The advent of computer automation and profile fitting techniques in powder diffraction., along with a general solution to the problem of preferred orientation, has opened a series of new horizons for this method. The new levels of accuracy attainable have brought us to the threshold of routine reliable qualitative phase identification, high precision quantitative analysis and the ability to perform crystal structure analysis on some of the most important technological materials. It has been primarily the question of accuracy which has held up these developments until now.

Different procedures used in precision measurements of lattice parameters are, strictly, only valid if they can be shown to give results that are mutually reproducible. For this purpose reproducibility is defined in terms of the parameters a. and standard deviations a. obtained for X-ray specimens of one or more reference materials. The requirement is that all systematic errors should be minimized to a level below that of the random measurement errors. Where these have a Gaussian distribution the significance of the difference, Δa°, between two , measurements can then be Let;Led by evaluating . Thus, if K < 2 the difference, Δa°, cannot be distinguished from the effects of random measurement errors. This condition should be met for specimens of the same sample if reproducibility is good. For K ≥ 3 the value of Δa° is then taken to reflect real differences in the crystalline Jattice of two X-ray specimens of a given compound. A basis is thus created for the study of solid solubility and for the precise characterization of crystalline compounds.

The two basic parameters traditionally employed in qualitative phase identification using the powder diffractometer are the diffracted peak maximum intensity and the interplanar spacing “d”. Moat routine powder diffractometry carried out today is performed with the parafocussing geometry, and this arrangement gives a diffraction pattern in terms of diffraction angle (2-theta) vs. intensity. During the course of obtaining a set of experimental 20 and intensity values from a specimen to be analysed and in the subsequent conversion of these data to a d/I list for qualitative phase identification, errors will of course accrue. Most qualitative search methods in use today give high credence to the d-value, since this is by far the most accurately known of the two search parameters, and d-values of a few tenths of a percent are reasonably easily obtained with a well aligned and properly calibrated diffractometer. Intensities, on the other hand, can be subject to errors of the order of tens of percent, and problems arise in qualitative analysis where the need arises to subtract an identified phase from a multi-phase pattern to allow identification of further phases.

The integrated and peak intensities of a series of silicon powder samples of various crystallite sizes were measured with a computer automated diffractometer and a profile fitting method (PFM). The accuracy of the PFM was better than 0.003% in computing the integrated intensities. The PFM gave more precise values than would be expected from counting statistics of the peak intensity. The average difference between each measurement and the average intensity was 0.5% with little dependence oo the absolute intensity. Crystallite sizes have a large effect and it is essential to rotate the specimen around the diffraction vector. The best results were obtained with <10 μm particles. Larger sizes decrease the absolute intensities and change the relative intensities. Structure refinement using the POWLS (powder least squares refinement) program showed the presence of (111) preferred orientation even in the <10 μm specimens. R(Bragg) decreased from 4.3% to 0.7% by including the preferred orientation correction in the refinement.

Standard Reference Materials (SRMs) from the National Bureau of Standards are samples or artifacts certified for one or more particular parameters. The NBS has produced SRHs since 1905 to aid commerce, to improve measurement technology and to assist in the enforcement of regulations. Today nearly 900 different SRHs are available to serve major segments of industry such as ferrous metals, nonferrous metals, mining, glass, primary chemicals, computer, nuclear power and electronics. In addition to the industrial customers, major SRM users include both federal and state governments, universities and nonprofit research organizations.

Lattice parameters, obtained by least-squares refinement of data from calibrated Guinier powder patterns, are compared in an effort to establish procedures for obtaining reproducible 2θ values with Guiniertype focusing camera techniques. The calibration procedure is discussed and a method of calculation to reduce loss of precision is proposed. Effects of particle size and crushing are also discussed as well as some sources of error such as use of only selected calibrant lines, film background, and mutual interference of powder lines.

