ADDISON-WESLEY METALLURGY SERIES MORRIS COHEN, Cidlity Guy Consulting Editor ELEMENTS OF X-RAY DIFFRACTION ELEMENTS OF PHYSICAL METALLURGY Norton ELEMENTS OF CERAMICS Schuhmann METALLURGICAL ENGINEERING VOL Wagner I: ENGINEERING PRINCIPLES THERMODYNAMICS OF ALLOYS ELEMENTS OF X-RAY DIFFRACTION by B D CULLITY Associate Professor of Metallurgy University of Notre Dame ADDISON-WESLEY PUBLISHING COMPANY, READING, MASSACHUSETTS INC Copyright 1956 ADD1SON-WESLEY PUBLISHING COMPANY, Inc Printed ni the United States of America ALL RIGHTS RESERVED MAY NOT BE THIS BOOK, OR PARTS THERE- ANY FORM WITHOUT WRITTEN PERMISSION OF THE PUBLISHERS OF, REI'RODl CED IN Library of Congress Catalog No 56-10137 PREFACE X-ray diffraction is a tool for the investigation of the fine structure of its beginnings in von Laue's discovery in 1912 This technique had matter that crystals diffract x-rays, the manner of the diffraction revealing the structure of the crystal At first, x-ray diffraction was used only for the determination of crystal structure Later on, however, other uses were developed, and today the method is applied, not only to structure determination, but to such diverse problems as chemical analysis and stress measurement, to the study of phase equilibria and the measurement of particle size, to the determination of the orientation of one crystal or the ensemble of orientations in a polycrystalline aggregate The purpose of this book is to acquaint the reader who has no previous knowledge of the subject with the theory of x-ray diffraction, the experi- mental methods involved, and the main applications Because the author is a metallurgist, the majority of these applications are described in terms of metals and method required for the examinatiorrof nonmetallic materials, is alloys However, little or no modification of experimental inasmuch as the physical principles involved not depend on the material investigated This book should therefore be useful to metallurgists, chemists, physicists, ceramists, mineralogists, etc., namely, to all who use x-ray diffraction purely as a laboratory tool for the sort of problems already mentioned Members of this group, unlike x-ray crystallographers, are not normally concerned with the determination of complex crystal structures For this reason the rotating-crystal method and space-group theory, the two chief tools in the solution of such structures, are described only briefly a book of principles and methods intended for the student, and not a reference book for the advanced research worker Thus no metalThis is data are given beyond those necessary to illustrate the diffraction For example, the theory and practice of determining orientation are treated in detail, but the reasons for preferred preferred lurgical methods involved orientation, the conditions affecting its development, tations found in specific metals and is orien- alloys are not described, because these topics are adequately covered in existing books tion is stressed rather than metallurgy The book and actual In short, x-ray diffrac- divided into three main parts: fundamentals, experimental methods, and applications The subject of crystal structure is approached through, and based on, the concept of the point lattice (Bravais lattice), because the point lattice of a substance is so closely related to its diffrac- PREFACE VI The entire book is written in terms of the Bragg law and can be read without any knowledge of the reciprocal lattice (However, a brief treatment of reciprocal-lattice theory is given in an appendix for those who wish to pursue the subject further.) The methods of calculating the intensities of diffracted beams are introduced early in the book and used tion pattern throughout Since a rigorous derivation of many of the equations for