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Structure and Bonding in Crystalline Materials GREGORY S. ROHRER
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Page 6 and 7: published by the press syndicate of
Page 8 and 9: vi CONTENTS 4. Crystal Structures 1
Page 10 and 11: CONTENTS Appendix 1A: Crystal and u
Page 12 and 13: x PREFACE where my knowledge was in
Page 14 and 15: B Periodic trends in atomic propert
Page 16 and 17: exceptions, we will use the periodi
Page 18 and 19: 6 1 INTRODUCTION Figure 1.3. Knowle
Page 20 and 21: 1 INTRODUCTION halogen, then it is
Page 22 and 23: 10 1 INTRODUCTION Table 1.2. Proper
Page 24 and 25: D Generalizations about crystal str
Page 26 and 27: structure is composed of many ident
Page 28 and 29: 16 1 INTRODUCTION Figure 1.9. Schem
Page 30 and 31: 18 1 INTRODUCTION p s s pz pz Figur
Page 32 and 33: 1 INTRODUCTION type of chemical bon
Page 34 and 35: 22 1 INTRODUCTION Table 1.9. The pr
Page 36 and 37: 24 1 INTRODUCTION Table 1.10. Super
Page 38 and 39: 26 1 INTRODUCTION (2) Consider Kete
Page 40 and 41: 28 1 INTRODUCTION [9] L. Pauling, T
Page 42 and 43: 30 2 BASIC STRUCTURAL CONCEPTS Figu
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Page 50 and 51: 38 2 BASIC STRUCTURAL CONCEPTS Tabl
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2 BASIC STRUCTURAL CONCEPTS the pri
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polyhedron bounded by these planes
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2 BASIC STRUCTURAL CONCEPTS Just as
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48 2 BASIC STRUCTURAL CONCEPTS Figu
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F The reciprocal lattice 50 2 BASIC
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2 BASIC STRUCTURAL CONCEPTS to the
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Figure 2.25. The relationship betwe
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4. Next, we find points with a z co
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metric tensor, (see Eqn. 2.17), we
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60 2 BASIC STRUCTURAL CONCEPTS we h
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62 2 BASIC STRUCTURAL CONCEPTS (a)
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2 BASIC STRUCTURAL CONCEPTS species
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2 BASIC STRUCTURAL CONCEPTS Figure
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74 2 BASIC STRUCTURAL CONCEPTS ya 2
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2 BASIC STRUCTURAL CONCEPTS is dete
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80 2 BASIC STRUCTURAL CONCEPTS the
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82 2 BASIC STRUCTURAL CONCEPTS (ii)
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(12) Show that the c/a ratio of the
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86 2 BASIC STRUCTURAL CONCEPTS [10]
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Chapter 3 Symmetry in Crystal Struc
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3 SYMMETRY IN CRYSTAL STRUCTURES nu
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ut with a ‘bar’ above. In Fig.
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94 3 SYMMETRY IN CRYSTAL STRUCTURES
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3 SYMMETRY IN CRYSTAL STRUCTURES th
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102 3 SYMMETRY IN CRYSTAL STRUCTURE
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3 SYMMETRY IN CRYSTAL STRUCTURES No
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3 SYMMETRY IN CRYSTAL STRUCTURES op
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3 SYMMETRY IN CRYSTAL STRUCTURES v
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3 SYMMETRY IN CRYSTAL STRUCTURES sh
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x. Trigonal and hexagonal groups Th
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3 SYMMETRY IN CRYSTAL STRUCTURES (x
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In closing this chapter, we note th
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136 4 CRYSTAL STRUCTURES Table 4.1.
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4 CRYSTAL STRUCTURES 1998, after fo
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diagonal 111 directions. In the hcp
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4 CRYSTAL STRUCTURES 142 Figure 4.6
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4 CRYSTAL STRUCTURES 144 Table 4.6.
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4 CRYSTAL STRUCTURES 146 Table 4.7
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4 CRYSTAL STRUCTURES 148 Table 4.8.
