Index [assets.cambridge.org]assets.cambridge.org/97811070/05877/index/9781107005877... · 2012. 8....

Index

Abelian group, 195absorption, 46, 265

coefficient, 556correction, 311edge, 266function, 557linear coefficient, 265mass coefficient, 265

absorption factor, 311acrylamide, 662acrylonitrile, 664actinide series, 30activation energy, 543active operator, 158adenine, 672adenosine, 672Advanced Photon Source (APS), 348aerogel, 642, 643agreement indices, 368Agricola, Georgius, 20akaganeite, 643, 644, 647alkali halide, 36, 562alkali metals, 30, 31alkaline earth metals, 30alkoxides, 642allotrope, 384allotropic, 430, 654allotropic forms, 644alumina, 576aluminates, 622aluminosilicates, 622, 624alunite, 650amethyst, 637Amici, Giovanni Battista, 151amorphons, 540amorphous, 531, 654

ice, 656solid, 531

amphiboles, 623

amphiphiles, 659andalusite, 622, 628andradite, 626angle

between atomic bonds, 84between lattice directions, 84

alternative method, 85, 578between planes, 112

angular momentum quantum number, 25anion, 561anisotropic, 14anomalous scattering, 351anti-bonding energy states, 442anti-bonding orbitals, 419anti-ferromagnetic, 330anti-fluorite structure, 447anti-phase boundary (APB), 455, 592

energy, 455anti-prismatic coordination polyhedron,

568anti-symmetry operators, 224aperiodic tiling, 403approximants, 490aquamarine, 624, 633Arago, Dominique François Jean, 151Archimedean, 413

solid, 387, 493tiling, 405–483

Archimedean tilings, 405Argand diagram, 300armchair carbon nanotube, 685aromatic hydrocarbons, 657arrangement, 49arrow of time, 170artificially modulated structure, 457asymmetric tetrahedron, 159asymmetric unit, 251, 356atactic, 664atom

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717 Index

energy level, 46first speculations, 44

atomicdisplacement, 460fraction, 432packing fraction, 430radii, 562scattering factor, 294, 336, 366, 444, 550

numerical computation, 297size, 31size factor, 432vibrations, 310volume, 430

atomic structure anisotropy (ASA), 546atomistic, 4Auger electron, 555Auger electron spectroscopy, 554Aurivillius, Bengt, 586Aurivillius phases, 586, 588austenite, 461average coordination number (ACN), 473average molecular weight, 661axial glide plane, 182axial vector, 171azimuthal quantum number, 25

backscattering phase shift, 557balancing subscripts, 54ball-and-stick representation, 359band theory, 433bandgap, εg, 419Barlow, William, 256barrelenes, 681basalt, 626basis vectors, 52

transformation direct to reciprocal,134

bcc derivative structure, 444beam line, 348beam stop, 283Bednorz, J. Georg, 598, 618Beer’s law, 265, 555benitoite, 632benzene, 657benzene crystal, 658Bergman, Torbern Olaf, 88

Bergman polyhedron, 493, 525Bernal, John Desmond, 559Bernal polyhedra, 537bertrandite, 623beryl, 623, 632binary phase diagram, 437binding energy, 34Binnig, Gerd, 618biological macromolecular crystals, 654biomimetic materials, 645biomineralization, 645, 649biotite, 624black-and-white symmetry, 67block copolymer, 659, 666boehmite, 646, 647Bohr, Neils, 23Bohr magneton, 321, 329Bohr’s atomic model, 23Boltzmann constant, 8bond length, 561bond strength, s, 566bonding energy states, 442bonding orbitals, 419borates, see mineral classesBorn, Max, 47, 120borosilicate, 633Boscovich, Ruggiero Giuseppe, 88Boyle, Robert, 44Bragg

angle, 274, 276equation, 320orientation, 277scattering vector, 520

Bragg, William Henry, 289Bragg, William Lawrence, 289Bragg’s law, 259, 337Bragg–Brentano diffractometer, 282braking-radiation, 261branched polymer, 661Bravais, August, 72Bravais lattice, 76, 77, 90, 230, 536

magnetic 2-D, 67magnetic 3-D, 67

Bravais nets, 63bremsstrahlung, 261Brewster, David, 151brick, 410






718 Index

brilliance, 348brittle mica, 634Brockhouse, Bertram N., 354Bronze Age, 1buckide salts, 678buckminsterfullerene, 41, 385buckyballs, 385buckytubes, 386, 681bulk amorphous alloys, 538, 541, 546bulk modulus, 437

Cahn, John Werner, 528calcite, 630capsid, 674capsomers, 674Carangeot, Arnould, 88, 150carbohydrate, 375carbon nanotubes (CNT), 415, 681carbonates, see mineral classesCardano, Gerolamo, 651Cartesian reference frame, 76, 77, 80Caspar, Donald L. D., 674cation, 561Cayley table, 195ccp, 40cementite, 461, 544central potential, 35centrosymmetric, 208ceramic, 561chabazite, 637, 638Chadwick, Sir James, 45, 321chain-reaction (addition) polymerization, 662chalcopyrite, 447characteristic radiation, 263charge transfer, 561charge transfer compound, 669charge-reversal operator, 226chemical potential, 32chiral angle, 415chiral carbon nanotube, 685chiral objects, 210chiral vector, 684chirality, 210choppers, 325Christian, Jack, 463Chu, Paul, 598class, 384

clathrate, 654, 658semiconducting, 658

Clebsch, Alfred, 401close-packed planes, 415close-packed structure, 40, 416close packing, 39, 415coherent scattering, 293cohesion, 88cohesive energy, 433, 466, 539coincident site lattices, 439coincidental equality, 159collimator, 280, 282color, 88color-reversal operator, 225color tilings, 408columnar micelles, 641combination, 663commensurate long-period structure, 460commensurate superlattice, 460commutative group, 195complex number notation, 260compound formation, 437compound structures

AB compounds, 442α′-CoFe, 444β-AlNi, 444β-AuCd, 444β-NiZn, 444β-brass, 444AlFe, 444AsGa, 446, 561, 575CoPt , 439CrFe(σ -phase), 486–487CsCl, 444, 571CuAu, 439CuTi, 439CuZn, 444FeCo, 572FePd, 439FePt , 439LiTl , 444MgO, 561NaCl, 442, 561, 571–574NiAs, 449, 584SiC, 561ZnO, 448ZnS, 446, 448, 574–576






719 Index

B1, 442, 571B2, 444, 571B3, 446, 574B4, 448, 576B81, 449, 584C6, 584L10, 439wurtzite, 576

ABC compounds, 447AlAsMg, 447

ABO3 compounds, 577BaTiO3, 4, 578CaCO3 (calcite), 630CaTiO3, 577LaCuO3, 588MgSiO3, 578NaxWO3 (tungsten bronze), 589SrTiO3, 4E21, 577perovskite, 577–580

