An improved deconvolution theory is presented for the resolution enhancement in powder diffraction spectra. In powder patterns, diffracted intensity, which is conceptually located at a single 2θ position, is actually distributed over a range of 2θ because of instrumental factors, crystal defects, beam penetration, and sample flatness. The location of the peak is usually taken as the peak maximum or the peak centroid. However, when interpreting complex spectra these approaches to locating peaks are not straightforward and deconvolution can be a useful tool. The method presented herein enhances resolution without altering peak area or peak position. Comparisons are made with results of other methods, with emphasis on deconvoluting spectra that contain random error. The discussion includes treatment of discrete data and analysis of the properties of the solution.

A program is presented that removes broadening from X-ray diffraction spectra. An instrumental spectrum can be used to describe empirically the broadening to be removed, or a Gaussian, Cauchy, or Pearson-VII distribution can be used to analytically describe it. In either case, singlet or doublet forms can be generated. The program returns the deconvoluted spectrum, the reconstructed spectrum, and a sum-of-squares difference between the original and reconstructed spectra. Deconvolution is accomplished using a combination of least-squares, background, and smoothing criteria that minimizes the effect of random counting errors.

In the Rietveld method for the analysis of powder diffraction data the entire pattern is calculated using a model for the positions of the peaks (the unit cell parameters), their intensities (dependent on the atomic positional and thermal parameters, preferred orientation, etc.) and their widths and shapes, together with a description of the background. The calculated pattern is then compared with the observed step profile, point by point, and the model parameters are adjusted by least-squares methods.

In order to ensure the best possible outcome of the refinement, a number of critical decisions must be made prior to the collection of the step intensities. For constant wavelength diffractometers, these decisions relate to the wavelength, beam collimation, range of diffraction angles, angular distance between steps, and counting time (X-rays) or monitor setting (neutrons) at each step. The effect of the first three of these factors is well known, but the selection of appropriate values for the counting time T (in effect, the intensity) and for the step interval (which, for a given scan range, determines the number of steps, N) is not straightforward. In fact, N and T are usually chosen more by tradition or by pressure of instrument time than by a consideration of their possible effect on the results of the analysis.

Since each measured step intensity is used in the Rietveld method, the number of ‘observations’, N, in a scan can be made arbitrarily large (independent of the number of Bragg reflections) by decreasing the step interval. It is, however, the intensities of the Bragg peaks that are the fundamental quantities in any structure analysis, not the step intensities themselves. Thus, although the precision of the peak intensity measurement is improved by increasing N or T, this only occurs up to the point where counting variance becomes negligible in relation to other sources of error; further increases provide no additional structural information.

Systematic studies of the effect of variations in T indicate that the optimum value of the maximum step intensity is only a few thousand counts. If significantly larger numbers of counts are accumulated, the accuracy of the structural parameters is not improved, time is wasted, and the usual weighting scheme based on counting variance becomes inappropriate (i.e., the parameter esd's reflect their precision rather than their accuracy). In the case of step width, the optimum value is between one-fifth and one-half the minimum full-width at half-maximum (FWHM) of well-resolved peaks, the exact value depending on T and the complexity of the diffraction pattern. Smaller steps provide little or no improvement in parameter accuracy (especially when step intensities are large) and, at the same time, introduce serial correlation between adjacent residuals in the profile, again leading to wasted time and corruption of the esd's.

In practice, it is the combination of N and T chosen for the experiment that is of greatest importance in determining the efficiency of the data collection strategy. If the pattern has many overlapping peaks, N should be large, corresponding to a step interval of about FWHM/5, to provide adequate peak resolution, and T should be correspondingly small to minimize serial correlation. For a fixed total data collection time, a given level of Rietveld precision can be achieved more efficiently by the use of large N and small T than by combinations of small N and large T. The implications of these restrictions for ‘real-time’ data collection are noteworthy.

Charles Barrett's work in phase transformation at the atomic level helped redefine the underpinnings of the science and practice of metallurgy. His work in low temperature physical chemistry has extended its range. And, perhaps more than anyone else, as a teacher and author, he has helped introduce the technique of X-ray diffraction to the present generations of practicing metallurgists.

The relevance of his contributions is demonstrated by the continuing utility of his widely translated metallurgical text, Structure of Metals, which, when it first appeared, made the understanding of metallurgy at the atomic level accessible to a wide audience. Today this book has become a compendium of first principles.

A systematic survey of phase formation in the Na2O-ZrO2-SiO2 system has revealed inconsistencies in the number and identity of ternary phases, and of their X-ray powder data. The phases Na2ZrSiO5, Na4Zr2Si3O12, Na2ZrSi2O7 and Na2ZrSi4O11 were prepared by solid-state reaction and their experimental X-ray diffraction patterns measured. Calculated X-ray diffraction patterns were generated by computer, using published crystallographic data, and critically compared with the experimentally observed values. The unit-cell constants were redefined to a greater accuracy than the presently accepted values published in the Powder Diffraction File. Only Na4Zr2Si3O12 produced an X-ray diffraction pattern which agreed with that previously published; those from the other phases were significantly different in both the intensities and positions of the reflections. Data for synthetic Na2ZrSi4O11 identical to the mineral vlasovite are reported.

The “hook effect” observed in the Warren-Averbach analysis of X-ray diffraction peaks from multiple layer thin films of copper has been investigated theoretically and experimentally. The strengths of the “hook effect” for films of different layer thicknesses were analyzed. The results showed definite correlation between the strengths of the “hook effect” and the grain size distributions in 1, 4, and 19-layer copper films.

X-ray powder diffraction was used as an analytical technique for the solid state synthesis of selective oxidation catalysts with large surface area. Qualitative analysis was used to determine the minimum temperature at which the synthesis was complete. Quantitative diffraction was used to analyze mixtures of isomorphous antimonates. Results indicated that the final mixtures are independent of the method of preparation, i.e., mixing or impregnation.

X-ray powder diffraction and single-crystal data are reported for a series of isomorphous compounds with the general chemical composition (Fe,Al)3(K,NH4,H3O)H14 (PO4)8·4H2O. The compounds are monoclinic with space group C2/c. Unit-cell parameters were determined on the mixed salt (Fe0.84,Al0.16)3KH14(PO4)8·4H2O, as obtained from sludge precipitated in commercial shipping-grade wet-process phosphoric acid. Single-crystal studies and refined powder diffraction data provided unit-cell parameters of a= 16.908(9) Å, b = 9.588(2) Å, c = 17.539(5) Å, and β = 91.06(4)°.

The following sixteen reference patterns of boride, silicide, nitride and oxide ceramics represent the second group of reference patterns measured at the National Bureau of Standards under the project “High Quality Reference Patterns and Total Digital Powder Patterns of Technologically Important Ceramic Phases”. Included in the sixteen reference patterns are data for two high Tc superconducting oxide phases (CuSr0.2La1.8O4 and Ba2Cu3YO7) plus one related phase (BaCuY2O5). In addition to these new phases, five other patterns represent phases previously not contained in the PDF and eight represent major corrections to data in the file. The general methods of producing these X-ray powder diffraction reference patterns are described in this journal, Vol. 1, No. 1, pg. 40 (1986).