Recently the X-ray wavelength scale has been put on a consistent basis by the selection of the W Kα1, line to be the wavelength standard foe the whole X-ray region of the electromagnetic spectrum. To help establish this scale, four other X-ray lines, which had been measured with a precision approaching 1 ppm, were selected as secondary standards. However, since the longest of these lines is the Cr Kα2 line at 2.293606 Å, other lines whose wavelengths are less precisely known have been used for calibration purposes. The most interesting of these is the Al Kα. line, which plays an important part in the effort to connect the X-ray wavelength scale to the basic standard of length. Two other often-used lines are the Cu La line at 13.339 Å and the O Kα line at 23.62 Å. It is, however, necessary to take several steps to trace the accepted values of these lines back to the basic X-ray wavelength standard. Furthermore, the uncertainties introduced by the effects of the chemical combination and the large natural line widths limit the precision obtainable. It has been suggested that the first resonance line of the Ne K edge in the 14-Å region would overcome both of these difficulties. It has also been suggested that the highfrequency limit of the bremsstrahlung radiation would make a particularly convenient reference mark. This method is discussed here, and it is shown that the accuracy obtainable by this method is better than that obtainable by means of some commonly used reference lines.

A portable, battery-operated X-ray fluorescence analyzer weighing 15 lb is described, consisting of a Nal(Tl) scintillation-counter probe and an electronic unit with a single-channel pulse-height analyzer and reversible scaler. Radioisotope X-ray sources are used for excitation of the sample and, where necessary, balanced filters for resolution of neighboring characteristic X-rays. Emphasis has been placed on designing and producing an instrument that is easy and convenient to operate in laboratory, factory, or field conditions and that can equally well be used to measure extended surfaces, such as rock faces, or finite samples in the form of powders, briquettes, or liquids. The feasibility of the following analyses has been studied by using for each determination the appropriate radioisotope source and filters: sulfur in coal; calcium and iron in cement raw mix; copper in copper ores; and vanadium, chromium, molybdenum, and tungsten in steels. Detection limits, based on counting statistics obtained in count times of 10 to 100 sec, range from 0.03% for copper in ores to 0.2% for sulfur in coal. Both matrix absorption and enhancement effects were encountered and were eliminated or reduced substantially by suitable choice of source energy, by the use of nomograms, or by semiempirical correction factors based on attenuation or scattering coefficients.

Radioisotope excitation, solid-state detection, and multichannel pulse-height analysis have been applied successfully to the determination of molybdenum in copper and molybdenum-process intermediates. Analytical data are presented, and comparisons are made with the conventional X-ray fluorescence approach. The equipment performed satisfactorily in molybdenum plant control and shows promise for other industrial applications with the development of suitable isotope sources.

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.

In the electron-probe microanalysis of thin alloy samples, particularly for areas which contain a high degree of solute segregation as are often obtained in extraction replicas or in electro chemically thinned foils, a correlation between the measured intensity and the sample microstructure has heen difficult to perform. The purpose of this study was to isolate the effect of micro segregation, i.e., segregation with respect to the beam size (∼2 μ) itself, on the characteristic intensity generated by a microvolurne. To accomplish this, a model system consisting of silver-powder particles (∼1 μ diameter) supported on an evaporated carbon film was investigated by using a thin-film microprobe accessory of an electron microscope (Hitachi HXA-1). The silver particles served as analogs to a highly concentrated segregation area, and the carbon film was analogous to the corresponding matrix. The simplicity of this system readily allowed for an analysis of the geometric positioning factor dependence of the generated intensity.

It was observed that the intensity measured for a given particle could vary by as much as 1000% depending only on the relative position of that particle within the electron beam. This variation was derived to be due to both the distribution of electrons within the beam and the amount of mass occupied by the particle at each distance from the beam center. A computer program was developed to perform the necessary calculation to predict the relative intensity as a function of position within the beam. These calculated intensities were found to compare favorably with the experimental measurements.

