihdZaZeqlh\h^hjh^emqr_Z[khj[bjm_lky\l_o<br />

kemqZyodh]^Zp_gljfZkkaZgylhcqZklbiehlghklbwe_dljhgguokhklhygbce_`bl[eb<br />

`_dmjh\gxwg_j]bbN_jfbDjhf_lh]hijbZ[khj[pbb\h^hjh^Z\[ebabZlhfZijbf_<br />

kbh[eZ^Zxs_]hfZ]gblguffhf_glhffZ]g_lbafmom^rZ_ljZkl\hjbfhklv\h^hjh^Z\<br />

kieZ\_ Bkke_^h\Zgby k\hckl\ Zlhfgh-djbklZeebq_kdhc kljmdlmju kieZ\h\ ihdZaZeb<br />

qlh k\hckl\Z \h^hjh^ghc khj[pbb lZd `_ aZ\bkyl hl khklZ\Z b kljmdlmju kieZ\Z GZ<br />

ijbf_j_kieZ\ZPdTakh[t_fghp_gljbjh\Zgghcl_ljZ]hgZevghcj_r_ldhc>@[uehmk<br />

lZgh\e_ghqlhijbjZaf_s_gbb\h^hjh^Z\ehdZevghfhdjm`_gbbZlhfh\iZeeZ^by_]h<br />

jZkl\hjbfhklv\ur_q_f\kljmdlmj_Pd 3 Ta.<br />

Ebl_jZlmjZ<br />

1. Xuezhi Ke, Gert Jan Kramer // Phys Condens Matter 16 (2004) 6267-6277<br />

2. Morinaga, H Yukawa // Materials Sci. And Engin., 268 (2002) A329-331<br />

3. Dmevdh\Z K.?., ?]hjmrdbg

190<br />

EHFHGHKH@<br />

JZkq_l nbabq_kdbo iZjZf_ljh\ fZehm]eh\uo mklZgh\hd y\ey_lky g_h[oh^bfuf<br />

gZqZevgufmkeh\b_fbokha^Zgby@<br />

>ZggZyjZ[hlZihk\ys_gZjZkq_lZfiZjZf_ljh\ijyfh]himqdZbboaZ\bkbfhklb<br />

hliZjZf_ljh\fZehm]eh\hcmklZgh\dbjZkk_ygbyg_cljhgh\JZkq_lu\uiheg_guf_lh<br />

^hfFhgl_-DZjehbZgZeblbq_kdb<br />

Ex[Zy fZehm]eh\Zy mklZgh\dZ khklhbl ba bklhqgbdZ g_cljhgh\ ^\modheebfZ<br />

lhjh\ jZkiheh`_gguo ihke_^h\Zl_evgh b ^_l_dlhjZ =_hf_ljbq_kdb_ jZaf_ju hkgh\<br />

guowe_f_glh\mklZgh\dbhij_^_ey_l__m]eh\h_jZaj_r_gb_<br />

JZkq_lu f_lh^hf Fhgl_-DZjeh ijh\h^bebkv k ihfhsvx ijh]jZffgh]h iZd_lZ<br />

McSats [3].<br />

GZhkgh\_wlh]hiZd_lZgZibkZguijh]jZffuihjZkq_lmbgl_gkb\ghklbijyfh]h<br />

imqdZdZdnmgdpbbm]eZjZkk_ygbyb\_dlhjZjZkk_ygbyIhj_amevlZlZfijh\_^_gguo<br />

jZkq_lh\ihdZaZghqlh<br />

Bkihevah\Zgb_djbh]_ggh]haZf_^ebl_eym\_ebqb\Z_lbgl_gkb\ghklvbmemqrZ<br />

_ljZaj_r_gb_<br />

Emqrbc \ZjbZgl dhgnb]mjZpbb mklZgh\db lbiZ XFH khhl\_lkl\mxsbc fZd<br />

kbfZevghcbgl_gkb\ghklbbfbgbfZevghfmm]eh\hfmjZaj_r_gbxj_Zebam_lkyijbmk<br />

eh\bbjZ\_gkl\ZjZ^bmkZi_j\h]hdheebfZlhjZ_]hdjblbq_kdhfmagZq_gbxjZkkqblZg<br />

ghfm\^ZgghcjZ[hl_<br />

JZkq_lu m]eh\h]h jZaj_r_gby f_lh^hf Fhgl_-DZjeh b ZgZeblbq_kdb ohjhrh<br />

kh\iZ^ZxlijbfZeuom]eZojZkk_ygby>ey[hevrbom]eh\jZkk_ygbyg_h[oh^bfhijb<br />

f_g_gb_f_lh^ZFhgl_-DZjeh<br />

1. K\_j]mg>BN_c]bgE:J_gl]_gh\kdh_bg_cljhggh_fZehm]eh\h_jZkk_ygb_F<br />

1986<br />

2. Jan Skov Pedersen, Dorthe Posselt, Kell Mortensen “Analytical treatment of the resolution<br />

function for small-angle scattering” // J. Appl. Cryst., 1990, 23 p. 321-333<br />

3. http://neutron.risoe.dk/mcstas/<br />

FH>?EBJHBNNMABHGGUOO:J:DL?JBKLBD

Ih^k_dpbynbabdbl\_j^h]hl_eZ 191<br />

gb_ hij_^_ey_lky \_ebqbghc Zdlb\Zpbhggh]h h[tzfZ y\eyxs_]hky kmffhc ^\mo kh<br />

klZ\eyxsboh[tzfZh[jZah\Zgbybfb]jZpbb^_n_dlh\G_fgh]hqbke_ggu_j_amevlZlu<br />

jZkq_lh\h[t_fh\fb]jZpbb^_n_dlh\iehohkh]eZkmxlkyf_`^mkh[hcbkwdki_jbf_g<br />

lZevgufb ^Zggufb >@ < ^Zgghc jZ[hl_ bkihevam_lky gh\Zy fh^_ev iha\heyxsZy<br />

jZkkqblu\Zlv h[t_fu h[jZah\Zgby b fb]jZpbb lhq_qguo ^_n_dlh\ \ djbklZeeZo ijb<br />

