In this paper an attempt is made to review in rather broad perspective the origins and history of quantitative methods in diffraction analysis, at the same time leaving an in-depth examination of the present state of the art to other better qualified contributors to this conference. Space limitations preclude mention of many significant contributions, for which I am very sorry. It will be possible to review only a number of pivotal historical events, while also taking note of certain other researches that seem representative of historical and present-day trends.

The birth of quantitatively meaningful analysis in the mid-1930s depended upon a realisation of, and allowance for, the alteration of the diffracted intensities resulting from absorption of x-rays by the specimen. Furthermore, advances in the art achieved during the past forty years have been closely related to improvements in the treatment of the absorption factor.

An updated d, I-MATCH procedure [Frevel and Adams, Anal. Chem., 40, 1335-1340 (1968)] is described which permits analysts to compare diverse powder-patterns in a quantitative,objective manner. Criteria are established for rating the quality of a diffraction standard. The d, I-MATCH program has been combined with an efficient SEARCH program to facilitate the quantitative matching of multiphase powder patterns.

Quantitative analysis by x-ray powder diffraction methods has become increasingly important in recent years with the availability of computer-controlled automatic powder diffractometers. All data gathering techniques require suitable reference standards to scale the measured data properly. One means of achieving this scaling is through the reference Intensity ratio which is defined as the intensity ratio of the strongest diffraction maximum of a substance to the strongest maximum of a reference material in a 1:1 mixture “by weight. These ratios may he measured or they may he calculated if the crystal structures of the materials are accurately known.

Beginning in December 1968, Type K expansive cements of both the shrinkage-compensating and self-stressing types, particularly ChemStress (a self-stressing cement) have been tested, and examined by X-ray diffraction in the Concrete Laboratory of the U. S. Army Engineer Waterways Experiment Station. They are interesting subjects for the study of mixtures by X-ray diffraction because they may contain as many as 14 identifiable phases, including most of the phases in portland cement. Their examination by X-ray diffraction is greatly assisted by chemical treatments, first with maleic acid in methanol, followed by treatment with ammonium chloride solution to remove the calcium sulfates and leave a residue that consists of tetracalcium trialuminate sulfate, quartz, corundum, and a few very minor substances which have proved to be unidentifiable.

Single crystal X-ray diffraction methods for the study of crystalline materials, although reliable, have been, mainly confined to the academic laboratory because of the rather lengthy and complex procedure necessary to determine the unit cell and the space group. The situation has now changed. Several recent developments give single-crystal methods considerable potential for routine Industrial use. They Include growth of the data base, advances in lattice theory, and automation of the single-crystal X-ray diffractometer. To identify an unknown, one can start with a single crystal, mount it on the diffractometer, determine a refined primitive cell, reduce the cell, and check against a file of known reduced cells. The entire procedure can be automated. As a result, the single-crystal X-ray diffraction method can now complement the powder method for the routine analysis of crystalline materials.

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.

X-Ray powder diffraction (XRPD) techniques are compatible with studies of the transplutonium elements and their compounds. Only limited amounts of these materials are available for study, and microchemical techniques exist for the preparation of samples suitable for X-ray analysis. The microscale syntheses, systems for annealing/ quenching to bring about phase transformations, and a modified powder diffraction camera are described. Examples of recent and current work are presented to illustrate some specific applications of XRPD to basic, transplutonium element research.

The Morgantown Energy Research Center of ERDA is studying fouling and slagging of pulverized coal fired boiler tubes resulting from mineral matter contained in the coal. The research is dependent on the development and application of reliable analytical techniques which can be applied to the coal and ash products to determine the mineral interactions responsible for fouling and slagging. X-ray powder diffraction is one of the techniques used to characterize the feed coals and their combustion products. A summary of the methods and techniques applied at MERC is the subject of this paper.

The mineralogy laboratory of the U.S. Geological Survey in Denver has developed a series of time-sharing oriented computer programs which aid in the identification of crystalline compounds from chemical and X-ray diffraction data. These programs operate on a data base compiled primarily from the Powder Diffraction File of the Joint Committee on Powder Diffraction Standards (JCPDS). Diagrammatic X-ray diffraction patterns and various search tables are products of these programs. Additional programs can retrieve information from the data base by chemical formula components or Powder Diffraction File number, and can search and match reflections of an unknown against reference patterns.

