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More About This Title Condensed Matter Physics, Second Edition
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This Second Edition of the unified treatment of condensed matter physics keeps the best of the first, providing a basic foundation in the subject while addressing many recent discoveries. Comprehensive and authoritative, it consolidates the critical advances of the past fifty years, bringing together an exciting collection of new and classic topics, dozens of new figures, and new experimental data.
This updated edition offers a thorough treatment of such basic topics as band theory, transport theory, and semiconductor physics, as well as more modern areas such as quasicrystals, dynamics of phase separation, granular materials, quantum dots, Berry phases, the quantum Hall effect, and Luttinger liquids. In addition to careful study of electron dynamics, electronics, and superconductivity, there is much material drawn from soft matter physics, including liquid crystals, polymers, and fluid dynamics.
Provides frequent comparison of theory and experiment, both when they agree and when problems are still unsolved
Incorporates many new images from experiments
Provides end-of-chapter problems including computational exercises
Includes more than fifty data tables and a detailed forty-page index
Offers a solutions manual for instructors
Featuring 370 figures and more than 1,000 recent and historically significant references, this volume serves as a valuable resource for graduate and undergraduate students in physics, physics professionals, engineers, applied mathematicians, materials scientists, and researchers in other fields who want to learn about the quantum and atomic underpinnings of materials science from a modern point of view.
English
English
Preface xix
References xxii
I ATOMIC STRUCTURE 1
1 The Idea of Crystals 3
1.1 Introduction 3
1.1.1 Why are Solids Crystalline? 4
1.2 Two-Dimensional Lattices 6
1.2.1 Bravais Lattices 6
1.2.2 Enumeration of Two-Dimensional Bravais Lattices 7
1.2.3 Lattices with Bases 9
1.2.4 Primitive Cells 9
1.2.5 Wigner-Seitz Cells 10
1.3 Symmetries 11
1.3.1 The Space Group 11
1.3.2 Translation and Point Groups 12
1.3.3 Role of Symmetry 14
Problems 14
References 16
2 Three-Dimensional Lattices 17
2.1 Introduction 17
2.2 Monatomic Lattices 20
2.2.1 The Simple Cubic Lattice 20
2.2.2 The Face-Centered Cubic Lattice 20
2.2.3 The Body-Centered Cubic Lattice 22
2.2.4 The Hexagonal Lattice 23
2.2.5 The Hexagonal Close-Packed Lattice 23
2.2.6 The Diamond Lattice 24
2.3 Compounds 24
2.3.1 Rocksalt—Sodium Chloride 25
2.3.2 Cesium Chloride 26
2.3.3 Fluorite—Calcium Fluoride 26
2.3.4 Zincblende—Zinc Sulfide 27
2.3.5 Wurtzite—Zinc Oxide 28
2.3.6 Perovskite—Calcium Titanate 28
2.4 Classification of Lattices by Symmetry 30
2.4.1 Fourteen Bravais Lattices and Seven Crystal Systems 30
2.5 Symmetries of Lattices with Bases 33
2.5.1 Thirty-Two Crystallographic Point Groups 33
2.5.2 Two Hundred Thirty Distinct Lattices 36
2.6 Some Macroscopic Implications of Microscopic Symmetries 37
2.6.1 Pyroelectricity 37
2.6.2 Piezoelectricity 37
2.6.3 Optical Activity 38
Problems 38
References 41
3 Scattering and Structures 43
3.1 Introduction 43
3.2 Theory of Scattering from Crystals 44
3.2.1 Special Conditions for Scattering 44
3.2.2 Elastic Scattering from Single Atom 46