ihfhsb f_lh^Z fhe_dmeyjghc klZlbdb b mqblu\ZxsZy kf_s_gby Zlhfh\ \ mijm]hc<br />

kj_^_hdjm`Zxs_cjZkq_lgmxyq_cdm<br />

< fh^_eb \aZbfh^_ckl\b_ Zlhfh\ hibku\Z_lky \ khhl\_lkl\bb k ihl_gpbZehf<br />

>`hgkhgZ>@.JZkq_lgZyyq_cdZkh^_j`bl^hZlhfh\Kf_s_gbyZlhfh\\mijm<br />

]hckj_^_\^Zebhl^_n_dlZhij_^_eyxlkymjZ\g_gb_f>@<br />

u=c· r/r 3 (1)<br />

]^_r –jZkklhygb_hl^_n_dlZ^hmaeZb^_Zevghcj_r_ldbk –dhgklZglZdhlhjZyjZk<br />

kqblu\Z_lky gZ hkgh\Zgbb j_amevlZlh\ fh^_ebjh\Zgby kf_s_gbc Zlhfh\ \ jZkq_lghc<br />

yq_cd_^eydhhj^bgZpbhgguokn_jgZoh^ysbokyijbf_jghihk_j_^bg_f_`^m^_n_d<br />

lhfb]jZgbp_cjZkq_lghcyq_cdb>Ze__\khhl\_lkl\bbkba\_klgufagZq_gb_fkkf_<br />

sZxlkyZlhfulj_lv_cahguhlghkbl_evghk\hboiheh`_gbc\b^_Zevghcj_rzld_J_Z<br />

ebah\ZgZ kZfhkh]eZkh\ZggZy bl_jZpbhggZy ijhp_^mjZ ihke_^h\Zl_evgh]h \uqbke_gby<br />

ZlhfZjghckljmdlmju\hdj_klghklb^_n_dlZbdhgklZgluk,oZjZdl_jbamxs_ckf_s_<br />

gb_ Zlhfh\ ih^ \ebygb_f ^_n_dlZ \ hdjm`Zxs_c jZkq_lgmx yq_cdm mijm]hc kj_^_<br />

DhgklZglZkkoh^blkydg_dhlhjhfmihklhygghfmagZq_gbxaZg_kdhevdhbl_jZpbc<br />

>Zgguc Ze]hjblf bkihevam_lky b \ kemqZ_ fb]jZpbb ^_n_dlZfh^_ebjh\Zgby<br />

kdZqdZZlhfZ\\ZdZgkbx>eywlh]hhkms_kl\ey_lkyihrZ]h\uci_j_ghkkhk_^g_]hk<br />

\ZdZgkb_cZlhfZ\gZijZ\e_gbbd\ZdZgkbbIjbq_fldijhbkoh^blgZjmr_<br />

gb_p_gljZevghckbff_ljbb^eyhij_^_e_gbykf_s_gbcZlhfh\bdhgklZgluk\\h<br />

^ylky^\Zp_gljZ^beZlZpbbI_j\ucp_glj^beZlZpbbjZkiheZ]Z_lky\\ZdZgkbbZ\lh<br />

jhckh\iZ^Z_lkgZqZevgufiheh`_gb_ffb]jbjmxs_]hZlhfZLZdbfh[jZahffh`gh<br />

jZaeh`blvihe_kf_s_gbcgZ^\_khklZ\eyxsb_hlghkbl_evgh^\momdZaZgguop_gljh\<br />

^beZlZpbb\deZ^dZ`^h]hbadhlhjuohij_^_ey_lky\_kh\uffgh`bl_e_f<br />

H[t_fu j_eZdkZpbb b fb]jZpbb \ZdZgkbb jZkkqblZgu gZ hkgh\_ ihemq_gguo<br />

agZq_gbcdhgklZglkihnhjfmeZfûV Œk[3] b V m Œk-k]^_kk –dhgklZglu<br />

^ey dhgnb]mjZpbb kbkl_fu k i_j_f_sZ_fuf Zlhfhf \ hkgh\ghc b k_^eh\hc ihabpbb<br />

khhl\_lkl\_ggh<br />

IhdZaZgh qlh kf_s_gby Zlhfh\ \[ebab ^_n_dlZ jZkkqblZggu_ gZ hkgh\Zgbb<br />

l_hjbb mijm]hklb kbevgh jZkoh^ylky kh kf_s_gbyfb ihemq_ggufb ijb fh^_ebjh\Z<br />

gbbkfjbk<br />

Kf_s_gbyZlhfh\:<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

JZkklhygb_^h\ZdZgkbb:<br />

Kf_s_gby<br />

Zlhfh\<br />

ihemq_ggu_ijb<br />

fh^_ebjh\Zgbb<br />

Kf_s_gby<br />

Zlhfh\<br />

jZkkqblZggu_gZ<br />

hkgh\Zgbbl_hjbb<br />

mijm]hklb

192<br />

EHFHGHKH@J_amevlZluihdZaZebqlhwlhl\deZ^ke_^m_lmqb<br />

lu\ZlvijbjZkq_l_h[t_fZfb]jZpbbldihZ[khexlghc\_ebqbg_hgij_\hkoh^blljZ<br />

^bpbhgghijbgbfZxsmxky\jZkq_lqZklv<br />

Ebl_jZlmjZ<br />

1. Kedves F.J., Erdelyi G. Diffusion under high pressure // Defect and Diffusion Forum,<br />

1989, v. 66-69, p. 175-188<br />

2. Philibert J. Diffusion under stress //Metal Physics and Advanced Tecnologies, 1999, v. 21,<br />

N1, p. 3-18<br />

3. Johnson R.A. InterVWLWLDOVDQGYDFDQFLHVLQ.LURQ3K\V5HYY‹$S<br />

1329-1336<br />

4. Nazarov A.V., Ganchenkova M.G., Mikheev A.A. Theory of diffusion under pressure//<br />

Defect and Diffusion Forum, 2001, p. 194-199<br />

M>D<br />

Ih^k_dpbynbabdbl\_j^h]hl_eZ 193<br />

Dhf[bgZpbywlbof_lh^h\iha\hey_lmq_klv^Zevgh^_ckl\mxs_coZjZdl_jwnn_dlb\gh<br />

]h\aZbfh^_ckl\bylhq_qguo^_n_dlh\bh[_ki_qblv\hafh`ghklvbamq_gbybo\aZbf<br />

gh]h\ebygbygZehdZevgu_^bnnmabhggu_oZjZdl_jbklbdb<br />

Nbabq_kdZyfh^_evjZajZ[hlZgZbkoh^ybahkgh\guoihgylbcnbabdbl\_j^h]h<br />

l_eZdjbklZeeblij_^klZ\ey_lkylj_of_jguffZkkb\hfdhhj^bgZlmaeh\\dhlhjuogZ<br />

oh^ylky Zlhfu f_lZeeZ ih^qbgyxsb_ky g_dhlhjhfm aZdhgm f_`Zlhfgh]h \aZbfh^_c<br />

kl\by>@Ijbh[jZah\Zgbb\ZdZgkbbbeb\g_^j_gbyZlhfZijbf_kb\kljmdlmjmijh<br />

bkoh^blbaf_g_gb_dZdwg_j]bbZlhfZlZdbwg_j]bbkbkl_fu\p_ehfAgZq_gb_\ukh<br />

lu ihl_gpbZevgh]h [Zjv_jZ ijb i_j_oh^_ ZlhfZ ba h^gh]h jZ\gh\_kgh]h iheh`_gby \<br />