The production of standard x-ray diffraction patterns at NBS imposes special requirements in the data processing of powder patterns. The patterns should be complete and have an overall accuracy of better than 0.01 degree two theta. To ensure completeness all the observable peaks should be indexed. To make certain that the sample is a pure phase, weak peaks have to be identified as well.

The indexing of all the peaks implies that the cell constants must be known and there should be a good agreement between all the calculated and observed peak positions. In practice this is achieved by a least-squares refinement of the unit cell parameters. This serves as a test of the assumed unit cell and also as an interpretation of the observed peaks. Finally, an attempt is made to identify the space group. This step also requires the identification of weak peaks. The agreement of a known space group with the observed reflections further confirms the purity of the sample.

This paper examines some of the concerns regarding the development of an algorithm for the refinement of X-ray diffraction profiles. The object of the algorithm is to provide a time efficient method of refinement through the choice of a suitable profile function and optimization technique.

Seven profile models were tested using a least-squares error criterion for refinement. Profile parameters were refined using non-linear Gauss-Newton, Marquardt and Simplex algorithms. The profiles were refined on a pattern digitally collected from an NBS 640A silicon sample.

The results of this study indicate the repetitive function evaluations are not necessarily the time consuming step in the profile fitting process. As the number of parameters needed to evaluate the profile and the number of points in the profile increases, the time required to perform the mathematics in the Gauss-Newton and Marquardt algorithms increases. Although the Simplex was most memory and time efficient, our Gauss-Newton optimization algorithm provided a more consistent set of refined values which were not as dependent on the initial estimates of the parameters.

The most favorable results were obtained by using the split Pearson VII profile with the alpha 2 reflection fixed in position and intensity with respect to the alpha 1 reflsction. This method generated the lowest residual error and was found to avoid some problems resulting from the alpha 1, alpha 2 line overlap.

This paper describes a set of interactive computer programs written in FORTRAN IV and implemented on a POP 11/34 equipped with RLO-2 ten Mbyte discs and an RSX-11M operating system to assist in x-ray diffraction phase analysis. The packing of the data base will be described along with the various interactive programs that access it. The search/match package is designed more as a set of aids for the diffractionist rather than as a single totally automated search/match program, the procedure adapted by many of the xray diffraction (XRD) equipment manufacturers. The approach taken allows the analyst to direct the analysis procedure by utilizing different search/match programs or specifying various options within a given program.

The Powder Diffraction File (PDF), published by the JCPDS-International Centre for Diffraction Data, is one of the most widely used scientific data bases. It currently consists of about 40,000 x-ray diffraction patterns, organized into 32 sets and 5 subfiles: metals and alloys, minerals, common phases, forensic patterns, and those from the National Bureau of Standards (NBS), New patterns are being added to the PDF at a rate of 2,000 patterns per year. The sources of these patterns are the literature, private contributions, grants in-aid projects, and the JCPDS Associateship at the NBS.

Interplanar spacings (d values) from X-ray powder diffraction data occur over a wide range of values for the phases that have been described to date. They are not; however, uniformly distributed; rather, the d values are concentrated near certain values and thinly distributed in other regions, We have investigated the possibility of utilizing this distribution of d's to develop a search/ match method for phase identification. We found that there exist single d values that can be unique or almost unique to a certain phase. Also, the number of phases that could be uniquely characterized by single d's was increased by limiting the classes of compounds that were searched. The use of such characteristic d values resulted in a simpler search/match procedure.

A simplified and effective computer Search/Match method is described in which no more than 12 largest d-value reflections regardless of intensities are used for the Powder Diffraction File standards. A quantitative procedure utilizing the figure-of-merit in the IBM Search/Match method was employed to show the applicability to inorganic, mineral and organic mixtures. The analyses gave the same results as the complete File but the standard databases and analysis time are reduced by about a factor of two. Search/Match without using intensities also gave the same results; this may be useful when instrument geometry and/or preferred orientation cause large errors in the relative intensities. The error limits in measuring the d-spacings were found to vary from ±0.1° to 0.5° (26) depending on the degree of overlaps.

