Rietveld Analysis on X-Ray powder diffraction data was used to build a comprehensive model of the structures in gallmm rich R-Ga systems (R is a rare earth between La and Gd). The ability to refine occupation factors as well as atomic positions allowed for the analysis of the e solid solution, its structural relation to the ordered ∊′ phase, and the unique role of the Ga-Ga pairs in these systems.

The recently developed code SHAPE allows the build-up of EDXRF spectra for collimated and monochromatic excitation. In this work the code is applied to investigate the Importance of the scattering corrections to the more intense XRF characteristic lines from low and medium Z elements. Results are given graphically for pure elements from Z=11 (Na) to Z=42 (Mo). Heavier element lines from a multi-component geological sample, where light matrix amplifies the influence of scattering, are studied.

A review is given of the main gas-discharge sources and auxiliary equipments which were used in soft and ultra-soft X-ray emission spectrometry. Special attention is paid to the basic principles and instrumentation of low-energy electron-induced X-ray spectrometry (LEEIXS) whose excitation source is an electron beam generated in a glow-discharge system. Capabilities of LEEIXS in surface and thin film analysis and characterization are illustrated by examples dealing with control and optimization of surface treatment and thin film deposition processes. Sensitivity of the technique down to the submonolayer range and influence of backscattering phenomena are shown.

A modified version of the Rietveld method has been developed for quantitative phase analysis in conjunction with crystallite size and microstrain determination.

Besides the information on the microstructural disorder in the different phases present in the sample, accurate phase analysis can be performed, even in presence of anisotropic crystallites, taking into account the non-instrumental peak broadening effect in a better way compared to conventional methods.

The method has been tested on binary mixtures of corundum, ceria stabilized zirconia and on a polyphase stabilized zirconia sample.

Sherman described the excitation of characteristic radiations by primary x-rays and by secondary excitation. The derivation has been made assuming a homogeneous sample. Criss and Birks inverted the problem from the calculation of fluorescent countrates to the quantitative XFA by means of fundamental parameters. Theoretical and instrumental developments enabled a reduction of the sample area and led to small area XFA and imaging XFA sytems. Depth profiling by means of XFA is a further development. We continue the original concept of variable take-off angle technique for the determination of film thicknesses without reference samples and apply the variation of the incidence angle to depth profiling.

The electron density distribution maps for CaF2 and TiO2 (rutile) were obtained from profile fitting of powder diffraction data by a Maximum Entropy Method (MEM) analysis. The resultant electron density maps show clearly the nature of the chemical bonding. In order to interpret the results, the nuclear density distribution was also obtained for rutile from powder neutron diffraction data. In the electron density map for rutile obtained by HEM analysis from the X-ray data, both apical and equatorial bonding can be seen. On the other hand, the nuclear density of rutile Is very simple and shows the thermal vibration of nuclei.

The X-ray fluorescence analysis of a trace element under a grazing incidence condition has been developed using synchrotron radiation. The interference effect plays an important role for determining the depth distribution of the elemental concentration. The elemental distribution above, on or below the material surface has been studied. The glancing angle dependence of the X-ray fluorescence signal around the critical angle strongly reflects the elemental distribution, and can be used to determine the position of the element of interest.

A Debye-Scherrer camera (radius 572 mm) was designed for the use at the Photon Factory BL-6A2. It uses 4 pieces of the Imaging Plate to cover 0° ∼ 160° in 2θ. The profiles measured by the camera had 0.083° full width at half maximum (FWHM) and were rather symmetric compared with conventional X-ray source. The observed profiles were well represented by either the split Pearson VII or pseudo-Voigt function. In order to examine the performance of the new camera, the whole powder data of LiF was analyzed by the Maximum Entropy Method(MEM). The MEM analysis of LiF was successfully accomplished using 20 measured structure factors and gave R(Bragg) 0.25%. The density distribution obtained represented a characteristic feature of ionic crystals and was consistent with the theoretical result of the self-consistent LCAO method.

This paper investigates the contributions of sample preparation to the analytical lower limits of detection and errors for the quantitative X-ray diffraction analysis of a simple, binary system of quartz and calcite. This study further demonstrates the danger of using only statistical and instrumental contributions to detection limits and analytical errors.

Reflection and fluorescence intensity profile curves for thin films were measured under the grazing incidence conditions using synchrotron radiation. A titanium layer and a carbon / titanium bilayer sputtered on a silicon wafer were subjected to heat treatment. The analysis of the reflection and fluorescence profile curves shows that the sample without the heat treatment has another high-density layer on the surface or interface, and that the heat treatment results in the removal of the high-density layer and the formation of a thick homogeneous layer.

Quantitative phase analysis (QPA) methods which employ only one diffraction line for each phase arc generally unreliable due to the influence of systematic errors such as preferred orientation and extinction. Gazzara and Messier (1977) proposed a multi-line QPA method using normalised line intensities for line j of phase i,

where Iij = measured Bragg intensity, m = multiplicity, Lp = Lorentz-polarisation factor, |F| = structure amplitude and Vi = cell volume. The method proposed here is a refinement of the Gazzara-Messier procedure. Phase compositions are calculated directly from the mean normalised Intensity for resolved lines which span the 2θ range of the instrument. The method makes use of the variance in to estimate standard deviations for the phase compositions. Test results are given for binaries of corundum-quartz and corundum-ceria.

