The formation of the spherical Guinier—Preston zones in an aluminum-silver alloy is governed by a metastable miscibility gap, which consists of two different sections. The lower section occurs below 170°C (η state), the higher section up to 420°C (∊ state). The zones in the two sections differ in their silver concentration and in their atomic order. To prove the change in order, a combination of X-ray small-angle scattering and electric resistivity measurements was used. As the resistivity depends on the zone size and the atomic order, the change in order can be found when the zone size is known. This size was measured by the X-ray technique. To complete the results, X-rays ingle-crystal diffraction patterns with monochromatic radiation were taken at different stages. According to these patterns, three different states must be distinguished.

The η′ state exists at room temperature after quenching from 550°C. The silver atoms prefer a layered arrangement in the zones, which is not very stable. It is destroyed after short annealings above 100°C. The η state is developed during annealing below 170°C. A three-dimensional atomic order is built up with increasing zone size, which results in a marked decrease in the resistivity. For the ∊ state (above 170°C), a nearly random atomic distribution exists. Step-quenching experiments prove that the ordered η state can also be developed at room temperature.

Values of the Debye temperature 0 for iron-manganese solid-solution alloys have been determined from X-ray diffracted intensity measurements of powder specimens at ambient temperatures of 310, 239, and 98°K. Corrections to 0 were made with respect to the temperature-dependence of Θ, temperature diffuse scattering, dispersion, volume expansion of the alloy, and the temperature gradient through the specimen. The variation of Θ with temperature has been found to be approximately linear, the value of Θ decreasing 3 % between 98 and SICTK. for a nominal Fe–4%Mn alloy.

Increasing the concentration of manganese in an iron-manganese solid-solution alloy decreases Θ in qualitative agreement with Lindemann's equation. The values of Θ for other s olid-solution alloys computed using Lindemann's equation also agree with reported experimental values of Θ. The Debye temperature of a nominal Fe-3%Mn alloy annealed for 2 hr at 300, 600, and 700°C has not been found to maximize at 600°C as has been reported by Il'ina et al. On the contrary, Θ decreases with increasing annealing temperature until, in the range 600 to 700°C, it reaches its true value; and at these temperatures the powder was found to be fully annealed.

In this work a detailed X-ray powder diffraction study of the reversible temperature transformation has been undertaken in several rare earth niobates MNbO4 M being lanthanum, cerium, neodymium, gadolinium, holmium, thulium, ytterbium, and yttrium. Both high-temperature diffractometer and film techniques were used. It was shown for the substances investigated that the low-high transformation is a continuous transition over the wbole temperature range from monoclinic at room temperature to tetragonal at the transition temperature. It was found that the rate of the overall transition is rapid, and also that the transition between any intermediate state occurs reversibly within minutes or seconds. The continuous transition and the rapid rate of attainment of equilibrium in the solid, even between intermediate states of the transformation, support the earlier assumption that it is a displacive-type order-disorder transition.

This paper presents the theoretical and practical aspects of measuring residual stresses by X-ray diffraction with emphasis on the analysis of aluminum alloys. The theoretical considerations of radiation) beam geometry, and peak location will be discussed in regard to establishing optimum analysis techniques. The precision and reproducibility of this technique have been investigated so that results can be applied accurately. The approach, however, is basically a practical one, with the intent of studying residual stress systems as they affect engineering applications. Residual stress systems produced by thermal and mechanical treatments have been determined and the effect of treatment modifications and variations on the resultant stress system have been analyzed. The effect of operational variables such as time and temperature on the developed stress system are shown. From this, the merits of a particular treatment can be determined with respect to its intended application.

Analysis of solution heat-treated and quenched 2014 aluminum has shown a significant effect of the quench temperature on the resultant residual stress system. The results obtained from shot-peening this alloy are presented, as well as the effect of time and temperature on the shot-peened stress gradient.

The broadening of powder pattern peaks of metals is normally caused by small crystallite size and by distortions within the crystallites as a consequence of dislocation configurations. In addition, the experimental diffraction geometry contributes to the line broadening. Using Cu Kα radiation, we recorded the peak profiles of the cold-worked and annealed filings of tungsten, niobium, aluminum, and silver-indium alloys with a standard focusing diffractometer. The Rachinger method was applied to separate the Kα1 and Kα2 peaks, and the Kα1 peaks were subjected to a Fourier analysis. Elimination of the instrumental broadening was carried out by the Stokes method, which does not require any assumptions concerning the mathematical description of the diffraction peak profile.

