A general expression for the method of QXRPD without standards is given in this paper to solve the problem of phase analysis on samples containing a non-crystalline component. Its application to some specific cases is discussed. The experiments have proved successful in the analysis of cement and sand-lime samples. The technique may also be applicable for the analysis of fly-ash, glass, ceramics, and metals. It is especially convenient in the study of kinetics and mechanism of reactions when the chemical composition of all samples does not change, because it is not necessary to know the mass absorption coefficient of samples. In the mathematical treatment of non-linear equations given in this paper, a method called linearized iteration procedure is first presented by the author.

A Fortran 77 computer program has been developed for the quantitative analysis of minerals by multiphase profile analysis of the complete powder diffraction pattern. Featured are full-matrix least-squares refinement of 14 Rietveld “instrumental parameters” (phase scales, asymmetry, preferred orientations (March model), linewidths, instrument zero, lineshapes and unit cell dimensions), Brindley particle absorption contrast factors and amorphicity corrections. The program uses a crystal structure Databank, which contains information on absorption coefficients, unit cell data and crystal structures for some 90 common minerals. New minerals can be easily added. Structure parameters are also refinable by a profile decomposition method using a program called STRUCT. The sum of the calculated patterns, derived from the crystal structure data, is fitted to the observed pattern by a program called TRACSCAL which runs in singlepass multiphase mode and, after the above corrections have been applied, the weight percentages of the component phases are calculated from the Rietveld scaling factors.

The program runs on an IBM-compatible AT computer with 640K of RAM, on an extended memory AT, or a mainframe system. Examples of its use are given with standard mixtures and naturally occurring specimens. On an AT computer with 20MHz clock speed a scaling run, including data input, reading of the pattern, processing of (hkl) files, calculation of the profile and one cycle of least squares fitting takes about 30 seconds for binary standard mixtures and about 2.5 minutes for a 7-phase natural bauxite pattern containing 320 independent (hkl) reflections.

The design and construction of Geiger-Müller counters which will respond reliably to Mo K x-rays is described. The impulses are amplified and recorded mechanically with the aid of a thyratron circuit. The amplifying and counting circuit, and the counting mechanism, are also described. The time of recovery of the counters has been determined by the use of an oscillograph and found to be less than 0.001 sec. when the proper values are used for the resistance and capacitance of the counter circuit. It is shown that for counting rates up to 600 per minute there is less than a 1 percent correction due to the fact that the impulses are random in nature. Several fundamental tests are described, which have been applied to the counter and the circuit. These tests have shown the counter and the circuit to be a reliable method of measuring x-ray intensities. Graphs are shown of the diffraction patterns of NaCl and KC1 taken by means of the counters. These graphs duplicate the well-known diffraction patterns of these materials, thus giving additional evidence of the reliability of the counters.

Pure phase reference intensity ratio determinations were completed on eleven biotites ranging in Fe composition from χFe = 0.058 to χFe = 0.695, where χFe = Fe/(Fe + Mg). The crystal chemistry of biotites requires that the intensity of diffraction for the 00l reflections, and thus the corresponding reference intensity ratio, correlate with the Fe, Mg and Al in the octahedral sites. As Fe occupancy increases in the octahedral site, the Lki for the 00l reflections increases as does the value of ∣F∣2 computed using the Takeda and Ross (1975) biotite model. The ∣F∣2 trend closely parallels the experimental regression of Lki = 6.359χFe + 1.513 (R = 0.91). Observed mass absorption measurements completed by X-ray transmission show a similar trend with μo = 69.36χFe + 47.85 (R = 0.97). Calculated values of μ from biotite chemical analyses agree well with the measured values. These relationships may be used to predict the appropriate Lki needed for quantitative analysis of biotite-bearing specimens if the Fe and Mg content of the biotite can be determined.

The kinetics of γ'-phase formation in a Ni-base superalloy were studied. The data (pairs of cps and 2θ) were processed by the deconvolution program (Wiedemann, Unnam and Clark, 1987), which was rewritten in FORTRAN and installed on an IBM/VM and a VAX/VMS host computer. Optimal program parameters were found. Pure nickel was used as a standard. The only evidence obtained from the raw data is that the early stage of the aging process is accompanied by broadening. Deconvolution resolved the peaks into three kinds of diffraction lines: Ni(γ), precipitate (γ'), and undefined lines which have been interpreted as satellites. The results show that our X-ray diffraction lines are composed of the main diffraction lines of nickel-base A1 type alloy and additive satellites. In an advanced stage of aging the satellites assume the typical diffraction pattern of γ' phase.

