Quantitative phase analysis by powder diffractometry requires accurate measurement of the integrated intensities of the diffracted, lines. When lines are isolated and on simple backgrounds, count integration techniques work very well. However, when one or more lines overlap the line of interest, or a complex background is present, profile fitting techniques are required in order to eliminate interferences.

Profile fitting involves choosing a mathematical model to represent the expected profile shapes. Experience has shown that the profile shapes obtained with a parafocusing powder diffractometer are not easily described and many models have been tried with varying degrees of success. Generally the more free parameters allowed In the model the ‘setter the fits, although, aesthetically one would like to keep the number of free parameters to a minimum.

The spherical wave theory of X-ray Pendellosung fringes in perfect crystals (N. Kato, Acta Cryst, 14: 526, 627, 1961) is extended to the case of crystals including a single stacking fault in an arbitrary way, Kelvin's stationary phase method is used extensively. The stationary phase condition gives us the trajectories of X-ray beams in the crystal. The phase and the amplitude along each trajectory are obtained by straightforward calculation. Based on this crystal wave field, the section patterns in X-ray diffraction topographs are obtained both for the direct and the Braggreflected waves. Characteristic fringe-patterns are expected. Through the image of a fault plane in a single section pattern, the geometrical configuration inside the crystal and the magnitude of the fault vector can be determined. Traverse patterns are also discussed. The fault image based on the plane wave theory (Whelan and Hirsch, Phil. Mag. 2: 1121, 1303, 1957) is also reformulated in the most general Laue case without the use of ad hoc assumptions on the shape of the dispersion surface.

SIROQUANT is a suite of personal ccmputer programs which runs on an IBM-compatible 386 or 486 personal computer, and gives phase quantification of mineral samples hy Rietveld refinement using the full XRD profile. Eight phases can be quantified in a mineral with the 640 K RAM version and 11 in the EM version.

New features have been added since the original description was written (J.C. Taylor, Powder Diffraction, 6, 2, 1991) including calculations of amorphous percentages using spiked samples, particle size calculations, use of “measured” as well as calculated patterns as standards, pre-programmed refinement “Stages” with different variables in each stage, and improved menus.

Some advanced applications of the system using these new features are described.

Nonmetallic crystals with a variety of structures and chemical compositions have been exposed to fission spectrum neutrons in a core position of the Low Intensity Test Reactor (LITR), Oak Ridge, and examined by X-ray diffraction techniques. Wherever possible, single crystals were employed, and the neutron dosages ranged between 1019 and 1021 neutrons/cm2 at a temperature of approximately 85°C. In no case was a special technique used for examining radioactive materials because the problem of heavy induced radioactivity was greatly reduced by working withcrystals weighing a milligram or less. Both film and counter measurements were employed.

To achieve increased case and precision of alignment, and to allow for convenient alteration between normal usage with filtered radiation and crystalmonochromated radiation, the G. E. goniometer has been mounted on milling machine beds allowing for x-y translation and 360° rotation; in addition the tube mount was repositioned. The usefulness of this apparatus has been demonstrated by accurately aligning the goniometer for usage with filtered radiation, with a new alignment procedure. As a demonstration of the accuracy and precision of alignment, the lattice parameter of silicon was determined from a powder sample. A least-squares analysis of the data gave a0 = 5.43046 Å with a standard deviation of ±0.00005 Å, in excellent agreement with the value of 5.43054 ± 0.00017 Å determined in a recent International Union of Crystallography test in many laboratories.

A monochromator housing has been built for use with all types of direct-beam monochromators and all radiations. This apparatus attaches to the new tube mount and was used to determine the optimum procedure for preparing the doubly bent LiF monochromator crystals designed by Warren to minimize the volume sampled in the reciprocal space of a single crystal. According to a suggestion made by Chipman, a doubly bent monochromator for use with poly crystalline specimens has been formed and its geometry and applications are presented. This monochromator gives about one-half as much intensity as that obtainable using filtered radiation and similar operating conditions ; this type of monochromator is therefore a powerful tool for use with powder specimens. A transmission diffracted-beam monochromator has also been constructed which attaches in a simple manner under the counter tube housing. Under similar operating conditions with a LiF monochromator, this yields intensities only one-tenth of those obtained using filtered radiation.