difis too lengthy and complex a matter for a book of this fracted intensity kind, I have preferred a semiquantitative approach which, although it does not furnish a rigorous proof of the final result, at least makes it physically reasonable This preference is based on my conviction that it is better for a student to grasp the physical reality behind a mathematical equation than to be able to glibly reproduce an involved mathematical derivation of whose physical meaning he is only dimly aware Chapters on chemical analysis by diffraction and fluorescence have been included because of the present industrial importance of these analytical In Chapter the diffractometer, the newest instrument for dif- methods fraction experiments, is described in some detail here the material on the ; various kinds of counters and their associated circuits should be useful, not only to those engaged in diffraction work, but also to those working with radioactive tracers or similar substances who wish to know how their measuring instruments operate Each chapter includes a set of problems Many of these have been chosen to amplify and extend particular topics discussed in the text, and as such they form an integral part of the book Chapter 18 contains an annotated books suitable for further study The reader should become familiar with at least a few of these, as he progresses through this book, in order that he may know where to turn for list of additional information Like any author of a technical book, to two of I am greatly indebted to previous acknowledge my gratitude my former teachers at the Massachusetts Institute of Technology, writers on this and allied subjects I must also Warren and Professor John T Norton: they will find many own lectures in these pages Professor Warren has kindly allowed me to use many problems of his devising, and the advice and encouragement of Professor Norton has been invaluable My colleague at Notre Dame, Professor G C Kuczynski, has read the entire book as it was written, and his constructive criticisms have been most helpful I would also like to thank the following, each of whom has read one or more chapters and offered valuable suggestions: Paul A Beck, Herbert Friedman, Professor B E an echo of their Hsu, Lawrence Lee, Walter C Miller, William Parrish, Howard Pickett, and Bernard Waldman I am also indebted to C G Dunn for S S the loan of illustrative material and to many graduate students, August PREFACE Vll in particular, who have helped with the preparation of diffraction patterns Finally but not perfunctorily, I wish to thank Miss Rose Kunkle for her patience and diligence in preparing the typed manuscript Freda B D CULLITY Notre Dame, Indiana March, 1956 CONTENTS FUNDAMENTALS CHAPTER PROPERTIES OF X-RAYS 1-1 Introduction 1-2 1-3 Electromagnetic radiation The continuous spectrum 1 1-4 The 1-5 Absorption 1-6 Filters 16 1-7 Production of x-rays Detection of x-rays 17 -8 characteristic spectrum 10 23 Safety precautions CHAPTER THE GEOMETRY OF CRYSTALS ^2-1 Lattices 29 Introduction J2-2 2-3 ^2-4 2-5 2-6 25 29 29 Crystal systems 30 Symmetry 34 36 Primitive and nonprimitive cells Lattice directions and planes * J Crystal structure 2-7 2-8 Atom 2-9 42 Crystal shape 2-10 37 Twinned crystals The stereographic projection 2-11 sizes 52 and coordination 54 55 CHAPTER DIFFRACTION 3-1 Diffraction THE DIRECTIONS OF DIFFRACTED BEAMS Introduction 3-2 I: 60 78 78 79 f ' ^3-3 3-4 3-5 The Bragg law 84 * 85 X-ray spectroscopy Diffraction directions 88 - methods 3-6 Diffraction 3-7 Diffraction under nonideal conditions CHAPTER DIFFRACTION II: THE INTENSITIES OF DIFFRACTED BEAMS 104 104 4-1 Introduction 4-2 by an electrons Scattering by an atom / Scattering by a unit cell */ 4-3 4-4 89 96 Scattering >, 105 108 Ill CONTENTS 4-5 Some 4-6 