ABO4 compoundsZnWO4 (sanmartinite), 589

AB2 compounds, 478BFe2, 478CO2 (solid), 656, 657CaF2, 447, 574CdI2, 584Cu2Mg, 479, 480–483MgNi2, 480, 484–485Mg2Pb, 446Mg2Si , 446Mg2Sn, 446MgZn2, 480, 483–484SiO2, 561TiO2 (rutile), 584, 585ZrO2, 561C1, 446C4, 585C14, 480, 483–484C15, 480–483C36, 484–485

AB2C compounds, 447AB2O4 compounds, 577

Fe3O4 (magnetite), 581MFe2O4, 581MgAl2O4, 580Mn3O4, 582

Mn0.5Zn0.5Fe2O4, 4Ni0.5Zn0.5Fe2O4, 583ferrite, 581–582spinel, 577, 580–583

AB3 compoundsAlCu3, 457AlFe3, 443, 447Al3Ti , 457Au3Cd, 441Au3Zn, 457BiF3, 443, 447Co3Al, 441Co3Pt , 450Cu3Au, 439Cu3Pd, 457Fe3Si , 443Ni3Fe, 441Ni3Sn, 449Pd3Fe, 441Pt3Sn, 441D03, 443D019, 449D022, 457L12, 439

A2B compounds, 447λ-Fe7Hf3, 546Co2Hf, 546Co2Zr, 546D2O, 655Fe2B, 544Fe2Hf, 546Fe2Zr, 546K2O, 447

A2BC compoundsCu2MnAl, 445GaNi2Mn, 446MnPt2Sb, 446MnPt2Sn, 446Ni2MnSb, 446L21, 445

A2B3 compoundsAl2O3, 561, 576–577corundum, 576

A3B compounds, 472Cr3Si , 473Fe3B, 544Fe3C, 544






720 Index

compound structures (cont.)Fe3Zr, 546Nb3Sn, 473Nb3Ti, 473Nb3Zr, 473W3O, 472A15, 472–475

A3B2 compounds, 477Al2Zr3, 477

A4B3 compounds, 476Al3Zr4, 476

A6B7 compounds, 488μ-phase, 488W6Fe7, 488

complex structuresα-Al-Mn-Si , 490–494β-Al3Mg2, 489δ-Co4Zr, 546A2(A′

n−1BnX3n+1) (Ruddlesden–Popperphases), 588, 589

AlH4Na, 462Al3Nb10Ni9 (M-phase), 489BaFe12O19 (magnetoplumbite), 586Bi2MoO6, 587(Bi2O2)2+(An−1BnO3n+1)2− (Aurivillius

phases), 586C6Cr23, 544Cd3Cu4, 489Cd2Na, 489Co5Cr2Mo3 (R-phase), 489Co23Hf6, 546Cr9Mo21Ni20 (P-phase), 489CuFeS2, 448FePtn, 459Gd3Fe5O12 (garnet), 627InGaAs2, 448La2CuO4, 588La3Cu2O7, 588Lan+1CunO3n+1, 588(MO)(Al2O3)6 (hexa-aluminate), 586(MO)(Fe2O3)6 (hexaferrite), 586Mg32(Al,Zn)49, 490–494PbBi2Nb2O9, 587Sr32Bi24+δAl48O141+3δ/2, 639SrBi2Ta2O9, 587Th6Mn23, 546Ti2CS, 591

E11, 448chalcopyrite, 448garnet, 626–627M-phase, 489P-phase, 489R-phase, 489

silicatesα-SiO2, 636β-SiO2, 636[Al(F,OH)]3SiO4 (topaz), 628Al2SiO5 (andalusite), 622, 629Al2SiO5 (kyanite), 622, 629Al2SiO5 (sillimanite), 622, 629Al2Si2O5(OH)4 (kaolinite), 635Al2Si4O10(OH)2 (pyrophyllite), 624Al3Si2O5(OH)4 (kaolin), 624BaTi(SiO3)3 (benitoite), 632Be3Al2Si6O18 (beryl), 624, 632–633Be4Si2O7(OH)2 (bertrandite), 623Ca2(Al,Fe)Al2Si3O13H (epidote), 629CaAl2Si4O12 · 6H2O (chabazite), 638CaFeSiO4 (kirschsteinite), 624, 628Ca3Fe2Si3O12 (andradite), 627Ca2Mg5(OH)2(Si4O11)2 (tremolite), 623CaMgSiO4 (monticellite), 622, 624, 628CaMg(SiO3)2 (diopside), 623Ca2MgSi2O7, 623Ca2Mg5(Si8O22)(OH)3 (tremolite), 633CaSiO3 (wollastonite), 630–631Ca2SiO4, 622, 624CaSnSiO5 (malayite), 622CaTiSiO5 (titanite), 622CoB2Si2O8 (danburite), 623Fe2SiO4 (fayalite), 624KAlSi2O6 (leucite), 624KAl3Si3O10(OH)2 (muscovite), 624, 634K(Mg,Fe)3AlSi3O10(OH)2 (biotite), 624M(Al , Si)4O8 (feldspar), 624(M2+

3 M3+2 )(SiO4)3 (garnet), 622

(Mg,Fe)2SiO4 (olivine), 622(Na,K)(Al ,Si)2 O4 (nepheline), 624MgSiO3 (enstatite), 623Mg2SiO4 (forsterite), 624–626Mg3Si2O5(OH)2 (serpentine), 624Mg3Si4O10(OH)2 (talc), 624Na4−5Al3Si3O12S (lazurite), 624Na8−10 Al6Si6O24S2−4 (lazurite), 639






721 Index

NaCa2Al5Si13 O36 · 14H2O (stilbite), 624NaAlSi2O6 (jadeite), 623, 631–632Na4Al3Si3O12Cl (sodalite), 624, 638Na2Al2Si3O10-2H2O (natrolite), 624SiO2 (quartz), 624, 636Zn4Si2O7(OH)2 · 2H2O (hemimorphite),

623ZrSiO4 (zircon), 622, 628–629

Compton modified radiation, 293Compton scattering, 293, 327concentration gradient, 15condensation polymerization, 664condenser lenses, 338conducting block, 598, 599confusion principle, 549congruent equality, 159congruent melting, 437congruent melting point, 437, 479constancy of interfacial angle, 100constructive interference, 271contact goniometer, 150continued fractions, 501continuous random network (CRN) model, 639convergent beam electron diffraction (CBED),