Jackson Laboratory is using computer searching of the powder diffraction file on an “in-house” IBM 365/65 computer for about 1000 searches per year. This paper will discuss our experiences with the search program.

A Philips Automatic Powder Diffractometer (APD), modified to communicate with an XDS Sigma 5 computer collects the data. A program in the Sigma 5 provides both hard copy output and a computer deck of punched cards for input to the JCPDS search program.

The JCPDS search program is indispensable for our large volume of samples . The majority of these samples are corrosion products which generally have “broad peaks, and frequently, preferred orientation.

A preliminary round robin test to evaluate available computer search/match has been carried out and comparisons made with handsearching techniques. Participants in the teat were all experienced diffractionists and a variety of data collection instrumentation was employed. Hand-searching and computer searching were found to be equally efficient, about 70-80%, for the mineral and inorganic samples provided that the quality of the “d” values was good (1 in 1000). Although the computer methods were much quicker, they were found to be much more sensitive to the quality of the “d” values. Where elemental data was used to assist in computer searching, much poorer “d“ values (3 in 1000) were acceptable. Hand-searching was found to be vastly superior to computer searching for the organic specimen.

Exposure of industrial workers to respirable crystalline silica is receiving considerable attention at present from industrial laboratories and regulatory agencies. Analytical methodology for rapid and accurate determinations of microgram quantities of silica is necessary. The X-ray diffraction method which has been recommended by NIOSH requires lengthy sample preparation.

An X-ray diffraction method has been developed for the quantitative analysis of α-quartz directly on polyvinyl chloride filters in the microgram range. The minimum detectable concentration of α-quartz is approximately 2μg/cm2. This represents a sensitivity comparable to that claimed using the Bumsted method. The necessity of ashing the filter and depositing the residue on silver membrane filters, as well as the addition of a standard, is avoided. This minimizes handling and alteration of the sample.

The reaction kinetics of forming TiB in a mixed powder compact were analyzed using internal standard and dilution methods. The dilution method was not successful due to insufficient dilution, while the internal standard method was satisfactory to confirm that diffusion is the rate controlling mechanism. Difficulties analyzing metal powders and diffusional film products in mixed powders are discussed.

The effect of the position of the X-ray unresolved Kα1 - Kα2 line doublets, diffracted from powder specimens, on the precision of the calculated lattice constant has been determined using a least-squares analysis. An analytical procedure to synthesize CuKα doublet X-ray diffraction peaks with X-ray characteristic lines (half widths ranging from 0.1° to 0.4° 26) has been applied in correcting the weighted wavelength of the doublet peak position. A series of correction curves was established from which the true 26 peak position of the weighted Kα wavelength could be determined from the measured 29 peak position.

This paper describes the principles, methods, instrumentation and results of EDXKD and a computer method of profile fitting to obtain corrected intensities and peak energies from isolated and overlapping reflections. The profile, P, of a diffraction peak is a convolution of the incident X-ray spectrum, X, the geometrical aberrations, T, the contribution from the specimen, S, and the detector resolution function, D.

The main characteristics of a new method of texture analysis are presented as well aa a comparative study of the results obtained with three different methods.

The “misorientation. contrast” which occurs at boundaries marking the relative displacement of adjacent subgrain reflections in x-ray diffraction images is shown by a stereographic projection method of analysis to be useful for deciphering x-ray images obtained by the Berg-Barrett and Lang techniques. Experimental results are given for subgrain structures observed in Zn and A1203 crystals.

X-ray diffraction topographs obtained in the anomalous transmission geometry contain images which are quite different from those obtained from thin crystals (μL<=l). In this paper various topographic images which are unique to thick crystals (μL>10) will be presented and discussed in terms of dynamical diffraction in imperfect crystals. First, it is observed in topographs that images of crystal imperfections caused by disruption of the anomalous transmission effect are slightly broader or more diffuse in the H-diffracted (Bragg-diffracted) beam than in the O-diffracted (transmitted beam). These observations have been made in both copper and nickel crystals. Such broadening can be explained by the presence of unique extinction terms in the expression for the intensity of the dynamically diffracted beam in an imperfect crystal.