Improvements on the semiquantitative analysis in a scanning electron-probe microanalysis will be discussed. Improvements have been attained by the development of a new content mapping attachment. By using this attachment, the X-ray intensity is indicated on a cathode-ray tube in nine steps of brightness. A discrimination operation on the intensity information can be done to help the observation of fine concentration variation in the specimen. The scanning image about an element in the specimen is displayed on the screen of the cathode-ray tube or on a paper tape by a typeout recording. The image is composed of 2500 picture elements. The brightness of each picture clement corresponds to an exponentially modulated X-ray intensity emitted from the corresponding point of the specimen surface. The correct information about the X-ray intensity to the observer is given by using this kind of modulation. In the image display on typewritten paper, the X-ray intensity is indicated with numbets from 0 to 9 according to the intensity grade. Each number is printed with an individual color to present a contour map of the element distribution. The time necessary to obtain one complete contour map is about 8.5 min.

Demonstrable diffraction (powder or single-cry still) with the use of zero-power isotopic sources would provide important data on such systems and may have implications in analysis (in this work, we fabricated 100-mCi 55Fe, acceleratorproduced, and 4-mCi 117Pm-Cu beta-excited sources). Powder-diffraction efficiency with the use of a special diffrac to meter adapted to these sources is about 10−5 (calculated) for the Mn Kα X-rays (55Fe) on the NaCl 200 plane. This beam flux at three times natural background intensity was experimentally achieved by using photon spectrometry with proportional counters and multichannel analysis. The Lip diffraction pattern was demonstrated with intensities roughly in agreement with prediction. Lithium fluoride single-crystal diffraction intensity (200 plane) exceeded by 250-fold that of powder. Powder main-peak intensity (θ = 31.5°) produced 9.2 photons per minute at the receiving slit versus 2.3 × 103 events for the single crystal. This single-crystal intensity with 60-sec runs provided a peak resolution of 0.29° full width at half maximum. The first-order Kα, Kβ1 first order, and Kβ1 second-order beams (θ = 31.5°, 28.3°, and 71.6°, respectively) were demonstrated, with 1900 events per minute in the main peak (Kα). X-ray noscreen emulsion was used to study photographic recording on the LiF single crystal with exposures as short as 2.5 hr. A 2-in.-diameter camera, newly designed for the 55Fe source, is collecting further emulsion data.

The isotopic source is stable, highly predictable in intensity, reliable, and compact. Requiring zero power, it thus has a potential for remote applications. Where its low output can be tolerated, it may hold promise for analysis, especially where its size, weight, and stability tire important criteria. Source work here points to possible 55Fe improvement in photon output of 102 over the source described here. Such an increase may make certain special analytical applications feasible.

An X-ray small-angle scattering instrument is described which is used for recording X-ray diffraction patterns or small-angle X-ray scattering curves in an angular region very close to the direct beam. The measurement of X-ray intensity is accomplished with standard geiger or scintillation counter techniques. The instrument is designed for use with a spot-focus or vertical-line X-ray source, In essence, it is a multiple-reflection double-crystal diffractometer, based on a concept developed by Bonse and Hart, employing two grooved perfect germanium crystals arranged in the parallel position. Multiple diffraction from these crystals produces a monochromated X-ray beam which can be several millimeters wide while still exhibiting extremely high angular resolution. As a result, effective sample volumes can be employed with maximum volume-to-thickness ratios. The principal features of the instrument are discussed with emphasis on the advantages of this device over those employing complex slit systems and film-re cording techniques, Data are presented to illustrate the operation, intensity, and resolution of the unit.

