DISLOCATION DYNAMICS AND
MECHANICAL PROPERTIES
OF CRYSTALS

E. NADGORNY

CONTENTS

Foreword										vii
List of Tables										 ix
Notation										 xi
1.   INTRODUCTION									  1
     1.1. Aims and Topics of the Treatise						  1
     1.2. Historical Background								  3
2.  THE FUNDAMENTALS OF DISLOCATION DYNAMICS						 11
     2.1. The Glide Resistance and Dislocation Shape					 11
	2.1.1.  Forces on a dislocation							 12
	2.1.2.  Drag resistance								 19
	2.1.3.  Lattice resistance and the kink-mode of dislocation motion		 21
	2.1.4.  Obstacle resistance and the bowing-mode of dislocation motion		 24
     2.2. Thermodynamics and Dislocation Dynamics					 36
	2.1.1.  General consideration							 38
	2.2.2.  The rate of activation over local obstacles				 41
	2.2.3.  The activation free enthalpy for surmounting obstacles			 50
	2.2.4.  The rate of activation over linear barriers				 54
3.  THERMALLY ACTIVATED DISLOCATION VELOCITY IN BOWING-MODE CRYSTALS			 64
     3.1. Two -Dimensional Thermally Activated Dislocation Glide through
		Randomly Distributed Obstacles						 66
	3.1.1.  Assumptions and approximations						 67
	3.1.2.  Thermally activated velocity						 72
     3.2. Statistics of the Thermally Activated Motion					 75
	3.2.1.  Statistical characteristics of moving dislocations			 75
	3.2.2.  Stationary distributions and dislocation velocity			 84
     3.3. Computer Simulation of Dislocation Motion					 90
	3.3.1.  Simulation procedures and algorithms					 91
	3.3.2.  Dislocation motion features revealed by computer simulation		 96
	3.3.3.  The dislocation velocity: computer simulation and experimental data	114
     3.4. Special Effects in the Dislocation Velocity					131
	3.4.1.  Dislocation viscosity and inertial contributions			132
	3.4.1.  Obstacle diffusion and dislocation drag					143
4.  THERMALLY ACTIVATED DISLOCATION VELOCITY IN KINK-MODE CRYSTALS			148
     4.1. Dislocation Motion in Ideal Kink-Mode Crystals				150
	4.1.1.  Thermally activated velocity						150
	4.1.2.  Experimental data and the comparison with bowing-mode crystals		158
     4.2. The mixed Kink-Obstacle Mode of Dislocation Motion				184
	4.2.1.  A collision kink regime							185
	4.2.2.  A collision-less kink regime with variations in dislocation shape	196
     4.3. Influence of Fine and Electronic Structure of Dislocations			206
	4.3.1.  Dissociation and fine structure of moving dislocations			206
	4.3.2.  The dislocation charge and electronic excitation			211
5.  VISCOUS MOTION OF DISLOCATIONS							221
     5.1. Dislocation Motion Features in the High-Velocity Region			223
     5.2. Phonon Drag									232
	5.2.1.  Abharmonic phonon drag							233
	5.2.2.  Other phonon contributions						244
     5.3. Electron Drag									251
	5.3.1  Electronic drag in normal metals						252
	5.3.2.  Drag in Superconductors							260
     5.4. Magnon Drag									264
     5.5. Extrinsic Dissipative Mechanisms						272
     5.6. Kink Drag									274
6.  EXPERIMENTAL RESULTS								277
     6.1. Techniques									278
	6.1.1.  Samples									279
	6.1.2.  Methods for revealing the dislocation motion				280
		6.1.2.1.  Etch pits							281
		6.1.2.2.  X - Ray topography						291
		6.1.2.3.  Transmission electron microscopy				293
		6.1.2.4.  Observation of slip lines in motion				298
	6.1.3.  Introduction of movable dislocations into the crystal			303
	6.1.4.  Methods of loading							305
	6.1.5.  Alternative methods of velocity measurement				306
	6.1.6.  Features and precautions in velocity measurement			314
     6.2. Bowing-Mode Crystals								317
	6.2.1.  Metals									317
		6.2.1.3.  FCC metals							318
		6.2.1.2.  BCC metals							321
		6.2.1.3.  HCP metals and ordered alloys					332
	6.2.2.  Ionic Crystals								336
     6.3. Kink-Mode Crystals								370
	6.3.1.  Elemental semiconductors						371
	6.3.2.  Compound semiconductors							386
     6.4. High Velocity Region								400
     6.5. Externally-Induced Effects							407
	6.5.1.  Influence of irradiation						408
	6.5.2.  Excitation effects							422
	6.5.3.  Hydrostatic pressure influence						428
7.  MOTION OF SLIP LINES								434
     7.1. Features of Array Motion and Smeared-out Obstacle Models of Arrays		435
     7.2. Discrete Obstacle Model							448
     7.3. Continuum Approximation							468
8.  Plastic Deformation and Dislocation Dynamics					470
     8.1. Plastic Deformation as a Dynamic Dislocation Process				471
	8.1.1.  Strain rate equations							472
	8.1.2.  The concept of internal stresses					477
	8.1.3.  Stress-strain curves							480
     8.2. Initial Stages of Plastic Deformation						487
	8.2.1.  Nucleation and motion of dislocations					487
	8.2.2.  Yield point and easy glide						497
     8.3. Work Hardening								502
	8.3.1  Stage I and dipole hardening						503
	8.3.2.  Stage II and forest dislocations					507
     8.4. Conclusions									512
APPENDICES										513
REFERENCES										517
SUBJECT INDEX										531