^jm]h_jZkkqblu\Z_lkyiml_fi_j_lZkdb\ZgbyZlhfZbah^gh]hmaeZ\^jm]hc\ZdZglguc<br />

ma_ebih^kq_lZwg_j]bbkbkl_fuihke_\uiheg_gbyijhp_^mjuj_eZdkZpbb\k_oZlhfh\<br />

kbkl_fu gZ dZ`^hf rZ]_>@KjZ\gb\Zy wg_j]bb i_j_oh^h\ ZlhfZ \ jZaebqguogZ<br />

ijZ\e_gbyofh`ghjZkkqblZlv\_jhylghklbkdZqdZZlhfZ\lhfbebbghfgZijZ\e_gbb<br />

GZ[hjlZdbo \_jhylghkl_ciha\hey_lihkljhblv ljZ_dlhjbx[em`^ZgbyZlhfZihdjb<br />

klZeebq_kdhcj_r_ld_kmq_lhf\ebygbygZ_]h^\b`_gb_ijbkmlkl\mxsbo\djbklZee_<br />

^_n_dlh\b\uqbkeblvwnn_dlb\gucdhwnnbpb_gl^bnnmabb>@<br />

GZ hkgh\_ wlhc fh^_eb jZajZ[hlZg ijh]jZffguc dhfie_dk ^ey \uqbke_gby<br />

wg_j]_lbq_kdbob^bnnmabhgguooZjZdl_jbklbddhfie_dkh\lhq_qguo^_n_dlh\JZkq_<br />

luijh\_^_gu^eykbkl_fNi-C.-Fe-C.-Fe-H.<br />

Fh^_ebjh\Zgb_lhq_qguo^_n_dlh\gZZlhfghfmjh\g_iha\hey_lg_lhevdhih<br />

emqblv bo wg_j]_lbq_kdb_ oZjZdl_jbklbdb gh b ijbh[j_klb agZgby b ihgbfZgb_ l_o<br />

ijhp_kkh\ dhlhju_ ijhbkoh^yl gZ fbdjhkdhibq_kdhf mjh\g_ b g_^hklmigu \bamZev<br />

ghfm gZ[ex^_gbx LZd ihemq_ggu_ j_amevlZlu ^ey kbkl_fu Ni-C ihdZau\Zxl qlh<br />

Zlhfm]e_jh^Zb\ZdZgkbyh[jZamxldhfie_dkdhlhjucfb]jbjm_l\k\yaZgghfkhklhy<br />

gbb>eykbkl_fu.-Fe-CihdZaZghqlh\ZdZgkbyijbly]b\Z_lZlhfm]e_jh^Z\j_amev<br />

lZl_ q_]h ijhbkoh^bl baf_g_gb_ _]h ^bnnmabhgghc ih^\b`ghklb ijbq_f ij_^\Zjb<br />

l_evgu_j_amevlZluihdZau\Zxlqlhijb\ukhdbol_fi_jZlmjZo\hafh`ghbmkdhj_gb_<br />

LZdbfh[jZahfbaf_gy_lkydZjlbgZ^bnnmabhgghcih^\b`ghklb\g_^j_gguoZlhfh\:<br />

gZ]jZnbd_aZ\bkbfhklbeh]ZjbnfZdhwnnbpb_glZ^bnnmabbhlh[jZlghcl_fi_jZlmju<br />

gZ[ex^Z_lkyhldehg_gb_hlijyfhebg_cghcaZ\bkbfhklb<br />

Ijh\_^_gh kjZ\g_gb_ ^bnnmabb dhfie_dkh\ \ZdZgkby-m]e_jh^ \ HPD b =PD<br />

kljmdlmjZo Z lZd`_ hkh[_gghklb ^bnnmabhggh]h ih\_^_gby dhfie_dkh\ \ZdZgkby-<br />

\h^hjh^\.-Fe.<br />

Ebl_jZlmjZ<br />

1. ;_r_jk>G©>bnnmabyijbf_k_c\g_^j_gby\f_lZeeZokh[t_fgh-p_gljbjh\Zgghc<br />

dm[bq_kdhc j_r_ldhcª K[ ©>bnnmaby \ f_lZeeZo k h[t_fghp_gljbjh\Zgghc<br />

j_r_ldhcªk<br />

2. OhfZg D>` ©>bnnmaby m]e_jh^Z \ .-`_e_a_ª K[ ©>bnnmaby \ f_lZeeZo k<br />

h[t_fghp_gljbjh\Zgghcj_r_ldhcªk<br />

3. :\QEODWW3-RXU3K\V$QG&KHPRI6ROLGV9RO‹SS-224.<br />

4. Ruda M., Farkas D., Abriata J. «Interatomic potentials for carbon interstitials in metals<br />

and intermetallics» // Scripta Materialia, 2002, Vol. 46, pp.349-355.<br />

5. K_e_ag_\Z E< GZaZjh\ :< ©Fh^_ebjh\Zgb_ ki_dljZ ihl_gpbZevguo [Zjv_jh\<br />

^eykdZqdh\Zlhfh\m]e_jh^Zb\ZdZgkbc\=PDgbd_e_mqblu\Zy\aZbfgh_\ebygb_<br />

^_n_dlh\ªK[gZmqguoljm^h\©GZmqgZyk_kkbyFBNB-ªlk-<br />

175.<br />

6. K_e_ag_\Z E< GZaZjh\ :< ©Fh^_ebjh\Zgb_ \ebygby \aZbfh^_ckl\by lhq_qguo<br />

^_n_dlh\gZ^bnnmabhggmxih^\b`ghklv\g_^j_gguoZlhfh\\HPD–kljmdlmjZoª<br />

K[gZmqguoljm^h\©GZmqgZyk_kkbyFBNB-ªlk-163.