An energy dispersive X-ray fluorescence spectrometer using pulsed X-ray excitation has been developed for use in large-scale environmental analysis programs. A grid controlled X-ray tube is coupled with variable secondary fluorescence targets to analyze for a wide variety of elements with almost optimum sensitivity. The operation of the pulsed tube in a feedback loop with the semiconductor detector spectrometer results in a substantial increase in output counting rates without pile-up. The loop functions by turning off the excitation immediately upon detection of an event by the spectrometer. Pileup events are virtually eliminated and the X-ray tube's available anode power is better utilized.

The electronic control of this feedback mode results in some unique features in the response of the system to varying sample mass. These features are discussed in detail. Experimental results for sensitivity and accuracy over the range of elements measured are presented. Early operating experience with the unit indicates increases of counting rates of a factor of five compared with similar conventional systems.

Quantitative analysis by x-ray fluorescence and photoelectron and Auger electron analysis can be effectively extended through a precise knowledge of the total aad subshell photoionization cross sections. Light element and intermediate element analysis, as based upon K and L series fluorescence respectively, involve x-ray interactions in the low energy region, Optimized analysis for essentially all the elements by x-ray induced photoelectron and Auger electron spectroscopy involves both x-ray and electron interactions in the low energy region. Unfortunately, theory and measurement for interaction cross sections in this 100-1500 eV region are difficult, particularly for the heavier elements. Nevertheless, recent advances in experimental and computerized-theoretical techniques for the determination of low energy interaction coefficients do permit establishing appreciatly more complete tabulations of cross sections than are currently available in this energy region.

In this paper, the types of interaction cross section data that are needed for quantitative x-ray and electron analysis are defined. Such data that are available from experiment and from theory are reviewed and compared. Some newer techniques for the measurement of cross sections are discussed. And finally, new “state of the art” tables are presented for the mass absorption coefficients of all of the elements and of some special laboratory materials. These are tabulated specifically for twenty-six of the most commonly applied characteristic wavelengths in the 8-110 A region and are based upon the best currently available theoretical and experimental data.

A review of the methods of characterization of materials using X-rays incident at grazing angles is presented. The rationale of all such methods is the need to obtain information from near-surface regions. The methods include grazing incidence diffraction, reflectivity, diffuse scatter and fluorescence. The experimental techniques are outlined, and the information obtainable and the methods of interpretation are discussed.

It is well known that all of the six independent components of the strain tensor can be calculated if the linear strains in six appropriate directions are known (e.g.). That calculation is to solve a system of linear equations, whose coefficients are defined by the orientations of the measured planes. The strains are determined by lattice plane distance measurements using X-rays.

The linear equation system can only be solved if the matrix of coefficients has rank. Whether this condition is met or not can be decided without calculating a determinant just from geometric relationships among the planes to be measured. A demand beyond that necessary condition is to make the matrix of coefficients so that the accuracy of the calculated strain tensor is best. From error calculation we know that there exist distinct ratios between the inevitable measurement errors and the errors of the calculated strain components. These ratios depend strongly on the geometric relationship among the lattice planes. It is the purpose of this paper to show how lattice planes should be chosen in order to get these ratios as small as possible i.e. to get a maximum of accuracy at a given number of measurements, or a minimum of experimental effort if a distinct limit of error is to be reached.

The broadening of powder pattern peaks has been studied by three methods—Fourier analysis, integral breadth measurements, and variance of the line profiles. The results obtained from the variances are compared with those obtained from the integral breadths and Fourier coefficients.

Tungsten filings were prepared at room temperature and their powder pattern peaks were recorded with a Norelco diffractometer using filtered Cu Kα radiation. The variances, integral breadths, and Fourier coefficients were calculated with the IBM 7094 computer. The results indicate that the variance is very sensitive to the range of integration s2 − s1 = (2θ2 − 2θ1) cos θ0/λ. An error of ± 10% in this range due to the difficulty in choosing the correct background changes the values of the variance significantly and the integral breadth to a lesser extent. However, the same error does not affect the values of the Fourier coefficients.