3.2.3 Wave Scattering from Many Atoms 47
3.2.4 Lattice Sums 48
3.2.5 Reciprocal Lattice 49
3.2.6 Miller Indices 51
3.2.7 Scattering from a Lattice with a Basis 53
3.3 Experimental Methods 54
3.3.1 Laue Method 56
3.3.2 Rotating Crystal Method 57
3.3.3 Powder Method 59
3.4 Further Features of Scattering Experiments 60
3.4.1 Interaction of X-Rays with Matter 60
3.4.2 Production of X-Rays 61
3.4.3 Neutrons 63
3.4.4 Electrons 63
3.4.5 Deciphering Complex Structures 64
3.4.6 Accuracy of Structure Determinations 65
3.5 Correlation Functions 66
3.5.1 Why Bragg Peaks Survive Atomic Motions 66
3.5.2 Extended X-Ray Absorption Fine Structure (EXAFS) 67
3.5.3 Dynamic Light Scattering 68
3.5.4 Application to Dilute Solutions 70
Problems 71
References 73
4 Surfaces and Interfaces 77
4.1 Introduction 77
4.2 Geometry of Interfaces 77
4.2.1 Coherent and Commensurate Interfaces 78
4.2.2 Stacking Period and Interplanar Spacing 79
4.2.3 Other Topics in Surface Structure 81
4.3 Experimental Observation and Creation of Surfaces 82
4.3.1 Low-Energy Electron Diffraction (LEED) 82
4.3.2 Reflection High-Energy Electron Diffraction (RHEED) 84
4.3.3 Molecular Beam Epitaxy (MBE) 84
4.3.4 Field Ion Microscopy (FIM) 85
4.3.5 Scanning Tunneling Microscopy (STM) 86
4.3.6 Atomic Force Microscopy (AFM) 91
4.3.7 High Resolution Electron Microscopy (HREM) 91
Problems 91
References 94
5 Beyond Crystals 97
5.1 Introduction 97
5.2 Diffusion and Random Variables 97
5.2.1 Brownian Motion and the Diffusion Equation 97
5.2.2 Diffusion 98
5.2.3 Derivation from Master Equation 99
5.2.4 Connection Between Diffusion and Random Walks 100
5.3 Alloys 101
5.3.1 Equilibrium Structures 101
5.3.2 Phase Diagrams 102
5.3.3 Superlattices 103
5.3.4 Phase Separation 104
5.3.5 Nonequilibrium Structures in Alloys 106
5.3.6 Dynamics of Phase Separation 108
5.4 Simulations 110
5.4.1 Monte Carlo 110
5.4.2 Molecular Dynamics 112
5.5 Liquids 113
5.5.1 Order Parameters and Long-and Short-Range Order 113
5.5.2 Packing Spheres 114
5.6 Glasses 116
5.7 Liquid Crystals 120
5.7.1 Nematics, Cholesterics, and Smectics 120
5.7.2 Liquid Crystal Order Parameter 122
5.8 Polymers 123
5.8.1 Ideal Radius of Gyration 123
5.9 Colloids and Diffusing-Wave Scattering 128
5.9.1 Colloids 128
5.9.2 Diffusing-Wave Spectroscopy 128
5.10 Quasicrystals 133
5.10.1 One-Dimensional Quasicrystal 134
5.10.2 Two-Dimensional Quasicrystals—Penrose Tiles 139
5.10.3 Experimental Observations 141
5.11 Fullerenes and nanotubes 143
Problems 143
References 149
II ELECTRONIC STRUCTURE 153
6 The Free Fermi Gas and Single Electron Model 155
6.1 Introduction 155
6.2 Starting Hamiltonian 157
6.3 Densities of States 159
6.3.1 Definition of Density of States D 160
6.3.2 Results for Free Electrons 161
6.4 Statistical Mechanics of Noninteracting Electrons 163
6.5 Sommerfeld Expansion 166
6.5.1 Specific Heat of Noninteracting Electrons at Low Temper-atures 169
Problems 171
References 173
7 Non-Interacting Electrons in a Periodic Potential 175
7.1 Introduction 175
7.2 Translational Symmetry—Bloch’s Theorem 175
7.2.1 One Dimension 176
7.2.2 Bloch’s Theorem in Three Dimensions 180
7.2.3 Formal Demonstration of Bloch’s Theorem 182
7.2.4 Additional Implications of Bloch’s Theorem 183
7.2.5 Van Hove Singularities 186
7.2.6 Kronig-Penney Model 189
7.3 Rotational Symmetry—Group Representations 192
7.3.1 Classes and Characters 198