A novel method has been investigated for the study of extended X-ray absorption-edge fine structures. The method takes advantage of the absorption of continuum X-rays that emerge at low takeoff angles from an electron-bombarded target. The extended fine structure is observed as undulations in the continuum X-ray intensity in the region of the self-absorption edge. Spectra from conventional X-ray diffraction tubes have been recorded for various values of kilovolts and takeoff angles. Spectra obtained by this method are compared with published data. Nearly all the features of the extended fine structures can be clearly resolved by this technique. In the case of iron ar.d copper targets, it is found, experimentally that the best contrast is obtained when using a 50-kV accelerating voltage. A takeoff angle of 3° yielded best results for copper, while an angle of 10° was best suited for iron. The Philibert absorption correction successfully used in electron microprobe analysis has been extended to account for the observed self-absorption effect where κΔλ = f(x)λ1/f(x)λ2. The primary advantage of the thick-target technique is in the ability to obtain absorption spectra without having to prepare thin films. The technique is essentially nondestructive in that the sample need not be pulverized or thinned.

The principal aim of this article is to develop in a clear and orderly manner a general relationship and show how it can be used to determine with a high degree of precision lattice parameters of tetragonal and hexagonal as well as cubic crystals. The introduction and extensive use of electron-probe microanalyzers provides a ready-made means of obtaining both Kossel and divergent X-ray beam patterns which could previously be produced only with specially constructed X-ray tubes. The present ease of their production as well as the continuing need for precise lattice parameters for the study of many problems associated with crystallized solids has stimulated a renewed interest in these two techniques. As has been recently shown by several experimental results limited to cubic crystals, these techniques are capable of giving lattice parameters with the same degree of precision as those obtained by the more classical means. The development of the general relationship is preceded by a brief historical review, a discussion of the relative merits of the methods, a short description of the nature of the diffraction patterns, and the geometrical conditions necessary for realizing precision parameter measurements. In conclusion, the advantages and disadvantages of the Kossel and divergentbeam methods compared with those of the classical powder techniques are enumerated and discussed.

X-ray diffraction angles are measured precisely, conveniently, and automatically by a specially designed instrument, the automatic precision X-ray goniometer connected on line to an Elliott 903B data processor. A monitor program controls two such instruments and two diffractometers simultaneously and allows a comprehensive set of experiments to be performed. The sensitivity is such that, when translated into terms of changes in the crystal-lattice parameter, a precision of 1 part in 10,000,000 is being attained, and indications are that absolute measurements are almost as good. The procedures, instrument, and automatic control are described, and the results of performance tests and some applications are given.

A computer search system utilising the Powder Diffraction File compiled by the Joint Committee on Powder Diffraction Standards, originally developed for an IBM 7074 in FORTRAN II and reported at the Pittsburgh (1966) conference, has beer. revised and extended to run on IBM 360/50. The system is now written in FORTRAN IV. This search system, which uses all the lines of the reference patterns, has successfully identified up to six standard reference patterns from a multiphase unknown X-ray diffraction pattern in less than 2 min running time. No chemical information is necessary for the system to run. In the revised program, the chemical composition of the patterns is now available from the magnetic tapes in immediate conjunction with the printout of the “most likely” components of the mixture. However, this chemical information is not used by the program itself in the search procedure since, if the unknown pattern is absent from the file, it is helpful to know those compounds which are isostructural with the unknown pattern. With the immediate use of chemical information, these patterns would be eliminated. An estimation of the relative concentration of each of the components, based on absolute intensities, is also calculated by the program. This identification system has been run on experimental data both of the Guinier type and of a less reliable type, with the present Powder Diffraction File on the search tape. Although the number of false matches was increased with the poorer quality of input data, the programs yielded excellent results for both single- and multiple-phase patterns even with poor data and the absence of any chemical information. A series of results from the Materials Research Laboratory of The Pennsylvania State University, illustrating the system in operation with increasingly difficult mixtures, will be given. With such a system in operation at such a small cost, the diffractionist can concentrate on the results and meaning of the identification rather than on the method of identification itself.

