Patterson, Bailey - Solid State Physics Introduction to theory

Index 711

Low Energy Electron Diffraction 611

Low temperature magnon specific heat 402

Lower critical field 462, 472, 504 Luminescence 579 Lyddane-Sachs-Teller Relation 574

M

Madelung constant 7, 38, 39 Magnetic anisotropy 383 Magnetic charge 426 Magnetic domains 420 Magnetic flux 257, 460, 504 Magnetic hysteresis 421 Magnetic induction 32 Magnetic interactions 116

Magnetic moment 164, 353, 422, 685

Magnetic phase transition 414 Magnetic potential 387

Magnetic resonance 353, 432, 613 Magnetic specific heat 365, 415,

454

Magnetic structure 353, 358, 393, 418

Magnetic susceptibility 164, 273, 277, 354, 370, 379, 454, 457

Magnetization 164, 168, 354 Magnetoacoustic 274 Magnetoelectronics 450 Magnetoresistance 273, 451, 453 Magnetostatic energy 386, 421 Magnetostatic self energy 387 Magnetostatic Spin Waves 404 Magnetostriction 425, 426 Magnetostrictive energy 421 Magnon-magnon interactions 394 Magnons 215, 392, 397

Mass defect in a linear chain 72 Mass of the electron 46, 158, 647 Mass of the nucleus 42

Maxwell equations 32, 263, 387

Mean field theory 353, 359, 366, 416

Medium crystal field 443 Meissner effect 419, 466, 504 Membranes 640

Metal Oxide Semiconductor Field Effect Transistor 350

Metal Semiconductor Junctions 334 Metal-Barrier-Metal Tunneling 619 Metallic binding 10

Metallic densities 135, 193, 242 Mg 272, 501

MgB2 459, 501 Microgravity 322, 606 Miller Indices 31 Minibands 622

Minority carrier concentrations 342, 348

Mobility gap 637

Models of Band Structure 319 Molecular Beam Epitaxy 613 Molecular crystals 2, 3, 215 Molecular field constant 360, 361,

405

Monatomic case 66 Monatomic Lattice 51 Monoclinic Symmetry 24 Monomer 641, 642, 643 Monovalent metal 130, 158 MOS transistors 350 MOSFET 337, 350, 633 Mott transition 173, 639 Mott-Wannier excitons 215

N

N 2, 502

N interacting atoms 59

Na 9, 56, 76, 155, 184, 271, 527, 596

NaCl 6, 9, 12, 28, 577, 596 NaKC4H4O6.4H2O (Rochelle salt)

516

Narrow gap insulator 293

712 Index

Narrow gap semiconductor 293, 615, 625, 626

N-body problem 59

Nd2Fe14B 431

Nearest neighbor repulsive interactions 8

Nearly free-electron approximation 173, 186, 201

Néel temperature 365, 368 Néel walls 428

Neutron diffraction 90, 95, 283, 368 Neutron star 289

Ni 188, 290, 359, 362, 405, 424 Noble metals 265, 271 Nonequilibrium statistical properties

218

Non-radiative (Auger) transitions 562

Normal coordinate transformation 4, 58, 77, 87, 649

Normal coordinates 51, 57, 76, 649 Normal mode 41, 49, 65, 649, 668 Normal or N-process 221

Normal subgroup 16

n-type semiconductor 334, 351 Nuclear coordinates 42

Nuclear magnetic resonance 433 Nuclear spin relaxation time 463,

464

O

O 335, 641

Occupation number space 79, 662 Octahedron 22

One-dimensional crystal 53, 207 One-dimensional harmonic

oscillators 3 One-dimensional lattices 47 One-dimensional potential well

210, 211

One-electron Hamiltonian 354 One-electron models 148 One-particle operator 116, 126, 663

Optic mode 64, 91, 233, 520, 524 Optical absorption 555, 597 Optical magnons 399

Optical phenomena 543

Optical phonons 216, 544, 569, 580 Orbital angular momentum operator

356, 661

Order parameter 416, 454, 465 Order-disorder transition 521 Orthogonality constraints 142 Orthogonalized plane wave 173,