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Figure 4.10. In the D0 3 structure
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4 CRYSTAL STRUCTURES Mn occupy the
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158 4 CRYSTAL STRUCTURES Example 4.
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4 CRYSTAL STRUCTURES the atoms. How
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168 4 CRYSTAL STRUCTURES Table 4.23
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4 CRYSTAL STRUCTURES mentioned earl
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176 4 CRYSTAL STRUCTURES Figure 4.2
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form symmetric arrangements, and to
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Figure 4.27. Ordered structures bas
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4 CRYSTAL STRUCTURES 4. Based on su
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4 CRYSTAL STRUCTURES The names for
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Because the intercalation or ion in
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4 CRYSTAL STRUCTURES random alloy n
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(a) (b) Figure 4.34. Penrose tiling
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4 CRYSTAL STRUCTURES iv. Amorphous
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198 4 CRYSTAL STRUCTURES (3) Test t
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4 CRYSTAL STRUCTURES 200 (19) The c
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(v) How many general equivalent pos
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204 4 CRYSTAL STRUCTURES [30] J.E.
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in the diffraction pattern is creat
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208 5 DIFFRACTION where 0x1 and the
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210 5 DIFFRACTION to the superposit
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Next, we want to use our definition
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214 5 DIFFRACTION Figure 5.4. Inten
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5 DIFFRACTION As demonstrated in Fi
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Bragg condition. The (101) plane in
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220 5 DIFFRACTION integrals represe
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5. So, the ratio of the measured in
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Figure 5.9. Systematic absences in
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226 5 DIFFRACTION which gives the c
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228 5 DIFFRACTION Figure 5.10 (a &
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230 5 DIFFRACTION Figure 5.10 (g-i)
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5 DIFFRACTION E Factors a¤ecting t
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the incident beam is , then the ang
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5 DIFFRACTION The atomic scattering
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238 5 DIFFRACTION Table 5.3. The mu
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5 DIFFRACTION values are determined
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5 DIFFRACTION F Selected di¤ractio
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244 5 DIFFRACTION the Debye-Scherre
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iii. Single crystal methods Most un
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248 5 DIFFRACTION Figure 5.20. Sche
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5 DIFFRACTION patterns produced by
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252 5 DIFFRACTION (i) Referring to
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254 5 DIFFRACTION Observed d-spacin
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5 DIFFRACTION 256 Figure 5.26. Sche
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258 5 DIFFRACTION Figure 5.27. Sche
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260 5 DIFFRACTION (vi) In both dias
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262 5 DIFFRACTION [6] B.D. Cullity,
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6 SECONDARY BONDING important role
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6 SECONDARY BONDING 266 Table 6.2.
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occupied and vice versa. To prevent
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6 SECONDARY BONDING 270 Table 6.3.
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272 6 SECONDARY BONDING The factor
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274 6 SECONDARY BONDING U1/2 V( i d
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276 6 SECONDARY BONDING increase wi
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d d where i or j1, 1 ij d d where i
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6 SECONDARY BONDING N. Thus, amines
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Within the simple interpretation pr
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energy parameters, and , for the N
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Chapter 7 Ionic Bonding A Introduct
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288 7 IONIC BONDING Table 7.2. Crit
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7 IONIC BONDING between ions with o
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atom binds the 4s electron more str
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7 IONIC BONDING H term for NeCl and
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296 7 IONIC BONDING To accurately d
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7 IONIC BONDING Furthermore, if the
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that the constant is properly defin
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7 IONIC BONDING deviates by 7.6% fr
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304 7 IONIC BONDING Figure 7.6. The
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7 IONIC BONDING and d x2-y2 orbital
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7 IONIC BONDING the bonding, lattic
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marginally preferable to NaCl and i
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7 IONIC BONDING iii. The influence
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7 IONIC BONDING 314 Table 7.15 Comp
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316 7 IONIC BONDING Figure 7.12. El
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the repulsion from next nearest nei
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320 7 IONIC BONDING Table 7.16. Def
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322 7 IONIC BONDING (ii) Explain ho
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324 7 IONIC BONDING [5] J.A.A. Kete
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Chapter 8 Metallic Bonding A Introd
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the properties that led to the form
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330 8 METALLIC BONDING In this expr
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332 8 METALLIC BONDING The boundary
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334 8 METALLIC BONDING arrangement
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336 8 METALLIC BONDING kF k0 E2 .