The use of X-ray topographic techniques for studying elastic strains in crystals deformed at their surfaces is becoming widespread, especially in the field of silicon semiconductor devices. Although the broad features of the phenomenological processes involved in producing the strain patterns on the X-ray micrographs are understood, little attention has been devoted to evaluating the detailed nature or range of the strain fields in the crystal. In this paper, an clastic model is proposed for cases in which a region of crystal surface is uniformly deformed over a thin layer. With this model, the associated strain field in the surrounding crystal, which is readily computed from elasticity theory, may be characterized by a single parameter. The model is in accord with observed strain patterns on topographs of abraded diamond surfaces and silicon surfaces onto which a strip of metal film has been evaporated. From the spatial range of the diffraction contrast, an estimate of the parameter characterizing the strain field may be made.

A double.crystal arrangement was employed in the symmetrical Laue arrangement [(+n, −n) setting]. A perfect BeO crystal was used for the first crystal of the double-crystal spectrometer. To obtain a high X-ray intensity, the thickness of the crystal was made to correspond to a maximum of Pendellosung interference. A slit was pieced between the first and second (specimen) crystals to select the X-rays which precisely satisfy the Bragg condition. The slit was adjusted to avoid significant Fraunhofer diffraction. In this method, the incident beam for the specimen crystal was parallel enough to obtain intrinsic rocking curves of the specimen crystal. As an application, the method was used for determination of the senses of slight strains in BeO crystals.

X-ray techniques employing film recording continue to play an important role in the routine determination of residual stresses in metals, particularly where heavy and bulky specimens are involved. The single-exposure technique in which the two diffraction patterns required are obtained simultaneously in a single X-ray exposure has several practical advantages over the more conventional two-exposure technique for many routine applications. Details of the method are discussed and an analysis is made of the factors influencing the reliability of the stress determination. An apparatus for stress measurement having some unique features is described and a practical application presented, illustrating the use of the single-exposure technique for the determination of the stress constant of a specimen of hardened steel. The specimen was subjected to a series of known stresses in bending, both in tension and compression. The measured diffraction-line displacements were plotted against the applied stress, and a line was fitted to the points by a least-squares calculation. From its slope, the stress constant was determined. The standard deviation of individual stress determinations from the “true” values given by the least-square line was calculated and was in excellent agreement with the value calculated from the errors of measurement. It is concluded that the single-exposure technique with its reduced time required for measurement and less demanding requirement of precise instrumental adjustment provides a reliable and practical method for many routine stress measurement applications.

One of the major problems that has plagued the tool and die maker for many years and more recently has come to the attention of the manufacturer of missiles and high-performance aircraft is the problem of shape distortion which occurs during heat treatment in the high-strength tool and die steels. Not only is shape distortion a problem in the heat treatment and use of these materials, but the origin of shape distortion has been a controversial issue among metallurgists for many years. The quantitative measurement of shape distortion on heat-treated steels is simply carried out hy machining standard shape samples, in this case, an L-shaped sample, and making a measurement of the variation after heat treatment from the 90° of the original 90° angle of the L. It is usually assumed that relief of residual stresses in heat-treated parts will occur by the shape changes which have been described above; however, it has been demonstrated that elastic residual stresses may still be present in heat-treated parts that have been tempered and theoretically should be stress free. By a very straightforward and simple application of the backreflection X-ray diffraction method for residual-stress determination, a very striking relationship has been demonstrated between the shape (angular) distortion of both A2 tool steel (air hardening) and O1 tool steel (oil hardening) and the residualstress pattern of these steels. Conversely, one could presumably utilize residualstress data at changes in cross section to estimate semiquantitatively the amount of shape distortion which occurs in rather complex parts.

Irradiation effects that have been observed in the structures of a number of ceramic materials are reviewed. Results of X-ray diffraction studies indicate that, to a great extent, the magnitudes of the crystallographic changes depend upon the type of crystal structure. However, the nature of the atomic bonding and the type of radiation can be the predominant factor in radiation stability in some materials. Damage mechanisms that have been investigated include: (1) fast-neutron and high-energy garnma-ray effects, (2) transmutation effects in high-neutron crosssection materials, and (3) lire effects of the (n, α) reaction in various bolide-containing structures. Some crystallographic changes observed include lattice parameter changes and structure damage of various magnitudes, the appearance of a transmutat. on product structure, and changes from the crystalline to the amorphous state.

