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32 2 BASIC STRUCTURAL CONCEPTS Figure 2.4. The cubic P lattice. (a) shows the unit cell boundaries and (b) shows a portion of the extended lattice. in Fig. 2.5 that the eight-fold coordination of each point is identical and, thus, this arrangement forms a Bravais lattice. The conventional cell contains two lattice points (see Fig. 2.5). The next distinct Bravais lattice, shown in Fig. 2.6, is the cubic F lattice (it is helpful to remember that there is a lattice point at the center of each face). In this case, the conventional cell contains four lattice points and each point has 12 nearest neighbors. Readers should note that the nomenclature used for lattices is carefully chosen to avoid confusion with crystal structures. The commonly used terms simple cubic, body centered cubic, and face centered cubic are reserved here exclusively for crystal structures (specifically, the crystal structures that are created when an elemental, monoatomic basis is added to each site of the cubic P, cubic I, and cubic F lattices, respectively). This distinction is essential for clarity. For example, while both rock salt and sphalerite have cubic F lattices, it would be a mistake to call either of them face centered cubic. Atoms in a face centered cubic structure have twelve nearest neighbors, atoms in the rock salt structure have six nearest neighbors, and atoms in the sphalerite structure have four nearest neighbors. The distinction between a lattice and a crystal structure is described further in Section D of this chapter. Having created new Bravais lattices by centering first the cube volume and
B THE BRAVAIS LATTICE Figure 2.5. The cubic I lattice. (a) shows the repeat unit with points at coordinates (0,0,0) and (1/2,1/2,1/2). (b) The extended structure demonstrates that the cube center (1) and the vertices (2) have an identical eight-fold coordination environment. Thus, this configuration is a Bravais lattice. Figure 2.6. The cubic F lattice. (a) shows the conventional unit cell lattice with positions at coordinates (0,0,0), (1/2,1/2,0), (1/2,0,1/2), and (0,1/2,1/2). (b) A portion of the extended lattice shows that each lattice point has 12 nearest neighbors. 33
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Page 5 and 6: Structure and Bonding in Crystallin
Page 7 and 8: Contents Preface ix 1. Introduction
Page 9 and 10: CONTENTS E. Electronegativity scale
Page 11 and 12: Preface This book resulted from lec
Page 13 and 14: Chapter 1 Introduction A Introducti
Page 15 and 16: B PERIODIC TRENDS IN ATOMIC PROPERT
Page 17 and 18: C BONDING GENERALIZATIONS BASED ON
Page 25 and 26: D GENERALIZATIONS ABOUT CRYSTAL STR
Page 33 and 34: E THE LIMITATIONS OF SIMPLE MODELS
Page 35 and 36: E THE LIMITATIONS OF SIMPLE MODELS
Page 37 and 38: F PROBLEMS and appreciated. For exa
Page 39 and 40: G REFERENCES AND SOURCES FOR FURTHE
Page 41 and 42: Chapter 2 Basic Structural Concepts
Page 43: B THE BRAVAIS LATTICE Figure 2.3. T
Page 47 and 48: B THE BRAVAIS LATTICE Figure 2.8. (
Page 49 and 50: B THE BRAVAIS LATTICE Figure 2.10.
Page 51 and 52: B THE BRAVAIS LATTICE Figure 2.12.
Page 53 and 54: C THE UNIT CELL 4. The scheme for f
Page 55 and 56: C THE UNIT CELL Figure 2.14. The co
Page 57 and 58: D THE CRYSTAL STRUCTURE. A BRAVAIS
Page 59 and 60: E SPECIFYING LOCATIONS, PLANES AND
Page 61 and 62: E SPECIFYING LOCATIONS, PLANES AND
Page 63 and 64: F THE RECIPROCAL LATTICE Figure 2.2
Page 65 and 66: F THE RECIPROCAL LATTICE graphicall
Page 67 and 68: F THE RECIPROCAL LATTICE Example 2.
Page 69 and 70: G QUANTATIVE CALCULATIONS INVOLVING
Page 71 and 72: H VISUAL REPRESENTATIONS OF CRYSTAL
Page 81 and 82: I POLYCRYSTALLOGRAPHY vertical line
Page 83 and 84: I POLYCRYSTALLOGRAPHY Figure 2.39.
Page 85 and 86: I POLYCRYSTALLOGRAPHY g Z 2 cos 2
Page 93 and 94: J PROBLEMS Table 2.3 CSL boundaries
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J PROBLEMS (4) Draw a [001]* projec
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K REFERENCES AND SOURCES FOR FURTHE
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K REFERENCES AND SOURCES FOR FURTHE
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B SYMMETRY OPERATORS Figure 3.1. Th
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B SYMMETRY OPERATORS Figure 3.4. (a
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C THE 32 DISTINCT CRYSTALLOGRAPHIC
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D THE 230 SPACE GROUPS Figure 3.17.
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D THE 230 SPACE GROUPS 2 P2 C2 Pm P
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D THE 230 SPACE GROUPS point groups
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Figure 3.31. The positions of the s
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E THE INTERPRETATION OF CONVENTIONA
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F PROBLEMS positions? If so, show t
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F PROBLEMS Table 3.5 AB crystal str
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G REFERENCES AND SOURCES FOR FURTHE
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Chapter 4 Crystal Structures A Intr
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B CLOSE PACKED ARRANGEMENTS Figure
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B CLOSE PACKED ARRANGEMENTS Figure
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C THE INTERSTITIAL SITES Table 4.5.
