Powder diffraction profiles of well crystallized compounds can be fitted to distributions of the type Iθ=I°(1 + k2x2)-n where k is a scale factor related to the half width of the profile. The value of n varies with the diffraction angle, 2θ, and is generally different for the low-angle and high-angle sides of the same profile. Limiting values of n for a specific Guinier camera-micro-densitometer combination are 1.2 ≤ n ≤ 2.3. Similar values are obtained for diffracto meter profiles after Ktt2 stripping. Line broadening due to departure from perfect crystallinity in the specimen affects the value of n a swell as that of k.

The above observations are interpreted interms of the convolution of a Gaussian with a Lorentzian distribution, the exponent n of the convolute being dependent upon the relative half widths of these two functions, expressed as the ratio bL/bG.

The residual stress induced by grinding or some thermal treatment has a large effect on the strength of ceramics. The X-ray technique can be used to nondestructively measure the residual stress in small areas on the surface of polycrystalline materials. The X-ray stress measurement is based on. the continuum mechanics for macroscopically isotropic polycrystalline materials. In this method, the stress value is calculated selectively from strains of a particular diffraction plane in the grains which are favorably oriented for the diffraction. In general, however, the elastic constants of a single crystal depend on the plane of the lattice, since a single crystal is anisotropic, The behavior of the deformation of individual crystals in the aggregate of polycrystalline materials under applied stress has not yet been solved successfully. Therefore, the stress constant and elastic constants for a particular diffracting plane should be determined experimentally in order to determine the residual stress accurately by X-ray diffraction.

The use of incomplete pole figures results in the loss of orthogonality relations among the associated Legendre functions, and necessitates explicitly evaluating integrals of products of these functions. The required indefinite integrals of associated Legendre functions and their products have been evaluated for cubic crystallographic symmetry and orthotropic physical symmetry through sixteenth order.

The solution has been particularized for {200}, {222}, and {110} back-reflection pole figures, where data are confined to the region not exceeding 60 degrees from the sheet normal direction.

Data obtained from a sample of low—manganese steel sheet are used to illustrate the method, and results are compared to those obtained using complete pole figures obtained with a composite sample of the same material.

The method described makes it possible to study crystallite orientation distribution as a function of distance from the sheet surface, by a series of pole figure measurements on the surface after successive material removals by polishing and etching.

The transition temperatures of solid-solid phase changes in selected polyalcohols, “plastic crystals,” can be adjusted by using interstitial and substitutional dopants. An investigation is under way of the structural changes in these during heating and cooling, and of the thermodynamic properties such as the transition, temperatures and enthalpy changes, as a function of the percent of dopant. The purpose of the investigation is to find and evaluate materials having potential value In thermal storage applications. Dopants for pentaerythritol discussed in this report are trimethylolpropane (TMP), ammonia, boron trifluoride, pentaglycerine (PG) and neopentylglycol (NPG).

Methods and instruments have been developed for efficient spectroscopic analysis in the 15 to 150 Å ultrasoft X-ray legion using specially designed Langmuir-Blodgett type multilayer analyzers with a flow proportional counter detection system. Simple adaptations of the basic Philips vacuum spectrograph are employed with a high-intensity, demountable, ultrasoft X-ray source to excite fluorescence in the lighter elements for chemical and valence band analysis.

The fluorescence x-ray method of the coating thickness measurement is theoretically studied. The theoretical formulas of the fluorescence x-ray intensity from the coating and from the substrate are obtained which include the enhancement effect between the coating and the substrate. The formulas are applied to the following examples and are confirmed experimentally: zinc on steel; tin on steel; aluminum on steel and on PMMA. The experimental results agree well with the theoretical results.

Our objectives in Instrument design & development are to improve the QUALITY OF THE DATA which can be obtained and presented to a computer system for analysis and to explore the corresponding choices which such improved data quality allows.

In usual EDXRF systems, the detector views the entire scattered and fluorescence radiation from a sample illuminated either by a direct beam or by a secondary target. In either case, the beam may be filtered before it strikes the specimen. Most efforts to mono-chromatize the exciting radiation or to reduce the background under the fluorescent peaks from the sample result in (a) decreases in X-ray flux available for excitation, (b) significant increases in power expended in the X-ray tube, or (c) extremely close coupling of the system components. These are NOT THE ONLY CHOICES AVAILABLE.