307, 343Cooper pairs, 597coordinate transformation, 135

direct space to Cartesian, 142direction vector, 136in direct space, 135in reciprocal space, 136inverse, 135metric tensor, 136reciprocal metric tensor, 137reciprocal space to Cartesian, 143summary, 137to Cartesian, 140

coordinates, 52coordination number, 470, 566coordination polyhedron, 470, 561coordination shell, 470copolymers, 666corundum, 576Coulomb force, 24Coulomb interaction, 36, 37, 41covalent bond, 38, 561

anti-bonding state, 39

bonding state, 38covalent ceramics, 561covalent radius, 39, 562Crick, Francis Harry Compton, 671, 685cristobalite, 636critical micelle concentration, 660critical radius ratio, 567cross-linking, 661cross product, 105crystal field, 563crystal growth, 150crystal habit, first law of, 88crystal radii, 563crystal structure, 49

definition, 49, 55crystal structures, see compound structurescrystal systems, 2, 57crystalline, 654crystalline electric fields, 41crystallographic basis vectors, 104crystallographic computations

angle between directions, 84angle between planes, 112bond angle, 84bond angle (alternative method), 85bond length, 82, 83length of a vector, 82length of reciprocal lattice vector, 112worked examples, 114

crystallographic orbit, 213crystallographic point groups, 383CrystalMaker, 428cube, 87, 388, 411cube crystal form, 97cubic close-packed structure, ccp, 415cubic close packing, 40cubic coordination, 563cubic zirconia, 628cuboctahedral, 567cuboctahedron, 97, 388, 413, 467, 469, 569cumulant function, 363cuprate conducting block, 598Curie temperature, 330Curl, Robert, 385, 402cut and project method, 504cyclic group, 196, 383cyclooctatetraene dianion, 396






722 Index

cyclosilicates, 623, 630cylinder

symmetry of, 187cytidine, 672cytosine, 672

Dalton, John, 44danburite, 623dart, 508Davisson, Clinton J., 352de Broglie, Louis, 7, 46de Broglie relation, 7, 8de Broglie wavelength, 321Debye scattering equation, 550Debye–Scherrer camera, 283

absorption, 312Debye–Waller factor, 51, 310, 363, 366,

557decagonal alloys, 410defects, 412deflated structures, 387deflation, 498, 502, 508degenerate energy states, 39degree of polymerization, 660Delaunay network, 537deltohedron, 420, 421Democritos, 43denaturation, 673dense random packing of hard spheres

(DRPHS), 534, 535density function, 506density functional theory, 34density of states, 466deoxyribonucleic acid, 654deoxyribose, 671depth shading, 358derivative structure, 439descent in symmetry, 212, 390destructive interference, 271detector, 18deuterium, 324dextro, 675diagonal glide plane, 182diamond, 39diaspore, 646differential scanning calorimetry (DSC),

547

diffraction, 20, 259angle, 275groups, 347order, 274pattern, 269

dihedral point groups, 199dioctahedral, 634diopside, 623, 644dip-coating, 643direct basis vectors, 105direct product, 385direct structure matrix, 140, 142, 147

example, 142direction indices, 95direction symbol [uvw], 75directional bond, 39directions, 90Dirichlet, Johann Peter Gustav Lejeune,

559Dirichlet domain, 66Dirichlet tessellation, 559disaccharide, 375disclination lines, 540disclinations, 412, 592disconnections, 592disilicates, 629dislocations, 592disorder–order, 439dispersion corrections, 351dispersion relation, 260dispirations, 592dissymmetric objects, 210distance between atoms, 83distance between points, 77distance pair correlation function, 553DNA, 654dodecagonal, 398dodecagonal quasicrystals, 498dodecahedron, 89domain

Dirichlet, 66ferroelectric, 580ferromagnetic, 330of an atom, 469Voronoi, 66

domain boundaries, 592domain of influence, 66






723 Index

Doppler energy shift, 557double diffraction, 341driving force for interatomic bonds, 34dry ice, 657dual method, 498duality, 407dumbbell substitutions, 466dummy index, 54dummy subscript, 54dynamical scattering, 336

early transition metal, 546eclipsed structure, 569edge model, 525Einstein, Albert, 7Einstein summation convention, 53, 79, 80eka-silicon, 44elastic magnetic neutron scattering, 322elastic nuclear neutron scattering, 322elastomers, 662electric dipole moment, 15, 67electrical conductivity, 10, 467electroceramic, 580electromagnetic wave, 259electron

affinity, 31charge, 335diffraction, 320discovery of, 23, 44energy state, 25mass, 335orbit, 25promotion, 39scattering factor, 336spin, 27

electron compounds, 433electron diffraction pattern, 341electron-doped, 603electron gas, 433, 466electron-to-atom ratio, 433electronegative, 561electronegativity, 31, 432

difference, 36, 38scales, 31

electropositive, 561electrostatic force, 36electrostatic potential energy, 24

elemental structuresα-Mn, 454α-Po, 428α-U, 454β-Mn, 454β-Sn, 452β-W, 472Ag, 428Al, 428Au, 428C, 441Co, 430Cu, 428Fe, 444Ge, 441Mg, 430Ni, 428Pb, 428Pd, 428Pt , 428Si , 441W, 429A1, 428, 429A2, 429A3, 430A3’, 451A4, 441A5, 452A6, 452A7, 453A8, 453A9, 453A10, 453A12, 454A13, 454A14, 454A15, 454A17, 454A20, 454diamond cubic structure, 441zinc blende, 441

elements, 44embedded atom method, 35emerald, 576, 624, 633emission, 46emulsion, 643enantiomerism, 210






724 Index

enantiomers, 675enantiomorphism, 210, 407enantiomorphous, 179endohedral fullerenes, 385energy band theory, 467energy bands, 419energy level, 46energy quantum, 46enstatite, 623entropy, 15envelope, 674epidote, 622, 629equilateral triangle, 411equivalence class, 384ester, 662ethylene, 662ethylene oxide (EO), 667Euclidean space, 412eukaryotes, 649Euler, Leonhard, 386, 414Euler’s formula, 260, 414, 470Euler’s theorem, 184, 193eutectic phase diagram, 437eutectic point, 437eutectic transformation, 437eutectoid decomposition, 486Ewald

circle (in 2-D), 276construction, 277

sphere (in 3-D), 259construction, 119

Ewald, Paul Peter, 119, 276exohedral, 385extended reciprocal lattice points, 286extended X-ray absorption fine structure

(EXAFS), 555external shape, 96

of a crystal, 51external surfaces, 592extinction, 300extinction rules, 482extraterrestrial minerals, 570extrinsic Frank stacking fault, 418

face model, 525family, 93, 96, 122, 143family of directions, 93

fayalite, 624fcc derivative structure, 442Federov, Evgraf Stepanovich, 151, 256Federov groups, 256feldspar, 624, 636feldspathoid, 624, 637Fermi energy, 467feroxyhyte, 646ferrihydrite, 644, 649ferrimagnetic, 330ferrite, 4, 461, 581ferritin, 645ferroelectric, 580ferroelectric materials, 580ferromagnetic, 330ferromagnetic shape memory alloy, 445Fibonacci

lattice, 498, 501numbers, 499, 501quasilattice, 502series, 501

Fibonacci, Leonardo Pisano, 499first Brillouin zone, 536first transition series, 29fluorescence detector, 555fluorite, 446focal plane, 340form, 51, 96

equilibrium, 150forms, 93formula unit, 357forsterite, 624four-index notation, 94–96

conversion to three-index notation, 95Fourier analysis, 378Fourier transform, 269, 378, 497, 505, 506fourth transition series, 30fracture, 88framework silicates, 624Frank, Frederick Charles, 468, 495Frank–Kasper phases, 383, 403, 425, 433, 466,

