Despite the advances of the electron mtcrodiflraction technique, the determination of unit cells of microcrystalline compounds still depends in many cases on the interpretation of the X-ray powder pattern. The feasibility of this interpretation depends strongly un the precision of the data, the present-day level of which is far from its physical limit. It could be improved by application of monochromators in diflractometry. Some possible methods are discussed. With regard to interpretation, a survey of existing methods is given (Lipson, Ito, de Wolff, Szoldos). Some of these techniques are suitable for computers, at least in the initial phase of the procedure. This is illustrated by application of a zone-finding program for the complete solution of a given pattern. Finally, the influence of impurities and other disturbing factors is discussed.

A modification of the theory of X-ray radial distribution analysis is presented. This modification can serve as a guide to the values of the unit cell dimensions and may be useful in indexing powder patterns of unknown structures, although the use of trial and error methods is not eliminated. This technique is shown to give consistent results with known structures and is applied to the indexing of powder patterns of Pu3Ru and Pu5Ru3. The powder pattern of Pu3Ru can be indexed on the basis of an orthorhombic unit cell with a0 = 6.216 Å, b0 = 6.924 Å, and c0 = 8.093 Å, and Pu5Ru3 on the basis of a tetragonal unit cell with a0 = 8.092 Å and c0 - 10.023 Å.

This paper briefly traces the study of the preprecipitation or cold-aging stage of the decomposition of supersaturated solutions by means of diffuse scattering of X-rays.

This part of the overall precipitation process is of considerable practical as well as theoretical interest because it is during preprecipitation that changes in many physical and mechanical properties take place without the formation of a precipitate phase.

Examples will be given to show the types of zones encountered during this stage in various age-hardening alloys. These will attempt to illustrate the contribution which the study of diffuse scattering of X-rays, guided by present-day concepts of crystal imperfections, has made toward a better understanding of the precipitation process in alloys.

A review of the crystal structures of the elements shows some prevailing tendencies of atomic arrangement. These are discussed as space, symmetry, and connection principles. Counteracting temperature and bond factors can be recognized.

The same principles and factors are responsible for the formation of alloy structures, taking into account additional factors due to the component's similarities and dissimilarities in size and electronegativity.

Similarity favors solid solution and dissimilarity favors compound formation. A q compound is here defined as a phase in a q-component system not connected with any other phase of the system by continuous solid solution. Similarly a q structure is defined as a structure type which needs only q components to be formed (considering present-day knowledge). For example, the binary compound Mg17Al12 has the elementary (1 ™) structure of α-manganese. As a rule, q compounds tend to form p structures with q > p.

A discussion of q structures with q = 1, 2, and 3 is given in some detail on the basis of known representatives to show: (1) the competition of geometrical principles and physicochemical factors in determining atomic arrangements of alloys; and (2) the value of rules for making guesses on the probable occurrence of compounds and their chemical composition in polycomponent systems yet unknown.

By means of a combined X-ray diffraction and metallographic study, two heretofore unrecognized phases, Zr4Fe and Zr2Fe, have been identified. Approximate verification of this finding has been made by Dr. David Levinson, using microprobe analysis. A tentative revision of the Zr-Fe phase diagram is proposed.

X-ray diffraction studies were made on the Ti–Ni system around the stoichiometric composition of the intermetallic compound TiNi to clarify some confusion which has existed about the phase diagram in this region, and to explain some anomalies in the physical properties of this material. Wrought and cast samples were examined at room temperature both before and after heat treatment and at temperatures both above and below ambient. The compound TiNi does exist at room temperature. The phase purity of the particular sample was found to be greatly affected by such factors as minor variations in composition, heat treatment, and method of sample preparation. Some confirming metallographlc and physical property data will also be presented.

The helium X-ray path has long been used, in spectrography to increase the intensity of the long-wavelength X-rays. The same principle has been applied to diflractometry. Up to threefold intensity increase is observed with chromium Ka radiation with very little increase In background. The peak to background ratio, therefore, is Improved by almost the same factor as the increase in intensity. Application of the technique is illustrated by analysis of gauge block steel for retained austcnite and macrostress.

The structure of ThPd4 has been determined by X-ray powder methods. It has the simple cubic Cu3Au (LI2) structure a = 4.110 ± 0.002 Å at 80 at. % palladium. Interatomic distances and the range of stability of this compound and of ThPd3 are discussed briefly.

Plastic deformation of metals produces a state characterized by the presence of residual elastic strains, small domains which diffract X-rays coherently, and often stacking faults; these effects may be studied with X-ray diffraction techniques. Changes in the lattice parameter, shifts in the relative positions of diffraction lines, and the broadening of diffraction lines were used to study the state of coldwork resulting in Cu-6.6 at.%Si-1.2 at.%Mn after deformation by filing, wiredrawing, and uniaxial tension at room temperature.

Both filing and wire-drawing produce large root-mean-square strains and stacking faults, whereas deformation by tension up to 22% extension fails to produce any clear evidence of faulting or root-mean-square strains. Tensile deformation causes fragmentation of coherent domains to an average dimension of 250 Å after 22% extension, and results in a radial, tensile, residual macrostrain arising from a smaller rate of work hardening in the surface layers than in the interior. Wire drawing also results in a residual macrostrain system. Deformation appears to enhance diffusion and promote solute clustering at room temperature.

