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Valim Levitin: Interatomic Bonding in Solids — 2013/10/2 — page 303 — le-tex

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303

Index

SymbolsNi3Al-based phases, 147

– atom vibrations, 147– elastic properties, 151– electron density, 154– simulation, 148

Aalkali halides, 252alloys

– Al3(Sc, Ti, V, Cr), 136– Fe-Mo, 206– Fe-W, 206– Zr-Pd, 208– Zr-Rh, 207– Zr-Ru, 207, 208

atom– argon, 36– manganese, 37

atom vibrations, 98– mean-square amplitude, 100, 147– spectrum, 99

atomic radius, 36, 38, 43atomic units, 21atoms in Periodic Table, 41augmented plane wave method, 127

Bband structure, 87

– construction, 90– one-dimensional case, 88

band theory, 86– evolution of dispersion relationship, 88– Kronig–Penney model, 82

bcc crystal lattice, 188binary intermetallic phases, 206blackbody radiation, 7Bloch theorem, see also Bloch wavesBloch waves, 64, 82

Born–Oppenheimer approximation, 110, 175Born–von Karman force constants, 179Bravais lattice, 49Brillouin zone, 59, 216bulk modulus, 98, 131, 137, 252

– noble gases, 244

Ccarbon atom, 93close-packed structures, 49cohesive energy, 103, 131

– alkali halides, 252– ice, 241– noble gases, 244, 245– silicon, 165– simple metals, 77

conductors, semiconductors, insulators, 91correlation energy, 72covalent bond, 43, 92

– in Si, 218creep, 253

– equations, 260– physical model, 258– structural parameters, 254

Dde Broglie equation, 8Debye temperature, 102density functional theory, 112, 115, 118, 149density of states, 135, 197, 200, 203, 205

– for gas of free electrons, 68dimerization, 238dispersion curve, 176

– Fourier transformation, 181, 297– K, 183– Mo, 186– Na, 176– Nb, 180

Interatomic Bonding in Solids: Fundamentals,Simulation,andApplications, First Edition. Valim Levitin.©2014 WILEY-VCH Verlag GmbH & Co. KGaA. Published 2014 by WILEY-VCH Verlag GmbH & Co. KGaA.

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Valim Levitin: Interatomic Bonding in Solids — 2013/10/2 — page 304 — le-tex

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304 Index

Eeigenfunction, 16, 21eigenvalue, 16, 21elastic constants, 95, 151, 162

– calculation, 293– matrix, 97

electron– energy, 19, 31– in a rectangular box, 18– in a square well, 16– spin, 25

electron shells, 37, 40– elements, 41

electronic structure– self-consistent calculation, 203

embedded-atom method, 166– calculated parameters, 170– embedding function, 168– modified method, 167

energy functional, 117, 119Euler formula, 11Evald sphere, 57exchange energy, 33, 39, 72exchange hole, 39exchange-correlation energy, 116, 119exchange-correlation functional, 118–120exchange-correlation hole, 72, 114

Ffatigue, 263

– crack growth, 270, 280– crack origination, 264– parameters, 281

Fermi energy, 66–68Fermi–Dirac function, 165first-principle simulation, 109, 131, 148fitting parameters, 168, 171Fourier

– series, 181– transformation dispersion curves, 181

Ggamma phase, 146graphene, 225

– applications, 227group velocity, 12, 183, 187, 290

HHamiltonian, 22, 80, 111

– single atom, 159Hartree theory, 34, 35, 37, 113Hartree–Fock theory, 39, 114Hohenberg–Kohn relations, 117

homogeneous electron gas, 63– bulk modulus, 69– energy, 70– notions, 69– parameters, 66

Hooke law, 95hybridization, 202hydrogen bond, 93, 236, 249

Iice, 239

– atomic vibration, 241– cohesive energy, 241– structure, 240

interatomic potentials, 171intermetallic compounds, 133, 136, 146interplanar force constants, 182ionic bond, 93

– Madelung constant, 251ionic compounds, 250

– bulk modulus, 252– cohesive energy, 252

ionization potential, 43

Jjellium model, 63

Kkinetic processes, 279

– system differential equations, 280Kohn–Sham approach, 118, 119Kohn–Sham equations, 125, 126Kronig–Penney model, 82, 291k-space, 20, 58

Llattice vibration, 175

– one-dimensional atomic chain, 181, 295linear combination of atomic orbitals, 44

Mmany-body problem, 21, 110

– milestones in solution, 112melting temperature, 102

– oxides, 133– transition metals, 193

metallic bond, 92metals, 131

– K, 183– Nb, 203– polymorphism, 211– Ru, 203– Ti, 197

Mo, 186, 187

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Valim Levitin: Interatomic Bonding in Solids — 2013/10/2 — page 305 — le-tex

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Index 305

modeling– system differential equations, 279, 284

molecular crystals, 233molecule-based networks, 248molecules

– bond types, 47– diatomic, 43– dipole moment, 233– hydrogen, 46

multi-electron atoms, 30, 34, 35

Nnanomaterials, 227nanotubes, 228, 231Nb, 186, 187Newton Second Law, 9noble gases, 242

Oone-electron atom, 22organic molecular crystals, 246

Ppair potential, 170

– Buckingham, 174– Lennard-Jones, 173, 233, 242– Morse, 172– Rydberg, 173

partitioning of space, 127Pauli principle, 30phase velocity, 12, 290phonon, 176

– L( 23 , 2

3 , 23 ), 187, 189

– energy, 187photon, 8Planck equation, 8plane wave, 13, 80, 122, 127polarizability, 235principal quantum number, 23probability density function, 26, 29, 30, 115program Wien2k, 128, 149property levels, 1pseudopotential, 75, 121

– self-consistent solution, 123

Qquantum numbers, 17, 19, 23, 24quantum physics

– experimental evidence, 8– fundamentals, 7

Rreciprocal lattice, 54–56

– diffraction, 57

renormalized atom, 197Runge–Kutta method, 280

SSchrödinger equation, 14, 16

– eigenfunction, 16– eigenvalue, 16, 22– for molecule, 44– for multi-electron atom, 33– solutions, 15, 23

– in polar coordinates, 23– three-dimensional, 18– time-independent, 16

self-consistent field method, 34, 40, 112, 124,125

semiconductors, 132, 215– band structure, 216– crystal structure, 216– fracture, 220, 223– strength properties, 219

shear modulus, 97shear strain, 97shielding, 32simple metals, 77, 78Slater determinant, 33standing wave, 11structure

– MgB2, 139– Ni3Al, 148– diamond, 50– entropy contribution, 212– GaS, 215– ZnS, 51

supercell, 134, 148, 149superconductivity, 138

– MgB2, 139surface energy, 105, 162

TTi, 197tight-binding approximation, 157

– applications, 161– bond integrals, 163– environment-dependent, 163

transition metals, 42, 193– bulk modulus, 195– cohesive energy, 195, 197– crystal structures, 205– internuclear separation, 195– melting temperature, 193

traveling wave, 11

Uuncertainty principle, 10

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Valim Levitin: Interatomic Bonding in Solids — 2013/10/2 — page 306 — le-tex

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306 Index

Vvacancy

– at fatigue crack, 272– energy formation, 105, 134, 161, 193,

260, 273– fit melting temperature, 105

– fatigue failure, 270van der Waals bond, 93, 233

Wwave equation, 11

wave function, 14, 15wave packet, 9, 290wave vector, 19Wigner–Seitz

– cell, 53, 75, 77– sphere, 195

ZZr, 187