A versatile beam-scanning system has been developed for use with the Electron Microprobe X-ray Analyzer manufactured by Applied Research Laboratories, Inc. It provides for the display of X-ray intensities from any of three spectrometers, three nondispersive detectors (either counters or scintiallation counters), as well as the current collected by the target or the current backscattered by the target. The electrostatic deflection system does not interfere with the use of the optical-viewing system and provides a maximum scanning area of only slightly less than field of view of the optical-viewing system.

A stepping motor, controlled from the readout console, has also been developed which permits automatic point-by-point analysis of a specimen with minimum operator attention. In the use of this attachement, measurements may be made for fixed time, fixed charge, or fixed counts (integrated intensity) at each point. As a result, the step-scanning motor facilitates accurate measurement of one-dimensional concentration fluctuations and is particularly useful for phase identification and studies of diffusion and segregation.

A systematic study of the production of characteristic X-rays by both light and heavy charged particles has been made. Using protons in the energy range 70-200 keV, data have been obtained for twenty-one X-ray lines encompassing a wavelength region from 1.44 to 44.00 Å from K-, L-, M-, and N-shells of elements with 6 ≤ Z ≤ 92. Additional X-ray production efficiencies have been measured in the K-, L-, M-, and N-shells using incident H2+, He++, N++, O++, and Ar++ ions in the energy range 90-400 keV. The ion beams were obtained from a 300 kV electrostatic accelerator, and beam analysis was obtained using a 7 kilogauss analysing magnet.

The data for proton excitation show that, for X-rays of a given wavelength, the X-ray production efficiency increases with the principal quantum number of the atomic shell being excited. These results contradict results reported by Sterk et al, but agree with results obtained earlier by Khan et al.

The results also show that the use of heavy ions (z > 5; obtains X-ray yields which are orders of magnitude higher than a repredicted by the direct scattering theory as used for protons and alpha particles.

Ion excitation of X-rays has been applied to the study of the oxidation kinetics of iron as part of a surface physics program. The wide range of target penetration depth as a function of both mass and energy of the ion has allowed us to study oxide film thickness as a function of oxidation temperature and impurity depth and concentration. Data are presented for protons and argon ions incident on high- purity ion with surface oxide films varying in thickness from 35 Å to 750 Å. Oxygen and carbon sensitivities to equivalents of fractional monolayers are routinely obtained using nondispersive analysis of the X-rays.

Our laboratory has been interested in the use of the X-ray spectragraph for routine rock analysis within limited rock types. This paper is meant as a progress report and to indicate the direction of our work on amphibolites to others interested ill the problem of rock analysis.

Even with the use of flow counters and pulse discriminators the intensities of the magnesium, aluminum and silicon peaks are quite low and most dilution techniques may not be used. The direct determination of major elements (except sodium) yields results directly comparable to the chemical results for potassium; manganese and titanium in the range from 0: 1 to 3% as the oxides. For iron (10-20%), calcium (8-12%) and silicon (45-52%) the accuracy is 2-3% but for each element occasional samples will be 5% from the chemical values. Aluminum and magnesium yield erratic results.

The use of ratios between elements occurring in. the samples yields slightly improved accuracies. The use of a strong absorber such as tungstic acid (40% by weight) greatly improves the ratios for aluminum and magnesium., without appreciably affecting their intensities. By a combination of the direct and tungstic acid techniques it is possible to attain accuracies of 2-3% with analysis time of two hours. At present we are attempting a combination with an internal standard method to yield greater accuracy.

X-ray, neutron or electron diffraction patterns of alloys with structural disorder (micro-crystalline, amorphous or liquid alloys) consist of few diffuserings or halos. The ratio Ia(K)/<f> 2, where Ia(K) is the elastically scattered intensity per atom, K = 4πsinθ/λ, and <f> is average scattering factor of the alloy, is the sum of the Laue monotonic scattering (<f2> - <f2>)/<f2>, the small angle scattering Is(K) and interference function I(K). For isotropic distribution of the atoms in the alloy, one can write:

and

where

ρ0 is the average atomic density, V(r) is the size factor , ci and fi are the atomic concentration and atomic scattering factor of element i, respectively. Iij(K) is called the partial interference function which is related to the number ρij(r) = cjρ0gij(r) of j-type atoms per unit volume at the distancer from an i-type atom.