A novel method using Fourier transform algorithm is proposed to determine each layer thickness of multi-layered thin films from interference oscillation observed in X-ray specular reflection. The peak position in Fourier space gives each layer thickness of the film. The principle of the present technique as well as its applications are described.

Chromium nitride hard coatings have been prepared by a plasma process by varying nitrogen partial pressure. The crystallographic structure of these samples has been investigated by XRD and their chemical composition and stoichiometry by Low Energy Electron Induced x-ray Spectrometry (LEEIXS).

A menu-driven IBM-PC/MS-DOS software system for quantitative XRF analysis was designed combining elements of pattern recognition (spectral “fingerprinting”) with mathematical correction models. The following topics are covered:

1. - pattern recognition method; N - dimension representation

2. - local empirical Lachance-Traill or Lucas-Tooth & Price models

3. - EGA/VGA intelligent driver for a calibration display

4. - dSASE III Plus “data files - accessed from dBXL/Quicksifver”, dBASE III Plus or from compiled BASIC equipped with “call subroutines”

5. - Examples of applications (stainless steels and ceramics).

In this approach, experimental alphas are computed utilizing the closest automatically preselected standards from available data files. Alpha values generated in this fashion we term “local alphas”. An intelligent software program is employed which automatically recognizes the resolution of tiie CRT display and delivers the best possible display for the available equipment. This new design also permits the utilization of dBXL/Quicksitver, dBASE III Plus or compiled BASIC resources for additional on site system customization programming. A dBASE III Plus file format is used for XRF data storage. This permits fast data exchange with a local ASCII database and also with all popular spreadsheet formats. Additionally, there are utility subroutines available which allow direct and rapid manipuiation of dBASE III Plus files in compiled BASIC. Application of this software system and graphics to stainless steels and engineered ceramic materials are demonstrated. RIGAKU Smax/PDP-11/73 and TRACOR X-RAY SPECTRACE 5000/Compaq 386 spectrometers are used in these studies.

A new approach to quantitative XRD by Partial Least Squares (PLS) used region(s) or the entirety of the diffraction pattern of calibration standards (also called a training set) in the model. The basic concept of this approach states that the information in many observed variables, expressed as matrix I = (i1, i2 … , ik,) is concentrated onto a few underlying latent variables, called factors, by the process of data compression. In XRD, the data points of the diffraction pattern are compressed to few factors T, computed according to their ability to explain the variation in the diffraction pattern or matrix I. The procedure incorporates into the model that part of I that is correlated to C concentrations. Data compression preserves the redundancy between variables due to collinearity and stabilizies the predictions against noise in I. The resulting calibration model allows for detection of outliers. Another important effect of data reduction is the ability to analyze muticomponent systems even when lines of the components are overlapped, Examples of quantitative analysis by PLS are demonstrated in the analysis of a commercial product.

An analytical framework for calculation of multiple scattering intensities emitted by a multi-layer sample are obtained with transport theory. The n-th order Flux solution of the Boltzsiann transport equation renders the iterative solution for multi-layers samples of thin or infinite thickness.

The first-order intensity is written for a generic sample with I layers and for the predominating interactions in the X-ray regime: the photoelectric effect, and the Compton and the Rayleigh scattering. As an example, the case of a thin deposit on an infinite thickness substrate is discussed.

The multiple scattering contributions to the emitted intensity of a thin homogeneous sample under X-Ray excitation are studied with recourse to the Boltzmann transport theory. The corrective terms to the XRF characteristic line due to a second collision of either the photoelectric effect (secondary XRF), or the Compton, or the Rayleigh scattering, are deduced for reflection geometry. Analytical expressions for the intensities are given that allow their computation for variable incidence and take-off beam directions and source wavelength.

At grazing incidence all X-ray techniques become surface sensitive. Far below the angle of total reflection the X-rays penetrate only 20 to 70 Å into condensed matter. X-ray reflectivity measurements give the density and the thickness of layers on substrates and the roughness of external and internal interfaces. The diffuse scattering in the vicinity of the specular reflection gives, besides the interface roughness, also the height-height correlation of the surface. From the angular dependence of the fluorescence intensity, emitted as a consequence of X-ray absorption, the depth profile of the absorbing species can be deduced. Artificial periodic multilayers give rise to Bragg reflexes and to standing X-ray wave fields, the angular dependence of which give the distribution of atomic species in the periodic stack. A number of examples illustrate the possibilities of the technique.

Precision X-ray reflectivity data were obtained with a high-resolution reflectometer equipped with a rotating anode X-ray source and Ge 220 channel monochromators (one placed before and the other after the specimen). The surfaces and buried interfaces of thin films were characterized by ieast-squares refinement of experimental data. Values of thickness, density, and/or roughness of Pt “single-layer” and Pt/Co based multiple-layer films were determined.

Variable sample exit angle x-ray fluorescence spectroscopy (VEA-XRF) employing the Lβ/Lα intensity ratio for transition metals and their oxides has been shown to be useful for non-destructively studying transition metal surfaces and oxidation, as well as, superconductors. Thus the theoretical formulation of the Lβ/Lα intensity ratio dependence on the sample exit angle, θe, is of some interest and we develop it here. We also present methods of obtaining parameters needed in the formulation, such as Lβ absorption coefficients, which are not available in the literature, for wavelengths greater than about 12Å.