A set of programs in Fortran 77 has been written to automate quantitative analysis on the Rigaku SMAX/PDP-11/73 XRF System. The spectrometer can be instructed and Trained to recognize spectral patterns of soda-lime glass or other materials.

The method of pattern recognition employed is based on the relative position of spectra-vectors in N-Dimension Euclidean feature space. The distance between 2 vector-points: is used as a classifier.

The software correlates between 2 Euclidean feature spaces:

• - Spectra Feature-Space

• - Chemistry Feature-Space

Quantitative results are extracted automatically and printed in laboratory report form. Mathematical modeling with associated software and the results obtained are presented.

The mass absorption coefficient is perhaps the most under-utilized parameter in x-ray diffraction analysis. Mass absorption measurements are often avoided in quantitative analysis by resorting to calibration curves of internal standards (e.g., Kung and Alexander, 1974, Sec. 7-2.1). However, Leroux et al. (1953) and Frevel and Roth (1982) directly utilized the mass absorption coefficient in multicomponent analysis, and suggested a "substrate diffraction" procedure for directly measuring the sample mass absorption coefficient. The reference intensity procedure of quantitative multicomponent analysis originally formulated by Frank Chung (1974) requires no explicit use of the mass absorption coefficient because all reference intensity ratios are determined relative to an "external" standard, generally corundum (Al2O3).

The background to the use of the Pearson VII function as a model for powder diffraction profiles was summarised in connection with the fitting of data obtained essentially from Guinier patterns (1). The algorithm developed for modelling single-wavelength profiles was found to be less effective when applied to diffractometer data generated by the Kα doublet. Diffractometer, rather than Guinier film data are generally to be preferred, however, for profile measurements. A new approach was accordingly made to devising an algorithm for this particular application. Numerical features of the method highlighted by this task are described below. Attention is also drawn to problems encountered when profiles are measured using a diffracted-beam monochromator (DBM).

One of the areas of X-ray powder diffraction receiving considerable attention in recent years is quantitative analysis. This analysis depends on an accurate measurement of integrated diffraction line intensities. In order to study the accuracy of these measurements we have calculated integrated intensities from single crystal data for single substance powders and compared them to experimental data obtained in our laboratory.

Numerous studies have been conducted into the microstructural origin of the instability and unpredictability of various energetic materials. Some of these materials are RDX/HMX, Ammonium Perchlorate, Aluminum, etc. Many techniques both destructive and non-destructive have so far been utilized in an attempt to quatify the energetic properties of their composites. These composites may contain one or more energetic constituents in an elastomeric binder. Non-destructive X-ray characterization techniques have been successfully employed to measure several microstructural parameters. Previous studies have shown considerable differences among various production grade RDX. These studies reveal marked differences in the amounts of residual elastic strain and the distribution of dislocations (residual plastic strain) in the constituent RDX phase.

The focus of this study is to develop a technique for quantitative constituent phase analysis of solid-propellant (fuel) composites using conventional diffractometry. The use of a Curved Position Sensitive Detector (CPSD) greatly enhances the technique and allows real time applications in production environments. Through the use of computer based Systems and "user friendly" software the required Operator, skill and training have been considerably reduced. The CPSD System has been successfully used to quantify constituent phases (peak heights) and the amounts of residual elastic strain (peak shifts) in these molecular crystal powder mixtures.

It is envisioned that rapid, automated, non-destructive X-ray characterization techniques will greatly facilitate production based propellant quality control. A thorough understanding of the relationship between the energetics and microstructural parameters can also he obtained.

On-stream X-ray fluorescence analyzers have been available for about 20 years. They have been used with great success and they have made an effective process control possible in many concentrators. They have, however, one severe drawback. Normally the sample that ought to be measured is in slurry form and it would be difficult and expensive to prepare it into more conventional form used in ordinary laboratory practice. The main constituent of slurry is water and normally some kind of plastic film is needed to keep slurry apart from the measuring system at least when the slurry system is malfunctioning. Already these two things are sufficient to set a limit to the lightest element that can be measured with reasonable accuracy and precision. This means that minerals that contain only such low atomic number elements as e.g. Mg, Al, Si and P remain out of reach. Difficulties arise also in cases where the interesting element is not only in the solid material but also in the solution part of the slurry. In great many cases the interesting element occurs in several minerals at the same time which causes certain problems with the accuracy. Fortunately this problem does not set such a basic limitation as a too low Z does unless only one of these minerals is of interest, which may make the whole method worthless.

