Systematic procedures are used for generating the geometrically possible close-packed ordered layers for any desired binary “ideal composition” and the various geometrically possible stacking sequences with a given number of layers of known structure. The known ordered close-packed cyrstal structure types in AB3 and AB4 alloys are characterized by the structure of the layer and by the stacking sequence. Their occurrence is reviewed in relation to pertinent variables, such as electron concentration and atomic size.

The crystal structures of elements and alloy phases in the B-metal region (B2(Zn) to B5(As) groups) have been classified into phase fields determined by their position in the periodic table. The limited number of equilibrium phases with element-like, disordered crystal structures and of extended terminal solid solutions has been more than doubled by the addition of metastable phases produced by ultra-rapid quenching from the melt (splat cooling). Strong structural correlations exist. Some high pressure phases have been included; in some cases, a qualitative discussion from the viewpoint of pseudopotential theory is given.

X-ray, neutron or electron diffraction patterns of alloys with structural disorder (micro-crystalline, amorphous or liquid alloys) consist of few diffuserings or halos. The ratio Ia(K)/<f> 2, where Ia(K) is the elastically scattered intensity per atom, K = 4πsinθ/λ, and <f> is average scattering factor of the alloy, is the sum of the Laue monotonic scattering (<f2> - <f2>)/<f2>, the small angle scattering Is(K) and interference function I(K). For isotropic distribution of the atoms in the alloy, one can write:

and

where

ρ0 is the average atomic density, V(r) is the size factor , ci and fi are the atomic concentration and atomic scattering factor of element i, respectively. Iij(K) is called the partial interference function which is related to the number ρij(r) = cjρ0gij(r) of j-type atoms per unit volume at the distancer from an i-type atom.

By varying the scattering factors of the elements through application of different radiations (x-rays, neutrons and electrons) and/or isotope enrichment, one can measure several I(K) which allow the evaluation of Iij(K) for a particular alloy. Assuming that gij(r) is independent of the relative abundance of the elements in the alloy , Iij(K) can also be obtained from several I(K) of the alloys with different concentratiora measured with a single radiation. This procedure has been applied to liquid Ag-Sn, Au-Sn and Cu-Sn alloys. The interference functions I(K), and their Fourier transforms, of vapor-quenched Ag-Ge and Ag-Cu films indicate that these alloys are micro polycrystalline with particle sizes of 15A in the Ag-52 at.% Cu alloy, 20A in the Ag-83 at.% Ge alloy and 24A in the Ag-64 at.% Ge alloy.

Protons and other energetic particles when back-scattered from a single crystal emerge with anisotropic Intensity distributions. There are minima In the intensities along crystallographic directions and planes. The indices of these directions and planes and the relative intensities of these crystallographic features can be readily established by photographing the pattern of emerging particles. The patterns disclose the symmetry of the scatterer but cannot be expected to reveal the presence or absence of a symmetry center, so that the symmetry of a pattern should be related to the symmetry of one of the 11 Laue-symmetry groups, Photographs made with 50-150 keV protons are found to differ not only for crystals that belong to different Laue groups, but also for crystals belonging to the same Laue group but having different space lattices. The patterns reveal a limited amount of structural information including information on orientation, crystal perfection, and axial ratios, but not unit cell dimensions, The interpretation of patterns on the basis of particle trajectories has had major successes in the past; interpretation on the basis of diffraction has also been proposed but the inherent complexities associated, with this are very severe. Some intensity relationships observed for various crystals a-re presented, and highly simplified approximate ways of predicting relative intensities of lines are compared with the observations.

It has been recently shown that particle size distributions can be determined from small angle x-ray scattering data. Size distributions have previously been measured in aluminum-zinc and aluminum-silver alloys containing spherical Guinier-Preston zones. Inorder to obtain the size distribution it is only necessary to calculate the Guinier radius and the Porod radius.

Dispersion hardened nickel alloys containing small spherical particles of thoria appear to be amenable to this type of analysis. A nickel-20% chromium-2% ThO2 alloy was selected for this study. The particle size distribution obtained by small angle x-ray scattering is compared with the transmission electron microscopy results found in the literature.