471Frankenheim, Moritz, 72, 151Franklin, Rosalind, 671, 685free electron theory, 433, 466Frenkel defect, 593Friauf polyhedron, 479, 480






725 Index

Friauf–Laves phases, 424, 433, 479Friedel’s law, 306, 345Frobenius, Georg, 191fructose, 375full width at half maximum (FWHM), 533Fuller, R. Buckminster, 385fullerene cluster assembled materials, 678fullerene grafted side-chain polymer, 671fullerene-containing macromolecules, 670fullerenes, 385fullerenoid oxide, 617, 637, 639fullerides, 654, 678, 681fullerites, 654, 677, 679fundamental reflections, 308, 351, 444

Galois, Evariste, 228Galois theory, 228gamma rays, 259garnet, 622, 626

structure, 627gas atomization, 541gas hydrates, 658Gaussian function, 314Gehler, Johann Carl, 88gel, 643gelation, 643gemstones, 620general positions, 212generating element, 196generating relationship, 388generator, 216, 383, 520

of a group, 197geodesic, 385, 412geology, 89Germer, Lester H., 352giant cell structures, 489Gibbs phase rule, 381glass-forming ability, 542glass transition temperature, Tg, 532glide plane, 181

axial, 182diagonal, 182, 239

glucose, 375goethite, 643, 644, 646Goldberg polyhedra, 387golden mean, 390, 410, 498, 517golden ratio, 498

golden rhomb, 500Goldschmidt, Victor Moritz, 380, 424Goldsmith, Julian Royce, 424goniometer

contact, 88, 150reflecting, 151two-circle, 102

Goudsmit, Samuel, 27graphene sheet, 681, 684graphite, 41, 324graphite sheet, 386graphite structure, 453Greninger chart, 288ground state, 26group

Abelian, 195closed set, 194commutative, 195cyclic, 196generator, 197homomorphism, 196isomorphism, 196proper subgroup, 197properties, 196subgroup, 197subgroup index, 197trivial subgroup, 197

guanine, 672guanosine, 672Guglielmini, Domenico, 87gypsum, 150gyromagnetic factor, 329

h–c notation, 417, 418halides, see mineral classeshalogens, 30hardness, 88Haüy, René Just, 51, 72, 102Haüy’s crystal models, 72hcp, 40hcp derivative structures, 449heat flux, 15heavy water, 324Heeger, Alan J., 669height labels, 359Heisenberg, Werner, 47Heisenberg uncertainty principle, 47






726 Index

Heitler, Walter, 34hematite, 571, 643hemimorphite, 623hemisubstitutional, 479hemoglobin, 645Hermann–Mauguin notation, 153, 195, 198, 383Hessel, J. F. C., 72, 228heterogeneity, 3heterogeneous, 12heterogeneous nucleation, 532heulandite, 638Heusler alloy, 445hexa-aluminate, 586hexaferrite, 571, 586hexagon, 411hexagonal

Miller–Bravais indices, 95prism, 87

hexagonal anti-prism, 471hexagonal close packing, 40hexagonal crystal system, 94

reciprocal lattice, 131zone equation, 131

hexagonal prismatic representation, 451hexahedron, 89, 97hexakaidecahedra, 658high-density polyethylene, 661high-resolution imaging, 342high-temperature superconductor (HTSC),

588, 597higher fullerenes, 386Hodgkin, Dorothy, 686hole-doped, 603homogeneity, 3homogeneous, 12homogeneous coordinates, 165homomorphism, 196homopolymers, 666Hooke, Robert, 150Hoover, Herbert Clark, 20human eye, 4

cones, 4fovea, 5lens, 4pupil, 4resolution of, 6rods, 4

Hume-Rothery, William, 463Hume-Rothery rules, 432, 461, 479, 543, 547humite, 622Hund’s rules, 327Huygens, Christian, 20Huygens’ principle, 20hybridization, 39

energy, 419gap, 419

hybridized sp3 orbital, 39hydrogen atom, 23hydrogen bonding, 653hydrogen storage, 462hydrogenic atom, 24hydrophilic, 659hydrophobic, 659hydroxides, 621hyperbolic surfaces, 412hyperoctahedral group, 524hypoeutectic, 547

I-beam, 622, 623I-beam structure, 623, 632, 644ice, 654ice clathrate, 658icosahedral alloys, 410icosahedral glass model, 525icosahedral short-range order, 535icosahedral symmetry, 187

generating matrices, 390groups, 384operators, 385

icosahedral twinning, 525icosahedron, 89, 387, 388, 411, 469, 500icosidodecahedron, 387, 413, 493identity matrix, 80, 134image plane, 340impermeability tensor, 15incoherent scattering, 293incommensurate superlattice, 460, 497inelastic neutron scattering, 322inelastic scattering event, 293inert gases, 28, 30infinite-layer structure, 589, 616inflation, 498, 499, 502, 508inflation–deflation method, 498initiation, 662






727 Index

inner shells, 29inosilicates, 623insertion devices, 350instrumental broadening, 534insulating layer, 598, 602, 616integral molecules, 72integrated intensity, 314interaction potential

central, 35pair, 35two-body, 35

interatomic force, 36interatomic potential, 35interference, 274

constructive, 271destructive, 271

interference function, 539intermediate solid solution phase, 432intermetallic compounds, 432International Centre for Diffraction Data, 282international notation, 153, 198International Tables for Crystallography, 55,

235interpenetrating lattice, 441, 444interplanar spacing, 112interstice, 415, 416

octahedral, 565, 567, 572, 573, 576, 580, 584tetrahedral, 565, 567, 572, 573, 576, 580

interstitial alloys, 461interstitial sites, 425interstitial solid solutions, 432intrinsic Frank stacking fault, 418invariant, 55, 155, 384inverse Fourier transform, 378inverse spinel, 581inversion, 160, 167

time-reversing, 175inversion boundaries, 592ionic bond, 36ionic ceramics, 561ionic compounds, 37ionic radius, 472, 561, 562ionization potential, 31Iron Age, 1isolated pentagon rule (IPR), 386, 387isomorphic, 390isomorphism, 196, 211

isomorphous groups, 196isotactic, 664isotopic substitution, 322isotropic, 14isotropy, 3itinerant ferromagnetism, 468

jade, 631jadeite, 623, 631, 644Jahn–Teller distortions, 577Jahn–Teller effect, 563jarosite, 643, 644Jordan, Camille, 191

Kagome net, 449, 482, 485Kagome tiling, 405, 475Kamerlingh Onnes, Heike, 597kaolin, 624kaolinite, 635Kasper polyhedra, 469, 470Kasper triangulated coordination polyhedra,

