Fluorescent X-ray spectrometers bave a high inherent reproducibility. It is possible to achieve results, on a routine basis, which have a coefficient of variation of less than 0.1%. Given extremely good chemical standards and the absence of interelemental effects, these readings can be interpreted into percentage concentrations with the same order of accuracy. Results, with this accuracy of analyses of copper in a straight brass will be given. With samples of greater complexity and more elements the interelement effects are large and have to be tackled. A correction method has been established and will be explained in detail.

As an example of the method it was decided to tackle the determination of chromium at high concentrations (7-32 %) in high-alloy steels containing additions in the following ranges: Si, 0.2-2.4%; Al, 0,07-5%; Cu, 1,3-3.6%; W, 0.25-3%; V, 0.1-0.3%; Nb, 0.1-0.3%; Mo, 0.1-4.4%; Ti, 0.05-1%; Mn, 0.35-10%; Ni, 0.2-24%. These very wide alloy specifications were a severe test on the accuracy of the chromium determination & the correction for interelement effects.

The broadening of powder pattern peaks of metals is normally caused by small crystallite size and by distortions within the crystallites as a consequence of dislocation configurations. In addition, the experimental diffraction geometry contributes to the line broadening. Using Cu Kα radiation, we recorded the peak profiles of the cold-worked and annealed filings of tungsten, niobium, aluminum, and silver-indium alloys with a standard focusing diffractometer. The Rachinger method was applied to separate the Kα1 and Kα2 peaks, and the Kα1 peaks were subjected to a Fourier analysis. Elimination of the instrumental broadening was carried out by the Stokes method, which does not require any assumptions concerning the mathematical description of the diffraction peak profile.

The Fourier coefficients, AL, were separated into the fraction produced by particle size, ALFF, and by strains, ALe, by the Warren-Averbach method and plotted as a function of the distance L = ndhkl, normal to the reflecting planes (hkl) of spacing dhkl. The negative, reciprocal initial slope of the ALPF vs. L curve is equal to the effective particle size Deff, which contains the effects of the true crystallite size and faulting. The coefficients ALβ = AL/ALPF are used to calculate the root mean square strain <∊L2>1/2. The sum of the ALPF, which is proportional to a reciprocal integral breadth, leads to a different particle size, DWAPF, which is also dependent upon the crystallite size and faulting. The sum of the AL6 values is a measure of the strain ƐWA.

The integral breadths bst, corrected by the Stokes method, i.e.,

are separated into a particle size term bstPF and distortion term bSts using the relations . It is found that only the first relation leads to particle sizes DG,StPF and strains ∊G,st similar to those obtained by the summation of the ALPF and AL6, i.e., DWAPF and ∊wA, respectively. The integral breadths of the cold-worked peaks Bew and of the annealed standards bA. were also calculated, using the Lauc definition of B equal to area per peak maximum. A comparison of the values of bst/Bcw with bA/Bew for bA/Bew < 0.6 shows that all data follow the parabolic relation b/Bew = 1 − bA2/Bew2. The maximum deviation of bst/Bew from the parabola is less than 10%.

A brief review of the different topographic methods is given in order to attempt a classification of the various types of contrast observed. Depending on whether the image is obtained by a reflection or transmission method, is simple or integrated, dynamic, direct, or intermediary, the contrast and image width vary greatly. A detailed analysis is given in the case of transmission section topographs.

X-ray diffraction (XRD) line-broadening analysis has been used to determine dislocation densities in zirconium alloys with hexagonal closepacked (hep) crystal structures and a complex distribution of dislocations reflecting the plastic, anisotropy of the material. The validity of the technique has been assessed by comparison with direct measurements of dislocation densities in deformed polycrystalline and neutron-irradiated single crystal material using transmission electron microscopy (TEM). The results show that-there is good agreement between the XRD and TEM for measurements on the deformed material whereas there is a large discrepancy for measurements on the irradiated single crystal; the XRD measurements significantly underestimating the TEM observations.