By varying the scattering factors of the elements through application of different radiations (x-rays, neutrons and electrons) and/or isotope enrichment, one can measure several I(K) which allow the evaluation of Iij(K) for a particular alloy. Assuming that gij(r) is independent of the relative abundance of the elements in the alloy , Iij(K) can also be obtained from several I(K) of the alloys with different concentratiora measured with a single radiation. This procedure has been applied to liquid Ag-Sn, Au-Sn and Cu-Sn alloys. The interference functions I(K), and their Fourier transforms, of vapor-quenched Ag-Ge and Ag-Cu films indicate that these alloys are micro polycrystalline with particle sizes of 15A in the Ag-52 at.% Cu alloy, 20A in the Ag-83 at.% Ge alloy and 24A in the Ag-64 at.% Ge alloy.

Humidity sensitive mineral phases change their structure when humidity varies resulting in X-ray pattern changes in intensity, position, and shape of lines. These structural changes in hydrous minerals are induced by dehydration and rehydration, which can lead to phase transformations or to steady depletion which may result in a total structure collapse. By means of X-ray diffraction with a special attachment, such reactions can be followed. The controlled relative humidity is provided in situ, in a closed cell, by a flow of moistened helium gas which is flushed through the cell during the XRD analysis. Humidity diffractometry allows studies of reaction rates of dehydration-rehydration reactions and their reversibilities, as well as effects of additives and impurities on these reactions. Potential applications in basic research and in industry are demonstrated using montmorilionite, ettringites, sodium carbonates and calcium sulfates.

Although widely recognized in the research community as one of the most accurate non-destructive methods for the determination of . residual stress in polycrystalline structural materials, x-ray diffraction has not been widely adopted in the field. This is partly due to the fact that such measurements require, most often, a well trained user with knowledge in both materials and mechanical sciences in addition to the specific know-how of the instrument. We believe that computer assistance could contribute to the promotion of this technique by increasing the productivity and accuracy of these measurements. We have developed a prototype expert system, using Nexpert Object's shell, to assist a non-trained operator in the validation and interpretation of X-ray diffraction residual stress data.

The present work describes this prototype which has been designed to confirm the feasibility of the concept. Its knowledge base contains relevant examples of the rules necessary for data validation. The prototype has also confirmed most of the concepts required for the implementation of a full-scale version by evaluating all of the major technical features such as graphics representation, external routines and database access.

Irregular backgrounds in time-of-flight neutron powder diffraction data and nonlinear backgrounds in angle dependent neutron powder diffraction data. were corrected by fitting fifth degree polynomials to those portions of the data most affected. The anomalous background intensities were in both cases due to non Bragg scattering. The polynomial fitting was carried out over a sufficiently widerange of the profile to avoid interfering with the Bragg peaks. The corrected data gave internally consistent results for the crystallographically nonequivalent (Si,Al) -0 (1) and(Si, Al) -0 (2) bond lengths in zeolite rho and compare favorably with previous refinements of this Zeolite in space group Im3m. Internal and external in consistencies of bond lengths are just as diagnostic of refinement difficulties as negative isotropic temperature factors or non positive definite an isotropic temperature factors are.

In the measurement of residual stresses via diffraction (using x-rays or neutrons) it is strains that are actually determined, by employing the interplanar spacing (dhkl) of the ﹛hkl﹜ planes as an internal strain gauge. The change in this spacing is measured from the shift of diffraction peaks (and Bragg's law) at several orientations of the sample to the incident beam, and the resultant strains are converted to stresses with the “diffraction elastic constants”, S1 (hkl) and S2 (hkl)/2. While these take on the values (- v/E) and (1 + v )/E respectively for an isotropic solid, in anisotropic materials their values depend on marry factors: preferred orientation, shape and orientation of second phases, interaction between grains. In fact there are reports of variation these constants with plastic deformation and theory predicts variations with morphology. While it is possible to calculate approximate values for these constants from theory and the single crystal elastic constants , Si and S2/2 are really not elastic constants in the strictest sense because or these other factors, and it is best to measure them. One of us (I. C. Noyan) has recently examined this problem in some detail , and we summarize his results here.