The relation of the X-ray small-angle scattering parameters to the results of transmission electron microscopy for spherical Guinier-Preston zones was investigated. Experimentally, the Guinier radius is found to equal (<R7>/<R5>1/2) and the Porod radius to equal <R3>/<R2>. These results were theoretically predicted by Baur and Gerold, A log normal distribution was found to be in close agreement with the experimental data. The use of this distribution allowed the size-distribution curve of spherical Guinier-Preston zones to be constructed from the X-ray parameters and from a knowledge of the metastable miscibility gap. This approach is used to follow the evolution of size distribution in both Al-Ag and Al-Zn alloys. The application of this approach to nncleation and growth as well as redistribution processes is discussed. Growth paths are established from the size distribution evolution curves through an Nv> construction. A brief discussion of the technique is included.

The intermetallic compound Au4V is known to be ferromagnetic at temperatures below 43°K. Its ferromagnetism, which has been attributed to long range order, can he destroyed by cold deformation. The present study was undertaken to determine how the Bragg and Williams long-range-order parameter of the fully-ordered alloy varied as a function of deformation by cold rolling. Because of complexities in the diffraction spectrum it was not possible to determine 5 by a simple ratio of integrated intensities as is frequently done in other ordered systems, A treatment was developed to handle these difficulties using a modification of a method developed by Giamei and Freise for determining volume fractions of mixed phases. These results are correlated with magnetic measurements made by Chin and coworkers at Bell Laboratories.

The antiphase boundary in a superlattice has been defined as the boundary between two neighboring zones which are out ofsphase with each other. This difference in phase is usually represented by a translation vector. In long-period superlattices, however, antiphase boundaries of the above mentioned type occur with regular spacings, thereby introducing another element of order which shows up as satellite peaks in the diffraction pattern. A second kind of antiphase boundaries may be defined in a one-dimensional long-period superlattice as the boundary between two neighboring zones which have different directions of repetition of the antiphase boundaries of the first kind. A theory of X-ray diffraction to obtain the size of the domains of the second kind in a one-dimensional long-period superlattice has been developed. An application of this theory to the ordered alloy Ag3Mg, known to have a one-dimensional long-period superlattice, is described and the results of the X-ray measurements are compared with those obtained by transmission electron microscopy.

Crystals with a dislocation density low enough so that individual dislocations can be resolved by X-ray diffraction contrast techniques should be regarded as highly perfect crystals. A complete description of the diffraction process, therefore, requires the approach of the dynamical theory of X-ray diffraction. In the Berg-Barrett arrangement each point on the crystal surface integrates the incident X-ray intensity over the angular range received from the X-ray source. For most experimental arrangements this range is about 1/2 degree and corresponds, therefore, to integrating over the entire range of reflection of the crystal, which is of the order of a minute or so of arc. The Berg-Barrett image is a recording of a localized integrated intensity, integrated over the complete range of incident angles. We consider as essential, however, primarily the range of total reflection, since it makes the major contribution to the integrated intensity.

The dynamical theory shows that the details of the diffraction process depend very strikingly on the boundary ocnditions at the crystal surface through two angles of incidence - one between the incident beam and the crystal surface, the other between the incident beam and the diffracting plane of atoms. Calculations of the parameters of the dynamical theory which describe the diffraction process in the Berg-Barrett arrangement show that the description depends very strongly on the details of the specific boundary conditions employed. In particular, two parameters seem especially important in dislocation image formation: 1) ΔθR, the angular range of the exit beam diffracted from the crystal, which we call the range of total rejection to distinguish It from ΔθA, the angular range over which the entrance beam is totally accepted, and 2) σe, the extinction coefficient, the parameter which describes the X-ray penetration depth. Both parameters are extremely sensitive to the specific boundary conditions employed.

This dynamical theory approach suggests that, by suitable choice of the experimental conditions, the boundary conditions can be advantageously adjusted so that satisfactory Berg-Barrett images can be obtained.

X-ray diffraction topographs were obtained from large arsenic single crystals. The camera employed copper Kα, radiation from a microfocus tube and an oscillating assembly of Soller slits limited the beam divergence. Reflections of the type (11) and (20) (primitive rhombohedral cell) were used to characterise dislocation Burgers vectors. The technique has been applied to arsenic single crystals grown from the vapour and from the melt. The majority of dislocations were found to belong to Burgers vectors <10>. Comparison has been made between dislocation etch pit patterns on (111) surfaces and X-ray topographs.