The Fourier coefficients, AL, were separated into the fraction produced by particle size, ALFF, and by strains, ALe, by the Warren-Averbach method and plotted as a function of the distance L = ndhkl, normal to the reflecting planes (hkl) of spacing dhkl. The negative, reciprocal initial slope of the ALPF vs. L curve is equal to the effective particle size Deff, which contains the effects of the true crystallite size and faulting. The coefficients ALβ = AL/ALPF are used to calculate the root mean square strain <∊L2>1/2. The sum of the ALPF, which is proportional to a reciprocal integral breadth, leads to a different particle size, DWAPF, which is also dependent upon the crystallite size and faulting. The sum of the AL6 values is a measure of the strain ƐWA.

The integral breadths bst, corrected by the Stokes method, i.e.,

are separated into a particle size term bstPF and distortion term bSts using the relations . It is found that only the first relation leads to particle sizes DG,StPF and strains ∊G,st similar to those obtained by the summation of the ALPF and AL6, i.e., DWAPF and ∊wA, respectively. The integral breadths of the cold-worked peaks Bew and of the annealed standards bA. were also calculated, using the Lauc definition of B equal to area per peak maximum. A comparison of the values of bst/Bcw with bA/Bew for bA/Bew < 0.6 shows that all data follow the parabolic relation b/Bew = 1 − bA2/Bew2. The maximum deviation of bst/Bew from the parabola is less than 10%.

When the accuracy of a lattice parameter determination is carried beyond about 0.01 % it becomes of special importance to consider the equivalence of λ and θ in solving the Bragg equation for d. A reference angle on the observed diffractometer profile must be identified with the corresponding wavelength, of the incident X-ray spectral distribution. Exact identity is not possible because the diffractometer profiles are broadened, distorted asymmetrically, and displaced from their correct positions by amounts dependent on the shape of the incident spectral lines, the angular separation of the Kα1,2 doublet lines, and the specimen, instrumental, and geometrical aberrations innerent in the experimental method. The aberration functions vary with the experimental conditions and are Bragg-angle-dependent, thereby introducing systematic errors which are not eliminated by extrapolation procedures.

Most of the published diffractometer measurements of lattice parameters have used as the reflection angle, 28, of the diffractometer profile the peak P(2θ) or the midpoint of chords at various heights above background M1/2(2θ), M2/3(2θ), etc., of the Kα1 line. The relationship between these various angular measures of the line profile is not constant; P(2θ) may be equai to, greater than, or less than M1/2(2θ), depending on the asymmetry of the line profile. The X-ray wavelengths currently used in diffractometry refer to the peak P(λ) of the spectral distribution. The use of P(λ) with different angular measures of the diffractometer profiles results in a range of d's from which different values of the lattice parameters are calculated. The selection of arbitrary methods of defining 2θ does not take into account the significant aspects of the diffraction process, nor does it facilitate the correction of the data for systematic errors inherent in the experimental measurements.

The problems associated with quantitative determinations and descriptions of preferred orientation are discussed and a method proposed to yield quantitative descriptions. A means of obtaining representative quantitative data using reflection techniques is described. The position of intensity minima in quantitative pole figure descriptions of preferred orientation is equal in importance to intensity maxima. Hence, rate-meter counting of diffracted intensity as the sample is continuously or semicontinuously rotated in a given spatial relationship is not satisfactory. Instead, sealer counting by fixed counts at a given spatial position yields more meaningful results; however, fixed-time sealer counting is used to reduce the time for data collection. The data are plotted in the form of normalized pole figures and analyzed.

To determine the relative volume of material associated with a given-texture component and an index of preferred orientation, the data are integrated. This is done by numerical integration or, alternatively, by graphical means. Integrating over the interval from ϕ = 0 to ϕ = π/2 and α = 0 to α = n/2 (where ϕ and α are spherical coordinates) will give the pole concentration per unit area for an ideally randomly oriented specimen for an octant of the sphere of projection. The relative volume of material associated with a given set of intensity maxima can be determined by integrating the intensity over the area of the maxima, summing these values, and dividing by the multiplicity to obtain the total intensity, It. The relative volume can be expressed as a ratio of It divided by random intensity. The texture strength can be expressed as the standard deviation from the random condition. Such information is vital to quantitative predictions of the anisotropy of properties

A brief and simple reciprocal space equation is derived for the X-ray camera setup, and the theoretical background necessary for graphical solutions is discussed. A typical graphical solution for powder patterns is carried out using the pattern of urea.

The determination of the orientation of a single crystal by Laue X-ray photographs is dependent on the identification of the indices of the spots. At the present time, the determination of indices is done by various methods, none of which is entirely systematical. A method for establishing the indices of the spots which avoids a trial-and-error approach is described here. The method is graphical, uses a specially compiled table of erystallographic angles and is not dependent on the complexity of the structure of the crystal or its symmetry. An example of the cubic system is included. With more complex crystal structures the method becomes very laborious and the help of computer methods is suggested.