It will be shown that there are different types of influence coefficients to correct for matrix effects in XRF analysis: the empirical coefficients calculated from regression analysis and valid for the standards on hand only; the theoretical binary coefficients that are essentially constant in a given concentration range; then the theoretical multi-element coefficients calculated from one given composition and valid for one specimen only.

With theoretical coefficients, however, a special calibration process is needed, because theory cannot take into account all the instrumental parameters. In the proposed calibration method it will be shown that the slope of the calibration curves is the link to correlate the theoretical formalism to the experimental reality; that the standards used do not have to be similar to the unknowns and that a few only are required; that the calibration curves can be extrapolated by a factor of two or three; that pure analytes are not required.

The performance of a room temperature mercuric iodide X-ray detector was investigated as a function of detector bias, amplifier time constant, and detector temperature. A Mn Kα line of 200 eV FWHM was obtained by using low noise electronics developed for Si(Li) detectors, including a cooled input PET. Measurements of the detector's resolution at various X-ray energies result in a Fano factor of 0.20.

The purpose of this investigation was to develop a rapid, accurate method of analysis for small amounts of calcium in wolframite concentrates. This analysis is necessary to determine if wolframite concentrates meet the U. S. National Stockpile Specification P-57R2, which limits the calcium content to 0.2 per cent.

Because of the small depth of sample analyzed in fluorescent x-ray spectrography the calcium Kα line intensity was found to be a function of the chemical composition of the calcium-bearing particle as well as the matrix composition. This particle-conn position effect was particularly important in this analysis because the calcium may be present as a carbonate, tungstate, phosphate, etc. Three methods of sample preparation were found to eliminate the variation of calcium Kα intensity with mineralogical occurrences: (1) Reduction in particle size by extensive grinding, (2) chemical fusion wtli sodium carbonate, and (3) solution of the calcium by an add.

Determinations by all three procedures are believed to be accurate to within ± 5 per cent for more than 0.30 per cent calcium and ± 10 per cent at the 0.1-per cent level. The lower limit of detectability is in the order of 0.005-0.01 per cent.

The operating characteristics of a gas-flow proportional counter used in conjunction with a pulse-height analyzer were studied in detail. This detector was found to have a high counting efficiency for calcium Ka radiation, to have a low counting efficiency for overlapping higher order radiation and to have counting stability equivalent to Geiger tubes.

The automation of analytical equipment is proceeding at a rapid pace, particularly since the introduction of inexpensive microcomputer systems. Most of this equipment has one characteristic in common, that is, they produce digital spectral data. The usual method of recording spectral data has been the strip chart recorder. Strip charts require the hand encoding of position and intensities of the spectral lines. This requires that all of the lines be on scale or that the sample be run several times in order to amplify weaker lines. This problem is eliminated by recording the data digitally. Digital data can then be rapidly plotted on a cathode ray terminal to any desired scale. The user of digital data has access to a great variety of automatic data reduction programs.

This paper examines the relationship between the lattice defects and crystallization process of synthetic diamonds. Diamonds synthesized by high pressure, high temperature methods as well as diamonds vapor deposited under metastable conditions are considered. High pressure crystals precipitated from Ni or Co solutions contain inclusions of metastable carbides and metal atoms distributed throughout a small fraction of the octahedral holes in the diamond lattice.

Diamonds are grown metastabily by a chemical vapor deposition process in which CH4 and H2 are excited by a microwave plasma. Such diamonds are deposited as individual micro-monocrystals or as solid poly crystalline films. The defects in such crystals are related to impurities such as Si and H which produce point defects and tend to nucleate graphite, which can generate planar defects. Nucleation of a diamond phase on β-SiC is also considered, because of the lattice matching between them.

Diamond structure is a prototype of a family of related phases such as cubic BN (sphalerite structure) and solid solutions of diamond and cubic BN, Cubic BN-diamond solid solutions (BN)x(C2)1-x,0<x<l are, in turn, a prototype of AIIIBV-CIV phases, of which (GaP)x(Si2)1-x,0<x<l is an example. Substitution of B-N (or Ga-P) by C-C (or Si-Si) atom pairs at lattice sites is characteristic of these solid solutions.