Index_1977_Diffraction-from-Materials

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Index 
A 
Absorption 
as analytical tool, 174-176 
chemical analysis by, 131 
correction, flat plate geometry, 274-275 
edge, fine structure, 432 
of χ rays, 131, 166-176 
Absorption, anomalous 
in electron diffraction, 486 
in neutron diffraction, 486 
in x-ray diffraction, 477-483 
Accuracy and precision in measuring 
spacings, 244-246 
Ag 3Sn, structure of, 288 
Air scattering, 521 
Amorphous solids, scattering from, 428-432 
Antinodal points, 484 
Argand diagram, 91 
Asymmetric unit, 16 
Atomic scattering factor, 143 
Atomic size, 3 4 - 3 6 
Auger transitions, 168 
Β 
Balanced filters, 172-174 
Beam monitors 
neutrons, 192 
xrays, 191, 519 
Berg-Barrett topography, 378 
Bernal chart, 217 
Bonse-Hart monochromator, 497 
Borrmann effect, 443, 470, 480 
physical interpretation, 483 
Bragg reflection from perfect crystals 
asymmetric geometry, 502 
attenuation factor, 497 
intensity of, 493 
Bragg's law, 84, 108 
Bravais space lattices, 20 
Bremstrahlung, 121-124, 140 
Buerger precession camera, 225 
C 
Characteristic radiation, 124-128 
Chemical analysis by absorption, 131 
Close packing, 35 
Clustering, 4 0 3 - 4 2 4 
Column approximation in electron diffraction,475 
Complex notation, 91 
Compton scattering, 153-156 
Convolution, 320 
Counters, 180-193 
Counting statistics, 188 
Crests, wave, 80 
Crystal classes, 32 
Crystal monochromatization, 244 
C u 20 , structure of, 286 
D 
Dead time, detectors, 191 
de Brogue's relation, 133 
553 
554 INDEX 
Debye-Scherrer camera, 243 
Detection of radiation, 179 
counting detectors, 180-188 
counting electronics, 180-188 
film techniques, 179-180 
Dielectric constant in a crystal, 446-448 
Difference Fourier synthesis, 341 
Difference Patterson synthesis, 346 
Diffraction 
effect of distortion on, 372-379 
Fourier analysis of, 304-310 
order of, 85 
precision of, 132 
from three-dimensional lattice, 99 -108 
Diffraction from perfect crystals 
Bragg geometry, 462 
Field amplitudes, 465 -470 
Laue geometry, 463, 467 
Diffractometer, 121, 229, 243-244 
with single crystals, 229-233 
Dirac delta function, 304 
Direct beam power, measurement of, 519-529 
Directions, indexing of, 49 
Dislocation, effects on diffraction, 372-379 
Dispersion surfaces, 456-458 
Distortion, effects of 
in electron microscopy, 372-379 
in x-ray diffraction, 379-385 
Dynamical theory of diffraction, 442-511 
Ε 
Electron density 
Fourier transform of, 307 
mapping, 308-317 
projections, 310-312 
sections, 310 
Electron diffraction, 252-255 
Electron microprobe, 137 
Electron microscopes, 137 
Electron scattering, 136-139 
factor, 157-158 
images and diffraction patterns in 
electron microscope, 139 
polarization of electrons, 158 
Electron units, 525 
Electrons, refraction of, 179 
Equipoint, rank of, 16 
Ewald sphere, 96 ,456 
EXAFS, 432 
Extinction 
primary, 279 
secondary, 280 
Extinction distance, 474 
F 
Faraday cage, 193 
Film shrinkage, 242 
Filters, 131, 172-174 
Fluorescent analysis, 128-129 
Form, 39, 48 
Fourier analysis, 296-308 
of peak shape, 379-385 
Fourier integral theorem, 299-300 
Fourier transform, 101 
one-dimensional, 300 
three-dimensional, 304 
Friedel's law, 307 
Full reflections, 485 
G 
Glide, 2 6 - 2 8 
Glide plane 
two-dimensional, 14-15 
three-dimensional, 2 6 - 2 8 
Greninger net, 207 
Group velocity, 148-149 
Η 
Habit, 39 
Hard-sphere diameter, 34 
Harker-Kasper inequalities, 338 
Harker sections, 325 
Hazards, 193 
Heavy atom techniques, 328 
Helical structures, 351-355 
Hexagonal indices, 4 9 - 5 1 
Honl correction, 149-150 
Hull-Davey chart, 237 
I 
Incoherent scattering of χ rays, 153-156 
Index of refraction, 448 
INDEX 555 
electrons, 179 
neutrons, 179 
xrays, 145-148 
Inelastic scattering, 367-368 
of xrays, 153-156 
Integrated intensity 
in Debye-Scherrer method, 282 -284 
in energy dispersive methods, 284 