433Kekule, Friedrich August, 658Kepler, Johannes, 422Kepler tilings, 405Kikuchi, Seishi, 352kinematical scattering, 336kirschsteinite, 624, 628kite, 508Klein, Felix Christian, 191, 400Klug, Aaron, 674, 676Kockel diagram, 236Kroger–Vink notation, 592Kronecker delta, 80, 105Kroto, Harold, 385, 402kyanite, 622, 628

lamellar micelles, 641lanthanide contraction, 381lanthanide series, 30lapis lazuli, 639late transition metal, 546lattice, 50

anorthic, 57base-centered, 63body-centered, 63cubic, 60






728 Index

lattice (cont.)face-centered, 63hexagonal, 58monoclinic, 58orthorhombic, 60rhombohedral, 58tetragonal, 60triclinic, 57trigonal, 58

lattice centering vector, 164lattice complex, 428lattice parameters, 55, 57, 77, 356lattice plane, 90lattice point, 52lattice sums, 435lattice translation, 67lattice vector, 52lattice vibrations, 310Laue class, 209, 306Laue pattern, 284

reflection mode, 285transmission mode, 284

Laves, George Ludwig Friedrich, 423Laves phase, 433, 479

Cu2Mg, 480–483MgNi2, 480, 483–484MgZn2, 480, 484–485

Laves tiling, 407Lavoisier, Antoine, 44layers, 588lazurite, 624, 639ledges, 605length unit

angstrom, 4nanometer, 4

Lennard-Jones potential, 37, 434, 468, 539, 565lens, 89Lenz’s law, 658lepidocrocite, 643, 644, 646Leucippus, 43leucite, 624levo, 675Lima-de-Faria, Jose, 652limiting sphere, 279line compound, 437, 446, 479linear absorption coefficient, 265, 312linear combination, 12

linear diblock copolymer, 666linear polymer, 661linear response theory, 10Linnaeus, Carolus, 101Liquidmetal, 549liquidus curves, 437local density functional theory, 437London, Fritz, 34London dispersion forces, 653long-range order, 532Lonsdale, Kathleen Yardley, 658Lorentz polarization factor, 315Lorentzian function, 314low-angle X-ray scattering, 459low-density polyethylene, 661lower fullerenes, 387Lucas numbers, 499luster, 88

Mössbauer effect, 557Mössbauer spectroscopy, 557Müller, K. Alex, 598, 618Ma’adim Vallis, 647Mackay, Alan L., 496Mackay icosahedron, 493, 540macromolecular solids, 654macromolecule, 660macroscopic, 4Madelung constant, 566Madelung sum, 566maghemite, 571magnetic anisotropy, 458magnetic Bravais lattice

derivation, 67nomenclature, 69

magnetic dipole moment, 15, 321, 329, 581magnetic domain, 330magnetic field, 15magnetic interaction vector, 331magnetic moment, 170magnetic nanowires, 641magnetic quantum number, 25magnetic space groups, 253, 330magnetic structure factor, 331magnetic symmetry, 15magnetite, 257, 571, 581magneto-optic Kerr rotations, 446






729 Index

magneto-optic materials, 545magnetocrystalline anisotropy, 458magnetoferritin, 649magnetoplumbite structure, 586magnetosomes, 649magnons, 322major ligand lines, 471major skeleton, 471, 480malayite, 622malformed, 100marching band, 50marialite, 624Martens, Adolf, 461martensite, 461mass absorption coefficient, 265, 555mass flux, 15Massalski, Thaddeus B., 464material property, 10materials paradigm, 1Maxwell, James Clerk, 7Maxwell–Boltzmann distribution, 324mean square end-to-end distance, 665mechanical alloying, 541mechanical milling, 541Megaw, Helen D., 594, 655meionite, 624Meissner effect, 597melt spinning, 540Mendeleev, Dmitri, 44Meridiani Planum, 647mers, 654, 660mesoporous silicates, 641metal–amorphous nanocomposite, 546metal–metalloid amorphous systems,

543metallic radii, 562metalloid, 461, 544metals, 33metasilicates, 623, 630metric matrix, 79metric tensor, 75, 79

explicit expressions, 81transformation of, 136

mica, 584mica group, 624micaceous, 584, 624micelles, 641, 659

microcrystalline model, 540microcrystalline short-range order, 535micrometer, 4microphase separation, 659, 666microscope

optical, 150polarizing, 151

microscopic, 4Miller, William Hallowes, 102Miller indices, 101, 104, 109, 122, 515

definition, 92examples, 92procedure, 92

Miller–Bravais indices, 94, 95Millikan, Robert, 44millimeter, 4mineral, 620mineral classes

borates, 621carbonates, 621halides, 621native elements, 621nitrates, 621oxides, 621phosphates, 621sulfates, 621sulfides, 621sulfosalts, 621tungstates, 621vanadates, 621

mineralogical phase rule, 381minor ligand lines, 471mirror, 166

time-reversing, 175mirror equality, 159mirror lines, 220mirror-rotation, 177mixed product, 105mixed valence compound, 602moderator, 324modulated structure, 459Mohs, Friedrich, 89molecular beam epitaxy (MBE), 450, 457molecular orbital theory, 34molecular quadrupole moment, 657molecular solids, 383molecular structure, 375






730 Index

molecular structuresC60, 384K3C60, 681MxC60, 681solid C60, 679–680solid C70, 680

monohedral tilings, 404monomers, 660monticellite, 622, 624, 628moonstone, 637morganite, 624Morse potential, 434Moseley, Henry, 44Moth–Bethe formula, 336motif, 50Mulliken, Robert S., 31Mulliken electronegativity, 41Mulliken electronegativity scale, 31multi-beam imaging, 342multi-walled nanotubes (MWNT), 682multiple twinning, 525multiplication table, 195multiplicity, 93, 94, 214, 239, 252, 312, 440muscovite, 624, 634

n-D tiles, 413Nagaoka, Hantaro, 44nanocomposite, 546nanocrystalline alloys, 533nanocrystalline structure, 533nanocrystallization, 350nanoglasses, 541nanoscale, 4nanotesttube, 641, 685native elements, see mineral classesnatrolite, 624, 638Néel temperature, 330nepheline, 624nephrite, 631nesosilicates, 622net, 50

centered rectangular, 63definition, 52hexagonal, 57oblique, 56rectangular, 57square, 57

net parameters, 55network formers, 641network glass, 639network modifiers, 641network polymer, 661, 662Neumann’s principle, 210neutron

discovery of, 24neutron diffraction, 321, 334neutron flux moderator, 324neutron scattering

elastic magnetic scattering, 322elastic nuclear scattering, 322inelastic scattering, 322isotopic substitution, 322

neutron scattering cross section, 326, 334neutron structure factor, 331neutrons

cold, 323fast, 323intermediate, 323slow, 323thermal, 323ultra-fast, 323

Newlands, John, 44Newton’s second law, 170Niggli, Paul, 423nitrates, see mineral classesnoble metals, 30node, 52non-conservative shears, 476non-crystallographic point group, 498non-metals, 33non-reentrant polyhedron, 470non-symmorphic, 240normal conductor, 597normal coordinates, 165normal spinel, 580, 581normal valency compound, 432normalized permutation symbol, 126nuclear magnetic resonance (NMR),