7.3.2 Consequences of point group symmetries for Schrödinger’s equation 201
Problems 203
References 206
8 Nearly Free and Tightly Bound Electrons 207
8.1 Introduction 207
8.2 Nearly Free Electrons 208
8.2.1 Degenerate Perturbation Theory 210
8.3 Brillouin Zones 211
8.3.1 Nearly Free Electron Fermi Surfaces 214
8.4 Tightly Bound Electrons 219
8.4.1 Linear Combinations of Atomic Orbitals 219
8.4.2 Wannier Functions 222
8.4.3 Geometric Phases 223
8.4.4 Tight Binding Model 226
Problems 227
References 232
9 Electron-Electron Interactions 233
9.1 Introduction 233
9.2 Hartree and Hartree-Fock Equations 234
9.2.1 Variational Principle 235
9.2.2 Hartree-Fock Equations 235
9.2.3 Numerical Implementation 239
9.2.4 Hartree-Fock Equations for Jellium 242
9.3 Density Functional Theory 244
9.3.1 Thomas-Fermi Theory 247
9.3.2 Stability of Matter 249
9.4 Quantum Monte Carlo 252
9.4.1 Integrals by Monte Carlo 252
9.4.2 Quantum Monte Carlo Methods 253
9.4.3 Physical Results 254
9.5 Kohn-Sham Equations 255
Problems 258
References 262
10 Realistic Calculations in Solids 265
10.1 Introduction 265
10.2 Numerical Methods 266
10.2.1 Pseudopotentials and Orthogonalized Planes Waves (OPW) 266
10.2.2 Linear Combination of Atomic Orbitals (LCAO) 271
10.2.3 Plane Waves 271
10.2.4 Linear Augmented Plane Waves (LAPW) 274
10.3 Definition of Metals, Insulators, and Semiconductors 277
10.4 Brief Survey of the Periodic Table 279
10.4.1 Nearly Free Electron Metals 280
10.4.2 Noble Gases 282
10.4.3 Semiconductors 283
10.4.4 Transition Metals 284
10.4.5 Rare Earths 286
Problems 286
References 291
III MECHANICAL PROPERTIES 293
11 Cohesion of Solids 295
11.1 Introduction 295
11.1.1 Radii of Atoms 297
11.2 Noble Gases 299
11.3 Tonic Crystals 301
11.3.1 EwaldSums 302
11.4 Metals 305
11.4.1 Use of Pseudopotentials 307
11.5 Band Structure Energy 308
11.5.1 Peierls Distortion 309
11.5.2 Structural Phase Transitions 311
11.6 Hydrogen-Bonded Solids 312
11.7 Cohesive Energy from Band Calculations 312
11.8 Classical Potentials 313
Problems 315
References 318
12 Elasticity 321
12.1 Introduction 321
12.2 Nonlinear Elasticity 321
12.2.1 Rubber Elasticity 322
12.2.2 Larger Extensions of Rubber 324
12.3 Linear Elasticity 325
12.3.1 Solids of Cubic Symmetry 326
12.3.2 Isotropic Solids 328
12.4 Other Constitutive Laws 332
12.4.1 Liquid Crystals 332
12.4.2 Granular Materials 335
Problems 336
References 339
13 Phonons 341
13.1 Introduction 341
13.2 Vibrations of a Classical Lattice 342
13.2.1 Classical Vibrations in One Dimension 342
13.2.2 Classical Vibrations in Three Dimensions 346
13.2.3 Normal Modes 347
13.2.4 Lattice with a Basis 348
13.3 Vibrations of a Quantum-Mechanical Lattice 351
13.3.1 Phonon Specific Heat 354
13.3.2 Einstein and Debye Models 358
13.3.3 Thermal Expansion 361
13.4 Inelastic Scattering from Phonons 363
13.4.1 Neutron Scattering 364
13.4.2 Formal Theory of Neutron Scattering 366
13.4.3 Averaging Exponentials 370
13.4.4 Evaluation of Structure Factor 372
13.4.5 Kohn Anomalies 373
13.5 The Mössbauer Effect 374
Problems 376
References 377
14 Dislocations and Cracks 379
14.1 Introduction 379
14.2 Dislocations 381
14.2.1 Experimental Observations of Dislocations 383
14.2.2 Force to Move a Dislocation 386
14.2.3 One-Dimensional Dislocations: Frehkel-Kontorova Model 386
14.3 Two-Dimensional Dislocations and Hexatic Phases 389