Structure-factor calculations 4-7 Application to powder Multiplicity factor 4-8 4-9 1-10 useful relations 118 ^ method 118 123 ' 124 124 Lorentz factor Absorption factor 129 130 factor 4-11 Temperature 4-12 4-13 Intensities of powder pattern lines Examples of intensity calculations Measurement of x-ray intensity 4-14 132 132 136 EXPERIMENTAL METHODS LPTER 138 LAUE PHOTOGRAPHS 5-1 Cameras 5-4 Collimators 5-5 The shapes 138 Introduction 5-2 5-3 143 Specimen holders kPTER of Laue spots POWDER PHOTOGRAPHS 146 149 149 Introduction 6-2 6-3 6-4 Debye-Scherrer method 6-7 6-8 6-9 144 6-1 6-5 6-6 138 Specimen preparation Film loading Cameras for high and low temperatures Focusing cameras Seemann-Bohlin camera Back-reflection focusing cameras Background radiation Crystal monochromators Measurement of line position Measurement of line intensity VPTER 156 157 160 163 165 166 168 173 173 177 DlFFRACTOMETER MEASUREMENTS 7-1 Introduction 7-2 General features 7-3 X-ray optics 7-4 Intensity calculations Proportional counters 7-7 156 6-11 7-5 7-6 154 Pinhole photographs 6-10 6-13 6-14 153 Choice of radiation 6-12 149 Geiger counters Scintillation counters 7-8 7-9 Sealers 7-10 Use monochromators 177 184 .193 188 177 - Ratemeters of 190 - 201 202 - 206 211 CONTENTS XI APPLICATIONS CHAPTER ORIENTATION OF SINGLE CRYSTALS Introduction 8-2 8-4 Laue method Transmission Laue method Diffractometer method 8-5 Setting a crystal in a required orientation 8-6 8-7 Effect of plastic deformation Relative orientation of twinned crystals 8-8 Relative orientation of precipitate and matrix 8-3 CHAPTER 9-1 215 8-1 Back-reflection ' 215 .215 THE STRUCTURE OF POLYCRYSTALLINE AGGREGATES Introduction 229 237 240 242 250 256 259 259 CRYSTAL SIZE 9-2 Grain 9-3 259 Particle size size CRYSTAL PERFECTION 9-4 Crystal perfection 9-5 Depth of x-ray penetration CRYSTAL ORIENTATION General Texture of wire and rod (photographic method) Texture of sheet (photographic method) 9-9 Texture of sheet (diffractometer method) 9-10 Summary CHAPTER 10 THE DETERMINATION OF CRYSTAL STRUCTURE 10-1 Introduction 10-2 Preliminary treatment of data Indexing patterns of cubic crystals 10-3 CHAPTER effect of cell distortion on the powder pattern Determination of the number of atoms in a unit cell Determination of atom positions Example of structure determination 11 Introduction Debye-Scherrer cameras Back-reflection focusing cameras 11-4 Pinhole cameras 11-5 Diffractometers 11-6 Method of least squares 297 297 299 304 311 314 316 PRECISE PARAMETER MEASUREMENTS 11-2 11-1 1-3 301 The 10-9 285 295 10-6 10-8 10-5 10-7 269 276 280 Indexing patterns of noncubic crystals (graphical methods) Indexing patterns of noncubic crystals (analytical methods) 10-4 263 272 9-7 9-8 9-6 261 317 320 324 324 326 333 333 334 335 ANSWERS TO SELECTED PROBLEMS CHAPTER X lOlrtsec1-7 cmVgm 1-1 4.22 1-5 1-11 1.54A 3.28 to X 2.79 , 1-14 0.000539 10~ in., A on section show 3-1 8.929 gm/cm 27S, 48E; (6) (r) ma 20 E 0.11 10 for 64/r for (h 42N, 26E; 45 80 0.43 mixed + k + F2 = indices; /) for (h an even multiple 1.76 of 2; + + k F~ - I) an odd multiple + for (h 32/r k 4-5 + 2k 3n 3n 3n 3n 3n 3n db + } (as 1, 3, 5, 8p(as8, 10,24 4(2/> 2(2p 8p 4(2p 3nl 3n db 3nl F2 / 2p + + + 1) ) (as 4, 12, 20, 2S 1) (as 2, (5, 10, 14 (as 1, 7, 9, 15, 17 1) d= + 4(fZn ) - 4(fZn ) ) 4(/Zn ) 3(/Zn (as 3, 5, 11, 13, 19, 21 ) 3(fZn /s) + /s + /s + fs + ) fs) 2 2 (/Zn-f/s) 8;; 4(2p 2(2p + + 0.707 0.31 0.14 0.22 0.43 CHAPTER = SB 750 500 250 F2 = strain 2-19 1000A h 1-18 B t 2-11 Shear 61 39S, 3-3 63.5 3-5 F* 10~ erg this CHAPTER = X 1-9 8980 volts 1-16 1000 watts, 0.55 will (T210) 20S, 30W; 45W;42S,63E 4-3 1.29 , 2-14 (a) 19S, 1&* sec' 10~ cm" X 3.88 CHAPTER 2-7 X 1.95 erg; cm /gm, (a) 30.2 - (/2n 1) (/zn l) n and p are any integers, including zero 4-8 Line hkl Gale