194<br />

EHFHGHKHD<br />

BKKE?>H

Ih^k_dpbynbabdbl\_j^h]hl_eZ 195<br />

Ebl_jZlmjZ<br />

1. B\Zgh\ GJ D<br />

196<br />

EHFHGHKH

Ih^k_dpbynbabdbl\_j^h]hl_eZ 197<br />

BGNJ:DJ:KG:YKI?DLJHKDHIBYDJ?FGBY<br />

E?=BJHZeb_\RODZeZg^Zjh\WD<br />

GZpbhgZevgucmgb\_jkbl_lMa[_dbklZgZbf_gbFbjahMem][_dZ<br />

Ba\_klghqlh\h[t_f_dj_fgbyihfbfhki_pbZevgh\\_^_gguoijbf_k_c\k_<br />

]^Z ijbkmlkl\mxl g_dhgljhebjm_fu_ ijbf_kb lZd gZau\Z_fu_ l_ogheh]bq_kdb_ ijb<br />

f_kbLZdbfbijbf_kyfb\dj_fgbby\eyxlkyZlhfudbkehjh^Zbm]e_jh^Z\k_]^Zijb<br />

kmlkl\mxsb_\_]hdjbklZeebq_kdhcj_r_ld_\\ukhdbodhgp_gljZpbyo^h 17 ÷10 18 kf -<br />

3 Hlf_lbf qlh oZjZdl_jghc hkh[_gghklvx Zlhfh\ dbkehjh^Z b m]e_jh^Z y\ey_lky<br />

kdehgghklv d jZaebqguf \aZbfh^_ckl\byf < k\yab k wlbf gZfb [ueh bkke_^h\Zgh<br />

\aZbfh^_ckl\b_Zlhfh\eZglZgZkZlhfZfbl_ogheh]bq_kdboijbf_k_c\dj_fgbb<br />

>eywdki_jbf_glh\\dZq_kl\_bkke_^m_fuoh[jZaph\bkihevah\Zekydj_fgbc n<br />

bp-lbiZijh\h^bfhklb\ujZs_ggucf_lh^hfQhojZevkdh]hkdhgp_gljZpb_chilbq_<br />

kdbZdlb\guodbkehjh^Zbm]e_jh^ZN 0 hil =6⋅10 17 kf -3 bN k hil = 2⋅10 16 kf -3 khhl\_lkl\_g<br />

ghIjbf_kveZglZgZ\\h^beZkv\dj_fgbc\ijhp_kk_\ujZsb\ZgbybajZkieZ\ZLhe<br />

sbgZihebjh\Zgguoh[jZaph\\aZ\bkbfhklbhlihklZ\e_gghcaZ^ZqbkhklZ\eyeZ÷2<br />

ff<br />

198<br />

EHFHGHKHD01.57<br />

FH>?EBJHBG?GBC<br />

F?LH>HF>BKDJ?LGH=HFH>?EBJHFih<br />

kjZ\g_gbx k f_lh^Zfb g_ij_ju\gh]h baf_g_gby hjb_glZpbhgguo bwg_j]_lbq_kdboiZ<br />

jZf_ljh\ ijb ]_g_jZpbb djbklZeebq_kdbo kljmdlmj y\eyxlky khdjZs_gb_ jZkq_lh\ b<br />

\hafh`ghklvdhg_qgh]hi_j_[hjZ\ZjbZglh\miZdh\hd[_aZijbhjgh]hagZgbyiZjZf_ljh\<br />

we_f_glZjghc yq_cdb @b>@ij_^eh`_gu Ze]hjblfu ]_g_jZpbb djbklZeebq_kdbo<br />

kljmdlmj ]hfhfhe_dmeyjguo kh_^bg_gbc kh^_j`Zsbo h^gm fhe_dmem b ^\_ fhe_dmeu<br />

k\yaZggu_p_gljhfbg\_jkbbgZijbfblb\gmxyq_cdmH^gZdhagZqbl_evgZyqZklvfhe_<br />

dmeyjguo djbklZeeh\ y\ey_lky ]_l_jhfhe_dmeyjgufb KemqZc dh]^Z gZ ijbfblb\gmx<br />

yq_cdmijboh^blky^\_bebljbkbff_ljbq_kdbg_aZ\bkbfuofhe_dmeujZkkfhlj_g\>@<br />

@Gb`_ijb\_<br />

^_gu g_dhlhju_ j_amevlZlu ]_g_jZpbb djbklZeebq_kdbo kljmdlmj ]b^jhoehjb^Z -<br />

ZaZ[bpbdeh>@mg^_dZgZ[jmllh-nhjfmeZ& 10 H 20 N 1<br />

1+ •Cl 1 1- >@GZjbkij_^klZ\e_<br />

gu rZjh-kl_j`g_\Zy fh^_ev ]_hf_ljbq_kdZy fh^_ev b ihebdm[ fhe_dmeu dZlbhgZ <<br />

lZ[eijb\_^_guiZjZf_ljuj_r_ldbwdki_jbf_glZevghcb[ebadhcdg_cfh^_evghc<br />

djbklZeebq_kdhckljmdlmjumdZaZggh]hobfbq_kdh]hkh_^bg_gby<br />

∗∗ >hdeZ^hlf_q_g`xjbdZdh^bgbaemqrbogZih^k_dpbb

Ih^k_dpbynbabdbl\_j^h]hl_eZ 199<br />

Z [ \<br />

JbkRZjh-kl_j`g_\Zyfh^_ev–Z]_hf_ljbq_kdZyfh^_ev–[bihebdm[fhe_dmeudZlbhgZ<br />

LZ[ebpZIZjZf_ljuj_r_ldbwdki_jbf_glZevghcbfh^_evghcdjbklZeebq_kdhckljmdlmju<br />

J_ndh^<br />

kljmdlmju<br />

a (Å) b (Å) c (Å) .]jZ^ ]jZ^ ]jZ^<br />

JK: F>F JK: F>F JK: F>F JK: F>F JK: F>F JK: F>F<br />

AZUDEC10 10.830 10.30 7.122 7.27 7.014 7.10 97.97 94.1 90.4 92.2 96.28 96.1<br />

< ^hdeZ^_ ij_^klZ\e_gu dhfie_dk dhfivxl_jguo ijh]jZff kha^Zgguo gZ hk<br />

gh\_ Ze]hjblfZ b ijb\_^_gu ijbf_ju _]h Zijh[Zpbb ^ey djbklZeebq_kdbo kljmdlmj<br />