14.3.1 Impossibility of Crystalline Order in Two Dimensions 389
14.3.2 Orientational Order 391
14.3.3 Kosterlitz-Thouless-Berezinskii Transition 392
14.4 Cracks 399
14.4.1 Fracture of a Strip 399
14.4.2 Stresses Around an Elliptical Hole 402
14.4.3 Stress Intensity Factor 404
14.4.4 Atomic Aspects of Fracture 405
Problems 406
References 409
15 Fluid Mechanics 413
15.1 Introduction 413
15.2 Newtonian Fluids 413
15.2.1 Euler’s Equation 413
15.2.2 Navier-Stokes Equation 415
15.3 Polymeric Solutions 416
15.4 Plasticity 423
15.5 Superfluid 4He 427
15.5.1 Two-Fluid Hydrodynamics 430
15.5.2 Second Sound 431
15.5.3 Direct Observation of Two Fluids 433
15.5.4 Origin of Superfluidity 434
15.5.5 Lagrangian Theory of Wave Function 439
15.5.6 Superfluid 3He 442
Problems 443
References 447
IV ELECTRON TRANSPORT 451
16 Dynamics of Bloch Electrons 453
16.1 Introduction 453
16.1.1 Drude Model 453
16.2 Semiclassical Electron Dynamics 455
16.2.1 Bloch Oscillations 456
16.2.2 k-p̂ Method 457
16.2.3 Effective Mass 459
16.3 Noninteracting Electrons in an Electric Field 459
16.3.1 Zener Tunneling 462
16.4 Semiclassical Equations from Wave Packets 465
16.4.1 Formal Dynamics of Wave Packets 465
16.4.2 Dynamics from Lagrangian 467
16.5 Quantizing Semiclassical Dynamics 470
16.5.1 Wannier-Stark Ladders 472
16.5.2 de Haas-van Alphen Effect 473
16.5.3 Experimental Measurements of Fermi Surfaces 474
Problems 477
References 480
17 Transport Phenomena and Fermi Liquid Theory 4S3
17.1 Introduction 483
17.2 Boltzmann Equation 483
17.2.1 Boltzmann Equation 485
17.2.2 Including Anomalous Velocity 486
17.2.3 Relaxation Time Approximation 487
17.2.4 Relation to Rate of Production of Entropy 489
17.3 Transport Symmetries 490
17.3.1 Onsager Relations 491
17.4 Thermoelectric Phenomena 492
17.4.1 Electrical Current 492
17.4.2 Effective Mass and Holes 494
17.4.3 Mixed Thermal and Electrical Gradients 495
17.4.4 Wiedemann-Franz Law 496
17.4.5 Thermopower—Seebeck Effect 497
17.4.6 Peltier Effect 498
17.4.7 Thomson Effect 498
17.4.8 Hall Effect 500
17.4.9 Magnetoresistance 502
17.4.10 Anomalous Hall Effect 503
17.5 Fermi Liquid Theory 504
17.5.1 Basic Ideas 504
17.5.2 Statistical Mechanics of Quasi-Particles 506
17.5.3 Effective Mass 508
17.5.4 Specific Heat 510
17.5.5 Fermi Liquid Parameters 511
17.5.6 Traveling Waves 512
17.5.7 Comparison with Experiment in 3He 515
Problems 516
References 520
18 Microscopic Theories of Conduction 523
18.1 Introduction 523
18.2 Weak Scattering Theory of Conductivity 523
18.2.1 Genera] Formula for Relaxation Time 523
18.2.2 Matthiessen’s Rule 528
18.2.3 Fluctuations 529
18.3 Metal-Insulator Transitions in Disordered Solids 530
18.3.1 Impurities and Disorder 530
18.3.2 Non-Compensated Impurities and the Mott Transition . . 531
18.4 Compensated Impurity Scattering and Green’s Functions 534
18.4.1 Tight-Binding Models of Disordered Solids 534
18.4.2 Green’s Functions 536
18.4.3 Single Impurity 539
18.4.4 Coherent Potential Approximation 541
18.5 Localization 542
18.5.1 Exact Results in One Dimension 544
18.5.2 Scaling Theory of Localization 547
18.5.3 Comparison with Experiment 551
18.6 Luttinger Liquids 553
18.6.1 Density of States 557
Problems 560
References 564
19 Electronics 567
19.1 Introduction 567
19.2 Metal Interfaces 568
19.2.1 Work Functions 569
19.2.2 Schottky Barrier 570
19.2.3 Contact Potentials 572
19.3 Semiconductors 574
19.3.1 Pure Semiconductors 575