The silicon diode array camera tube, recently developed for PICTURFPHONE® service, was modified to permit X-ray imaging. High quantum efficiency is attained without the use of a phosphor screen, since each photon absorbed in the silicon target generates several hundred hole-electron pairs for each keV of its energy, most of which can he usefully collected. The sensitivity and resolution are adequate to allow a continuous television display of the diffracted intensity as a crystal is oriented. Particular advantages of this technique include; high resolution (< 25 μm); electronically variable magnification; direct oscilloscope measurement of X-ray spot Intensity profiles and relative spot intensities because signal current is directly proportional to photon flux; high sensitivity in the range of 0.6 to 5.0 Å, potentially limited only "by counting statistics; integration times variable from < 1/60 second to minutes; and expected low cost, since the camera tube has no complicated electron imaging, and is directly interchangeable Mith a standard television vidicon. Applications which are described include crystal orientation and X-ray topography.

By the electron microprobe Kossel technique, an a-precipitate at a grain boundary of a Cu-45wt% Zn alloy was found to consist of only one crystal and the orientation relationship between the a precipitate and one of the grains beside the grain boundary was (110)β//(111)α and <111>β//<110>α. This is the same relationship as the case α a precipitates in β-phase grains. A little deviation from the exact coincidence of above orientation relationship was observed. The vacancy model for the production of a denuded zone in the same alloy was confirmed by a line scanning analyses using an electron microprobe. An effect or orientation differences was observed on the specimen current of the electron microprobe. This effect was attributed to a channelling phenomenon. The influence of ths channelling effect on quantitative analyses by electron microprobe was considered for the precipitated a-phase and matrix β-phase, and the massive a precipitates were found to consist of many crystallites having different orientations. From the lattice constant of the g-phase determined by the Kossel patterns, the concentration of zinc at the target point was obtained in good agreement with the value obtained by quantitative analyses using an electron microprobe. Thus, in some cases, the Kossel technique can be utilized for the quantitative analysis of a small portion without any corrections which are necessary In the case of electron microprobe.

A transmission Kossel camera unit has been built for the Cambridge Mark II electron probe. It replaces the standard specimen stage assembly, and is useful also for regular electron probe microanalysis and projection microradiography.

Its design extends the attainable precision of lattice parameter measurements to near-ultimate practical limits, while providing special features for research studies, and speed, flexibility, and convenience of operation for routine analytical use on a wide variety of specimens, particularly semiconductor materials.

The most significant feature is a novel X-ray projection box structure which casts index-mark images on each pattern. From these images, the exact source distance and pattern-center positions are determined for each exposure. Precise crystal-piane spacings can be measured, therefore, from conic intersections anywhere on the exposed area of the plate. Since the conics need not be in any particular favorable location, it is not necessary to achieve an exact orientation of the sample. Precise lattice dimensions in several different crystallographic directions are obtainable from a single pattern exposure if their various sensitive conics appear anywhere on the pattern. The need for a reference measurement of “fixed” conics is eliminated, being replaced by a much more precise measurement of very sharp, high contrast, widely spaced index-mark images.

Camera length is 12.5 cm and exposed pattern area is 9.4 cm square. Glass photo plates are used to eliminate errors due to film shrinkage and warp. A removable cassette holds ten 4″×5″ glass plates, interchangeableiunder vacuum. The X-ray shutter has ten positions for making exposure-time sequences. The specimen stage is thermostatted to ±0.01° C, controllable from room temperature up to 200° C, and;temperature is measured to +0.005° C. Stage movement range is 25mmx50mn, with coordinates shown on external digital dials. Interchangeable inserts provide for a wide range of specimen sizes and shapes. Electrical contacts to the specimen are available.

An externally adjustable plate holds 24 different target foils or target-filter combinations for pseudo-Kossel patterns. An open position provides for true Kossel work and for scatteredelectron image viewing.

A method of Fourier analysis of x-ray line broadening is presented whereby microstrain, incoherent particle size, and fault probability can be calculated using only first-order peaks. This method can thus be used in studies of catalysts, vapor- and electrodeposits or heavily textured specimens for which second-order peaks are too broad or weak, in cases where the effect of particle size is not the same for all orders of a peak, or for multiphase specimens where overlap of peaks sometimes occurs. Examples of deformed FCG and BCC metals and alloys are presented, with comparisons to the method of multiple orders.