^Zggh]hdeZkkZ<br />

JZ[hlZ\uiheg_gZijbih^^_j`d_Jhkkbckdh]hnhg^Znmg^Zf_glZevguobkke_^h\Zgbc]jZgl‹-<br />

02-16835.<br />

Ebl_jZlmjZ<br />

1. FZe__\ :< JZm hde :G KKKJ L ‹<br />

K<br />

2. FZe__\:

200<br />

EHFHGHKH@y\ey_lky<br />

h^gbfbaf_lh^h\]_g_jZpbbdjbklZeebq_kdbokljmdlmj>Zggucf_lh^hkgh\ZggZaZ<br />

f_g_ZiijhdkbfZpbbfhe_dme^bkdj_lgufbfh^_eyfbihebdm[Zfb>@<br />

@ [ueh hlh[jZgh iylv<br />

ihebdm[h\<br />

>ey hlh[jZgguo ihebdm[h\ [ue<br />

\uiheg_g jZkq_l \k_o \hafh`guo \ZjbZglh\ bo miZdh\dbijb mkeh\bb qlh \ we_f_g<br />

lZjghcyq_cd_bf_xlky^\Zihebdm[Z k\yaZggu_p_gljhfbg\_jkbb>@dhwnnbpb_gl<br />

miZdh\db\Zjvbjh\Zekyhl^heyihemq_gguo\ZjbZglh\miZdh\dbihebdm[h\jZkkqblZgufh^_ebdjbklZeeb<br />

q_kdbokljmdlmjbijh\_^_ghbomlhqg_gb_<br />

:gZebaj_amevlZlh\fh^_ebjh\Zgby[m^_lij_^klZ\e_g\^hdeZ^_<br />

Ebl_jZlmjZ<br />

1. FZe__\ :< JZm hde :G KKKJ L ‹K<br />

1382.<br />

2. FZe__\ :< ©=_g_jZpby fhe_dmeyjguo kljmdlmj ;jZ\w f_lh^hf ^bkdj_lgh]h<br />

fh^_ebjh\ZgbymiZdh\hdªDjbklZeeh]jZnbyL‹K<br />

3. FZe__\:D<br />

BKKE?>HBG?GBCKu 1+X SF?LH>HFYDJ 63,65 Cu<br />

KZnhgh\:GIh]hj_evp_\:BFZlmobg

Ih^k_dpbynbabdbl\_j^h]hl_eZ 201<br />

abq_kdbok\hckl\b\qZklghklb^eybkke_^h\Zgbyf_oZgbafh\k\_joijh\h^bfhklb<<br />

gZklhys_c jZ[hl_ ij_^klZ\e_gu j_amevlZlu bamq_gby kh_^bg_gbc Ku 1+x S (x = 1÷1.4)<br />

f_lh^hfy^_jgh]hd\Z^jmihevgh]hj_ahgZgkZgZy^jZof_^bYDJ 63,65 Ku).<br />

Bkke_^h\Zgby ki_dljh\ YDJ 63,65 Ku ijh\h^bebkv gZ bfimevkghf YDJ ki_dljh<br />

f_lj_\l_fi_jZlmjghf^bZiZahg_-DHkgh\mkljmdlmjudh\_eebgZCuSkhklZ\<br />

ey_l ]_dkZ]hgZevguc ijhkljZgkl\_ggZy ]jmiiZ K 3 /mms lj_okehcguc iZd_l ABA.<br />

Kehc:keZ]Z_lkyl_ljZw^jZfbCuS 4 Kehc

202<br />

EHFHGHKHD<br />

LHQ?QGU?=JMIIUDJBKL:EEH

Ih^k_dpbynbabdbl\_j^h]hl_eZ 203<br />

M>D<br />

BKKE?>H

204<br />

EHFHGHKHD<br />

?E?GB?IHEYJBA:PBB<<br />

;?KIJBF?KGUO FHGHDJBKL:EE:OSBNBSBN:CrK_<br />

Fh\qbdh\Z::FZeurdbgZHeybkke_^h\Zgby<br />

iheyjbaZpbb\]em[hdbokehyoh[jZaph\g_h[oh^bfhbkihevah\Zlvgbadb_qZklhlufh<br />

^meypbb l_ieh\h]h ihlhdZ \ wlhf kemqZy h[uqgu_ baf_j_gby kbkihevah\Zgb_f<br />

\hevlf_ljZkj_^gboagZq_gbcg_\hafh`guihwlhfmgZfbij_^eh`_gpbnjh\hcf_lh^<br />

h[jZ[hldbkb]gZeZ.<br />

D<br />

:G:EBAG?IJ?JU:IHEMQ?GBY=:EE:F<br />

S?EHQGUOF?L:EEH<<br />

Ebl\bgh\

Ih^k_dpbynbabdbl\_j^h]hl_eZ 205<br />

e_gbys_ehqguof_lZeeh\hkgh\ZgZgZZfZev]Zfgh-h[f_gghff_lh^_\dhlhjhfh^gbf<br />

ba hkgh\guo dhfihg_glh\ y\ey_lky ZfZev]ZfZ eblby Lj_[h\Zgby d wdheh]bq_kdhc<br />

[_ahiZkghklb hij_^_ebeb g_h[oh^bfhklv jZajZ[hldb gh\uo f_lh^h\ jZa^_e_gby bk<br />

dexqZxsbo ijbf_g_gb_ \ukhdhlhdkbqghc jlmlb < gZklhys__ \j_fy ij_^eh`_gh bk<br />

ihevah\Zlvgh\u_h[f_ggu_kbkl_fu\dhlhjuojlmlvaZf_g_gZgZwdheh]bq_kdb[_ah<br />

iZkguc]Zeebc<br />

< gZklhys_f khh[s_gbb ij_^klZ\e_gZ nbabdh-fZl_fZlbq_kdZy fh^_ev hibku<br />

\ZxsZyg_ij_ju\gucf_lh^ihemq_gby]ZeeZfueblbyF_lh^aZdexqZ_lky\ijhp_kk_<br />

^bnnmabbeblby\]Zeebcijbg_ij_ju\ghfijhoh`^_gbbdZi_ev`b^dh]h]Zeebyih^<br />

^_ckl\b_f kbeu ly`_klb q_j_a kehc jZkieZ\e_ggh]h eblby JZkkfZljb\Zebkv ke_^mx<br />