392nucleation, 532nucleation and growth, 543nucleocapsid, 674nucleoside, 672nucleotide, 671, 672






731 Index

number average molecular weight, 661number of lattice points, 430

object plane, 340objective lens, 338oblate rhombohedron, 518obverse setting, 81octagonal prism, 396octagonal quasicrystals, 498octahedral coordination, 563octahedral interstice, 416octahedral interstitial site, 416octahedral sheets, 587octahedron, 87, 97, 388, 411, 416octahedron crystal form, 97oligoclase, 637oligomer, 660olivine, 643olivine series, 622, 624optical activity, 151optical gyration constant, 15optical opacity, 39orbit, 25, 213orbital, 27ordered solid solution, 439ordered structure, 439organic, 653organic chemistry, 653organo-metallic compounds, 642orientation variant, 456orientations, 455orthogonal projection, 357orthopyroxene, 644orthosilicates, 622, 624oxidation number, 33oxides, see mineral classesoxyhydroxide, 621, 643, 646

π meson, 321packing fraction, 431pair correlation function, g(r), 535pair potential, 35parawollastonite, 630parity, 171particle–wave duality, 46partitionless freezing, 543passive operator, 158

path difference, 274pattern, 49Patterson function, 379Patterson symmetry, 248Pauli exclusion principle, 27, 35, 37Pauling, Linus Carl, 34, 41, 594Pauling’s rules, 446, 562, 566, 641Pearson, W. B. , 463Pearson symbol, 426, 427Peierl’s theorem, 669Penrose, Roger, 507Penrose rhombs, 410, 507Penrose tile, 403, 498, 507pentagon, 383pentagonal anti-prism, 471pentagonal dodecahedron, 386–388, 411, 491,

658pentagram, 499percentage ionic character, 41perfect conductivity, 597peridot, 626periodic approximants, 501periodic table of the elements, 28, 44periodic tiling, 403peritectic phase diagram, 437peritectic point, 437peritectic transformation, 437permanent dipole moment, 579permanent material response, 10permutation symbol, 126Perovski, Count Lev Aleksevich, 577perovskite, 577, 589, 597

B setting, 578structure, 578

perpendicular recording media, 458perspective projection, 358phase, 271phase diagram, 3, 437phase difference, 272phase field, 437phase transformation, 135phonon density of states, 310phonons, 322phosphates, see mineral classesphosphodiester bonds, 672photoelectric effect, 7, 554photoelectron, 554






732 Index

photon, 259phyllosilicate, 624, 634, 635piston and anvil, 532pitch, 178planar flow casting, 540Planck, Max, 46Planck’s constant, 46plane group, 231plane tiling

definition, 403plane wave, 261plasma torch synthesis, 541plate, 89Plato, 2Platonic solids, 2, 386–388, 390, 411, 412point charge, 88point group, 197, 230, 383

2-D, 221black-and-white, 223dihedral, 199gray, 222Hermann–Mauguin notation, 195international notation, 195non-crystallographic, 383, 398non-magnetic, 222notation, 198polar, 209Schoenflies notation, 195Shubnikov, 223two-color, 223

point symmetry, 186polar point groups, 209polar vector, 171polarization, 40polarization factor, 293polyacetylene, 668polyacrylamide, 662polybutadiene, 664polychloroprene, 664polyester, 662polyethylene, 660, 662polygonal reciprocal lattices, 515polyhedral representation, 360polyisoprene, 664polymer, 660polymerization, 662polymers, 654

polymethyl methacrylate, 664polynucleotide, 671, 672polypropylene, 663polysaccharides, 654polystyrene, 662, 664polytope, 403

regular, 412polytypes, 415, 417, 418polyvinyl acetate, 664polyvinyl chloride, 663polyvinylidene chloride, 664potential energy, 24potential range, 437Powder Diffraction Files, 282powder diffraction pattern, 18, 360, 363, 369,

372Poynting flux, 347Poynting vector, 347precipitation, 643Priestley, Joseph, 44primary crystallization temperature, Tx1, 532primary layers, 471primary nanocrystallization, 547primitive basis vectors, 536primitive unit cell, 61, 536principal quantum number, 25prism, 89prismatic, 568projection method, 498prokaryotes, 649prolate rhombohedron, 518propagation, 662proper motions, 160properties of groups, 196propylene oxide (PO), 667proteins, 654proton, 321

discovery of, 24, 45prototile, 403pseudo-binary phase diagram, 624pseudo-scalar, 171pseudo-translations, 410pseudo-Voigt peak shape, 367pulsed laser deposition (PLD), 457purines, 672pyramid, 89pyrimidines, 672






733 Index

pyrophyllite, 624pyrosilicates, 623, 629pyroxene, 643pyroxene mineral, 631pyroxene mineral group, 644pyroxenoid group, 630pyrrhotite, 647Pythagoras’ theorem, 76

quantum chemistry, 34quantum mechanics, 45quantum numbers, 25quantum of energy, 46quantum theory, 25, 45quantum well structures, 459quartz, 4, 193, 383, 624quartz compensator, 151quasicrystal, 383, 497

decagonal, 515dodecagonal, 498, 515octagonal, 498, 515polygonal, 514

quasicrystal alloysAlMnSi, 524AlZnMg, 524Ti56Ni23Fe5Si16, 521TiNiSi , 524UPdSi , 524

quasicrystalline alloys, 410quasicrystallography, 403quasilattice constant, 522quasilattices, 410, 496, 515quasiperiodic, 410quasiperiodic Fibonacci lattice, 501quasiperiodic functions, 498quasiperiodic structure, 497quasiperiodic tiling, 403quasiperiodicity, 460, 497quasiregular solids, 413QuasiTiler, 410quaternary system, 547, 624

radial distribution function, 535radical initiator, 662radius

covalent, 431ionic, 431

metallic, 431van der Waals, 431

radius of gyration, 665Ramsdell notation, 417random copolymer, 666random distribution, 581random walk, 665rare earth elements, 30rare earth–transition metal system

amorphous, 543, 545rare-earth-like metals, 30Raveau, Bernard, 617reciprocal basis vectors, 105, 261

in terms of direct basis vectors, 134simple procedure, 134

reciprocal lattice, 108, 271, 407reciprocal lattice parameters, 110reciprocal lattice vector, 276reciprocal metric tensor, 110

definition, 110reciprocal permutation symbol, 126reciprocal space, 104reciprocal structure matrix, 140, 142, 147

example, 143reduced glass-forming temperature, Trg, 542reduced intensity function, 539, 553reduced Lennard-Jones potential, 434reduced Morse potential, 434reference frame