The analysis of thin insulating films occurring in various stages of the manufacture of integrated circuits has in the past been difficult, if not impossible. Their dimensions usually preclude analysis by conventional chemical techniques, hence very little is known concerning their relative stoichiometrics. However, by microprobe analysis, films as thin as 540 Å (∼18μg/cm2) have been successfully analyzed. In general, two different approaches are taken, depending on the film thickness. Usually, films thicker than 2500 Å (∼50μg/cm2) are analyzed by conventional microprobe techniques. A computer program, called MAGIC, has been written, which converts the raw X-ray intensities to chemical composition. All data are corrected for dead time, background, absorption, atomic number effects, and fluorescence by characteristic radiation, if required. A minimum of input is required, only the chemical symbols. X-ray lines employed, and the accelerating voltage being necessary in addition to the raw X-ray intensities. All constants such as atomic weights, critical excitation potentials, X-ray wavelengths, and absorption coefficients are stored or calculated internally, which reduces the errors and time associated with looking up and key-punching these values. New fluorescent yields are used for K and L radiation. No fluorescence correction is made for M radiation. The use of this correction program generally gives results, accurate to about 2 to 4%, relative to the amount present. For films thinner than 2500 Å, a new model is proposed which allows the X-ray spectra from the film and substrate to be unfolded to give the composition of the film only. To accomplish this, the atomic number correction of Duncumb and deCasa employed in MAGIC has been used in conjunction with a mean electron energy concept. Results obtained to date through the use of this model have been surprisingly good, being of the order of 5% relative to the amount present. Potential errors and uncertainties are discussed, and results given which illustrate the accuracy of the two methods.

A pragmatic, easily applied theory of the extended X-ray absorption fine structure found on the high-energy side of absorption edges is developed. This simple model can be successfully applied to determinations of interatomic distances, and it accounts for differences in Kronig structure on different absorption edges in the same material. Quantitative agreement with experimental data is good.

A monochromatic source of X rays for sample excitation permits the use of pure elemental standards and relatively simple calculations to convert the measured fluorescent intensities to an absolute “basis of weight per unit weight of sample. Only the mass absorption coefficients of the sample for the exciting and the fluorescent radiation need be determined. Besides the direct measurement of these absorption coefficients in the sample, other techniques are considered which require fewer sample manipulations and measurements, These fundamental parameters methods permit quantitative analysis without recourse to the time consuming process of preparing nearly identical standards.

The fitting of a parabola by least squares regression to the upper portion of diffraction peaks is commonly used for determining lattice spacing in residual stress measurement. When Kα techniques are employed, the presence of the Kα doublet is shown to lead to significant potential error and non- linearities in lattice spacing as a function of Sin2ψ caused by variation in the degree of blending of the doublet. An algorithm is described for fitting Pearson VII distribution functions to determine the position of the Kα component, eliminating errors caused by defocusing of diffraction peaks of intermediate breadth. The method is applied to determine the subsurface residual stress distribution in ground TI-6 AI- 4 V, comparing directly the use of parabolic and Pearson VII peak profiles, and is shown to provide precision better than ± 1%% in elastic constant determination.

We calculate the extended X-ray absorption fine structure by treating the ejected photoelectron as a spherical wave which expands in the lattice and is partially scattered by neighbors of the absorbing atom. The neighboring atoms are treated as point scattered and the total scattered wave is summed from the waves scattered by each atom. The fine structure is determined from the dipole transition matrix between the initial K-state and the final photoelectron state. Calculations compare favorably with experimental data.

Physical and chemical analysis, X-ray astronomy and high temperature plasma diagnostics which utilize the ultrasoft X-radiations hare made evident a strong need for filling the gap in measured absorption coefficient data for the radiations between the conventional X-rays and the extreme ultraviolet. More than one hundred new coefficients have been measured in this laboratory on the gas state, atomic or molecular, containing He, C, N, 0, F, Ne, S, Cl, Ar, Kr and Xe using eleven fluorescent, characteristic wavelengths Al-Kα (8.34 A) through Be-K (113.8 A). The radiations were isolated by Bragg reflection from multilayer analyzers of the Langmuir-Blodgett type and by pulse height discriminating proportional counter intensity measurements.