190, 203

Orthorhombic symmetry 24 Oscillating polarization 380 Oscillator strength 512, 553, 558,

585

Overlap catastrophe 375

P

Padé approximant 415 Pair tunneling 506

Parabolic bands 296, 322, 553 Paraelectric phase 517, 518 Parallelepiped 17, 22, 84, 159 Paramagnetic Curie temperature

361

Paramagnetic effects 355 Paramagnetic ions 358, 442 Paramagnetic resonance 597 Paramagnetic susceptibility 355,

413

Paramagnetism 166, 355, 365, 413 Particle tunneling 506, 507 Particle-in-a-box 154

Partition function 61, 99, 167, 415, 457

Passivation 335

Pauli paramagnetism 135, 355, 601 Pauli principle 120, 129, 168, 288 Pauli spin paramagnetism 164 Pauli susceptibility 413

Peierls transitions 279, 282 Peltier coefficient 254, 256

Index 713

Penetration depth 466, 471, 473, 502, 578

Perfect diamagnetism 506 Periodic boundary conditions 48,

51 Permalloy 428

Permittivity of free space 4, 234 Permutation operator 120 Perovskite 29, 517 Perpendicular twofold axis 26 Perturbation expansion 44, 667 Phase space 182, 245

Phase transition 203, 279, 359, 406, 414, 454, 517, 522

Phonon 41, 61, 62, 82, 556 Phonon absorption 229 Phonon current density 223

Phonon density of states 98, 228 Phonon emission 229

Phonon frequencies 222 Phonon radiation 222

Phonon-phonon interaction 41, 113, 219, 221

Phosphorescence 579 Photoconductivity 585, 597 Photoelectric effect 172, 347 Photoemission 172, 543, 578 Photoluminescent 579 Photon absorption 551 Photons 172, 563, 579 Photovoltaic effect 344, 347 Physical observables 77 Piezoelectric crystals 516 Pinned 208, 336, 439

Planar defects 589 Planck distribution 579

Plane polarized light 582, 611 Plane wave solution 132, 210 Plasma frequency 216, 265, 515,

527, 564, 583

Plasmons 136, 216, 527, 611 Platinum 291

pn-junction 331, 338, 344 Point defects 587, 597

Point group 13, 17, 22, 23, 26, 27, 39, 442

Point scatterers 32, 36 Point transformations 17 Poisson bracket relations 76 Polar crystals 216, 516 Polar solids 544

Polaritons 569

Polarization 234, 509, 514, 523, 563, 572, 583

Polarization catastrophe 520 Polarization vectors 89, 91, 111,

229, 238

Polarons 216, 232, 241 Polyhedron 22, 184 Polymers 1, 610, 640, 641 Polyvalent metals 265 Population inversion 626

Positive definite Hermitian operator 114

Positrons 213

Potential barrier 336, 338, 556, 605 Potential gradients 307

Primitive cells 17

Primitive translation 17, 23, 84, 269, 610, 655

Principal threefold axis 26 Projection operators 179 Propagators 666

Proper subgroup 15, 16 Pseudo binary alloys 320 Pseudo-Hamiltonian 200

Pseudopotential 178, 190, 194, 265, 318, 319, 500, 611

p-type semiconductor 335, 336, 337 p-wave pairing 501

Pyroelectric crystals 516

Q

Quantum conductance 609, 620 Quantum dot 609, 615, 616 Quantum electrodynamics 217,

233, 479, 666

Quantum Hall Effect 165, 632

714 Index

Quantum mechanical inter-band tunneling 344

Quantum wells 325, 609, 626 Quantum wires 609, 615, 636 Quasi Periodic 21

Quasi-classical approximation 344 Quasicrystals 21

Quasi-electrons 135, 136, 217, 484 Quasi-free electron 113, 158, 509 Quasi-particles 135, 217, 666

R

Radiation damage 587 Radiative transitions 562, 626 Raman scattering 96, 580, 613 Rare earths 265, 378, 383, 405,

430, 443

Rayleigh-Ritz variational principle 114

Real orthogonal transformation 88 Real solids 6, 173, 243, 388 Reciprocal lattice 31, 36, 37, 84,