Comparing the particle sizes and strains obtained by the three methods, it was found that the strains agreed remarkably well. The particle size calculated from the variance was smaller (DeW = 150Å) than that evaluated from the initial slope of the Fourier coefficients (De – 210Å) and from the integral breadths 2De ≃ D1 = 430Å.

Three powder mixtures, each composed of four or more phases, were submitted for phase identification by x-ray diffraction. Laboratory technicians supplied tables of “d” values and of relative intensities as obtained separately and independently by use of the diffractometer, the Debye camera and the Guinier camera. These tables of diffraction data were “solved” by utilization of the Joint Committee search manuals and reference to the Joint Committee Powder Diffraction File (P.D.F.). The same tables of data were then submitted to the 2dTS:Diffraction Data Tele∼Search for a computer printout of results. Experimental data are also presented which provide a quantitative comparison of the accuracy of measurement of “d” values and of the resolution of Debye cameras vs Guinier cameras, since this information is necessary for efficient search procedures whether by manual or computer methods.

The incorporation of carbonate in the apatite causes a decrease in crystallite size as demonstrated in precipitated apatites prepared at 37°C. Carbonate disturbs the crystallization of the growing apatite crystallites to such an extent that materials with more than 15 wt% CO3 gives an ‘amorphous’ x-ray diffraction pattern. The incorporation of carbonate in precipitates prepared at 100°C. causes a shortening of the a-axis and a lengthening of the c-axis which is proportional to the carbonate content, supporting the concept that in these apatites, CO3 substitutes for PO4 (11). X-ray diffraction linebroadening studies of CO3-apatites precipitated at 100°C and electron micrographs show that the size and shape of the crystallites change from long needles to smaller rods to tiny spheroids, depending upon the amount of CO3. Carbonate causes the bonding in the apatite to become weaker and more isotropic, which results in the small spheroidal crystals.

This paper reports the effect of carbonate on lattice parameters and morphology of carbonate-apatites which have been prepared by the conversion of rnonetite, CaHPO4 in hot carbonate solutions. The structural effects of CO3 on the apatite is further reflected by the modification of the vibrations of the PO4 groups in the infrared absorption spectra. The morphology of ‘amorphous’ CO3- containing apatitic precipitates and that of CO3∼apatite with high CO3 content (prepared at 100°C) is similar, i.e., spheroidal in shape, but greatly differing in crystallite size.

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.

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.

Precision X-ray reflectivity data were obtained with a high-resolution reflectometer equipped with a rotating anode X-ray source and Ge 220 channel monochromators (one placed before and the other after the specimen). The surfaces and buried interfaces of thin films were characterized by ieast-squares refinement of experimental data. Values of thickness, density, and/or roughness of Pt “single-layer” and Pt/Co based multiple-layer films were determined.

Dislocations, Inclusions, and Precipitates. Impurity precipitated after growth and foreign particles accidentally included during growth both produce intense local strain fields which give rise to diffraction contrast effects resembling those seen in electron microscope images of precipitates. The relationship between the dislocation configuration and these localized strain centers can show whether the latter arise from inclusions or precipitates. Precipitates will generally be found strung along the grown-in dislocations, decorating them. On the other hand, inclusions often generate dislocations by lattice closure errors; such dislocations then fan out from the inclusion in the general direction of advance of the growth interface.

Twin Boundaries and Fault Surfaces. The cases when the twins have parallel lattices, such as in Brazilian and Dauphiné twinning in quartz, are interesting. When the crystals on either side of the twin boundary are both Bragg reflecting, the twin boundary may exhibit ‘stacking fault’ type fringes. From an analysis of the variation of visibility of these fringes in different reflections, the fault vector at the twin boundary and its variation with boundary orientation may be found. In quartz, other types of fault surfaces producing fringe contrast may lie parallel to growth horizons or they may mark growth sector boundaries. In synthetic quartz, they can also mark cell boundaries under conditions of cellular growth.

Internal Magnetic Domain Structures. In plates of Fe + 3% Si roughly parallel to (110), a variety of previously undetected domain structures has been discovered and analyzed. Diffraction contrast is produced by 90° domain walls but not by 180° walls. The 90° walls produce strong diffraction contrast even though the magnetostriction of silicon-iron is only about 10−5. In plates parallel to (112), the main lamination pattern below the complex pattern of surface closures can be revealed and, in favorable cases, interpreted.