Int 10.0 200 17 4-10 Ill and 200 110 211 3.3 220 1.1 The ratio is 2100 to 506 fs) +/s ) + I) of 2; odd 507 ANSWERS TO SELECTED PROBLEMS CHAPTER cm 6-1 0.67 (6) third for (111); 0.77 cm 5-3 (a) Third, fourth for (200) and fifth; and fourth CHAPTER 6-1 38 minutes AS 6-3 6-5 (a) 144; (b) 67; (c) 12.3 cm A20 6-7 1.58 to CHAPTER 7-4 (a) 1.14 (Co) to 7-1 0.44 (Ni); (6) 10.5 CHAPTER 16S, 64W CHAPTER 8-3 26 about beam axis, clockfrom crystal to x-ray source; about EW, clockwise, looking from 8-6 Habit about NS, counterclockwise, looking from N to S 69E; 60S, 46W 26N, 14W; 14S, 100} 8N, 23E; 74S, 90E; 8-1 wise, looking E to plane W; is j 9-1 45,000 psi listed in the order in 9-3 Diffractometer 9-5 (6) 0.11, 0.18, 0.28, and 0.43, which the incident beam traverses the layers CHAPTER 10 10-1 Ill, 200, 220, 311, 222, 400, 331, 420, 422, and 511 (333); a = 4.05A 10-6 Ill, 220, 311, 400, 331, 422, 511 (333), 10-4 100, 002, 101, 102, 110 10-8 100, 002, 101, 102, 110, 103, 440 Diamond cubic; a = 5.4A; silicon 200, 112 Hexagonal close-packed; a = 3.2A, CHAPTER 11-1 =bl.7C 11-3 4.997A 11-5 c = 11 Near CHAPTER 12 CHAPTER 12-1 13 0.0002A 13-2 0.0015 5.2A; magnesium = 30 ANSWERS TO SELECTED PROBLEMS 508 CHAPTER 14-1 BaS 14-3 Mixture of 14 Ni and NiO 14-5 12.5 volume percent austenite CHAPTER 16-1 (a) quate, A20 = 1.75 NaCi inadequate, (mica), 1.20 (6) (LiF), 0.81 A20 =1.41 Mica and LiF adequate, NaCl inadequate CHAPTER 16-1 2.20 mg/cm 16-3 0.00147 (NaCl) Mica and LiF ade- (LiF), 0.75 16-3 0.0020 in (mica), 16 in CHAPTER 17-1 dblSOOpsi 15 17 1.05 (NaCl) INDEX Absorption of x-rays, 10 Absorption analysis (see Balanced filters, 211 BARRETT, CHARLES Chemical anal- S., 454 Absorption coefficients, table, 466 10, 11 Body-centered cubic structure, 43 BRAGG, W H., 8, 79, 177 Absorption edges, 464 BRAGG, W Bragg law, ysis by absorption) table, L., 79, 82, 177, 297, 82, 456 84 BRAVAIS, M A., 31 Bravais lattice, 31 Absorption factor, Debye-Scherrer, 129 diffractometer, 189 for reflection from flat plate, 189 table, Broad for transmission through flat plate, 31 lines, measurement of, 447 BUERGER, M J., 456 BUNN, C W., 309 287 ALEXANDER, LEROY E., 455 ALLISON, SAMUEL K., 456 Bunn Annealing texture, 273 Annealing twins, 55 Applied Research Laboratories, 410, 418 Asterism, 246 chart, 309 Caesium chloride structure, 47 Calibration method (for lattice parameters), 342 on powder pat- thermal, 505 ASP, E T., 285 Cell distortion, effect A.S.T.M., diffraction data cards, 379 grain size number, 260 Characteristic radiation, tern, wavelength table, 464 Chemical analysis by absorption, 423 absorption-edge method, 424 direct method, monochromatic, 427 polychromatic, 429 Chemical analysis by diffraction, 378 Atomic scattering factor, 109 change near an absorption edge, 373 table, 474 Atomic weights, Atom AuBe sizes, table, 481 52 qualitative, 379 structure, 49 AuCu, ordering in, AuCus, ordering in, quantitative, 388 direct comparison method, 391 370 363 internal standard method, 396 Austenite determination, 391 Automatic spectrometers, 417 Background radiation, powder method, 166 Back-reflection focusing camera, 160 errors, 333 Back-reflection Back-reflection Laue camera, 140 Laue method, 90 for crystal orientation, 215 Back-reflection pinhole camera, 163 errors, 333 314 single line method, 389 Chemical analysis by fluorescence, 402 automatic, 417 counters, 414 intensity and resolution, 411 nondispersive, 419 qualitative, 414 quantitative, 415 spectrometers, 407 wavelength range, 406 Chemical analysis by parameter meas- urement, 388 semifocusing, 443 509 INDEX 510 Debye-Scherrer method (continued) film loading, 154 Choice of radiation, 165 CLARK, GEORGE L., 455 intensity equation, 132 Clustering, 375 specimen preparation, 153 DECKER, B F., 285 Defect structures, 317, 353 Coating