A method for using synchrotron-radiation parallel-beam X-ray diffractometry for precision measurement of scattering angles and lattice parameters is described. The important advantages of the method are the high P/B made possible by wavelength selection and high source intensity, the symmetrical profiles and the absence of most systematic errors making it unnecessary to use standards. Profile fitting with a pseudo-Voigt function is used to determine 2θ to 0.0001º. The zero-angle correction and lattice parameter were determined from least-squares refinement and the average accuracy of observed-calculated 2θs was 0.0020°. Average values of ∆d/d = ∆a/a directly calculated from the individual hkl measurements ranged from 2x 10-5 to 5.7 x 10-5. The precision estimated from the standard deviation of the mean is in the 10-6 range and 1 ppm precision was obtained for Si. The determination of the exact wavelength selected remains to be solved, but ratios of lattice spacings to standards such as NBS SRM 640a can be determined.

Synchrotron radiation was used to obtain a high-resolution powder diffraction pattern of the high-density form of BeH2, a material whose unit-cell dimensions have not previously been determined. The observed d-spacing values were presented to three different computer indexing programs. All three programs returned as best solution a body-centered orthorhombic unit cell with a = 9.082, b = 4.160, c = 7.707 Å and V = 292 Å3. Interpretation of the three-dimensional Patterson led to 12 BeH2 molecules per unit cell; thus, the theoretical density is 0.755 g/cm3. The molecular structure is based on a network of corner-sharing BeH4 tetrahedra rather than flat, infinite chains with hydrogen bridges previously assumed.

Discussions exist in the literature concerning the application of single x-ray diffraction profile analysis to determine the average particle size, particle size distribution and root mean squared strain in catalytic systems. Nandi et al. have shown that the single order analysis can give erroneous strain results and is subject to error in the large particle size range. They further indicated that the initial slope of Stokes corrected Fourier coefficients gives more reliable average p article size than that which is calculated from single order peak shape analysis. There is apparent agreement that the average particle size and the particle size distribution measured by single order profile analysis, in small metal particle systems, are reliable.

In order to reveal the mechanism of the negative c-axis expansion in cordierite (4 MgO 4 Al2O3 10 SiO2), the thermal expansion of cordierite containing small amounts of Cs, Li, B, Ge, Sc and Ni-cations was investigated by time-of-flight neutron diffraction at temperatures between 22 and 750°C. The samples were prepared by melting the constituent oxides followed by quenching and devitrification to obtain the hexagonal form (Indialite). Using the neutron powder diffraction data, the atom positions in the space group P6/mcc were refined by Rietveld least squares analyses.

The expansion behavior of the cordierite structure could be explained in terms of the various kinds of constraints and the interatomic bond strengths of the structure. It was found that cordierite doped with Cs-cations shows the largest volume expansion, followed by the Li-doped sample. So-doped cordierite has the lowest volume expansion. All cordierite samples show positive expansion along the a-axis and negative expansion along the c-axis, except the Cs-doped sample which has positive expansion in both directions.

The following study is an evaluation of several different types of instrumentation available for use in powder x-ray diffraction work. The particular units used are those at the Dow Chemical Company x-ray diffraction lab. The variety of instrumentation allows analyses from routine phase identification to more specialized work such as low-angle x-ray diffraction of polymers and high-resolution analysis for cell parameter refinements.

The purpose of this work is to compare the relative capabilities of these different instruments under typical day-to-day operating conditions. While not a comprehensive study, the conclusions drawn should be applicable to powder x-ray diffraction in general.

The presented paper describes design and operational characteristics of a new high-temperature camera. The design is developed from the widely used Anton Paar camera, but several of its major disadvantages were eliminated.

The specimen is directly mounted on an electrically-heated metal strip. The most important improvement over the original camera is a provision for the compensation of the thermal expansion of the heating strip. Fig. 1 shows a Ta-heater after using it at temperatures above 2000°C without adequate compensation; the specimen, which is mounted at the center of the strip, is considerably displaced during the measurement and large errors occur in the measurement of the reflecting angles.

The improved overall design allows temperatures (at the heater) above 3000°C to be reached. The highest temperature measured so far at a tungsten strip was 3350°C, which is only 40° below its melting point.