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8 METALLIC BONDING Example 8.1 We w
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340 8 METALLIC BONDING r 0 U c (r
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342 8 METALLIC BONDING Considering
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344 8 METALLIC BONDING The variable
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346 8 METALLIC BONDING Table 8.6. C
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8 METALLIC BONDING isolated K atom
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So, K is approximately continuous,
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usually [110]. Band structure diagr
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354 8 METALLIC BONDING there is no
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8 METALLIC BONDING 356 Figure 8.13.
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local density of electrons will not
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360 8 METALLIC BONDING electronic k
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362 8 METALLIC BONDING 1980). Chapt
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9 COVALENT BONDING in practice. For
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9 COVALENT BONDING be used to estim
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crystal, we will examine the princi
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370 9 COVALENT BONDING would occupy
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formation (this is also the energy
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374 9 COVALENT BONDING 1 V 3 ( 2s
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electron near either one of the two
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378 9 COVALENT BONDING If the cryst
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380 9 COVALENT BONDING Figure 9.6.
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382 9 COVALENT BONDING are actually
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384 9 COVALENT BONDING Table 9.4. D
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386 9 COVALENT BONDING As before (E
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388 9 COVALENT BONDING higher energ
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On the other hand, as the bands bec
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392 9 COVALENT BONDING value. For d
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394 9 COVALENT BONDING H 11 p e i
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9 COVALENT BONDING was not intended
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9 COVALENT BONDING Example 9.3 Cons
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9 COVALENT BONDING 400 Figure 9.18.
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9 COVALENT BONDING 402 Figure 9.20.
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9 COVALENT BONDING 404 Figure 9.22
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9 COVALENT BONDING F The distinctio
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9 COVALENT BONDING 408 p-orbitals o
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1 2 2 2 2 E (4Z)( V bond V2,h V3,
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cohesive energy decreases with an i
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J The bandgap 414 9 COVALENT BONDIN
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9 COVALENT BONDING L References and
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422 9 COVALENT BONDING [31] W.A. Ha
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Chapter 10 Models for Predicting Ph
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10 MODELS FOR PREDICTING PHASE STAB
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478 APPENDIX 1A: CRYSTAL AND UNIVAL
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Appendix 2A Computing distances usi
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Appendix 2B Computing unit cell vol
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484 APPENDIX 2C: COMPUTING INTERPLA
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486 APPENDIX 3A: THE 230 SPACE GROU
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Appendix 3B Selected crystal struct
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490 APPENDIX 3B: SELECTED CRYSTAL S
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Appendix 5A Introduction to Fourier
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514 APPENDIX 5A: INTRODUCTION TO FO
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516 APPENDIX 5B: COEFFICIENTS FOR A
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Appendix 7A Evaluation of the Madel
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520 APPENDIX 7A: EVALUATION OF THE
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APPENDIX 7B: IONIC RADII FOR HALIDE
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APPENDIX 7B: IONIC RADII FOR HALIDE
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Appendix 7C Pauling electronegativi
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528 APPENDIX 9A: COHESIVE ENERGIES
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530 APPENDIX 9B: ATOMIC ORBITALS AN
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532 APPENDIX 9B: ATOMIC ORBITALS AN
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534 INDEX Br, 10 Bragg, 205 conditi
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536 INDEX GaP, 414 GaSb, 414 Ga 2 Z
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538 INDEX nearest neighbour, 40, 84
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540 INDEX transmission electron mic
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