thickness, 421 COCHRAN, W., 456 COHEN, M U., 338 Cohen's method, 338 for cubic substances, 339 for noncubic substances, 342 Coherent scattering, 105, 111 Cold work, 263 modified radiation, 108, 111 Conservation of diffracted energy, 131 Continuous spectrum, COOLIDGE, W D., 17 Coordination number, 53 COSTER, D., 404 Ratemeter) use with diffractometer, 211 Crystal perfection, 100, 263 Crystal rotation during slip, 243 Crystal setting, 240 Crystal shape, 54 table, 485 Crystal-structure determination, 297 example of, 320 Crystal systems, 30 table, 334 general features, 177 intensity calculations, 188, 389 optics, 184 specimen preparation, 182 use in determining crystal orientation, 237 Diffusion studies, by absorption measurements, 428 of elements, table, 482 CsCl 31 Disappearing-phase method, 354 Doublet, Electromagnetic radiation, Electron diffraction, 272, 486 Energy level calculations, 13 Errors, back-reflection focusing method, structure, 47 DAVEY, W P., 305 DEBYE, P., 149 333 Debye-Scherrer method, 326 diffractometer method, 334 pinhole method, 333 Debye-Scherrer camera, 149 high-temperature, 156 in ratemeter CuZn, ordering in, Laue method, 502 powder method, 500 rotating-crystal method, 499 Diffraction lines, extraneous, 299 Diffraction methods, 89 by parameter measurements, 388 Crystal structure, 42 compounds, 131 of, Diffraction and reciprocal lattice, errors, (see Crystal monochromators, reflection, 168 transmission, 171 of Diffracted energy, conservation absorption factor, 189 201 Counting-rate meter 23 structure, 48 Diffractometer, 96 Counters, Geiger, 193 proportional, 190 scintillation, Diamond Diffraction, 79 107 effect, of x-ray penetration, 269 Detection, of superlattice lines, 372 Depth of x-rays, Collimators, 144, 152 Complex exponential functions, 115 COMPTON, ARTHUR H., 107, 456 Compton Compton Deformation texture, 273 Deformation twins, 58 Densities, table, 466 369 Debye-Scherrer method, 94 errors, 326 random, 332 measurements, 208 measurements, 204 systematic, 332 in sealer INDEX 511 EWALD, P P., 490 Ewatd construction, 498 HENRY, N F M., 456 HEVESY, GEORQ VON, 404 Excitation voltage, Extinction, 399 Hexagonal close-packed structure, 43 transformaHexagonal-rhombohedral tion, 462 back-reflecfunctions, tion focusing method, 333 Extrapolation Debye-Scherrer method, 329, 330 diffractometer method, 334 pinhole method, 330 High-temperature cameras, 156 HULL, A W., 149, 305 Hull-Davey chart, 305 IBM Face-centered cubic structure, 43 Ferrite, 51 FeSi structure, 49 Fiber axis, 276 Photographic film) 16 (see Filters, balanced (Ross), 211 table, 17 Fluorescent analysis ysis by (see of planes, 38 measurement with Chemical anal- fluorescence) Focal spot, 22 Focusing cameras, 156 37, 41 Fourier Indices, of directions, 37 Integrated intensity, 124, 132, 175 Fluorescent radiation, 12, 111 Fluorescent screens, 23 Form, 386 noncubic crystals, analytical, 311 graphical, 304 Fiber texture, 276 Film diffraction data cards, Incoherent scattering, 108, 111 Indexing powder patterns, cubic crystals, 301 sealer, 205 Integrating camera, 165, 294 Intensifying screens, 142 Intensities of powder pattern lines, in Debye-Scherrer camera, 132 in diffractometer, 188, 389 Intensity calculations, CdTe, 320 copper, 133 series, 319 ZnS (zinc blende), 134 FOURNBT, GERARD, 456 FRIEDMAN, H., 177 Fundamental lines, 363 Intensity measurements, photographic, Geiger counter, 193, 414 counting losses, 197 with scintillation counter, 201 Internal stress (see Residual stress*) efficiency, 200 quenching, 199 GEISLER, A H., 293 General Electric Co., 179, 409 Goniometer, 143 Grain growth, 266 Grain 259 GRENINGER, A B., 217 Greninger chart, 218 173 with Geiger counter, 193 with proportional counter, 190 Interplanar angles, cubic system, 72 equations, 460 Interstitial solid