174, 221

Reciprocal lattice vectors 35, 268, 610

Reciprocal space 36, 176 Reducible representation 445 Reflection coefficient 545 Reflection High Energy Electron

Diffraction 612 Reflection symmetry 18, 19

Reflectivity 203, 547, 564, 576 Refractive index 509

Registry 613

Regular polyhedron 22 Relativistic corrections 116, 192,

193, 204, 243, 660, 661 Relativistic dynamics 287 Relativistic effects 43 Relativistic pressure 288 Relaxation region 565

Relaxation time 171, 172, 250, 307 Relaxation time approximation 250,

253, 264

Remanence 420, 427 Renormalization 414, 416, 484, 665 Reptation 642

Repulsive force 3, 6

Resonance frequencies 313, 509 Resonant tunneling 614, 625 Rest mass 193, 287, 660 Restrahl frequency 68, 576 Restrahlen effect 510

Reverse bias breakdown 344 Reversible processes 8 Richardson-Dushmann equation

603

Riemann zeta functions 401 Rigid ion approximation 229, 230 RKKY interaction 378

Rochelle salt 516 Rotary reflection 18

Rotation inversion axis 26 Rotational operators 81

Rotational symmetry 18, 20, 81, 90, 188, 419

Rubber 641

Rushbrooke inequality 417

S

Saturation magnetization 405, 409, 420, 428

s-band 179, 184, 407 sc lattice 38, 210 Scaling laws 415

Scanning Auger microscope 612 Scanning Electron Microscopy 429,

612

Scanning Tunneling Microscopy 612

Scattered amplitude 40 Schoenflies 26, 27

Schottky and Frenkel defects 588 Schottky Barrier 334

Schottky emission 605 Screening 535 Screening parameter 533

Screw axis symmetry 19, 20

Index 715

Screw dislocation 599, 600, 601 Second classical turning point 605 Second quantization 124, 662 Secondary Ion Mass Spectrometry

612

Second-order phase transitions 414 Secular equation 50

Selection rules 225, 228, 569 Self-consistent one-particle

Hamiltonian 126 Semiconductor 293, 555, 568, 587,

590, 637

Seven crystal systems 23 Shallow defects 296, 589, 591 Shell structure 115

Shockley diode 339, 344 Shockley state 587 Short range forces 3

Si 29, 191, 315, 318 Similarity transformation 445 Simple cubic cell 25

Simple cubic lattice 181, 210, 392, 422

Simple monoclinic cell 24 Simple orthorhombic cell 24 Simple tetragonal cell 24

Single crystal 273, 325, 424, 590 Single domain 420

Single electron transistors 615 Single particle wave functions 141 Single-ion anisotropy 385, 386 Singlet state 373, 501

SiO2 335, 633

Skin-depth 274

Slater determinant 120, 664 Slater-Koster model 205, 596 Slow neutron diffraction 228 SmCo5 431

Sn 265, 290

Soft condensed matter 1, 609, 640 Soft mode theory 517, 521

Soft x-ray emission 210

Soft x-ray emission spectra 168 Solar cell 294, 345

Solid state symmetry 17 Solitons 353, 456

Space degrees of freedom 43 Space groups 13, 23, 28 Specific heat of an electron gas

135, 161

Specific heat of an insulator 52, 97 Specific heat of linear lattice 61 Specific heat of spin waves 400 Specific heat of the one-dimensional

crystal 61

Speed of light 32, 635, 660 Speromagnetic 430 Spherical harmonics 187 Spin 1/2 particle 43

Spin coordinate 119, 373 Spin degeneracy 602 Spin density waves 283

Spin deviation quantum number 397, 402

Spin diffusion length 451 Spin glass 353, 430, 454 Spin Hamiltonian 373 Spin polarization 450

Spin wave theory 364, 389, 413, 417

Spin-lattice interaction 222 Spin-orbit interaction 204, 443, 660 Spin-polarized transport 450 Spin-spin relaxation time 433, 437 Split-off band 320