Cartesian, 140standard Cartesian frame, 140

reflection, 160, 166, 272reflection condition, 307refraction, 272regular continued fractions, 499regular polygons, 404regular polytopes, 412regular tilings, 404, 428

derivation, 404regular vertex, 407residuals, 368resistivity tensor, 15resonance, 39reverse setting, 81rhombic dodecahedron, 72, 536rhombic triacontahedron, 491, 500, 522, 527rhombicosidodecahedron, 414, 493






734 Index

rhombicuboctahedron, 414rhombitruncated cuboctahedron, 414rhombitruncated icosidodecahedron, 414rhombohedron, 87ribonucleic acid, 654Rietveld method, 369right-hand rule, 15, 170, 173RNA, 654rocksalt blocks, 598rocksalt structure, 442Romé de l’Isle, Jean Baptiste Louis, 87root-mean-square end-to-end distance, 665rotation, 160

angle, 162axis, 162matrix, 154order, 162time-reversing, 174

roto-inversion, 175rubbers, 662ruby, 576Ruddlesden–Popper phases, 588rule of rational indices, 161Rutherford, Ernest, 44rutile, 357, 585Röntgen, Wilhelm Konrad, 317

sandwich structure, 459sanmartinite, 590sapphire, 576satellite reflections, 459saturated, 580scalar product, 77scalars, 171scalenohedron, 88scanning tunneling microscopy, 605scapolites, 624, 636scattering cross section, 326Scherrer broadening, 533Scherrer’s formula, 315, 534Schläfli symbol, 404, 405Schoenflies, Arthur Moritz, 190, 256Schoenflies notation, 153, 195, 383Schottky defect, 592Schrödinger, Erwin, 47Schrödinger equation, 25, 34, 47schwertmannite, 643, 644

screw axis, 178handedness, 179pitch, 178

screw dislocation, 605second transition series, 29secondary crystallization, 532section method, 498Seitz, Frederick, 72Seitz symbol, 166, 210

for rotations, 166for translations, 166

self-assembly, 441, 641, 654, 659, 666, 674,676

self-similarity, 508semi-crystalline, 654semiconducting materials, 419separating layer, 598, 602serpentine, 624set, 53

closed, 194shape, 88Shechtman, Daniel, 528Shechtmanite, 497sheets, 588shell, 27Shockley stacking fault, 418Shoemaker, Clara Brink, 380, 381Shoemaker, David P., 380, 381short wavelength limit, 263short-range order, 532Shubnikov point groups, 223Shull, Clifford Glenwood, 322, 353silicate glasses, 639Silicon Age, 1sillimanite, 622, 628siloxane, 643simple closed surface, 414simple cubic structure, sc, 428simple sugars, 654single crystal monochromator, 555single-walled nanotubes (SWNT), 682site symmetry, 212, 233, 252Slater, John C., 34small angle neutron scattering, SANS, 323Smalley, Richard Errett, 386, 401Snell’s law, 273snub cube, 414






735 Index

snub dodecahedron, 414sodalite, 624, 637sodalite cage, 624, 638sodalite group, 624, 636sol, 642sol-gel synthesis, 642solid CO2, 654solid benzene, 654solid solution, 458sorosilicates, 623, 629sp2 bonding, 657sp3 bonding, 657space group, 231, 356

magnetic, 253symbol, 248, 428

space groups, 383space lattice, 52, 75

definition, 52space-filling representation, 359spacing layer, 598, 602spallation, 324spallation source, 324special points, 214specific weight, 88spectral lines, 26spectroscopy, 44sphalerite, 446, 574spherical coordinate system, 24spherical micelles, 641spherical space, S2, 412spherical surfaces, 412spin quantum number, 27spin-coating, 643spinel

inverse spinel, 581normal spinel, 581random spinel, 581structure, 581

spinel-type magnetic oxides, 257spiral growth, 605splat cooling, 532splat quenching, 540spray pyrolysis, 643square, 411stacking fault, 418, 592stacking sequence, 416

A)α(ACB)β(BAC)γ (CB, 483

AB)β(BAC)γ (C, 483ABAB, 416, 567ABAC, 449ABC, 417ABC notation, 417ABCABC, 416, 567ACAB, 451A+B+C+, 483A+B−, 483A+B−A−C+, 485BBCC, 448BC, 449XYXY . . ., 481XYXZXYXZ . . ., 481XYZXYZ . . ., 481α(ABC)γ (CBA)α(ACB)β(BCA), 485βBbB, 478μ-phase, 489h-c notation, 417Ramsdell notation, 417Zhdanov notation, 417

staggered, 568staggered structure, 569standard Cartesian frame, 140Stanford Positron Accelerating Ring (SPEAR),

348star, 518star extension, 499statistical mechanics, 665stellation, 499Stensen, Niels, 87step-reaction (condensation) polymerization,

662stereo-chemistry, 664stereographic projection, 101, 122, 150

conversion to Cartesian coordinates, 146net, 150

stilbite, 624stoichiometry, 503Stone Age, 1Stoney, J., 23strain, 15stress, 15structural groups, 622structure factor, 291, 300, 444

A15, 474body-centering, 302






736 Index

structure factor (cont.)CsCl, 307example, 307face-centering, 303glide plane, 306inversion symmetry, 304primitive structure, 301screw axis, 305single face centering, 301ZnS, 575

structure prototype, 428structures, see compound structuresStrukturbericht symbol, 426, 427styrene, 662subgroup, 197

index, 197sublattice, 438, 455subshell, 27subsilicates, 622, 624, 628substitutional solid solution, 432sulfates, see mineral classes, 649sulfides, see mineral classessulfosalts, see mineral classessunstone, 637superconducting transition temperature, Tc, 597superconductivity, 468, 597superconductor, 475

0201 T’ phase, 6030201 T* phase, 6031201 phase, 613, 6141212 phase, 613, 6141212C phase, 6051223 phase, 613, 614123 phase, 6041234 phase, 6132201 phase, 607, 610, 6112212 phase, 607, 610, 6112223 phase, 607, 610, 6112224 phase, 6072234 phase, 610Ag1−xCuxBa2Can−1CunO2n+3−x, 598,

615AgBa2Ca3Cu4O10, 615Ba1−xKxBiO3, 599BaPb1−xBixO3, 597, 599(Ba,Sr)CuO2, 616(Bi ,Pb)2Sr2Ca2Cu3O10+x, 598

