Druck-Materie 20b.qxd - JUWEL - Forschungszentrum Jülich

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γ r ( 0) ≅ 2 2 2 T erf e ( ) / 2 2 2 2 ⎪⎧ π ⎛ ⎞ 0 0 0 / 2 T / 8 T 0 T 0 / 2 ⎪⎫ ⎨ ⎜ ω ⎡ ⎛ ω ⎞⎤ ω ⎡ ⎤ − ω ω −σ ω ⎛ω −σ ω ⎞ 1 2 1 erf ⎟ −ω σ σ + + e ⎬ / K ⎪⎩ 2 ⎜ ⎢ + ⎜ ⎟⎥ ⎢ + ⎥ 2 ⎜ 2 ⎟ ⎟ ⎝ σ ⎣ ⎝ σ ⎠⎦ σ ⎢⎣ ⎝ σ ⎠⎥⎦ ⎠ ⎪⎭ whereω kT / h , K is the normalization constant, and the Debye-Waller factor for rotations T = 2 hQ 2Wr = γ r ( 0) ; Mr = M / ar . 2M C) Vibrational modes r In our description of molecular vibrations, we use the Einstein model to represent those high frequency modes [9]: a v Z v ( ω ) ∑c jδ ( ω −ω j ) , = j where ωj denotes the eigenfrequency of the j-th vibrational mode, and cj its relative weight. The width function for this model is: = j v iω jt −iω jt { [ n( ω ) + 1] e + n( ω e } c j −1 γ v ( t) ∑ ω j j j ) a but, under the assumption that kT
Q0 denotes the (modulus of) momentum transfer for elastic scattering, m is the neutron mass, ϑ the scattering angle, and 3φ1 ( θ ) γ r ( 0) Γ = + + hω A hA D B) Inelastic scattering s r ∑ ( hω ) A j v j −1 j ; Ak = Mk / m The inelastic component of the scattering law according to the present formulation is given by: ⎡ 3 p ( s) 3 k ( r ) ( ) inel −2( W + W + W ) ( 2W ) G p ω s ( 2Wr ) Gk ( ω) s r v S3 ( Q, ω) ≅ e ⎢∑ + ∑ ⎢⎣ p= 1 p! h k = 1 k! h 4WsWr ( s) ( r) ( s) ( r ) ( s) ( r ) ⎤ + { G1 ⊗ G1 + W 1 ⊗ 2 + 2 ⊗ 1 } 2 rG G WsG G h ⎥⎦ where the index ´3´ reminds us that we are limiting the actual component to a three-phonon expansion. 3. THE SYNTHETIC MODEL FOR MOLECULAR SOLIDS Having introduced an approximate formulation to describe the interaction of slow neutrons with molecular solids, we wish to extend its validity over the complete thermal energy range. This will be our final prescription for a Synthetic Model for Molecular Solids (SMMS), and it will be required to behave as the Synthetic Model for Molecular Gases when the energies involved in the scattering process are much larger than the characteristic Debye energy of the solid lattice. We propose el [ 1− R ( E) ]{ σ SSF −σ } σ 3 inel σ = + R(E): a function of the total Debye-Waller factor, with R(E→0)→1, R(E→∞)→0. For the double-differential cross section, we have 1/ 2 N i inel ⎛ E' ⎞ σ σ , ⎝ E ⎠ i 4π S inel E b inel ( E, E', ϑ) = ⎜ ⎟ ∑ ni S E ( Q ω ) el inel ( Q, ω ) = [ 1− R( E) ]{ 1− σ ( E) / σ ( E) } T ( Q, ω; E) + S3 ( Q, ω) SSF where E, E’, and ϑ are the incident, the final neutron energies, and the scattering angle, respectively. As in the case of the original SSF, this pseudo scattering law also depends on the incident neutron energy, E. 47 with
Page 1 and 2: ACoM - 6 6th 6 International Worksh
Page 3 and 4: Forschungszentrum Jülich GmbH Inst
Page 5: Preface These are the Proceedings o
Page 8 and 9: List of participants, cont’d. Kü
Page 10 and 11: Pepe M. 43 Petriw S. 43 Picton D.J.
Page 12 and 13: Experimental background, results an
Page 14 and 15: • Light water ice as H(H2O) at T
Page 16 and 17: In Table 2 a survey is given about
Page 18 and 19: sigma-T in barns/molecule Figure 4.