Spontaneous emission 579 Spontaneous magnetism 359 Spontaneous polarization 517 Spontaneously broken symmetry

419, 505

Stark-Wannier Ladder 623 Steel 290, 639 Stereograms 26, 39 Stokes line 580

Stoner criterion 412 Stoner model 406, 450 Strained layer 622 Strong crystal field 443

716 Index

Structure factor 35, 38, 177, 201 Subgroup 16, 23, 39 Substitutional atoms 70, 589 Superconducting metals 460 Superconducting wave function

468, 472 Superconductive state 459 Superconductivity 464 Superconductors 459 Superlattice 622, 623, 626 Surface defects 587 Surface reconstruction 612

Surface states 335, 345, 350, 636 s-wave pairing 501

Symmetry operations 17, 18, 23, 26, 192

Symmorphic 23

T

Tamm states 587

Tensor effective mass 158 Tetragonal Symmetry 24 Tetrahedron 22

Thermal conductivity 99, 169, 223, 246, 254

Thermal energy 172, 561 Thermal neutrons 30, 228 Thermal resistance 52, 222 Thermionic emission 135, 601 Thermodynamic fluctuations 359,

416

Thermodynamics of irreversible process 255

Thermoelectric power 255 Thomas-Fermi approximation 531 Thomas-Fermi-Dirac method 137 Three-dimensional lattice vibration

47, 85 Three-dimensional periodic

potential 148 Threefold axis 20, 26 Ti 291

Tight binding approximation 113, 173, 178, 184, 190, 207

Total cohesive energy 8 Total exchange charge 129 Total reflection 568

Transistors 294, 328, 338, 350, 615, 636

Transition metals 265, 273, 639 Translation operator 80, 655 Translational symmetry 17 Transmission coefficient 605, 619 Transmission Electron Microscopy

429, 612

Transport coefficients 218, 246 Transverse and longitudinal acoustic

modes 229

Trial wave function 115, 190, 243, 490, 493, 541

Triclinic Symmetry 23 Triglycine selenate 516 Triglycine sulfate 516 Trigonal Symmetry 25 Triplet state 373

Triplet superconductivity 284 Two-atom crystal 50 Two-body forces 3, 42 Two-dimensional defect 590 Two-fold axis of symmetry 26

Two-fold degeneracy 4, 150, 444 Two-particle operator 116, 121, 663 Type I superconductors 461, 471,

505

Type II superconductors 459, 471, 504

U

UAl2 284

UBe13 284, 501, 503 Ultrasonic absorption 274 Ultrasonic attenuation 463 Ultrasonic wave 274 Ultraviolet photoemission 578

Index 717

Umklapp process 221, 232, 251, 483

Uncertainty principle 5 Unit cells 17

Unitary transformation 88, 207, 451 Unrestricted force constants

approach 47

Upper critical field 462, 470, 502

V

Vacancies 285, 587, 588, 596, 598 Valence band 590

Valence crystalline binding 12 Valence crystals 11, 12, 371 van der Waals forces 4, 6 Van Hove singularities 559 Varactor 332

Variational principle 114 Variational procedure 140

Vector potential 165, 166, 465, 550 Velocity operator 195

Verdet constant 584 Vertical transitions 554 Vibrating dipoles 4 Virgin curve 427

Virtual crystal approximation 320 Virtual excited states 2

Virtual magnons 501

Virtual phonons 233, 237, 501, 502 Volume coefficient of thermal

expansion α 100 Vortex region 462

W

W 291

Wall energy 424, 425 Wannier excitons 561 Wannier function 207, 407 Wave vector 55

Weak crystal fields 443 Weak superconductors 505

Weiss theory 359, 361, 406, 415 Whiskers 599

White dwarf 286 Wiedeman-Franz Law 169 Wigner-Seitz cell 184, 186, 231 Wigner-Seitz method 9, 184, 187 WKB approximation 557, 605, 620

X

X-ray photoemission 578

X-rays 30, 96, 168

Y

YBa2Cu3O7 502, 503

Z

Zeeman energy 388

Zener Breakdown 344, 556 Zero point energy 5, 62 Zincblende 295, 320, 323 Zn 290