A new quantitative X-ray powder diffraction (QXRPD) method has been developed to analyze polyphase crystalline mixtures. The unique approach employed in this method is the utilization of the full diffraction pattern of a mixture and its reconstruction as a weighted sum of diffraction patterns of the component phases. To facilitate the use of the new method, menu-driven interactive computer programs with graphics have been developed for the VAX series of computers. The analyst builds a reference database of component diffraction patterns, corrects the patterns for background effects, and determines the appropriate reference intensity ratios. This database is used to calculate the weight fraction of each phase in a mixture by fitting its diffraction pattern with a least-squares best-fit weighted sum of selected database reference patterns.

The new QXRPD method was evaluated using oxides found in ceramics, corrosion products, and other materials encountered in the laboratory. Experimental procedures have been developed for sample preparation and data collection for reference samples and unknowns. Prepared mixtures have been used to demonstrate the very good results that can be obtained with this method.

The Powder Diffraction File (PDF) is a collection of single phase X-ray powder patterns, maintained and distributed by the JCPDS-International Centre for Diffraction Data. Over the past 10 years there has been increasing use of the PDF in computer readable form, but the limited amount of disk space available on most commercial powder diffractometer systems has limited use to a small subset of the total PDF. The recent availability of low-cost Compact Disk Read Only Memory (CD-ROM) systems offers an attractive alternative to conventional disk media. This paper describes a low-cost Personal Computer/CD-ROM system, “PC-PDF”, having a total available storage of 550 Mbytes. While seek times are relatively slow – typically, 0.5 seconds are required to traverse the complete PDF – by use of optimum packing and access algorithms, search strategies based on PDF numbers, chemistry, strongest d-spacing, etc., operate at a speed causing no great inconvenience to the user.

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.

Tabular untwinned crystals of colorless transparent armstrongite from the Strange Lake Alkalic Complex, on the Quebec – Labrador boundary, Canada are monoclinic, space group choices I2/m, I2, Im (diffraction aspect I*/*), with refined unit-cell parameters a = 13.599 (9), b = 14.114(9), c = 7.833 (4) Å, β = 103.41 (5)°, V = 1462.4 (±3.0) Å3. a:b:c = 0.9635:1:0.5550, Z = 4 and D(x) = 2.696 g/cm3. A fully indexed X-ray powder pattern is presented. Averaged electron-microprobe analyses suggest a theoretical formula of CaZrSi6O15 · 3 H2O. The Strange Lake armstrongite is biaxial negative, α = 1.567 (1), β = 1.576 (1), γ = 1.577 (1), 2V (meas.) = 39 (1)°, 2V (calc.) = 37°, Z∥b, X Λc = +4°, with no absorption and weak dispersion r < v.

The intensity diffracted by a low-mass sample with negligible absorption may be expressed as It = I∞ (B/2μ*)/G, where I∞ = intensity diffracted by a bulk sample, B = cross section of the primary beam, μ* = mass absorption coefficient, and G = mass of the sample. Measurable intensity may be obtained from samples with less than 1 μg mass. In order to improve the limit of detection, the primary beam should be collimated so as to irradiate the sample and only a minimum volume of the sample support. The optimum spreading area of a low-mass sample is S sinθ≅10μ*. Comminution of low-mass samples to 1 — 2μm particles is adequate for reasonable intensity measurements.

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.

Calculations of crystal size distributions in oriented clays (montmorillonite and kaolinite) are carried out utilizing X-ray diffraction data together with a method based on information theory. Two different procedures for dealing with the available data are compared. One of them involves some points of the corresponding spectrum, the other correlates the data by means of their moments.

A headlamp of a vehicle involved in an accident was examined in order to assess whether or not it was lit during the collision. In the examination it was found that the headlamp bulb was heavily blackened in an unusual way and its two filaments burnt out. Applying X-ray powder diffraction by diffractometer, the black deposit present in the bulb was identified to consist of a mixture of β-tungsten and the ordinary α-tungsten.