Bi-2223, 598CuO2 plane, 602, 604HgBa2CaCu2O6+x, 614HgBa2Ca2Cu3O8+x, 598, 614(La,Ba)2CuO4, 588La1−xBaxCuO4, 598La2CuO4, 602(La,Sr)2CuO4, 588La1−xSrxCuO4, 598La2−xSrxCuO4, 598, 602Nb3Ge, 597Nb3Sn, 597Nd2CuO4, 603RuSr2GdCu2O8, 616Tl-2223, 598TlBa2CaCu2O7, 613Tl2Ba2CaCu2O8+x, 610TlBa2Ca2Cu3O9, 613Tl2Ba2Ca2Cu3O10+x, 598, 610TlBa2Ca3Cu4O11, 613Tl2Ba2Ca3Cu4O12+x, 610TlBa2CuO5, 612Tl2Ba2CuO6+x, 610YBa2Cu3O7−x, 598, 604–605ACBCCO, 615BPBO, 599BSCCO, 598, 606–608HBCCO, 598, 613–614infinite-layer, 616LBCO, 598, 602LSCO, 598, 602nomenclature, 598rutheno-cuprate, 615–616TBCCO, 598TBCCO (double-layer), 608–610TBCCO (single-layer), 611–613YBCO, 598

supercooling, 468superexchange, 581supergroup, 197superlattice, 438, 439

commensurate, 497incommensurate, 497

superlattice reflections, 308, 351, 444superlattice structures

n × 1, 459superspace groups, 257






737 Index

superstructure, 439surface coordination number, 470surfactant, 659symmetric variants, 159symmetry, 3, 13symmetry operation, 152symmetry operator

decomposition, 169time-reversing, 173

symmorphic, 240synchrotron radiation, 347syndiotactic, 664synthetic modulated structure, 457systematic absences, 301systematic extinctions, 301

talc, 624Taylor expansion, 9tectosilicates, 624, 635temperature, 51temperature difference, 15tensor, 12

second-rank, 136termination, 662tessellated, 471tessellation, 403tetragonal distortion, 440tetrahederstern, 469, 474, 489tetrahedral coordination, 563tetrahedral interstice, 416, 467tetrahedral interstitial site, 416tetrahedral oxides, 637tetrahedron, 411, 416tetrakaidecahedra, 658tetrathiafulvalene, 669texture, 364texture analysis, 364theorem of Lagrange, 197theoretical density, 430, 431theory of electromagnetism, 7theory of quasi-equivalence, 674thermal conductivity, 39thermal emission, 262thermal motion, 51thermal vibration, 51thermodynamics, 14thermoelectric properties, 659

thermoplastic polymers, 662thermosetting polymers, 662thin-film deposition, 541third transition series, 30Thomson, George Paget, 352Thomson, Joseph John, 23, 44Thomson equation, 291, 312three-index notation

conversion to four-index notation, 95thymidine, 672thymine, 672tile

definition, 403tiling

2-uniform, 406k-uniform, 4062-D periodic, 4033-D Penrose, 498Archimedean, 405colored, 408edge-to-edge, 404monohedral, 404regular, 404uniform, 405

time reversal, 67time-reversal operator, 170time-reversal symmetry, 17time-reversing translation, 67titanite, 622tobacco mosaic virus, 675topaz, 628topological close packing (TCP), 466, 468, 469topologically close-packed phases, 433topologically close-packed structures, 467tourmalines, 633trace

of a matrix, 384transformation

direct to reciprocal space, 133of coordinates, 135reciprocal to direct space, 133

transition metal systemamorphous, 543

transition metal–metalloid systemT23M6, 544

translation, 160, 164time-reversing, 67






738 Index

translation variant, 456translation vector, 52, 75, 536translational symmetry, 55transmission electron microscope, 338transparency, 88transuranic elements, 30tremolite, 623, 633triangulated coordination polyhedron, 469triangulation number, 421, 675triblock copolymers, 667tridymite, 636trigonal prism, 568trioctahedral, 634truncated cube, 388, 413truncated dodecahedron, 387, 388, 413truncated icosahedron, 387, 388, 413, 491truncated octahedron, 97, 388, 413, 536, 658truncated pentagonal prism, 392truncated tetrahedron, 413, 484truncation, 413TTT diagram, 543tungstates, see mineral classestungsten bronze, 589twinned cuboctahedron, 467, 469twins, 88two-color symmetry, 67two-dimensional point groups, 220Type I clathrate, 658Type II clathrate, 658

Uhlenbeck, George Eugene, 27ultra-high molecular weight polyethylene,

661ultraviolet rays, 259ultramarine, 639uncertainty principle, 47undercooling, 531, 539undulators, 350uniform coloring of regular tilings, 408uniform tilings, 405unit cell

non-primitive, 61primitive, 61volume, 105Wigner–Seitz, 65

unit cells, 2universal behavior, 436universal binding curve, 437

universal binding potential, 566

vacancies, 592valence, 33, 404, 407

of a tile, 404valence bond theory, 34van der Waals

force, 41, 653radius, 431

Van Leeuwenhoek, Anton, 150vanadates, see mineral classesvector

attributes, 75cross product, 126

examples, 129general definition, 127

dot product, 78, 80scalar product, 78, 80transformation direct to reciprocal, 134transformation reciprocal to direct, 134

Vegard’s law, 361, 432velocity of light, 259vertex

model, 525regular, 407truncation, 413valence, 407

vibration amplitude, 51vibration ellipsoid, 310virion, 674virus, 674

complex symmetry, 674helical, 675–677icosahedral, 674–675

volume exclusion, 537volume of unit cell, 105von Groth, Paul Heinrich Ritter, 150von Kármán, Theodore, 120von Laue, Max Theodor Felix, 318Voronoi, George Feodosevich, 558Voronoi construction, 537Voronoi domain, 66Voronoi polyhedron, 469, 537

Watson, James Dewey, 671, 685wave

phase of, 271wave function, 25, 47






739 Index

wave lengthelectron, 7neutron, 8

wavevector, 259, 276wave–particle duality, 7wavelength, 4, 260weight, average molecular, 661Weiss, Christian Samuel, 89Weiss indices, 102Werner, Abraham Gottlob, 88wet gel, 642, 643wide bandgap, 419wide-bandgap semiconductor, 415Wiener, Christian, 191wigglers, 350Wigner, Eugene Paul, 72Wigner–Seitz cell, 65, 408, 469Wigner–Seitz primitive cell, 536Wigner–Seitz radius, 436Wilkins, Maurice Hugh Frederick, 671, 685Wollaston, William Hyde, 151, 630wollastonite, 630Wulff, Yuri Victorovich (George), 150Wulff net, 124Wulff plot, 150wurtzite, 448wüstite, 571Wyckoff letter, 252

Wyckoff position, 214, 307Wyckoff symbol, 252

X-ray absorption, 554edge, 351

X-ray absorption fine structure (XAFS), 554X-ray absorption near-edge spectroscopy

(XANES), 555X-ray absorption spectroscopy (XAS), 555X-ray filters, 266X-ray fluorescence, 554, 555X-ray photoelectric effect, 555xerogel, 642, 643xerogel film, 642

Zachariessen’s rules, 641zeolite, 624, 637zeolite family, 636Zhdanov notation, 417, 418zigzag carbon nanotube, 685zinc blende, 446, 574zincite, 448Zintl line, 30, 33zircon, 622, 628zone, 125, 130zone axis, 125, 130zone equation, 130






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