sb_ ijhp_kku dZie_h[jZah\Zgb_ ]jZ\blZpbhggh_ hkZ`^_gb_ dZi_ev ^bnnmabhggu_<br />

ijhp_kku<br />

206<br />

EHFHGHKHey<br />

\k_obamq_gguof_lZeeh\gZ[ex^Z_lkyihgb`_gb_nhlhwfbkkbhggh]hlhdZj n bih<br />

\ur_gb_jZ[hlu\uoh^Zwe_dljhgZijbZ^khj[pbb\h^hjh^Z<br />

Jbk Baf_g_gb_ ^Z\e_gby G 2 nhlh<br />

lhdh\bjZ[hlu\uoh^ZlZeby\aZ<br />

\bkbfhklbhl\j_f_gbgZl_dZgby\h^hjh<br />

^Z\dZf_jmλ gf<br />

JbkBaf_g_gb_^Z\e_gbyG 2 nh<br />

lhlhdh\bjZ[hlu\uoh^Zheh\Z<br />

\ aZ\bkbfhklb hl\j_f_gb gZl_dZgby \h<br />

^hjh^Z\dZf_jmb- λ gfbλ<br />

gf<br />

Bah[jZ[hldbj_amevlZlh\djb\uoZ^khj[pbbhij_^_e_gukj_^gyywg_j]byZ^<br />

khj[pbb \h^hjh^Z gZ ihebdjbklZeebq_kdhc ih\_joghklb f_lZeeZ b \j_fy j_eZdkZpbb<br />

kbkl_fuih\_joghklv-]Zah\ZynZaZ<br />

Ebl_jZlmjZ<br />

1. HklZlhqgu_ ]Zau \ we_dljhgguo eZfiZoFZl_jbZeu i_j\h]h b \lhjh]h f_`^mgZ<br />

jh^gh]h kbfihabmfh\ b]] Ih^ j_^ DLG =e_[h\Z => F ©Wg_j]byª<br />

]<br />

2. DZeZ`hdh\ OO bk gZ khbkd mq kl dn-fg<br />

GZevqbdD;=M]k<br />

M>D<br />

L?FI?J:LMJG:YA:BYHEH

Ih^k_dpbynbabdbl\_j^h]hl_eZ 207<br />

juh[jZapZkaZ^ZgghckdhjhklvxhldhfgZlghc^hl_fi_jZlmjuieZ\e_gbyb\ur_<<br />

ijhp_kk_ ih\ur_gby l_fi_jZlmju h[jZapZ ijhba\h^beZkv g_ij_ju\gZy j_]bkljZpby<br />

l_fi_jZlmjubnhlhwe_dljbq_kdh]hlhdZ

208<br />

EHFHGHKHD<br />

WFBKKBY;HEVRBODE:KL?JH<<br />

IJBBHGGHFJ:KIUE?GBBF?L:EE:<br />

DhqdbgK:<br />

Ihfhjkdbc]hkm^Zjkl\_ggucmgb\_jkbl_lbfF@dh<br />

lhjuc ^ey klhedgh\_gbc bhgh\ k wg_j]byfb ihjy^dZ g_kdhevdbo dw< b kj_^gbo fZkk<br />

Zlhfh\ b bhgh\ khklZ\ey_l \_ebqbgm ihjy^dZ ^\hcdb m – fZkkZ ZlhfZ<br />

U<br />

2 3<br />

N<br />

= σ S<br />

N<br />

= δ N –wg_j]byk\yabdeZkl_jZkf_lZeehf>@δ -bf__lkfukewg_j]bb<br />

k\yabdeZkl_jZhlg_k_gghcdh^ghfmZlhfm\khklZ\_deZkl_jZb\hh[s_]h\hjyδhl<br />

ebqZ_lkyhl∆

Ih^k_dpbynbabdbl\_j^h]hl_eZ 209<br />

D<br />

N<br />

=<br />

∑<br />

Q<br />

⎪<br />

⎧<br />

exp⎨−<br />

⎪⎩<br />

1<br />

2<br />

( Q − Q0<br />

)<br />

2<br />

( ∆Q<br />

) +<br />

N<br />

2<br />

⎪<br />

⎫<br />

⎬,<br />

β ⎪⎭<br />

3 1 3<br />

2 3<br />

m Θ⎛V<br />

⎞ 3<br />

4 3 2<br />

⎜ ⎟<br />

2<br />

e<br />

1<br />

( ∆Q<br />

) =<br />

γ N,<br />

N<br />

π<br />

!<br />

⎝N<br />

⎠<br />

2 3<br />

e 1 3<br />

1 3<br />

3 m ∆µ<br />

⎛V<br />

⎞<br />

Q0<br />

=<br />

γ N<br />

4 3 2<br />

⎜ ⎟ ,<br />

π ! ⎝N<br />

⎠<br />

]^_ m<br />

e<br />

-fZkkZ we_dljhgZ ahgu ijh\h^bfhklb V -h[t_f deZkl_jZ Θ -l_fi_jZlmjZ<br />

fbr_gb γ -\Ze_glghklvZlhfh\f_lZeeZ ! -ihklhyggZyIeZgdZ β -iZjZf_ljkhhl<br />

\_lkl\mxsbcd\Zglh\ufnemdlmZpbyfaZjy^Zijbgme_\hcl_fi_jZlmj_fbr_gb ∆ µ -<br />

jZaghklvf_`^mmjh\gyfbN_jfb\f_lZee_b\deZkl_j_<br />

hklb]gmlhohjhr__kh]eZkb_kwdki_jbf_glZfb<br />

:\lhju[eZ]h^ZjguFbgh[jZah\ZgbxJNaZnbgZgkh\mxih^^_j`dmjZ[hlurbnj]jZglZ:-2.9-<br />