Using a standard laboratory X-ray powder diffractometer under very stable environmental conditions, it has been found that measurements of the positions and heights of sharp diffraction maxima can be made with a precision of order 2 × 10 −4° in 2θ and 0.1% in height (for ∼ 2 × 105 counts per point at the peak). Under normal conditions, however, displacements of order 0.02° in 2θ and 3% in height are observed. These shifts have been attributed to changes in the diffraction geometry, in particular the sourcedivergence slit configuration, brought about by changes in ambient temperature and by changes in the temperature of the liquid used to cool the X-ray tube.

Magnesium-chlorophoenicite may be differentiated from the Mn-analogue chlorophoenicite, because for magnesium-chlorophoenicite at 7Å, whereas for chlorophoenicite.

In a review of the literature for the Mineral Powder Diffraction File by Bayliss et al. (1980), powder X-ray diffraction data could not be found of the mineral species magnesium-chlorophoenicite, (Mg,Mn)3Zn2(AsO4)(OH,O)6. Dunn (1981) states that the powder X-ray diffraction data of magnesium-chlorophoenicite is essentially identical to that of chlorophoenicite (Mn analogue) and confirms that the minerals are isostructural.

With the crystal structure parameters determined by Moore (1968) for a Harvard University specimen from New Jersey of chlorophoenicite, a powder X-ray diffraction pattern was calculated with the programme of Langhof, Physikalische Chemie Institute, Darmstadt. The calculated pattern was used to correct and complete the indexing of the powder X-ray diffraction data of chlorophoenicite specimen ROM M15667 from Franklin, Sussex County, New Jersey, U.S.A. by the Royal Ontario Museum (PDF 25-1159). With the correctly indexed data of ROM M15667, the unitcell parameters were refined by least-squares analysis and are listed in Table 1.

The most magnesium-rich magnesium-chlorophoenicite found in the literature is a description of Harvard University specimen 92803 from Franklin, Sussex County, New Jersey, U.S.A. by Dunn (1981), where Mg is slightly greater than Mn. A 114.6 mm Debye-Schemer film taken of HU92803 with Cu radiation and a Ni filter (CuKα = 1.5418Å) was obtained from Dr. P. Dunn and measured visually. The unit-cell parameters, which were refined by least-squares analysis starting from the unit-cell parameters of PDF 25-1159 in space group C2/m(#12), are listed in Table 1, and give F28 = 4.1(0.050,136) by the method of Smith & Snyder (1979).

The hkl, dcalulated, dobserved and relative intensities (I/I1) of HU92803 are presented in Table 2. With the atomic positions and temperature factors of chlorophoenicite determined by Moore (1968), the Mn atomic positions occupied by 50% Mg and 50% Mn, and the unit-cell parameters of HU92803, a powder X-ray diffraction pattern was calculated and Icalculated is recorded in Table 2. A third powder X-ray diffraction pattern was calculated with the Mn atomic positions fully occupied by Mg. Because the atomic scattering factor of Mn is more than twice greater than Mg, chlorophoenicite may be differentiated from magnesium-chlorophoenicite based upon the calculated intensities of the first three reflections given in Table 3.

Although the a, c and β unit-cell parameters of chlorphoenicite are similar to those of magnesium-chlorphoenicite, the b unit-cell parameter of chlorophoenicite is significantly greater than that of magnesium-chlorophoenicite (Table 1). The b unit-cell parameter represents the 0–0 distance of the Mn octahedra (Moore, 1968). Since the size of Mn is greater than that of Mg, chlorophoenicite may be differentiated from magnesium-chlorophoenicite based upon the b unit-cell parameter given in Table 1.