solutions, 51, 351 lonization chamber, 191 lonization devices, 25 size, GUINIER, AN&ais, 455, 456 Habit plane, 256 HANAWALT, J JAMES, ty W., 456 Keysort diffraction data cards, 385 KLUG, HAROLD P., 455 kX u" t, 87 ; D., 379 Hanawalt method, 379 HARKER, D., 285 Lattice, 29 Lattice parameters, 30 table, INDEX 512 Lattice-parameter measurements, 324 with back-reflection focusing camera, 333 Multiple excitation (in fluorescence), 416 Multiplicity factor, 124 with Debye-Scherrer camera, 326 with diffractometer, 334 table, NaCl with pinhole camera, 333 LAUE, M VON, 78, 367, 457 Laue cameras, back-reflection, 140 477 structure, 47 National Bureau of Standards, 386 Neutron diffraction, 375, 486, specimen holders, 143 transmission, 138 487 Nondispersive analysis, 419 Nonprimitive cells, 33, 36 North America Philips Co., Laue equations, 497 \f Laue method, 89, 502 back-reflection, 90, 215 Optimum specimen diffraction spot shape, 146 experimental technique, of, 417 thickness, 164 Order, long-range, 363 parameter, 366 38 transmission, 89, 229 Least squares, method 179, short-range, 375 Order-disorder transformations, 363 335 Leonhardt chart, 231 in AuCu, 370 Limiting sphere, 501 in AuCu Line broadening, due to fine particle size, 97-99, 262 in CuZn, 369 , 363 Ordered solid solutions, 52, 363 due to nonuniform strain, 264 LIPSON, H., 456 Long-range order, 363 Long-range order parameter, 366 LONSDALE, KATHLEEN, 455 Orientation of single crystals, 215 Lorentz factor, 124 Parametric method, 356 Particle size, 261 by back-reflection Laue method, 215 by diffractometer method, 237 by transmission Laue method, 229 Lorentz-polarization factor, 128 table, 478 Particle-size broadening, 97-99, when monochromator is used, 172 Low-temperature cameras, 156 262 PEISER, H S., 455 Penetration depth (x-rays), 269 Phase diagrams, determination of, 345 Macrostrain, 431 Photoelectrons, 12, 111 Macrostress, 264, 447 Photographic Matrix absorption (in fluorescence), 415 Microabsorption, 399 Photographic measurement of intensity, 173 Microphotometer, 174 Photomultiplier, 201 Microstrain, 431 Physical constants, table, 480 Pinhole method, cameras, 163 Microstress, 264, 447 film, 24 MILLER, W H., 38 conclusions from film inspection, 294 Miller-Bravais indices, 40 Miller indices, 38 errors, Monitors, 206 Monochromators (see chromators) Mosaic structure, 100 MOSELEY, H G J., 402 Moseley's law, Crystal 333 measurement, 333 under semifocdsing conditions, 443 for stress measurement, 441 for texture determination, 276, 280 Plane-spacing equations, table, 459 for parameter mono- Plastic deformation, effect photographs, 242 on Laue 513 INDEX Plastic deformation (continued) effect Point Sealers, 179, on powder photographs, 263 lattice, errors, 202 204 use in measuring integrated intensity, 29 205 Polarization factor, 107 when monochromator is used, 172 Scattering (see X-ray scattering) 149 Pole figure, 274 SCHERRER, Polycrystalline aggregates, 259 crystal orientation, 272 crystal perfection, 263 crystal size, 259 Polygonization, 249, 266 Powder method, 93, 149, 500 Scherrer formula, 99 SCHULZ, L G., 290 Preferred orientation (see Texture) Short-range order, 375, 376 Primitive cells, 33, Principal stresses, P., 414 Seemann-Bohlin camera, 157 Scintillation counter, 201, Setting a crystal in a required orientation, 36 436 240 Short-wavelength SIEGBAHN, M., Proportional counters, 190, 414 Pulse-height analyzer, single-channel 193 limit, (sin 0)/X values, sin B values, tabk, Slip, 472 469 table, , 86 9, 243 Slip plane, determination of indices, Pulse-height discriminator, 192 254 Small-angle scattering, 263 Quadratic forms of Miller indices, tabk, 471 Quartz, determination in dust, 398 chloride structure, 47 Solid solutions, defect, 317, 353 Sodium interstitial, 51, 351 ordered, 52, 