Over the past fifteen years two basic computer search/match strategies have evolved. The exhaustive search approach of Johnson and Vand (1) uses a sequential file structure whereas Nichols (2) developed a strategy which uses an inverted file, examining only those patterns containing lines of interest. Frevel (3) was the first to attempt to relate the quality of the reference patterns to the search strategy using a very restricted data base. These “first generation” search/match algorithms were forced to use very wide d and I windows due to the poor quality of the unknown and reference patterns.

Snyder (4) wrote the first “second generation” search/match procedure which takes advantage of high quality of data in the JCPDS data base when it is present. Recently, a minicomputer optimized version of the Johnson-Vand strategy has been incorporated into this search system enabling a chance to compare these two strategies under similar conditions.

Preferred orientations in powder diffraction specimens can cause large errors in measured intensities. An extreme case is shown in Figure 1, Smith and Barrett (1979) reviewed the various methods which have been proposed for reducing this effect. Subsequently, two methods which are used commercially for aggregating finely divided solids have been proposed for preparing powder diffraction specimens (Smith, Snyder, and Brownell, 1979; Calvert and Sirianni, 1980). In one of these, spray drying, a finely divided solid is suspended in a liquid together with small quantities of a deflocculent and a binder. This mixture is pulled by venturi action through a nozzle into a heated chamber. The spherically shaped aggregates dry before falling to a collection surface. The apparatus is fairly large (3 X 3 X 4 ft. at NBS), and operating parameters must be carefully chosen.

Preferred orientation has long been considered the primary source of systematic error involved in quantitative analysis by X-ray powder diffraction. Techniques of spherical agglomeration have been shown to eliminate preferred orientation provided that the agglomerate size is made sufficiently larger than the particle size. These techniques invariably employ the surface energy minimization of a liquid phase dispersed within a second fluid to create the spherical form desired. Spray drying has been the only method to date which has been successfully used to prepare spherical agglomerates suitable for X-ray diffraction. This study was undertaken to investigate possible deleterious effects of spray drying as a diffraction sample preparation technique.

Solid solutions are pervasive in minerals and in industrial inorganic materials. The analyst is often called upon to provide qualitative and quantitative X-ray phase analysis for specimens containing solid solutions when all that is available are Powder Diffraction File (PDF) data or commercial standards for the end members. In an earlier paper (1) we presented several examples of substantial errors in accuracy of quantitative analysis that can arise when the crystallinity and composition of the analyte standard do not match those of the analyte in the sample of interest. We recommended that to obtain more accurate quantitative analyses, one should determine the analyte composition (e.g., from XRF on grains seen in a SEM or from comparison of cell parameters with those of the end members) and synthesize an analyte standard with this composition and with a crystallinity approximating that of the analyte (e.g., as determined from peak breadth or α1/ α2 splitting).

X-ray diffraction has been shown to provide an accurate qualitative and quantitative determination of the pigment composition of paint films. This analysis, however, is frequently complicated by the presence of pigments with plate-like crystallites which show a marked tendency to orient in preferred directions in drying paint films. The variability in the degree of orientation causes line intensity variations not attributable to pigment concentration.

A technique based on a summation of the intensities of many lines has been used to correct for the effects of preferred orientation in the analysis of retained austenite in certain steels. This method is shown to be applicable to the quantitative analysis of mica in paint films.

In the steel hardening process, steel is heated to a temperature where a face-centered-cubic solid phase called austenite is formed. After a stabilization period, the steel is quenched into a medium which transforms the austenite into a metastable, body-centered-tetragonal solid phase called martensite. On occasion the austenite is not entirely transformed into martensite and some austenite remains. This untransformed (retained) austenite is sometimes detrimental to the finished product, and often there are requirements as to the amount of retained austenite permitted In the finished product.

X-ray diffraction procedures (XRD) are normally used to determine the amount of retained austenite and this paper describes the preparation and characterization of the Standard Reference Materials used to calibrate x-ray diffraction units.