American Museum of Natural History (New York, N.Y., U.S.A.) specimen 28942 from Sterling Hill, Ogdensburg, New Jersey is composed of willemite, haidingerite and magnesian chlorophoenicite. A spectrographic analysis of the magnesian chlorophoenicite shows As, Mg, Mn and Zn. Powder X-ray diffraction data (PDF 34-190) of the magnesian chlorophoenicite was collected by diffractometer with Cu radiation and a graphite 0002 monochromator (Kα1 = 1.5405) at a scanning speed of 0.125° 2θ per minute. The unit-cell parameters, which were refined by leastsquares analysis starting from the unit-cell parameters of PDF 25-1159, are given in Table 1. Specimen AM 28942 is called chlorophoenicite, because of its large b unit-cell parameter (Table 1), and the I/I1 of 25 for reflection 001 and of 50 for reflection 201 compared to the Icalculated in Table 3.

Described is an improved Gandolfi camera which overcomes the disadvantages of the adjustment procedure of the conventional instrument. The basic principle of the new construction is the introduction into a camera of a complete goniometer head as sample holder with two 45° rotation axes. Particular advantages of the modified Gandolfi camera are a simple and time saving centering technique as well as convenient combination possibilities of powder and single crystal investigations.

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.

The International Centre for Diffraction Data has an ongoing program to ensure the quality of data in the Powder Diffraction File (PDF) reflects current requirements of the powder diffraction community. Annual updates are made available, comprising of around 1800 new patterns and 200 replacement patterns, but current statistics indicate that only about 20% of users of the PDF take advantage of these updates. This paper reviews changes which have been inplemented in the editorial review process to continuously monitor and review pattern quality and gives examples of better data which have resulted from these changes.

In the Bragg-Brentano X-ray powder diffractometer geometry the Automatic Divergence Slit (ADS) provides a fixed area of illumination on a flat specimen. For this case, the “constant volume” diffraction, appropriate for a Constant Divergence Slit (CDS) diffractometer, is not applicable and intensities must be corrected by a sinθ factor before comparison to CDS data.

It is shown that for thin layers the diffraction pattern may be treated as a “constant volume” diffraction case when the ADS is used. Moreover, the derivation of the unit cell dimensions using a common least-square procedure can result in excellent lattice parameters without using internal standards, because the transparency aberrations are minimized.

ADS data were obtained for a variety of reference materials including several NBS SRM powders. It was found that thin samples made of powder mixed with vaseline gave “constant volume” diffraction, less angular aberration, and yet had line intensities only somewhat less than bulk samples.

Three main benefits arise using a combination of thin layers and ADS: (a) The amount of material needed for routine chracterization is small, (b) The relative experimental intensities are approximately the same as those obtained from bulk specimens using a CDS. (c) The measured (Bragg) scattering angles are more accurate compared with those measured from bulk specimens.

A Siemens D500 powder diffractometer has been modified to accommodate data collection and storage by an IBM microcomputer. The interface mechanism, described in detail, is simple, versatile and relatively low cost. The system performance is evaluated and further enhancements suggested.

50-50 atomic percent lead telluride (Altaite), grown by the vapor transport method, was examined with a well aligned Rigaku horizontal beam diffractometer. PbTe is cubic (precise lattice parameter ao = 6.4591(5)Å) with an space group and a calculated density of 8.253 g/cm3. Fully indexed powder diffraction data are presented.

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 ε-phase is hexagonal, space group P63/mmc. For the composition Pb7Bi3 the following data were determined, a = 3.5058(1) Å c = 5.7959(5) Å, Vol. = 61.687 Å3(5), Dc = 11.17 Mg m−3. Filings from single crystal material were used to obtain powder data by the Guinier method and the X-ray results were in accordance with single crystal neutron diffraction data. Transition to the superconducting state took place in the interval 8.3 K–8.55 K.

The Level III Powder Diffraction File Computer Database can be used for many purposes beyond phase identification. The data file as received from the ICDD must be implemented via a data management system for efficient utilization. The results of one such implementation, and applications using the Mineral Powder Diffraction Subfile are reported. The applications include studies of space group statistics and density distributions as well as searches for cubic sulfide and uniaxial potentially pyroelectric minerals.