19.3.2 Semiconductor in Equilibrium 578
19.3.3 Intrinsic Semiconductor 580
19.3.4 Extrinsic Semiconductor 581
19.4 Diodes and Transistors 583
19.4.1 Surface States 586
19.4.2 Semiconductor Junctions 587
19.4.3 Boltzmann Equation for Semiconductors 590
19.4.4 Detailed Theory of Rectification 592
19.4.5 Transistor 595
19.5 Inversion Layers 598
19.5.1 Heterostructures 598
f 9,5.2 Quantum Point Contact 600
19.5.3 Quantum Dot 603
Problems 606
References 607
V OPTICAL PROPERTIES 609
20 Phenomenological Theory 611
20.1 Introduction 611
20.2 Maxwell’s Equations 613
20.2.1 Traveling Waves 615
20.2.2 Mechanical Oscillators as Dielectric Function 616
20.3 Kramers-Kronig Relations 618
20.3.1 Application to Optical Experiments 620
20.4 The Kubo-Greenwood Formula 623
20.4.1 Bom Approximation 623
20.4.2 Susceptibility 627
20.4.3 Many-Body Green Functions 628
Problems 628
References 631
21 Optical Properties of Semiconductors 633
21.1 Introduction 633
21.2 Cyclotron Resonance 633
21.2.1 Electron Energy Surfaces 636
21.3 Semiconductor Band Gaps 638
21.3.1 Direct Transitions 638
21.3.2 Indirect Transitions 639
21.4 Excitons 641
21.4.1 Mott-Wannier Excitons 641
21.4.2 Frenkel Excitons 644
21.4.3 Electron-Hole Liquid 645
21.5 Optoelectronics 645
21.5.1 SolarCells 645
21.5.2 Lasers 646
Problems 652
References 656
22 Optical Properties of Insulators 659
22.1 Introduction 659
22.2 Polarization 659
22.2.1 Ferroelectrics 659
22.2.2 Berry phase theory of polarization 661
22.2.3 Clausius-Mossotti Relation 661
22.3 Optical Modes in Ionic Crystals 664
22.3.1 Polaritons 666
22.3.2 Polarons 669
22.3.3 Experimental Observations of Polarons 674
22.4 Point Defects and Color Centers 674
22.4.1 Vacancies 675
22.4.2 F Centers 676
22.4.3 Electron Spin Resonance and Electron Nuclear Double Res-onance 677
22.4.4 Other Centers 679
22.4.5 Franck-Condon Effect 679
22.4.6 Urbach Tails 683
Problems 684
References 686
23 Optical Properties of Metals and Inelastic Scattering 689
23.1 Introduction 689
23.1.1 Plasma Frequency 689
23.2 Metals at Low Frequencies 692
23.2.1 Anomalous Skin Effect 694
23.3 Plasmons 695
23.3.1 Experimental Observation of Plasmons 696
23.4 Interband Transitions 698
23.5 Brillouin and Raman Scattering 701
23.5.1 Brillouin Scattering 702
23.5.2 Raman Scattering 703
23.5.3 Inelastic X-Ray Scattering 703
23.6 Photoemission 703
23.6.1 Measurement of Work Functions 703
23.6.2 Angle-Resolved Photoemission 706
23.6.3 Core-Level Photoemission and Charge-Transfer Insulators 710
Problems 716
References 719
VI MAGNETISM 721
24 Classical Theories of Magnetism and Ordering 723
24.1 Introduction 723
24.2 Three Views of Magnetism 723
24.2.1 From Magnetic Moments 723
24.2.2 From Conductivity 724
24.2.3 From a Free Energy 725
24.3 Magnetic Dipole Moments 727
24.3.1 Spontaneous Magnetization of Ferromagnets 730
24.3.2 Ferrimagnets 731
24.3.3 Antiferromagnets 733
24.4 Mean Field Theory and the Ising Model 734
24.4.1 Domains 736
24.4.2 Hysteresis 739
24.5 Other Order-Disorder Transitions 740
24.5.1 Alloy Superlattices 740
24.5.2 Spin Glasses 743
24.6 Critical Phenomena 743
24.6.1 Landau Free Energy 744
24.6.2 Scaling Theory 750
Problems 754
References 757
25 Magnetism of Ions and Electrons 759
25.1 Introduction 759
25.2 Atomic Magnetism 761
25.2.1 Hund’s Rules 762
25.2.2 Curie’s Law 766
25.3 Magnetism of the Free-El ectron Gas 769
25.3.1 Pauli Paramagnetism 770