from flat plate polycrystal, 280-282 
from flat plate single crystal, 273-276 
in omega scan, 277 
from small crystal, 270-273 
in theta-two-theta scan, 277 
Intensity, 91 
Intensity inequalities, 337-341 
Intensity statistics, 332-336 
acentric distribution, 335 
centric distribution, 333 
Interference 
constructive, 80, 9 3 - 9 5 
destructive, 80, 9 3 - 9 5 
function, 93 
partial, 80, 9 3 - 9 5 
Inversion 
one-dimensional, 4 
two-dimensional, 6 
three-dimensional, 24 
Interstitial sites, 3 5 - 3 6 
Κ 
K-absorption edge, 126 
K-shell ionization, 126 
kx units, 132 
L 
Lattice, 2 
Lattice parameters, evalution of, 2 4 4 -
248 
Laue conditions, 105 
Laue monotonic scattering from alloy, 161 
Laue patterns, 201 -214 
back-reflection, analysis of, 205-208 
transmission, analysis of, 208 
uses of, 204, 212 
Laue reflection from perfect crystal 
exit beams, 463 ,490 
integrated intensity, 492 
position of, 463 
width of, 458, 490 
Least squares refinement, 293-296 
Leonhardt chart, 208 
Light scattering, 82 
Limiting sphere, 107 
Liquids, scattering from, 428 -432 
Local order, 4 0 3 - 4 2 4 
Lorentz factor, 276 
Lorentz-polarization factor, 276 
Μ 
Magnetic spin, 32 
Maxwell's equations, 449-451 
Miller-Bravais indices, 49 -51 
Miller indices, 4 6 - 4 7 
Mirror planes, 6 
Monitor counter, 191,519 
Monochromators, 131, 242 
Mosaic, effects on diffraction, 372-385 
Moseley's law, 125 
Multichannel analyzers, 187-188 
Multiplicity, 48 
Ν 
NaCl, structure of, 286 
Nelson-Riley extrapolation function, 245 
crystal, 2 
Greninger, 207 
Wulff, 6 4 - 6 6 
Neutron absorption, 176-178 
Neutron detectors, 192 
Neutron scattering, 133-136 
factor, 158-161 
incoherent scattering due to 
thermal vibrations, 162 
magnetic scattering, 162-166 
scattering cross sections, 162 
spin and isotope scattering, 160 
spin incoherent scattering cross section, 162 
Neutrons 
collimation of, 136 
detection of, 136 
diffraction, 135 
monochromatization of, 134 
Nondispersive diffraction, 187 
Nuclear reactors, 134 
556 INDEX 
Ο 
Octahedral site or hole 
bcc, 36 
fee, 35 
Optical transformations, 315 
Omega scan, 277 
Orienting crystal using diffractometer, 2 2 9 -
233 
Oscillating crystal method, 220 
Ρ 
Parseval's theorem, 298, 302 
Particle accelerators, 134 
Path difference, 82, 8 5 - 8 6 
Patterson synthesis, 317, 328 
Pendellosiing effect, 473 
Permittivity, 447 
Phase difference, 90 
Phase velocity, 148-149 
Plane, normal to wave, 52 
Planes 
indices, 4 6 - 4 7 
parametric, 46 
rational, 46 
Point group 
one-dimensional, 4 
two-dimensional, 5 - 9 
three-dimensional, 20 -25 
Point symmetries, 3 
Points, indexing of, 49 
Polarization of χ rays, 140-142 
Polarization states, 453 
Poles, 5 7 - 5 9 
Position sensitive detectors, 185 
Powder method, 233-252 
analytical procedures for indexing, 238-240 
cameras, 240-244 
card file, 248 
charts for indexing, 236-238 
energy analysis, 249-252 
experimental details, 240-244 
resolution of peaks in, 243 
sample preparation for, 235 
systematic errors in, 245-246 
uses of, 247-248 
Poynting's vector and energy flow in crystal, 
470 -476 
Precision lattice constant determination, 
244-248 
uses for, 247-248 
Precession method, 223-229 
nonzero layers, 228 
zero layer, 224 
Primitive lattice, 10 
Proportional counters, 182-185 
Pulse height analyzer, see Single channel 
analyzer 
R 
Radial density distributions, 428-432 
Radius of gyration, 425 
Ranks of equipoint, 16 
Reciprocal lattice vectors, 5 3 - 5 7 , 105 
Reciprocal space, 96 
one-dimensional, 96 
three-dimensional, 106 
Reflecting sphere, see Ewald sphere 
Reflection 
one-dimensional, 3 - 4 
two-dimensional, 6 - 7 
three-dimensional, 22 
Refraction 
index of, 178 
Refraction of χ rays, 178 
Reliability index, 295 
Rocking curve, 458 
Rotating crystal method, 214-220 
Rotation 
one-dimensional, 3 - 4 
two-dimensional, 7 - 8 
three-dimensional, 2 0 - 2 2 