363 Radiography, Random substitutional, 51, 352 352 x-ray scattering from, 367, 376 Ratemeter, 179, 206 calibration, 210 errors, 208 Rational indices, law of, 54 Reciprocal lattice, 454, 490 solid solution, 50, Recovery, 266 Recrystallization, 250, 266 Recrystallization texture, 273 stress, 263, 431 in weldments, 432, 453 Resolving power, for plane Residual spacings, 151, 159, 161 for wavelengths, 162, 411 slits, 185, 408 Space groups, 319 Specimen holders, for Laue method, 143 for texture determination, 286, 291 Seller Specimen preparation, Debye-Scherrer method, 153 diffractometer method, 182 Spectrometer, 85 automatic, 417 curved reflecting crystal, 409 curved transmitting crystal, 409 flat crystal, 407 Sphere of reflection, 498 SPROULL, WAYNE T., 456 Standard projections, 71, 73, 74 Retained austenite determination, 391 Stereographic projection, 60 Rhombohedral-hexagonal transformation, 462 Rock-salt structure, 47 Stereographic ruler, for back-reflection ROENTGEN, W C., ROOKSBY, H P., 455 Ross filters, 211 Rotating-crystal method, 92, 314, 499 Laue, 227 for transmission Laue, 235 Straumanis method, 154 Stress measurement, 431 applications, 451 biaxial, 436 INDEX 514 Stress measurement Uranium (continued) calibration, 449 camera technique, 441 WALKER, CHRISTOPHER WARREN, B E., 262 434 when lines are broad, 447 Structure factor, 116 of BCC element, 119 of of of FCC HCP of characteristic lines, element, 119 element, 122 NaCl, 121 Superlattice, 52, 363 Surface deposits, identification table, of, 387 elements, 34 A., Wulff net, 64 WYCKOPP, RALPH W G., 458 Temperature factor, 130, 389, 395 Ternary systems, 359 Texture (preferred orientation), 272, 398 Texture determination, of sheet, diffractometer method, 285 photographic method, 280 of wire, photographic method, 276 Thermal asterism, 505 Thermal vibration, 130 Thomson equation, 107 Time constant, 207 Time width of slit, 210 depth of penetration detection of, 23 269 fluorescent, 12, 111 production of, 17 safety precautions, 25 X-ray scattering, 12 by amorphous solids, 102 by an atom, 108 Compton modified, 108 by an electron, 105 by gases and liquids, 102 by random solid solutions, 367 at small angles, 263 Transmission Laue camera, 38 Transmission Laue method, 89 for crystal orientation, 229 75 determination of composition plane, 250 temperature-diffuse, 131 by a unit cell, 111 X-ray spectroscopy, 85 X-ray tubes, gas type, 21 hot-filament type, 17 rotating-anode type, 23 X unit, 87 Twins, annealing, 55 deformation, 58 YUDOWITCH, KENNETH Unit Zone, 41 ZnS 29 Unit-cell volume, equations, of, incoherent, 108 TIPPEL, T L., 455 Torsion, 244 cell, 10 coherent, 105 Thickness of specimen, optimum 164 THOMSON, J J., 105 crystals, of, continuous, Temperature-diffuse scattering, 131 Twinned 464 Wire texture, 276 WOOSTER, W A., 456 X-rays, absorption characteristic, 456 tofcfe, F., 35 TAYLOR, 456 274 Widmanstatten structure, 257 WILSON, A J C., 455 WEVER, ZnS Symmetry B., Wavelengths, of absorption edges, 464 (zinc blende), 134 Substitutional solid solutions, 51, 352 of 46 Vector multiplication, 490 Vegard's law, 352 diffractometer technique, 444 focusing conditions, 442 uniaxial, structure, 460 L., 457 (zinc-blende) structure, 49 Zone law, 41, 495 table, .. .ELEMENTS OF X-RAY DIFFRACTION by B D CULLITY Associate Professor of Metallurgy University of Notre Dame ADDISON-WESLEY PUBLISHING COMPANY, READING,... properties of x-rays and the internal structure of crystals its two chapters as necessary preliminaries to the the diffraction of x-rays by crystals which follows described in the cussion of first... Variation with wave- length of the energy per x-ray quantum and of the mass absorption coefficient of nickel PROPERTIES OF X-RAYS 12 [CHAP termed hard, while long-wavelength x-rays are easily absorbed