Upload
others
View
3
Download
0
Embed Size (px)
Citation preview
�
�
Valim Levitin: Interatomic Bonding in Solids — 2013/10/2 — page 303 — le-tex
�
�
�
�
�
�
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.
�
�
Valim Levitin: Interatomic Bonding in Solids — 2013/10/2 — page 304 — le-tex
�
�
�
�
�
�
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
�
�
Valim Levitin: Interatomic Bonding in Solids — 2013/10/2 — page 305 — le-tex
�
�
�
�
�
�
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
�
�
Valim Levitin: Interatomic Bonding in Solids — 2013/10/2 — page 306 — le-tex
�
�
�
�
�
�
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