X-ray studies indicate that mixed iron and nickel “amalgams” are reactive even at room temperature. By distilling off the mercury from these amalgams at temperatures between 400 and 100°C, ultrafine iron-nickel alloy powders are readily obtained. X-ray studies show that these powders possess equilibrium structures corresponding to the temperature of preparation. Alloy powders belonging to many alloy systems and having controlled composition, purity, and particle size may be prepared by this process. One special use of the process is in the preparation of homogeneous alloy powders for studying solid state equilibria below 400°C, particularly in alloy systems with sluggish transformations, the process being invaluable in the temperature range between 200 and 100°C, Another is in the preparation of ultrafine metal and alloy powders with equally fine, if not finer, dispersions of other phases, suited for studying dispersion-strengthening. Both of these special uses are currently under investigation,

Compositions in the tantalum-carbon system were prepared by carburizing high-purity tantalum wires. The microstructures so produced exhibit regions of a characteristic striated structure identical to those observed by earlier investigators. There are disparities in the literature as to the origin of such structures in the tantalum—carbon system. They have been variously described as “twins,” “striated structure,” “precipitate,” and “structure of unknown origin.” This paper presents conclusive evidence that the structures in question are the result of precipitation on cooling. In addition, a coherent precipitation model is applied in which it is shown that the lattice relationship {0001}Ta2C‖{Klll}TaC can exist with less than 0.5% misfit. This relationship is shown to completely explain the occurrence and characteristic appearance of the observed micro structures. Correlations between chemical analysis, X-ray diffraction results, metallography, and microhardness measurements confirm the proposed precipitation model.

The lattice parameters of single-crystal SrTiO2 were determined by X-ray diffraction as a function of temperature from 4.2 to 300°K. Three significant regions were found: from 65 to 110°K a tetragonal modification, exists (c/a = 1.00056); from 35 to 55°K, line splitting consistent with orthorhornbic symmetry was observed, and at 10°K an anomalous maximum in the lattice parameter vs. temperature curve was found which suggested a third structure transformation. In the tetragonal region (at 78°K) the formation of a domain structure was observed with a polarising microscope. The low-temperature X-ray technique and X-ray cryostat are described.

Helical dislocations and vacancy aggregates have been reported in lithiumdoped germanium and in diffused silicon. In the present study, defects related to an excess vacancy concentration are examined in as-grown silicon. X-ray topography, etch techniques, and Hall effect are used in determining the conditions of formation of these imperfections. Two distinct types of defects are observed: (1) helical dislocations and (2) dislocation loops. The helical dislocations are identified in the X-ray topographs and correlated to their etch figures. The diameters of the helices in various crystals range from less than 10 to 100 μ. The largest concentration of helices are observed in the initial growth, but prismatic loops or helical segments are also present in the low dislocation density regions of some crystals. The dislocation loop image consists of a pair of opposed arcs. The lengths of images vary from 30 to 400 μ, and the axis of the loop is usually parallel to <110> linage contrast changes with changes in sample orientation, but conclusive Burgers vector determinations are incomplete.

The formation of these defects is shown to be directly related to the heat treatment during crystal growth. The total acquisition of vacancies during growth is quite high and is attributed to the “orbital” growth process. In the “orbital” method, the seed check rotates 8-9 rpm about the center of the crucible as the growing crystal rotates 50-60 rpm. A linear relationship exists at room temperature between the vacancy concentration and the antimony impurity concentration. Impurity concentrations were determined independently by chemical and mass spectrograph techniques. A defect complex involving V− and Sb+ in thermal equilibrium is employed to explain this effect.

A study utilizing an application of X-ray diffraction analysis has been made to determine the depth of surface damage in s ingle-crystal wafers of germanium. Damage was introduced by mechanical lapping and sawing. A scintillation-counter double-crystal diffractometer system was used with a 3-m evacuated collitnator. This experimental arrangement employed the (220) reflection, from a silicon monochromator, using Cu Kα1 radiation. All wafers were taken from dislocation-free crystals which were subsequently centerless ground, sawed, lapped, and etched. Half-widths were determined for the sawed and lapped conditions. Successive etchings were used to remove the damaged surface layer with the resulting halfwidths being plotted as a function of thickness removed and etching time.

