Andrew M. Wims

Quantitative X-Ray Powder Diffraction Method Using the Full Diffraction Pattern

A new quantitative X-ray powder diffraction (QXRPD) method has been developed to analyze polyphase crystalline mixtures. The unique approach employed in this method is the utilization of the full diffraction pattern of a mixture and its reconstruction as a weighted sum of diffraction patterns of the component phases. To facilitate the use of the new method, menu-driven interactive computer programs with graphics have been developed for the VAX series of computers. The analyst builds a reference database of component diffraction patterns, corrects the patterns for background effects, and determines the appropriate reference intensity ratios. This database is used to calculate the weight fraction of each phase in a mixture by fitting its diffraction pattern with a least-squares best-fit weighted sum of selected database reference patterns. The new QXRPD method was evaluated using oxides found in ceramics, corrosion products, and other materials encountered in the laboratory. Experimental procedures have been developed for sample preparation and data collection for reference samples and unknowns. Prepared mixtures have been used to demonstrate the very good results that can be obtained with this method.

A quantitative X-ray microanalysis thin film method using K-, L-, and M-lines

We have developed an improved quantitative X-ray microanalysis method using new relative intensity factors and ionization cross section equations. The method uses K-lines from Z=11 to 60 and all measurable L- and M-lines. Our most important improvement over existing procedures is in the equation for ionization cross section which takes the form Q x ~ b ln ( c U x ) / E x 2 U x d ; where Ex=excitation energy, U=overvoltage (E0/Ex), and b, c, and d are functions of atomic number. We obtained experimental k values on particulates of eight stoichiometric compounds using a STEM at 100 and 200 kV. These data and selected values from the literature were used to obtain the following functions for b, c and d: bK(Z⩽30)=8.874-8.158 ln Z+2.9055 (ln Z)2—0.35778 (ln Z)3; bK(Z>30)=0.661; bL=0.2704+0.00726 (ln Z)3; bM= 11.33-2.43 ln Z; cK=cL=cM=1; dK = 1.0667—0.00476 Z; dL = dM = 1. Precision and accuracy data obtained on eight samples using a variety of line combinations gave an overall relative accuracy of±4.4%.

Use of full diffraction spectra, both experimental and calculated, in quantitative powder diffraction analysis

The use of the full powder diffraction trace over a selected diffraction range for quantitative analysis has advantages over using single peaks in that it compensates for the effects of peak overlap and low levels of preferred orientation. Using a data base composed of experimental and calculated traces, the phase composition of an unknown may be determined by determining the least-squares best-fit sum of the appropriate data base patterns to the pattern of the unknown. Weight fractions are calculated from the pattern weighting factors using the reference-intensity-ratio method.

An automated, laser light-scattering photometer (0.1 to 170° range) with a single photon counting system

Abstract A light-scattering photometer has been developed which is particularly useful for the determination of particle sizes (0.1 to 50 μm). The light sources for the photometer are a 6-mw helium-neon laser with wavelength of 0.6328 μm and a 10-mw argon laser that provides wavelengths of 0.5480, and 0.4880 μm. A typical two-pinhole receiving system provides angular resolution of 0.2°. The photomultiplier output pulses from single photoelectrons are fed into an amplifier, discriminator, and high speed scaler that handle rates of up to 10 7 counts/sec. The digital data are obtained automatically as a function of angle on punched paper tape at a teletype terminal which is also used as a time sharing device for the computer processing of the data. Experimental scattering curves for several latex standards agree well with the Lorentz-Mie theoretical curves. The Sloan method was used to obtain particle diameters for latex standards which are in agreement with the certified values; this method of data analysis is rather insensitive to differences in particle shape, to concentration, and to refractive index. The measurement of the molecular weight (51,000) of a polystyrene standard in 2-butanone with the small pinhole system mentioned above shows the versatility and high sensitivity of this photometer.

A Method for Determining Reaction Kinetics by Differential Scanning Calorimetry

Knowledge of the degree of cure and the optimum molding conditions of thermosetting materials is important for molding good parts using minimum processing time. From the practical point of view, analytical data in the form of isothermal composition curves (concentration or percent cured vs. time) are the most valuable. These curves are used by the processor to determine the temperature and time required for a particular degree of cure. A number of experimental techniques and studies relating to thermosetting cure reactions have been reported in the literature with emphasis on the chemical, physical, and mechanical property changes with time at constant temperature. These methods have recently been enumerated by Sourour and Kamal (1). However, these traditional methods use the approach of measuring a particular chemical, physical, or mechanical property of a large number of molded parts which have been cured under different conditions of time and temperature. While this approach does lead to the desired isothermal composition curves, it requires a long time period during which valuable production equipment is tied up before the „optimum“ cure conditions can be found.

Determination of size distribution of Rayleigh—Gans scatterers by forward scattering lobe method

Abstract The value of light-scattering measurements in the forward lobe for determining the size of monodisperse scatterers has been previously documented. The applicability of the method for determining the size distribution of Rayleigh—Gans scatterers was studied because it was uncertain which average size is actually determined for polydisperse scatterers. To generate the theoretical curves for polydisperse scatterers, the Rayleigh—Gans and the Mie scattering equations were used with the zero-order-log-normal and the Gaussian distribution functions. These curves were plotted using a modified Sloan plot (log I sin2 θ/2 vs log sin θ/2). The ratio of the fifth to the fourth moments (z + 2 average radius) of the distribution can be calculated from the maximum in the plot. The breadth parameter of the distribution (σ0) can also be determined by using a master plot of a family of curves generated for different values of σ0 and any fixed value of the modal radius.

Interactive Dialog for Phase Identification by the Johnson/Vand Program for X-Ray Diffraction Data

A new, convenient program has been designed and implemented on a VAX computer to facilitate the use of the Johnson/Vand program (Version 21) for identifying components in crystalline mixtures by X-ray diffraction. (The data base of references is distributed solely by the JCPDS – International Centre for Diffraction Data.) This new program uses an easy-to-follow conversational mode of communication for setting up the input file for the identification program from a remote terminal. The program is menu driven with screens for input of sample information, for change of default computational parameters, and for handling the experimental diffraction data. Many of the input screens can be readily bypassed when the default parameters are acceptable. An editor feature is provided for viewing the final input file and for correcting the diffraction data.

Size distribution analysis of large scatterers by the forward scattering lobe method

Abstract The value of light-scattering measurements in the forward scattering lobe (FSL) has been increased for large polydisperse scatterers. The Mie equation and the Airy disk equation along with the ZOLD and Gaussian distribution functions were used to represent polydisperse scatterers. A Sloan plot (logIθ2 vs logθ) is used to present data in the FSL. The z average radius can be calculated from the maximum in the Sloan plot (within 5% for most cases) for large scatterers. The breadth parameter (σ0) can also be estimated by using a master plot of a family of curves generated for different values of σ0) and any fixed value of the modal radius. The shape and maximum of the Sloan plot, except for a few cases, was also shown to be independent of the refractive index ratio.