At the moment, the time required to obtain a pole figure is about three hours, and generally several pole figures are needed to make a texture analysis. Therefore the time and the cost of texture measurement are widely increased.

Now, new position sensitive X-Ray detectors are appearing, which allow to record at one and the same time the whole 2Θ spectrum, i.e. the beams diffracted by several (hik1l1) lattice planes. So with this kind of detector, it will be possible to get simultaneously several pole figures.

To understand how a material evolves - its crystal growth, topotaxy, twinning, phase transformation, plastic deformation, microstress, etc. - it is important to know the crystal orientations, either between them or in respect to the sample.

The crystal texture of the material is quantified by the Orientation Distribution Function (O.D.F.). This function represents the part of the material volume having a given orientation. To compute this O.D.F, we must first measure one or several complete or incomplete pole figures and then analyse them either with Roe-Bunge's harmonic method or with Vadon, Ruer, Baro's vector method. In the case of a very sharp texture, the results obtained with the harmonic method are not good because developing a DIRAC function in spherical harmonics requires a high rank, hence a large number of pole figures. On the contrary, with the vector method, the results are good since discretizing amounts to developing on a step-function basis.

Programs exist to compute X-ray diffraction patterns (angles and intensities) for specified atomic arrangements using mainframe computers. We report here a microcomputer version (in Basic, to n m on a standard Apple ][ computer with two disk drives and optionally a printer). Additionally, the program offers considerable flexibility in entering atomic positions and using symmetry relations to simplify the input for complex unit cells, and provides a visual display of the unit cell in any orientation.

There are a variety of search-match algorithms that compare measured powder diffraction patterns to previously determined standards, such as the JCPDS powder diffraction file. These have been implemented on computers ranging from mainframes to microcomputers, with tradeoffs in the practical size of the standards file and the speed of the search.

Several factors have long been known to affect the intensity measurements of X-ray powder diffraction. The characterization of these effects has been impeded by difficulties in their isolation and the statistical nature of the data in which they manifest themselves. The most celebrated, and most detrimental, of the these effects is that of preferred orientation. This error can be eliminated with the spherical agglomeration of the sample (1). The spray drying process offers this result and is considered to have the broadest range of applicability to materials encountered by the powder diffractionist.

Due to the current high interest in characterizing epitaxially deposited thin films required by the electronics industry as well as the increased attention in elucidating reactions between solid surfaces and the environment (e.g., corrosion), investigators have increased their efforts in developing X-ray procedures for analyzing films and surfaces less than 2 μm thick. For example, an entire session of the 1985 Denver Conference on Applications of X-ray Analysis was devoted to this subject and an excellent review of X-ray diffraction techniques for characterizing thin films was recently published by Segmuller (1). Specific techniques include grazing incidence diffraction (2, 3), double crystal diffraction (3), and the use of the Seemann-Bohlin focusing geometry (4, 5).

During the past quarter-century, the field of high pressure research has undergone a quiet revolution. This has resulted from the creation and development of the diamond-anvil cell (DAC). Because diamonds are the hardest known materials, the highest static pressures can be attained and indefinitely held in these devices, recent pressure records have surpassed 400 GPa.

The lattice parameters of sol-gel derived Pb(ZrxTi1-x)O3 powders were determined as a function of temperature using a microcomputer automated Picker x-ray diffractometer. The spontaneous strain was calculated from the lattice parameters, and used with other experimental data to develop a thermodynamic phenomenological theory for the PZT solid solution system. A second tricritical point, where the transition changes front first to second order, was found to occur near or possibly at the morphotropic phase boundary between the tetragonal and high temperature rhombohedral phases. Using an equation derived from the theory, the spontaneous tilt angle of the oxygen octahedra in the low temperature rhombohedral phase was calculated from the experimental spontaneous strain data.

Metallic glasses are mostly produced by fast quenching from a melt. The glass forming composition range in binary materials is thereby restricted to the area around eutectics. The production of metal-metal binary glasses in a much wider composition range is possible by employing a technique called 'mechanical alloying'. Using this technique the metallic class is produced as a powder which can be manufactured into any shape to make use of the properties the material exhibits in the amorphous state. During compacting, and also in some applications of the finished product, the glass has to endure elevated temperatures which might cause devitrification. Since this crystallization of a metallic glass usually results in the loss of properties essential for a certain application it is necessary to investigate this crystallization behaviour and thus receive information about a material's prospective performance in a particular application.