The depths of damage—8.0 ± 0.7 μ for sawing and 3.0 ± 0.7 μ for lapping—were indicated by the depth at which the line breadth measurements reached a limiting value. For crystals used in this study, the median value for this limiting half-width was 28″. The experimental data expressing the rate of etching indicates the presence of two separate rates—one for the damaged material and one for the undamaged substrate. An unexpected finding is a faster etch rate for the undamaged material than that observed for the damaged layer. Quite good correlation is obtained between the depth of damage as determined by X-ray and etching techniques.

Accurate measurement of the electrical and mechanical properties of polycrystalline oxide ceramics has revealed anisotropy in a number of properties. The source of this anisotropy may be attributed to a number of causes, however, with oxides having anisotropic crystals, preferred orientation of the crystallites may be suspected. Aluminum oxide and beryllium oxide ceramics samples of high purity and density were formed by slip casting, dry pressing, isostatic pressing, and extrusion. Pole figures for the (113), (110) and (030) planes in aluminum oxide and (100) and (103) planes in beryllium oxide were prepared by using a Siemens automatic pale figure goniometer.

It was found that both slip-cast oxide samples and dry-pressed aluminum oxide samples and dry-pressed beryllium oxide samples showed sufficient preferred orientation to prepare a pole figure from the data. The actual preferential orientation of the crystallites in these two oxides is discussed and the pole figure information presented. The effect of furnace atmosphere and surface contaminants on re crystallization at an exposed surface is covered briefly.

A series of four types of glasses was supplied for investigation. Six individual filaments of each glass (each filament ranged between 7 and 10 μ in diameter) were extracted and the ultimate tensile strength determined for each. The ultimate average tensile strength was then used in the determination of the tensile load applicable to the investigation.

Two methods of examination were used—the Laue and a modified rotation camera. The results of the investigation seem to indicate that a reconstructive transformation in three of the four glasses studied was in process. These results have not been confirmed, due to time limitations. In the case of the E glass investigated, a series of rings were faintly produced after 15 days under 35% of the ultimate average tensile strength. These rings, actually egg-shaped ovals, appeared at 15, 20, and 30 mm from the point of contact of the incident beam. In the other modified E glass and in the YM-31A (BeO) glass, the egg-shaped configuration did not appear in the rotation camera, but did appear in the Laue examination as a semioriented series of spots.

The structural aspects of the precipitation of MgFa in LiF have been studied in LiF crystals containing up to 3 wt. % MgFs. The precipitate particles appear to be rodlike, having a sawtooth morphology. The rods lie in two directions on matrix planes which are close to but not precisely {111}LIF.

The lattice orientation relationship between MgF2 and LiF has been established by X-ray techniques as

(111)LIF‖(100)MgF2

Laue photographs of slowly cooled crystals show diffuse X-ray scattering effects which are associated with the precipitation process.

Excellent matching of atoms at the interfaces between the precipitate and matrix is postulated on the basis of a hard-sphere atomic model. The results suggest that phase coherency obtains during the early stages of growth, and that growth is controlled by dislocation interfaces.

Rapid quenching retains all MgF2 in solution. Upon subsequent aging a transition structure forms which is based essentially on the LiF lattice but with a cell size of 8.20 Å, roughly double that of LiF. With further aging the transition structure is replaced by the normal MgF2 tetragonal structure.

Solid solutions of AlCl3 and TiCl3 were formed in all proportions by milling together dry powders of AlCl3 and TiCl3 (delta crystalline modification). For each composition, X-ray diffraction showed a single phase having a high degree of layer stacking disorder. These materials, including milled AlCl3, were isomorphous with the so-called delta modification of TiCl3.

The presence of solid solutions was investigated primarily by lattice parameter measurements made with a diffractometer and carried out with the aid of internal standards. For the milled materials, lattice parameter changes were observed not only with changes of composition, but also with the crystallite size. In terms of the system of hexagonal axes used for α TiCl3, the a parameter for the milled samples decreased with decreasing crystallite size, whereas the c parameter increased. In the samples examined, this effect was about the same order of magnitude as that due to changes in composition. In order to evaluate the effects due to composition alone, a correction was made for the effect of crystallite size, and the lattice parameters were then expressed as the limiting values one would obtain for very large crystals.

With increasing AlCl3 content, the a parameter decreased from 6.168 Å for no AlCl3 to 6.162 Å for 20 mol.% AlCl3. For higher AlCl3 content, a showed a relatively rapid and almost linear decrease to 5.921 Å for 100% Aids. The c parameter decreased from 17.73 Å for no AlCl3 to about 17.61 Å for 35 mol.% AlCl3, and thereafter decreased slowly to 17.58 Å for 100% AlCl3. The layer stacking disorder appeared to increase the lattice parameters in solid solutions containing less than 25 mol,% AlCl3. However, at 25% and 100% AlCl3, no significant effect was observed.