The compounds BaR2O4, where R = La, Nd, Sm, Gd, Eu, Dy, Ho and Er have been prepared from a stoichiometric mixture of BaCO3 and lanthanide oxides, and characterized by X-ray powder diffraction. Standard X-ray patterns of these phases were prepared. In general, BaR2O4 crystallizes in the pervoskite-related CaFe2O4 structure which is orthorhombic with a space group Pnam. The cell parameters of these compounds from R = Er to La range from 10.3729(12) to 10.668(2) Å for a, 12.0699(11) to 12.642(2) Å for b, from 3.4356(4) to 3.7037(10) Å for c, and from 450.14(5) Å3 to 499.51 Å3 for V respectively. A monotonic, linear relationship is obtained when V is plotted against the cube of the ionic radius of R. When R = Tm, Lu and Yb, the BaO·R2O3 composition produced the mixture Ba3R4O9 and the unreacted lanthanide oxide. Under the present experimental conditions, the compound BaRO3 was the predominant component when R = Ce, Pr, and Tb.

X-ray diffraction has many applications in the chemical and metallurgical industries, but its techniques have been confined until recently to the laboratory and to highly trained personnel. Conventional procedure entails photographic exposure, processing, and density comparisons of the finished film strips.

The Geiger counter spectrometer described below measures x-ray intensities and diffraction angles directly, without intermediate photographic steps. It is simple enough for unskilled operators performing routine industrial processes yet also meets the precise requirements of laboratory research. The instrument was developed at the Naval Research Laboratory, where it has been in regular use for the past two years.

A comparison between the results of ab initio structure determination from X-ray powder diffraction data of a new cadmium hydroxide nitrate, Cd5(OH)8 (NO3)2·2H2O (SG C2/m), and those obtained from single crystal data is presented. The powder diffraction pattern has been analysed by an indexing method and fitting techniques. A total of 119 unambiguously indexed reflections has been extracted and used in subsequent treatment. The power of powder techniques to index the pattern and to find the structure model by normal Patterson and Fourier methods is clearly shown. The refinement of approximate coordinates has been carried out by the Rietveld method (444 reflections). The comparison of results with those obtained from single crystal data (2218 reflections) shows that the precision of positional parameter values is lower by a factor of 10, on average, in the powder study. These results are discussed in terms of crystallographic parameters (number of reflections used, number of parameters to refine, contrast between atoms) and, also, in terms of sample dependent properties (preferred orientation effect, impurity). Finally, the crystal structure has been derived from powder data with a precision probably sufficient for most purposes.

Methods for precise control of the cutting angles of quartz by x-ray measurements are described. The quartz must first be oriented by some other method (usually optically) before the x-ray method can be applied. The sense of direction of the cut is indicated by an arrow drawn on the outer surface of the test cut at the saw and this direction is preserved in making the x-ray measurement. The x-ray technique is an adaptation of the Bragg ionization chamber method and involves measuring the angle between the surface of the test cut or blank and an atomic reference plane parallel (or nearly parallel) to the surface. All measurements are direct, and require no computation. A Gieger-Muller tube operated in the proportional counter region is employed. Accuracy of the method is approximately ±1.5′, the measurement requires about 10-15 seconds, and is used by unskilled help. The procedures for calibrating the x-ray goniometer and measuring various types of cuts are described in detail. Methods involving precise angular adjustments of sections approximately oriented by other methods and the use of reflection intensity differences of certain planes on either side of the optic axis for detecting usable portion of electrical twins and negative and positive directions from Z are described. The methods are applicable to other fields.

2 Hydroxymethyl-2 methyl-1,3 propanediol tetrahydrate has been crystallised from aqueous solutions in the form of transparent tetragonal thin plates. The cell parameters of the unit cell were determined as a = 9.102(1) Å, c = 47.654(6) Å and the space group is I41/ a.

Solid liquid and reverse transformations have been studied by DSC, and a melting enthalpy of 185 kJ.kg−1 at 29.8° C determined.

A procedure for Sr-analysis of vein barites by X-ray powder diffraction is described. It is based on the measurement of barite d210 spacing change referenced to NaCl as the internal standard. This procedure covers a range of Sr isomorphic substitution of 0 to 12% SrSO4. Comparison with other values, derived from literature data, shows they are in good agreement with the experimental ones. Statistical analysis of the results yields a maximum absolute error of ±0.50 %SrSO4 in Sr determination. This measurement error proves to be acceptable for most studies of barite in mineral deposits. The effect of Pb-substitution is smaller, in most cases, than this error.

The reported method has the advantage of being fast and simple. It can routinely handle large number of samples as well as small samples isolated from large crystals. Moreover, it allows the recovery of the original sample after the analysis by dissolving the NaCl in water. The main disadvantage is that fair amounts of quartz interfere with the measurement of the position of the barite 210 line.