The lattice parameter-composition curves for several nickel solid solutions and for some chromium and. iron solid solutions are discussed. It is shown that the size effect may be the predominating influence on the change of lattice parameters in these systems. This is demonstrated by comparing observed and calculated data employing various methods. A new scheme for evaluating the atomic size in solid solutions is proposed, based on regarding the atom, as an incompressible core surrounded by a smeared-out compressible volume. The suggestion that classical elasticity theory may be used as a basis for understanding the size effect in solid solutions is justified by examination of the Ag-Pd system for additions of Ag from 0 to 100 at. %.

Oxygen was introduced into a single crystal of titanium in successive stages. The intensities of the h00 and 00l reflections were measured with a single-crystal diffractometer. The observed variation of the intensities with oxygen concentration was attributed to three factors: (1) the additional scattering from the oxygen atoms, (2) a change in the Debye-Waller factor, and (3) an exponential factor originating from the distortion around the oxygen atom. The theory of X-ray scattering from crystals containing centers of distortion was applied to the hexagonal titanium containing interstitial oxygen atoms. Using the variation of the lattice constant with oxygen concentration, it was possible to predict the intensity reduction due to lattice strains. It was concluded that it would have been possible to obtain an estimate of the defect concentration from the X-ray measurements of lattice expansion and intensity reduction.

The counter tube diffractometer method for determining d spacings is often rejected for precision work because of lack of information concerning the nature and significance of the inherent errors. Errors concerned with the geometry of the method, the nature of the X-ray source, and the technique of collecting data have all been analyzed previously in some detail. The findings of these analyses, which are scattered throughout the literature, are reviewed briefly. Errors arising from imperfections in the instrument and misalignment of the X-ray source with respect to the diffractometev have been studied experimentally. The results are presented and discussed in terms of the resultant error in the determination of the lattice parameter of a cubic crystal. Errors determined both analytically and empirically are discussed in relation to the extrapolation procedures commonly used for diffractometers. It is shown that, depending on the construction of the instrument, the effect of imperfections in the gears may almost double the error in the final extrapolated value of a lattice parameter.

Large single crystals can be examined by conventional X-ray diffraction procedures only at their surface or by destructive sectioning. Within the limitations inherent in polychromatic X-ray photography, high-voltage Laue pictures arc shown to give some information on the internal quality of large crystals.

Asterism in conventional Laue photographs is contrasted, with streaks due to geometric effects in Laue patterns of large crystals. Detail within the streaks reveals subgrain structure. A primary extinction effect can be used as striking proof of good crystals being capable of scattering coherently over large distances.

The effect of substructural perfection on the accumulation of irradiation damage in aluminum was examined. Large single crystals with extensive substructure and crystals essentially free of substructure, all with faces cut parallel to crystal planes, were subjected to neutron irradiation. Subsequent examination by X-ray diffraction revealed pronounced changes in integrated intensity and Debye-Waller temperature factor for the substructure-free crystals; these effects disappeared upon re-etching of the surface. Laue photographs showed that the normal single-crystal pattern was partially obscured by a polycrystalline effect which also disappeared upon etching. Crystals with extensive substructure showed no such effects.

This diffraction evidence supports the view that irradiation-induced defects in aluminum migrate to and collect at the crystal surface if no internal trapping sites exist.

A simple gradient heating apparatus was developed and used successfully in growing oriented single crystals of high-purity aluminum suitable for X-ray dinfraction analysis.

The Debye-Waller factor for CuaO and the atomic scattering factor for copper were determined independently of each other at one temperature from measurements of both the diffuse scattering and the integrated intensities of the Bragg maxima. The scattering factor agreed well with that computed from theory. The characteristic temperature computed from the Debye-Waller factor at 298°K was found to be 182°K. At 88°K its value is 152°K.

Similar measurements of the Bragg maxima with a powder sample of UO2 were not useful because of preferred orientation. However, the diffuse intensity is not so sensitive to preferred orientation and may be used to determine the characteristic temperature. Its value for UO2 was found to be 188°K at room temperature.

Art X-ray diffraction study has been conducted on the emissive coating (Ba, Sr, CaO) of experimental diodes from which thermionic emission data were taken before X-ray analysis. The tubes were then opened and the oxide protected by special techniques in order to prevent the formation of the hydroxide. In addition to X-ray diffraction, other techniques were used to give a complete description of the structures present.

Several methods for the routine determination of crystallite size by means of X-ray diffraction line-broadening have previously been reported. Although these techniques have proven useful and reliable when utilized with the single X-ray diffractometer and instrumental geometry used to originally develop the methods, it was not known whether other instruments would provide similar reliability. Therefore a study was performed to evaluate the applicability of routine methods of crystallite size analysis to other X-ray diffraction units. A series of six beryllium oxide powder specimens, whose average crystallite sizes ranged stepwise from about 35 to nearly 3000 Å, were used to test a number of X-ray diffractometers. By using a predetermined diffraction geometry for each instrument tested, measured crystallite sizes were found to be quite reproducible and well within the limits of experimental error. The testing procedure, instrumental conditions, and individual performance results are presented in this paper.