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D NAMING CRYSTAL STRUCTURES apex of
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E CLASSIFYING CRYSTAL STRUCTURES E
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F IMPORTANT PROTOTYPE STRUCTURES F
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(a) (b) Figure 4.8. Two AB structur
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F IMPORTANT PROTOTYPE STRUCTURES Ta
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Figure 4.11. The L2 1 structure. Al
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F IMPORTANT PROTOTYPE STRUCTURES Fi
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G INTERSTITIAL COMPOUNDS G Intersti
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H LAVES PHASES Table 4.30. The C14
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H LAVES PHASES Table 4.32. Selected
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I SUPERLATTICE STRUCTURES AND COMPL
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J EXTENSIONS OF THE CLOSE PACKING D
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L NONCRYSTALLINE SOLID STRUCTURES (
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L NONCRYSTALLINE SOLID STRUCTURES F
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L NONCRYSTALLINE SOLID STRUCTURES F
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M PROBLEMS Figure 4.37. (a) Silica
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M PROBLEMS (ii) Do you think this s
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M PROBLEMS (vii) Compare this struc
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N REFERENCES AND SOURCES FOR FURTHE
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Chapter 5 Di¤raction A Introductio
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C THE SCATTERING OF X-RAYS FROM A P
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D THE RELATIONSHIP BETWEEN DIFFRACT
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E FACTORS AFFECTING THE INTENSITY O
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F SELECTED DIFFRACTION TECHNIQUES A
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G PROBLEMS Figure 5.23. The L1 0 st
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G PROBLEMS (10) Consider the reacti
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G PROBLEMS Figure 5.25. Three exper
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G PROBLEMS (iii) Define the orienta
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H REVIEW PROBLEMS (iv) Based on the
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I REFERENCES AND SOURCES FOR FURTHE
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Chapter 6 Secondary Bonding A Intro
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A INTRODUCTION Table 6.1. Inert gas
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B A PHYSICAL MODEL FOR THE VAN DER
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C DIPOLAR AND HYDROGEN BONDING Tabl
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D THE USE OF PAIR POTENTIALS IN EMP
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E PROBLEMS Figure 6.12. Two possibl
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F REFERENCES AND SOURCES FOR FURTHE
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A INTRODUCTION Table 7.1. Lattice e
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B A PHYSICAL MODEL FOR THE IONIC BO
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C OTHER FACTORS THAT INFLUENCE COHE
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D PREDICTING THE STRUCTURES OF IONI
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D PREDICTING THE STRUCTURES OF IONI
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E ELECTRONEGATIVITY SCALES E Electr
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E ELECTRONEGATIVITY SCALES A comple
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F THE CORRELATION OF PHYSICAL MODEL
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H PROBLEMS interacts with the other
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H PROBLEMS the lattice energies of
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A INTRODUCTION Table 8.1. The cohes
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B A PHYSICAL MODEL FOR THE METALLIC
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D ELECTRONS IN A PERIODIC LATTICE F
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D ELECTRONS IN A PERIODIC LATTICE t
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F EMPIRICAL POTENTIALS FOR CALCULAT
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G PROBLEMS Figure 8.14. The energy
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H REFERENCES AND SOURCES FOR FURTHE
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Chapter 9 Covalent Bonding A Introd
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A INTRODUCTION Table 9.1. Tetrahedr
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B A PHYSICAL MODEL FOR THE COVALENT
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Antibonding orbitals --- s2〉 - 1
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Antibonding orbitals Anion orbital
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C A PHYSICAL MODEL FOR THE COVALENT
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D A PHYSICAL MODEL FOR THE COVALENT
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E BANDS DERIVING FROM D-ELECTRONS s
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E BANDS DERIVING FROM D-ELECTRONS
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E BANDS DERIVING FROM D-ELECTRONS t
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G THE DISTINCTION BETWEEN COVALENT
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G THE DISTINCTION BETWEEN COVALENT
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H THE COHESIVE ENERGY OF A COVALENT
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I OVERVIEW OF THE LCAO MODEL AND CO
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K PROBLEMS bandgaps that can be pro
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K PROBLEMS (iv) What happens to the
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K PROBLEMS (i) Draw a sketch showin
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L REFERENCES AND SOURCES FOR FURTHE
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L REFERENCES AND SOURCES FOR FURTHE
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B MODELS FOR PREDICTING PHASE STABI
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Figure 10.7. Atomic parameters used
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C FACTORS THAT DETERMINE STRUCTURE
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Table 10.5. Atomic parameters for t
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D STRUCTURE STABILITY DIAGRAMS char
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D STRUCTURE STABILITY DIAGRAMS Figu
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D STRUCTURE STABILITY DIAGRAMS Tabl
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E PROBLEMS E Problems Figure 10.18.
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F REFERENCES AND SOURCES FOR FURTHE
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Appendix 1A Crystal and univalent r
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APPENDIX 1A: CRYSTAL AND UNIVALENT
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APPENDIX 2A: COMPUTING DISTANCES US
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Appendix 2C Computing interplanar s
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Appendix 3A The 230 space groups Ta
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APPENDIX 3A: THE 230 SPACE GROUPS T
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APPENDIX 3B: SELECTED CRYSTAL STRUC
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APPENDIX 5A: INTRODUCTION TO FOURIE
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Appendix 5B Coeªcients for atomic
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APPENDIX 5B: COEFFICIENTS FOR ATOMI
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N e L 21 2 APPENDIX 7A: EVALUATION
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Appendix 7B Ionic radii for halides
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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 9A Cohesive energies and b
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Appendix 9B Atomic orbitals and the
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APPENDIX 9B: ATOMIC ORBITALS AND TH
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Index -MoO 3 , 130, 491 -quartz, 31
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INDEX D0 24 structure, 154, 156 D5
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INDEX L2 1 structure, 147, 151 La 2
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INDEX reflection, 88, 90 Rh 2 O 3 ,
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