25.3.2 Landau Diamagnetism 771
25.3.3 Aharonov-Bohm Effect 774
25.4 Tightly Bound Electrons in Magnetic Fields Ill
25.5 Quantum Hall Effect 780
25.5.1 Integer Quantum Hall Effect 780
25.5.2 Fractional Quantum Hall Effect 785
Problems 791
References 794
26 Quantum Mechanics of Interacting Magnetic Moments 797
26.1 Introduction 797
26.2 Origin of Ferromagnetism 797
26.2.1 Heitler-London Calculation 797
26.2.2 Spin Hamiltonian 802
26.3 Heisenberg Model 802
26.3.1 Indirect Exchange and Superexchange 804
26.3.2 Ground State 805
26.3.3 Spin Waves 805
26.3.4 Spin Waves in Antiferromagnets 808
26.3.5 Comparison with Experiment 811
26.4 Ferromagnetism in Transition Metals 811
26.4.1 Stoner Model 811
26.4.2 Calculations Within Band Theory 813
26.5 Spintronics 815
26.5.1 Giant Magnetoresistance 815
26.5.2 Spin Torque 816
26.6 Kondo Effect 819
26.6.1 Scaling Theory 824
26.7 Hubbard Model 828
26.7.1 Mean-Field Solution 829
Problems 832
References 835
27 Superconductivity 839
27.1 Introduction 839
27.2 Phenomenology of Superconductivity 840
27.2.1 Phenomenological Free Energy 841
27.2.2 Thermodynamics of Superconductors 843
27.2.3 Landau-Ginzburg Free Energy 844
27.2.4 Type I and Type II Superconductors 845
27.2.5 Flux Quantization 850
27.2.6 The Josephson Effect 852
27.2.7 Circuits with Josephson Junction Elements 854
27.2.8 SQUIDS 855
27.2.9 Origin of Josephson’s Equations 856
27.3 Microscopic Theory of Superconductivity 858
27.3.1 Electron-Ion Interaction 859
27.3.2 Instability of the Normal State: Cooper Problem 863
27.3.3 Self-Consistent Ground State 865
27.3.4 Thermodynamics of Superconductors 869
27.3.5 Superconductor in External Magnetic Field 873
27.3.6 Derivation of Meissner Effect 876
27.3.7 Comparison with Experiment 879
27.3.8 High-Temperature Superconductors 881
Problems 888
References 890
APPENDICES 895
A Lattice Sums and Fourier Transforms 897
A. l One-Dimensional Sum 897
A. 2 Area Under Peaks 897
A. 3 Three-Dimensional Sum 898
A. 4 Discrete Case 899
A.5 Convolution 900
A. 6 Using the Fast Fourier Transform 900
References 902
B Variational Techniques 903
B. l Functionals and Functional Derivatives 903
B. 2 Time-Independent Schrodinger Equation 904
B. 3 Time-Dependent Schrodinger Equation 905
B. 4 Method of Steepest Descent 906
References 906
C Second Quantization 907
C. l Rules 907
C. 1.1 States 907
C. l.2 Operators 907
C. l.3 Hamiltonians 908
C.2 Derivations 909
C.2.1 Bosons 909
C.2.2 Fermions 910
Index
English
"In this text intended for a one-year graduate course, Marder (physics, U. of Texas, Austin) comments in the preface that this second edition incorporates the many thousands of updates and corrections suggested by readers of the first edition published in 1999, and he even gives credit to several individuals who found the most errors. He also points out that "the entire discipline of condensed matter is roughly ten percent older than when the first edition was written, so adding some new topics seemed appropriate." These new topics - chosen because of increasing recognition of their importance - include graphene and nanotubes, Berry phases, Luttinger liquids, diffusion, dynamic light scattering, and spin torques. The text also gives more leisurely attention to the topics of primary interest to most students: electron and phonon bond structures." (Reference and Research Book News, February 2011)