X-ray Moiré Patterns. The most direct method of observing X-ray moiré patterns—by topography of one crystal closely superimposed upon another—involves considerable theoretical complexities and produces a variety of curious diffraction patterns. However, it shows promise of providing a means for the comparison of lattice spacings to about one part in 107 and for mapping strain fields very sensitively.

Fundamental-parameters calculations can be made on a laboratory microcomputer fo r automatic treatment of interelement absorption and enhancement effects in x-ray fluorescence analysis. A new software package, called XRF-11, uses an efficient combination of fundamental parameters and alpha factors to compensate for any lack of measured reference materials, while taking full advantage of whatever standards are available, even just pure elements. In many cases, one multi-element standard is enough for accurate analysis.

The new XRF-11 software uses the same data base of absorption coefficients, fluorescence yields, etc. as the big-computer program NRLXRF, and combines theory with experiment in a consis tent way that is similar to, but more efficient than, the treatment used in NRLXRF.

In epitaxial single crystal growing it happens very often that the composition of the grown film, say AxB1-x C, is not known exactly. Usually it would be possible to find out that compositions imply by determining the lattice constants of the film. The problem of such a measurement lies in the fact of internal and unknown stresses in the film. On the other side the knowledge of the state of stress σ and strain ε can also be of great importance. To calculate the stresses from X- ray measurements we need the lattice constants in the unstrained condition.

Hornstra and Bartels have shown that the lattice constant can be det ermined by X-ray measurements if the strain is isotropic in the film plane. In the following we show that the lattice constant and the full strain tensor can be calculated fromat least four X- ray measurements also in the general case.

A method is described for determining the magnitude and sense of systematic errors in x-ray diffractometer stress measurements produced by focusing aberrations during diffraction from imperfect specimen contours and wide horizontal beam divergences. Corrections for such systematic errors are presently not made. However, if the highest accuracy and/or absolute values of stress are desired, these must be either taken into account or minimized by control of beam geometry. Equations and computer data are presented to indicate the errors in 2θ and stress (σ) resulting from use of flat, various convex and concave curvatures for primary beam divergences of 1° to 3°, Stress errors are calculated for both the parafocus technique of beam focusing and the stationary or non-focusing method.

The results show that convex and flat specimens always produce negative 2θ deviations from the condition of perfect focus and thus a net positive or tensile stress error. The magnitude of this error increases as the radius of the convex shape decreases and/or the ψangle and beam divergence is increased. Concave specimens with curvatures less than the radius of the concave shape required for perfect focus (see body of report) produce positive 2θ deviations and, therefore, negative or com-pressive stress errors.

The stationary or non-focusing technique produced systematic errors which were 1/3 of those produced by focusing aberrations with the parafocus technique. Fortunately, in both cases the actual errors are not very large (less than ±7.5 ksi), even with divergent beams as large as 3° and convex radii as small as 125”.

The possibility that primary recrystallization textures are influenced by local inhomogeneities of deformation induced in the regions of grain boundaries has been confirmed by comparing the cold rolling and the annealing textures of polycrystalline pure irons which were different in the grain size prior to cold rolling. Analyses were made for the effects of deformation on crystals, namely storage of lattice strain and orientation spread, with application of X-ray diffraction techniques, in order to elucidate the role of in homogeneities of deformation on recrystallization texture formation. Apparent correspondence was found between the orientation dependence of stored strain energy and the textural change on recrystallization. This is a scribed to oriented nucleation in high energy blocks, in the case of originally large-grain material in which the effects of inhomogeneities of deformation are small. But discrepancies arise on this basis in originally small - grain material in which the effects of inhomogeneities of deformation are thought to be considerable. The discrepancy is inferred to arise as an effect of local inhomogeneities of deformation, from the change in the trend of rotational orientation spreads from, a stable orientation and the extent of development of potential nuclei of recrystallization at high energy blocks in the orientation spreads. The change is considered to give rise to the variation in amount of microstrain distribution, which is expressed in recovery characteristics of lattice strains and in the dependence of microstrains on the column length as analyzed by following the procedure of Warren-Averbach.