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Hematite (α-Fe2O3) powder compacts have been subjected to controlled, quantitative high pressure shock loading at peak pressures from 8-27 GPa and preserved for post shook analysis. The broadened x-ray diffraction peak profiles have been analyzed to determine the residual lattice strain and the coherent crystallite sizes. Maximum modification effects are observed near 17 GPa with strain values near 3 x 10-3 and size values near 200 Å suggesting annealing at higher shock pressure, resulting from the higher shock temperature.
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.
Preferred orientations in powder diffraction specimens can cause large errors in measured intensities. An extreme case is shown in Figure 1, Smith and Barrett (1979) reviewed the various methods which have been proposed for reducing this effect. Subsequently, two methods which are used commercially for aggregating finely divided solids have been proposed for preparing powder diffraction specimens (Smith, Snyder, and Brownell, 1979; Calvert and Sirianni, 1980). In one of these, spray drying, a finely divided solid is suspended in a liquid together with small quantities of a deflocculent and a binder. This mixture is pulled by venturi action through a nozzle into a heated chamber. The spherically shaped aggregates dry before falling to a collection surface. The apparatus is fairly large (3 X 3 X 4 ft. at NBS), and operating parameters must be carefully chosen.
Several kilometers of drill core are sometimes obtained when the geology of a particular area is explored. The cores are visually inspected and a limited number of samples are taken for laboratory analysis. Accurate chemical analyses are usually performed on only a small number of core sections because of the expense involved. A chemical profile along the core may provide useful information not available by any other means. This information may be of primary value for geological investigations or it may provide an additional basis for selecting samples for detailed laboratory analyses.
Neutron powder diffraction techniques have been used to characterize the pseudo-macro (PM) residual stresses in ZrO2(CeO2)/Al2O3 ceramic composites as a function of ZrO2(CeO2) volume fraction and fabrication procedures. The diffraction data were analyzed using the Rietveld structure refinement technique. From the refinement, we found that the CeO2 stabilized tetragonal ZrO2 particles were in tension and the Al2O3 matrix was in compression. Different sintering time had little impact on the PM stresses. On the other hand, the magnitude of the PM stresses in both ZrO2 and Al2O3 decreased linearly with the increase of their volume fractions.
Techniques for the computer-assisted evaluation of crystallographic data have been developed to improve the data compilations of the NBS Crystal Data Center and the JCPDS—International Centre for Diffraction Data. The resulting computer program, NBS*ATDS80, can be used for the analysis of unit-cell and powder data by the general scientific community as well. NBS*AIDS80 is written in FORTRAN to permit implementation on a wide variety of computers, and input may be from cards or from a terminal. The research and analysis components that will be of use to the individual scientist include the following:
1) Calculation of the Crystal Data cell, determinative ratios, and space group for the comparison and reporting of unit cell parameters in a standard setting and for the identification of unknowns.
2) Determination of the reduced cell, reduced form number, and the unit cell with the highest metric symmetry.
3) Calculation of the molecular weight from the formula using the most recent atomic weights, and comparison of the density calculated by the program with the measured density.
4) Generation of d-spacings and indices for any input cell and crystal system.
5) Comparison of input powder data with calculated d-spacings, indexing of lines based on known unit cell parameters, and calculation of figures of merit.
This paper reports and discusses the results of a computer modeling study on powder diffraction profile analysis for crystallite size and strain of polycrystalline materials. The results of this computer modeling show that if the spans of diffraction profiles in reciprocal space (1/d) are not carefully chosen, an overestimation on size and an underestimation on strain may result in analysis by both the Warren-Averbach and the Hall-Williamson methods. A general way to eliminate such errors based on profile fitting and regeneration is presented and discussed in this paper.
The beryllium diamond-anvil pressure cell described by Weir, Piermarini and Block has been mounted on a Bond diffractometer equipped with an orienter of the fixed-x type. Molybdenum radiation is used to penetrate the diamonds and beryllium of which the cell is constructed, and special techniques are required to retain adequate precision in measuring cell parameters using diffraction angles in the low 2θ range. The method described provides high sensitivity in determining peak positions and eliminates the effect of centering errors on measured values of 2θ. Under favorable conditions, diffraction angles are measured with an accuracy of ±0.001° in 2θ. The method has been tested by measuring the lattice parameter of vacuum float zone refined silicon. Measurements of the compressibilities of silicon and of α-Pb(N3)2 (orthorhombic) have been carried out using the method of Barnett, Block, and Piermarini to determine pressure by measuring the shift in the R-line fluorescence spectrum of ruby.
As a result of interest in the characterization of materials with large d-spacings and layer periodicities, it has become necessary to develop a low-angle diffraction material which has welldefined diffraction peaks down to very small 2θ angles. The use of silver behenate, CH3(CH2)20COO-Ag, was introduced by one of the authors (TB) at the 1991 International Centre for Diffraction Data (ICDD) Annual Meeting and was shown to have a set of well-defined (001) diffraction peaks down to 1.5° 2θ when using CuKα radiation. The silver behenate diffraction peaks were observed to be slightly asymmetric with relatively long tails at the low angle side of the peaks. The average crystallite size along the c-axis was estimated using the Scherrer equation and was found to be 900 Å.
A task group of the JCPDS-ICJDD Data Collection and Analysis Subcommittee was established with the charge of investigating the use of silver behenate as a possible low-angle calibration material for diffraction applications. Utilizing several data collection and data analysis techniques, d001 long-period spacings in the range of 58.219-58.480 Å were obtained. Using the same collected data and one data analysis refinement calculation method resulted in long-period spacing with a range of 58.303-58.425 Å. Data collected using a silicon internal standard and the same singular data analysis calculation method provided d001 values with a range of 58.363-58.381 Å.
The formation of a full-range 2θ diffraction sample was also investigated. Silver behenate and inorganic powders were mixed with an epoxy binder to form a permanent sample which provides diffraction peaks over the entire 2θ range of a powder diffractometer.
Depth profiles of intrinsic in-plane, biaxial stresses were obtained as a function of τ, the 1/e penetration depth, in a 1.0 um thick planar d. c. magentron sputter deposited molybdenum film using asymmetric grazing incidence x-ray diffraction (GIXD). τ was varied between 20 and 276 Å. The stresses σ11 and σ22 were characterized in the directions parallel and perpendicular to the long axis of the cathode respectively using a cos2φ method. The results show that starting from τ=17Å, σ11 and σ22 are compressive and become rapidly more compressive with a minimum at τ ∼ 20 - 40 Å thereafter increasing gradually toward tensile values. The reasons for the shape of the stress gradient are not well understood but may be related to the relaxation of the stresses at the tops of the columnar Zone T-type microstructure and to the oxygen gradient in the film.
The real-time x-ray powder diffractometer control system AUTO incorporates several advances in data collection and analysis. Counting procedures for selected area data collection are optimized to achieve either a preselected statistical error in minimum time or a minimum error in fixed total time. Run files are employed to greatly simplify quantitative analysis procedures and for controlling repetitive runs. External calibration curves for 20 are used to eliminate all but sample dependent aberrations to peak positions. A generalized data file structure is used to document the instrumental variables and sample parameters.