Roto-inversion, 24 
Roto-reflection, 24 
S 
Safety precautions, 193 
S ay re' s relation, 340 
Scattered intensity, 91 
Scattering 
from crystal, 104 
isotopic, 160 
magnetic, 162-166 
by one electron, 140-143from periodic two-dimensional array, 107 
INDEX 557 
from row of atoms, 89 
small-angle, 424-427 
spin incoherent, 160 
thermal diffuse, 363-372 
Scattering cross section, 164 
Scattering factor, 149-152 
electrons, 157 
neutrons, 159 
xrays, 149-152 
Scattering power, 273 
Scintillation counters 
xrays, 185 
Screw axes 
definition of, 2 8 - 2 9 
detection of, 3 9 - 4 0 
Short-range order, 403 -424 
Sign triple products, 339 
Single channel analyzer, 183 
Slit correction, 385-392 
Small-angle scattering, 424-427 
Solid-state detectors 
neutrons, 193 
xrays, 186 
Space groups 
one-dimensional, 4 
two-dimensional, 11-18 
three-dimensional, 2 5 - 3 3 
Space lattice 
one-dimensional, 2 
two-dimensional, 9 -11 
three-dimensional, 18-20 
Special conditions for diffraction, 111 
Special positions, 16 
Spinels, 37 
Stacking faults, 392-403 
Stacking pattern, 36 
Static atomic displacements, 153, 370, 406-424 
Stereographic projection, 5 8 - 7 4 
Stoke's correction, 385-392 
Straumanis mounting, 242 
Structure factor, 98, 103, 108-111 
Subgrain size, effects on diffraction, 372-385 
Surface markings, traces, 7 2 - 7 3 
Surface roughness, 521 
Symmetry elements, 4 
Symmetry factor, 328 
Symmetry operations, 3 
Synchrotron radiation, 432 
Systems 
one-dimensional, 3 - 5 
two-dimensional, 9 -11 
three-dimensional, 18 -20 
Τ 
Temperature effects 
anisotropic factor, 294 
depression of peaks, 152-153 
dispersion curves, 368-369 
elastic constants, 370 
inelastic scattering, 367-368 
neutron inelastic scattering, 367-368 
phonons, 367-369 
soft modes, 370 
T D S , 363-372 
Termination errors, 309, 322 
Tetrahedral site or hole 
fee, 35 
bcc, 36 
Texture, analysis of, 247 
Thermal diffuse scattering, 363-372 
Thermal vibrations 
effect on elastic scattering, 158 
effects of, 152-153, 363-372 
Theta-two-theta scan, 277 
Thomson formula for one electron, 142-143 
Tie point, 458 
Time-averaged intensity, definition of, 91 
Time-of-Flight powder method, 250-252 
resolution of, 251-252 
Total reflection, 495 
Darwin curve, 496 
Darwin-Prins curve, 496 
Transformations 
axes, 5 6 - 5 7 
cell, 57 
Traveling wave, 80 
Two-surface analysis, 7 2 - 7 3 
U 
Unit cell 
Primitive, 2 
one-dimensional, 2 
two-dimensional, 11 
three-dimensional, 18 -20 
Unit translation 
one-dimensional, 2 
558 INDEX 
Unit translation (cont.) 
two-dimensional, 5 
three-dimensional, 18-20 
Unitary structure factor, 335 
W 
Warren-Averbach analysis of peak shape, 
379-392 
Warren short-range order parameter, 404 
Wavelength dispersion, 132 
Waves, 82, 8 5 - 8 6 
Weighting factors, 294 
Weissenberg method, 220-223 
White radiation, 121 
Wulff net, 6 4 - 6 6 
X 
X-ray diffraction, discovery of, 83 
X-ray equation, 169 
X-ray interferometer, 486 
X-ray scattering 
Laue monotonic scattering from alloy, 161 
Thomson formula for one electron, 142-143 
X-ray topography, 503-511 
Berg-Barrett technique, 503-509 
Bormann technique, 508 
contrast in, 508 
Lang technique, 508 
X-ray tubes, 119 
line focus, 130 
microfocus, 130 
spot focus, 130 
take-off angle, 130 
target dimensions, 130 
Xrays 
absorption of, 131, 166-176 
absorption coefficient, 169-171 
absorption by multicomponent materials, 171 
balanced filters, 172-174 
Bremstrahlung, 121-124, 140 
characteristic radiation of, 124-130 
chemical analysis by absorption, 131 
Compton scattering, 153-156 
discovery of, 118 
filters, 131, 172-174 
generation of, 119 
Honl correction, 149-150 
inelastic scattering of, 153-156 
minimum wavelength, 122 
monochromator, 131 
polarization of, 140-142 
refraction of, 178 
scattering factor, 149-152 
theory for, 124-128 
white radiation, 121 
Ζ 
Zone axis, 55 
A 
Β 7 
C 8 
D 9 
Ε 0 
F 1 
G 2 
Η 3 
I 4 
J 5