One part of the procedure, first demonstrated by Pines and Sirenko, provides for reducing the effects of truncation on the Fourier coefficients. As a result, larger particle sizes can be analyzed and the integrated intensity can be determined more precisely. Application to determinations of volume fraction are given.

The recovery and recrystallization of cold rolled copper during reverse bending fatigue at room temperature has been studied with x-ray diffraction, optical microscopy and transmission electron microscopy techniques. Recovery of x-ray line breadth was recorded as a function of number of cycles at all strain amplitudes investigated. Recrystallization was observed to take place only at small strain amplitudes (life of 106 to 107 cycles). The rate of nucleation of the recrystallized grains increases with increasing strain amplitude and is a linear function of the number of cycles. The formation and growth of the grains was confined to regions near the surface of the specimen. Since comparable thermal recovery occurs at approximately 435°F it is concluded that the dynamic generation and migration of numerous point defects during fatigue is responsible for the room temperature recrystallization.

Distinct X-ray intensity peaks corresponding to a stacking fault structure have been observed in the plastically deformed ctbrass (30% Zn). TITO sets of intensity peaks were present simultaneously: one set corresponding to the f.c.c. structure of annealed a-brass, the second set was displaced with respect to the first set in accordance with the Paterson pattern for a stacking fault structure. With Increasing plastic deformation the height and width of the stacking fault peaks increased, while the height of f.c.c. peaks decreased. Finally, only the intensity peaks of the stacking fault structure were observed. The positions of the stacking fault peaks and the original structure peaks remained constant and were independent of the amount of plastic deformation.

A general computer program has been written in basic Fortran language and tested for computing average particle size, strain, and particle size distribution according to the Fourier method of B. E. Warren.

The program provides such optional features as input data and Fourier coefficient print out, automatic background correction, the choice of fixed count or fixed time input mode, the synthesized diffraction peaks deconvoluted with respect to the instrumental diffraction peak, and a variable amplification range of particle Size. Included in the analysis is a polynomial fitting procedure for the scattering factor. The authors have attempted to write this computer program to be as self-explanatory as possible for general applicability. This program is available on request.

This Fourier analysis program has been tested using known distribution functions, and has been used for measuring average particle size, particle size and strain distribution in heattreated boron-doped graphite samples.

Uniaxial Plastic Deformation (UPD) has been known to produce anomalies in residual stress measurements based on x-ray diffraction techniques. This study was undertaken to determine the magnitude of the effects, if any, on residual stress calculations from various materials subjected to UPD. An x-ray diffraction study using the two-exposure method ( ψ = 0° and ψ = U5°) was made on several iron, aluminum, and titanium alloys (AISI 4340, 4330M, 4130; 2024-13, 7075-T611; Ti-6Al-4V) before and after these alloys were deformed plastically by bending on a U-bend test fixture. The x-ray peak shifts, Δ2θ0-ψ, were recorded and the x-ray stress factors, Ki, calculated by three different methods. The results indicate that UPD of the calibration specimens will increase or decrease Ki depending on the alloy. These results are discussed together with observations on the additivity of residual and applied stresses, and the per cent differences in the stress measurements based on stress factors calculated by three different methods.

Residual stresses in several batches of heat-treated 4-79 molybdenum Permalloy finished laminations were measured by X-ray diffraction technique. This involved determination of macrostresses from line shift of (331) reflection by the two-exposure diffractometric technique as well as the determination of microstresses from half breadth of the same line profile. It was observed that the residual stresses In all batches of laminations were small and the variations in residual stresses from one batch of laminations to another were not appreciable, considering the scatter in laminations within each individual batch. Simultaneous magnetic measurements showed considerable variation in magnetic properties from batch to batch; e.g., a five-fold variation in normalized hysteresis loop and a two-fold variation in the magnetic “softness” parameter. On subjecting individual batches of laminations to various thermal and thermomagnetic treatments below 650 C, considerable change in magnetic properties was achieved without significantly changing residual stresses. The variation in magnetic properties in finished laminations was ascribed to the difference in effective crystal anisotropy and uniaxial anisotropy caused by variations in thermal and thermomagnetic annealing treatments. The study showed that the variation was not due to any major variation in stress induced magnetostrietive anisotropy.