A unified matrix-flushing theory and its practical applications for quantitative multicomponent analysis by X-ray diffraction are presented.

In this method, a fundamental “matrix-flushing” concept is introduced; the calibration curve procedure is shunted; the matrix (absorption) effect is totally eliminated; all components, crystalline or amorphous, can be determined.

In spite of the wide availability of automated diffractometers and advanced data reduction software, numerous traditional problems still exist that make highly precise and accurate quantitative analyses of complex mixtures difficult. The problems include particle statistics, primary extinction, microabsorption, preferred orientation, overlapping and broad reflections, variation in standard data with composition, availability of pure standards, and detection of amorphous and trace phases. Our analyses of rocks use the matrix flushing method on < 5μm particle-size material mixed with a 1.0-μm corundum internal standard to minimize the first four effects. Integrated intensities are used, and we employ several peaks from each phase whenever possible. We overcame overlap problems through iterative calculations using integral, multiple peaks or with profile refinement. Use of observed and calculated diffraction patterns for every phase enables us to predict the effects of composition and preferred orientation on RIRs. This allows us to correct for these effects if reference intensity ratios (RIRs) are known as a function of composition and orientation. Detection of amorphous phases is a significant problem, and standard mixtures reveal that amounts of amorphous components below 30% are difficult to detect. The poor detection limit and the nature of the diffraction band from amorphous phases make internal standard or spiking methods the best approach for analyzing samples containing amorphous materials. The Rietveld method of quantitative analysis has the potential to minimize all of the above problems. This method requires a knowledge of the crystal structures of all component crystalline phases, but no calibration data are necessary, structural and cell parameters can be varied during the refinement process, so that compositional effects can be accommodated and precise cell parameters can be obtained for every phase. Since this method fits the entire diffraction pattern and explicitly uses all reflections from every phase, complex, overlapped patterns can be easily analysed. In addition, this method presents the opportunity to correct for preferred orientation and microabsorption during data analysis.

The residual stress left on the fracture surface is one of the important parameters in X-ray fractography and has been used to analyse fracture mechanisms in fracture toughness, stress corrosion cracking and fatigue tests especially of high strength steels.

In this study, the distribution of residual stress near fatigue fracture surfaces made in air and in 3.5% NaCl solution was measured by the X-ray diffraction method. The effect of aqueous environment on the plastic deformation near fatigue fracture surfaces was discussed on the basis of the residual stress distribution.

Optimized vacuum spectrographic measurement of low-energy fluorescence has been found to yield counting rates and peak-to-background ratios which are enough to permit the extension of fluorescence analysis for elementary chemistry into the light-element range—sodium through boron. This is accomplished with an efficient, demountable ultrasoft X-ray source, with close coupling among source, crystal, and detector, with KAP and multilayered stearate analyzers, and with, optimized flow-propordonal counting. Specific methods for achieving peak-to-background ratios on practical samples containing these light elements are presented. The extension of these methods of light-element analysis with the use of curved long-spaced crystals for X-Ray macroprobe and electron microprobe measurements is discussed. The design and construction of multilayered soap film “crystals” for long-wavelength X-ray analysis is described.

Residual stresses are expected to lead to a linear dependence of the interplanar spacing, d, on sin2ψ (where ψ is the sample tilt) and the stress can be obtained from the slope of this line, As a result of the linear dependence a two-tilt method is often employed to obtain the stress. However, when a specimen is subjected to extensive plastic deformation large deviations from a straight line can occur and a two-point method can lead to an erroneous stress determination. The results reported here show that: (1) this is more likely to occur in homogeneous materials than in multiphase materials (2) the oscillations follow closely the variation in peak intensity due to texture (3) the oscillations are caused by microstresses which are due to an "orientation" effect as suggested by Weidemann,

A simple, easy-to-use procedure has been developed and tested to correct the data and obtain the correct macrostress.