918).<br />

Ebl_jZlmjZ<br />

1. FZl\__\D<br />

FH>?EBJHBNNMABHGGUOO:J:DL?JBKLBD<br />

LHQ?QGUO>?N?DLH

210<br />

EHFHGHKHey hibkZgby f_`Zlhfguo \aZbfh^_ckl\bc \ ^Zgghc jZ[hl_ ijbf_gzg f_lh^<br />

wfibjbq_kdbofgh]hqZklbqguoihl_gpbZeh\@y\eyxsbckyijb[eb`_gb_f\lhjh]hihjy^dZl_hjbbkbevghck\yab>Zg<br />

gucih^oh^hij_^_ey_lwg_j]bxZgkZf[eyZlhfh\ke_^mxsbfh[jZahf<br />

N<br />

N<br />

N<br />

1<br />

E = ∑Nij<br />

( Rij<br />

) − ∑ f ( ρ<br />

i<br />

), ρi<br />

= ∑ϕ(<br />

Rij<br />

) , (2)<br />

2<br />

i≠<br />

j=<br />

1<br />

i=<br />

1<br />

]^_N ij –iZjgZyhl\_qZxsZyaZhllZedb\Zgb_qZklvihl_gpbZeZ3 ij –\deZ^\we_dljhg<br />

gmxiehlghklv\ihabpbbZlhfZihlhdjm`ZxsboZlhfh\j, ! i –we_dljhggZyiehlghklv\<br />

ihabpbbZlhfZi, f –fgh]hqZklbqgZynmgdpbyR ij –f_`Zlhfgh_jZkklhygb_<br />

>eyjZkqzlZmdZaZgguo^bnnmabhgguooZjZdl_jbklbd\^ZgghcjZ[hl_bkihevah<br />

\ZgZgh\Zyfh^_evhkgh\ZggZygZbkihevah\Zgbbf_lh^Zfhe_dmeyjghcklZlbdb^eyhi<br />

j_^_e_gbyZlhfZjghckljmdlmju\hdj_klghklb^_n_dlZIjbwlhfjZkqzlgZyyq_cdZmk<br />

eh\ghjZa^_ey_lkygZljbahguey<br />

wlh]hhkms_kl\ey_lkyihrZ]h\uci_j_ghkkhk_^g_]hk\ZdZgkb_cZlhfZ\gZijZ\e_gbb<br />

gZb[he__iehlghcmiZdh\dbHPDj_rzldbd\ZdZgkbbIjbwlhfkf_s_gbyZlhfh\<br />

i_j_klZxl[ulvbahljhigufbb^eyhij_^_e_gbydhgklZgluK\\h^blky^\Zp_gljZ^b<br />

eZlZpbbI_j\ucp_glj^beZlZpbbjZkiheZ]Z_lky\\ZdZgkbbZ\lhjhckh\iZ^Z_lkgZ<br />

qZevguf iheh`_gb_f fb]jbjmxs_]h ZlhfZ LZdbf h[jZahf fh`gh jZaeh`blv ihe_<br />

kf_s_gbcgZ^\_dhfihg_gluhlghkbl_evgh^\momdZaZgguop_gljh\^beZlZpbbeyhij_^_e_gbywlbo^h[Z\hd[uebkihevah\Zggh\ucih^<br />

oh^mqblu\ZxsbcaZ\bkbfhklvwg_j]bbkbkl_fu\lqkbkl_fuk^_n_dlhfhl^Z\e_<br />

gby>@@:gZeh]bqgh \ jZfdZo ^Zggh]h ih^oh^Z<br />

fh`ghihemqblvkhhl\_lkl\mxs__\ujZ`_gb_^eykemqZyfgh]hqZklbqguo\aZbfh^_c<br />

kl\bc<br />

j=<br />

1<br />

(4)

Ih^k_dpbynbabdbl\_j^h]hl_eZ 211<br />

∆V<br />

Em<br />

p N −body<br />

= −<br />

1<br />

3K<br />

0<br />

N<br />

∑<br />

i<br />

⎡<br />

⎢<br />

⎢⎣<br />

( f ′+ f ′)<br />

i<br />

N<br />

1 ⎡<br />

ϕ<br />

⎤<br />

0 ∂<br />

0 ∂Φ<br />

∂f<br />

+ ∑⎢( f ′)<br />

+ ⎥ ′<br />

i′+<br />

fs<br />

Ris<br />

Ris<br />

f ≡<br />

3K<br />

0 i ⎢⎣<br />

∂R<br />

0<br />

R<br />

∂R<br />

0<br />

R ⎥⎦<br />

∂ρ<br />

is<br />

is<br />

A^_kvD 0 –fh^mev\k_klhjhgg_]hk`Zlby:gZeh]bqgufh[jZahfmqblu\Z_lkyaZ<br />

\bkbfhklvwg_j]bbhl^Z\e_gby^eyh[tzfZh[jZah\Zgby\ZdZgkbb<br />

J_amevlZlubkke_^h\Zgby^bnnmabhgguok\hckl\^\moHPDf_lZeeh\ ij_^klZ\<br />

e_gu \ lZ[ebp_ OZjZdl_jbklbdb .-Fe bkke_^h\Zebkv k ihfhsvx iZjgh]h ihl_gpbZeZ<br />