Page 20 and 21: 2.3 Liquid water Compared to the so
Page 22 and 23: presented. The corresponding experi
Page 24 and 25: 3.2 Gaseous hydrogen and deuterium
Page 26 and 27: Rho(Omega) normalised 160 140 120 1
Page 28 and 29: elatively free and can also suffer
Page 30 and 31: Figure 16. Heat Capacity for Solid
Page 32 and 33: o-D2 and p-H2 at 5K for an ucn ener
Page 34 and 35: Figure 22. UCN Upscattering Rates i
Page 36 and 37: ho(omega) normalised 40 35 30 25 20
Page 38 and 39: derived from Walker [52]. The neutr
Page 40 and 41: Since there is only a small gain of
Page 42 and 43: 7. CALCULATION OF SCATTERING LAW DA
Page 44 and 45: For the validation of these data se
Page 46 and 47: [36] Nielsen, M.: Phonons in Solid
Page 48 and 49: 2. THE CASE OF MOLECULAR SOLIDS An
Page 52 and 53: 4. PRELIMINARY APPLICATION Solid Me
Page 54 and 55: [5] Meeting on Moderator Concepts a
Page 56 and 57: state. Conversely, the monatomic hy
Page 58 and 59: Note that the equilibrium trihydrog
Page 60 and 61: para hydrogen system under irradiat
Page 62 and 63: [12] T. E. Fessler and J. W. Blue,
Page 64 and 65: tion of neutron intensities, partic
Page 66 and 67: varied between calculations but the
Page 68 and 69: 5. THE OPTIMISATION OF MULTIPLY GRO
Page 70 and 71: Figure 7. A comparison of time dist
Page 72 and 73: 4.8 cm hydrogen slab in front of a
Page 75 and 76: ACoM - 6 6 th Meeting of the Collab
Page 77 and 78: the moderator is annealed every 12
Page 79 and 80: The method requires two additional
Page 81 and 82: ABSTRACT ACoM - 6 6 th Meeting of t
Page 83 and 84: Heat transfer processes across phas
Page 85 and 86: 3. TWO-PHASE FLOW PATTERN IN THE MO
Page 87 and 88: continuous phase dominating, and a
Page 89 and 90: Also the velocity pattern has chang
Page 91 and 92: Figure 8. Methane pellets concentra
Page 93 and 94: ACoM - 6 6 th Meeting of the Collab
Page 95 and 96: sample volume and the nominal densi
Page 97 and 98: The results presented in this paper
Page 99: Table 10. Summary of energy transfe
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2. EXPERIMENTAL Methane hydrate was
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Figure 4. Energy levels of methane
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102
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phase transitions from phase II to
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After melting phase I in the cryost
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4. SOLID PHASES OF MESITYLENE-D0 AN
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G(ν) [a.u.] 8 6 4 2 Phase II Phase
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112
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A not quite as perfect cold spectru
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2.2 Inelastic neutron scattering Th
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Figure 4. Inelastic spectra at the
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3.2 Moderator performance The resul
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122
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Figure 2. The methane pelletizer, m
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Figure 5. The cryogenic hopper fill
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128
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ture
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The charging device scheme could be
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Table 1. Data of irradiation of met
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5. METHODS OF PROCESSING OF RAW EXP
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of radicals, that is, before a burp
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6.2 Condition for thermally stimula
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Table 4. Estimated values of an ene
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• Nine spontaneous burps were obs
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APPENDIX Some useful relations and
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APPENDIX. Graphs of burps. 148
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150
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152
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154
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2. EXPERIMENTAL SETUP Fig. 1 will g
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All these parameters are kept const
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4. CONCLUSIONS We demonstrated that
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JESSICA (Juelich Experimental Spall
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The moderator system consists of th
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to change the temperatures and to p
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168
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supplied from the high pressure bom
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10 9 10 8 10 7 10 6 Para35%[Experim
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174
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2. TIME OF FLIGHT SPECTRA AND ENERG
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When applying this transformation t
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data were analyzed in more detail.
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182
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First of all, we should conclude th
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The equation (a) may also describe
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Even at h=0.01 mm which is too smal
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model and some consequences of its
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methane and 0.7-1.5% for water ice
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case: the sample of infinite size.
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196
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200
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202
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206
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208
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210
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Phase Diagram of the CH4-H20 system
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Reaction Chamber for Hydrate Produc
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Analysis: X-ray diffraction pattern
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Comparison with non-hydrate forming
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Mechanical Tests: Apparatus 220
Page 226 and 227:
Morphology of Indium Jacket 222
Page 228 and 229:
Schriften des Forschungszentrums J
Page 230 and 231:
Schriften des Forschungszentrums J
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