The object of the Rietveld method is to produce refined values of crystal structural parameters from powder diffraction data. Many materials of great interest can not be made available for study in single crystal form. This may be because it is not possible to prepare a single-crystal form at all (e.g., human tooth enamel) or because the single-crystal form differs from the polycrystalline form with the properties of interest (e.g., catalysts). Thus, our basic understanding of the atomic scale mechanisms is limited on the structural side by the information that can be deduced from powder diffraction patterns. (Only diffraction and EXAFS are direct probes of the spatial arrangements of atoms.) The Rietveld method has greatly extended the amount of structural detail that we can obtain routinely from powder diffraction patterns. In this method, structural parameters such as atom coordinate, thermal motion, and site occupancy parameters are adjusted in a least-squares refinement procedure until the best fit is obtained between entire calculated and observed powder diffraction patterns, as a whole.

A technique and apparatus are described for obtaining the elastic constant E/(1 + v) in selected crystaliographic directions for the purpose of calibrating x-ray diffraction residual stress measurement methods. The preparation of a simple rectangular beam specimen with two active electrical resistance strain gages applied to the test surface is described. Samples are clamped in a diffractometer fixture designed to minimize displacement errors, and loaded in four-point bending to several stress levels below the proportional limit. A method is described for calculating E/(l + v) and an estimate of the experimental error.

Values of E/(l + v) obtained for several alloy-(hkl) combinations are presented. The results indicate that several alloys of current commercial interest exhibit significant elastic anisotropy.

In recent years considerable success has been achieved in the development of detectors for the localization of ionizing radiation. One dimensional position sensitive detectors have a number of uses in nuclear physics and in biological studies utilizing small-angle scattering. Detectors are now capable of providing position information of high resolution with a high count rats capability and a simple readout system. We report here on the feasibility of employing a position sensitive proportional counter (PSPC) for the measurement of residual stresses with X-rays.

Comparisons of the accuracy and time of data accumulation between a scintillation detector and a PSPC have been performed on stress relieved, shot peened steel specimens, and specimens deformed in tension.

The ability of obtaining the entire profile at once is somewhat offset by the lower efficiency of the PSPC when compared to a scintillation detector, but this is counteracted by the fact that motion of the detector is eliminated with the PSPC, It will be shown that a PSPC system provides a speed of data accumulation currently not available in any other way, while still remaining a versatile and accurate method.

The fundamental parameter method for quantitative analysis of composite elements has been a powerful technique for x-ray spectrochemical analysis in which the x-ray intensity and spectral distribution from x-ray spectrographic tubes are the moste ssential factors in the calculating process based on x- ray physics.

Various electro-optical systems have been reported which permit intensification of X-ray diffraction patterns and thus a decrease in exposure time for recording and display of the X-ray images. Prior to 1966, all such electro-optical systems incorporated a large format X-ray image intensifier of the same type as conventionally used for medical and industrial fluoroscopy. In the past four years, a number of different systems have been reported which are superior to those developed prior to 1966. These systems may be grouped into two main categories, the large format variety for Laue diffraction applications, and the small format variety for topographic applications.

The purpose of the present paper is to describe the particular characteristics of both the large format and small format systems and to discuss the advantages and disadvantages associated with each type. Based on actual performance characteristics it will be shown that:

1. 1. A multiple stage image intensifier system coupled to an external fluorescent screen is the most sensitive and only truly instantaneous system; it can be used with very weak X-ray intensities, the resolution is currently limited by the external fluorescent screen to 42μ the system is extremely versatile in that it can be used both for large format recording of Laue patterns as well as for small format recording of X-ray topographe; the system has a very long lifetime since nothing is altered by X-radiation.

2. 2. An X-ray sensitive vidicon is the least sensitive; it must be used with extremely high intensity X-rays or long exposure times; the resolution is the highest at approximately 15μ and is limited by either bandwidth of the television system, the thickness of the X-ray sensitive target or the size of the electron beam at the target; due to the small size of the X-ray sensitive target the system can only be used for small format recording of X-ray topographs; the lifetime of the system is short since X-radiation causes degradation of the target.