Diffraction peak broadening analyses were carried out on diffraction profiles of several reflections from hot-pressed α-Al2O3 containing 29, 18 and 10 volume % β-SiC whiskers. The data were analyzed and compared using four different integral breadth methods for microstrain and crystalline size. All four methods gave comparable results, within an order of magnitude, for the microstrains in each phase: (2-15 × 10−4 for the matrix and (6-19 × 10−4 for the whiskers). Microstrains in both matrix and whiskers decreased with decreasing volume % of whiskers for all four methods. Trends in the crystallite size were less consistent but for the matgrix, an incrfease from ∼665 to 1565Å was found with decreasing whisker content using DeKeijser's method.

A new preparation procedure to obtain tetragonal pure zirconia powders is reported together with a detailed analysis of the profile of X-ray Diffraction (XRD) peaks. The crystallization kinetic up to 800°C is described through r.m.s. microstrain and crystallite size distributions. The results of two methods of profile analysis are compared. After thermal treatments up to 100°C the samples of amorphous gel prepared crystallize in the tetragonal structure. The monoclinic phase occurs only above this temperature. Moreover the tetragonal to monoclinic transformation has a strong effect in changing the shape of the distributions. Studying the crystallite size distributions we can infer a critical size of about 300 Å for the tetragonal crystallites to transform. The shape of the mean crystallite of a fully tetragonal sample is also described.

The linear coefficient of thermal expansion for three silicon single-crystal samples, taken from the head, middle, and tail of the same boule, and their powder samples have been measured at room temperature by using an X-ray powder diffractometer. All samples yield the same expansion value α=2.45 (± 0.04) × 10−6 °C at 25 °C. The results of this experiment show that the linear coefficient of thermal expansion of silicon at room temperature is not dependent on its single-crystal state or its powder state.

Crystal data and results of structure refinements for MnSi are reported. The material is cubic, P213, with a = 4.5603(2) Å, Vd = 94.84(1) Å3, Z = 4, Dx = 5.815 Mg/m3. Intensity data were obtained from a Stoe transmission type diffractometer equipped with a position sensitive detector. CuKα1 radiation, λ = 1.5405981 Å was employed. Germanium was used as an internal standard for the determination of the lattice constant (aGe= 5.6582 Å). The structure was refined by the Rietveld method by aid of three different programs.

Simple relationships exist between the individual phase scale factors derived from Rietveld analysis of multiphase mixtures and (i) the ‘reference intensity ratio’ used in traditional methods of discrete-peak phase analysis, (ii) the phase abundance itself and (iii) the relative pattern intensities in simulated powder patterns. These relationships are shown to follow naturally from the fundamental integrated-intensity phase-analysis equations provided in standard texts. In the event that preferred orientation, crystallinity, extinction and/or microabsorption cannot be adequately incorporated into the Rietveld models for individual phases, it is demonstrated that the Rietveld ab initio ‘pattern intensity constants’ can be scaled/calibrated experimentally, as in other whole-pattern methods of analysis, while retaining all the advantages of the Rietveld method.

Described is a method of sample preparation for multiple Guinier Cameras (DeWolff, 1948). This technique practically eliminates cross-contamination of adjacent samples and is easy to employ.

Samples for Guinier cameras are usually applied to a thin adhesive coated foil. For multiple Guinier cameras, however, samples pose some technical problems. Manufacturers usually supply a slotted die for sample preparation. Figure 1 shows schematically such a die for a Seifert/Huber camera. For this type of camera, the manufacturer recommends application of the powdered sample by means of a small brush, or by dusting while the adjacent slots are covered by adhesive tape (Seifert, undated). These methods are simple, but easily result in sample being spilled into an adjacent slot. The following method, though involving more steps, eliminates this problem.

Citation analysis of the articles that appeared in the first five volumes of the journal Powder Diffraction showed that it is clearly a journal of crystallography with strong ties to materials science, mineralogy and analytical chemistry. This specific orientation makes Powder Diffraction invaluable in the existing network of scientific journals.

Tacrine hydrochloride monohydrate, velnacrine maleate and suronacrine maleate have been investigated by means of X-ray powder diffraction. The unit cell dimensions, determined by single-crystal diffraction data, agree well with those of powder diffraction analysis, which is characterized by good figures of merit for the three drugs. Present work assures that single-crystals are good representatives of the commercial powdered samples, since experimental and simulated (from structure determination) powder patterns are practically identical.

Diffracted intensities from an X-ray diffractometer operating with fixed or variable divergence slits were compared, following a reported systematic deviation from the theoretical 1/sinθ intensity ratio between these two slit configurations. The theoretical relationship was found to hold over a wide 2θ range provided the anti-scatter slit did not obstruct the beam at higher diffraction angles as the variable slit increased beam divergence. Such obstruction was found to be a possible explanation for the reported deviation.