>`hgkhgZbfgh]hqZklbqgh]hihl_gpbZeZWdeZg^ZAckland>@JZkqzlu^ey-Zrijh<br />

\h^bebkv k ihfhsvx fgh]hqZklbqgh]h ihl_gpbZeZ MbeevyfZ-FZkkh[jbh Willaime-<br />

Massobrio) [4].<br />

LZ[e<br />

OZjZdl_jbklbdb<br />

Fgh]hqZklbqgucihl_g<br />

pbZeWdeZg^Z<br />

s<br />

.-Fe<br />

R<br />

W<br />

is<br />

∂ϕ<br />

∂R<br />

W<br />

Ris<br />

+ R<br />

W<br />

is<br />

∂Φ<br />

∂R<br />

IZjgucihl_gpbZe<br />

>`hgkhgZ<br />

W<br />

Ris<br />

⎤<br />

⎥+<br />

⎥⎦<br />

(5)<br />

-Zr<br />

Fgh]hqZklbqgucih<br />

l_gpbZeWM1<br />

f<br />

Ev<br />

, w< 1,70 2,91 1,55<br />

m<br />

Ev<br />

, w< 0,79 0,69 0,32<br />

E , w< 2,49 3,78 1,87<br />

SD<br />

v<br />

V rel<br />

∆ / Ω -0,159 -0,132 -0,472<br />

E f<br />

V p<br />

∆ / Ω 0,021 0,015 0,014<br />

V / Ω 0,862 0,854 0,542<br />

f<br />

v<br />

0<br />

( V′<br />

rel<br />

Vrel<br />

)<br />

∆ −∆ / Ω 0,009 0,011 10 -4<br />

E m<br />

V p<br />

∆ / Ω 0,041 -0,032 0,089<br />

m<br />

Vv<br />

/ Ω 0,050 -0,022 0,089<br />

V / Ω 0,912 0,832 0,631<br />

SD<br />

v<br />

BalZ[ebpu\b^ghqlh\_ebqbgZg_ljZ^bpbhggh]hkeZ]Z_fh]hh[tzfZfb]jZ<br />

pbb\nhjfmeZohljbpZl_evgZqlh]h\hjbl\_jhylghhg_Z^_d\Zlghklbfh^_ebiZj<br />

guo ihl_gpbZeh\ Khhl\_lkl\mxsZy \_ebqbgZ ihemq_ggZy ^ey fgh]hqZklbqgh]h ih<br />

l_gpbZeZ WdeZg^Z ohjhrh kh]eZkm_lky k ba\_klgufb hp_ghqgufb agZq_gbyfb >ey<br />

pbjdhgbywg_j]bbh[jZah\Zgbybfb]jZpbb^h\hevghfZeuZagZq_gb_Zdlb\Zpbhggh]h<br />

h[tzfZfb]jZpbbhlghkbl_evgh\ukhdh<br />

Ebl_jZlmjZ<br />

1. Finnis M.W., Sinclair J.E. A simple N-body potential for transition metals. Philosophical<br />

magazine A, 1984, Vol. 50, No 1, p. 45-55.<br />

2. Nazarov A.V., Ganchenkova M.G. and Mikheev A.A. Theory of diffusion under pressure,<br />

Defect and Diffusion Forum, 2001, Vol. 194-199, p 49.<br />

3. Ackland G.J., Bacon D.J., Calder A.F., Harry T. Computer simulation of point defect<br />

properties in dilute Fe-Cu alloy using a many-body potential. Philosophical magazine A,<br />

1997, Vol. 75, No 3, p. 713-732.<br />

4. Willaime F., Massobrio C. Development of an N-body interatomic potential for hcp and<br />

bcc zirconium. Physical review B, 1991, Vol. 43, No 14, p. 11653.

212<br />

EHFHGHKHD<br />

FH>?EBJH?E?GBY<br />

WE?DLJHGGHCIEHLGHKLB

Ih^k_dpbynbabdbl\_j^h]hl_eZ 213<br />

dZgkbyfb jZkiheh`_ggufb \h \lhjuo dhhj^bgZpbhgguo kn_jZo hlghkbl_evgh ^jm]<br />

^jm]Zjbk[g_y\ey_lky_^bgufh[t_dlhfbfh`_ljZkkfZljb\ZlvkydZd^\_fhgh\Z<br />

dZgkbbqlhih-\b^bfhfmbihdZ`_lf_lh^ihabljhgghcZggb]beypbb\^ZgghfkemqZ_<br />

Z) [)<br />

JbkJZaghklgu_nmgdpbbjZkij_^_e_gbywe_dljhgghciehlghklb\hdj_klghklb[b\ZdZgkbcZ\Z<br />

dZgkbbgZoh^ylky\i_j\uodhhj^bgZpbhgguokn_jZohlghkbl_evgh^jm]^jm]Z[\ZdZgkbbgZoh<br />

^ylky\h\lhjuodhhj^bgZpbhgguokn_jZohlghkbl_evgh^jm]^jm]Z<br />

Ebl_jZlmjZ<br />

1. G_fhrdZe_gdh NbabdZ l\_j^h]h l_eZ AhggZy l_hjby f_lZeeh\ Db_\ GZmdh\Z<br />

^mfdZ–k<br />

2. Turner D.E., Zhu Z.Z., Chan C.T., and Ho K.M. Energetics of vacancy and substitutional<br />

impurities in aluminum bulk and clusters. // 1997, Phys. Rev. B, 55, 13842.

214<br />

EHFHGHKH?J@:GB?<br />

Ij_^bkeh\b_.................................................................................................................. 3<br />

Ih^k_dpby<br />

J:>BHNBABDB<br />

Klj–38<br />

>BNJ:DPBHGGU?IHL?JB?E?GB?WE?DLJBQ?KDBOA:JY>H

Kh^_j`Zgb_ 215<br />

EBGUJ?AHG:LHJ:G:G?EBG?CGMX>BG:FBDM<br />

:;KHEXLGHCIMQDH

216<br />

EHFHGHKHHH

Kh^_j`Zgb_ 217<br />

BKKE?>H:<br />

HFWIJ<br />

**>zfbgHFWE?DLJHFB=J:PBB<br />

Dmlmjh\:GFZke_ggbdh\:KIHFHSVX<br />

IHJBKLH=HDJ?FGBY<br />

;_eh]hjhoh\B:Jy[qbdh\X< ......................................................................... 64<br />

L?OGHEH=BYIHEMQ?GBYG:GHA:AHJH:<br />

Ayabg:K ................................................................................................................. 66<br />

IEHLGHKLVWE?DLJHGGUOKHKLHYGBCZgbebg::............................................................................................................ 67<br />

J?E:DK:PBYWG?J=BBWE?DLJHGGH=H?GBYH?E?GB?DHGP?GLJ:PBBEHD:EBAH:D?EV

218<br />

EHFHGHKH

Kh^_j`Zgb_ 219<br />

I?J?K?D:XSB?KY6-;J:GUB:GBAHLJHIGU?FH>?EBL?FGHC<br />

WG?J=BB<br />

**Hjeh\>=............................................................................................................. 106<br />

IHKLJH?GB?>BHGUO=BI?J;J:GF?LH>HFP?IHQ?DLH>U<br />

Hjeh\>=................................................................................................................. 107<br />

LHQGHBGL?=JBJM?F:YFH>?EV;:EEBKLBQ?KDHC:=J?=:PBB<<br />

PBEBG>JBQ?KDHCBKN?JBQ?KDHCKBFF?LJBB<br />

:g^jb_\kdbc::.................................................................................................... 109<br />

WE?DLJHGGU?I?J?OH>UIJB?CKL<br />

Eukh\J< ................................................................................................................ 115<br />

IJBF?G?GB?NHJF:EBAF:GVXF?G:-I?GJHMA:DA:>:Q:F<br />

G?EBG?CGHCWE?DLJH>BG:FBDBH

220<br />

EHFHGHKH

Kh^_j`Zgb_ 221<br />

HKH;?GGHKLBF:=GBLGUOK

222<br />

EHFHGHKHH

Kh^_j`Zgb_ 223<br />

KV-HJH><br />

Afb_gdh>K ............................................................................................................ 186<br />

I?JHH

224<br />

EHFHGHKHBKDJ?LGH=H<br />

FH>?EBJHBNNMABHGGUOO:J:DL?JBKLBDLHQ?QGUO<br />

>?N?DLH

Kh^_j`Zgb_ 225

logo

products

Resources

Company

Terms of service
Privacy policy
Cookie policy
Cookie settings
Imprint
Change language
Made with love in Switzerland
© 2024 Yumpu.com all rights reserved

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!