Aging processes exhibiting cluster to precipitate transitions were studied in polycrystalline line austenitic iron-base alloys with a Siemens' Guinier camera. This camera combines the Seemann-Bohlin focusing geometry with a curved-crystal monochromator arid thus maximizes the resolution of observed sidebands and the weak precipitate lines. Growth studies encompassing a cluster-size range of 15 to 70 unit cells were followed. For the systems of interest, this coincided with a variation from detectable hardness increase to a stage of maximum hardness immediately preceding precipitation, Cluster sizes were calculated on the basis of the Guinier model; variation with time and temperature permitted calculations of an apparent activation energy in the one system where decomposition was spontaneous. An iron-nickeltitanium alloy was used to study aging in a ternary system. Behavior was classic in that the cluster size present on quenching grew with aging coincident with a simultaneous hardness increase. Calculation of activation energies indicated strongly that transportation of nickel to, or iron from, the cluster was rate determining. Upon overaging, the nickel-titanium enriched clusters gave way to the hexagonal Ni2Ti phase. An iron-nickel-chromium-niobium quaternary, in addition to presenting a clustering system similar to the above ternary, showed two rather interesting phenomena. First, chromium was necessary for precipitation; the ternary ironnickel-niobium did not age. Secondly, a stable Pe2Nb Laves phase present upon quenching from 2200°F disappeared on aging in favor of nickel-niobium clusters; an incubation time for the formation of these clusters existed, and its duration was about 4 hr. An asymmetry was noted in the diffraction intensities about the (311)γ line in both systems. In the iron-nickel-titanium case, the asymmetry was only in intensity, whereas, with the iron-nickel-chromium-niobium alloys, the asymmetry existed in both intensity and position. Interpretation of these observations is made on the basis of anticipated variations in scattering factors, lattice spacings, and cluster sizes.

Qualitative evaluation of preferred orientation in 10-rml Hastelloy N seamless tubing was carried out by obtaining conventional pole figures for several samples with the modified Schulz reflection technique. This established the texture as a (110)[112]. Quantitative determination of this texture was achieved for a large number of samples by a radial traverse of an azimuthally averaged (110) stereographic projection. This was accomplished with a Schulz goniometer by rotating the sample rapidly in its own plane while slowly varying the tilt angle ϕ. The first minimum observed in the resultant pattern approximates the pole density of the randomly oriented component of the sample. A scan obtained from a randomly oriented sample and suitably scaled to match pole density at these minima serves to distinguish the random from the oriented component of the sample. A ratio of the oriented to the random component as a function of the tilt angle ϕ is independent of the instrumental effects of defocusing and absorption. This ratio is proportional to the pole density of the oriented component since the pole density of the random component is a constant by definition. The same constant of proportionality yields a pole density of unity for the random component. Integrating the pole density for die random component over the surface of a reference sphere of unit radius gives the value 4π for the number of randomly oriented poles NR. The number of poles corresponding to the oriented component is obtained by evaluating the integral

In this equation, R(ϕ) is the ratio of the oriented to the random component, Φ is the tilt angle corresponding to the first minimum in the sample scan, and m is a multiplicity factor which compensates for integration over just one 110 face of each grain. Evaluation of this integral may be made by plotting it with the aid of a family of sine curves and measuring the area under the curve.

The per cent of volume of the oriented component is then calculated by the relationship

This method entails about 30min of an analyst's time and 40 to 120 min of machine time, depending on the grain size of the sample. Further information on the angular breadth of the texture may be obtained from the plot of the integrand. This technique is subject to the limitations that the material have a single texture and it must be possible tc prepare the specimens so that a suitably chosen pole figure contains a central concentration of poles which are delineated from other regions of pole concentration by a surrounding minimum in pole density. This is generally not too difficult in the case of sheet textures but requires that the specimen normal be parallel to ths fiber axis for a fiber texture.

Roe's method for deriving the crystallite orientation distribution in a series of generalized spherical harmonics is applied to the analysis of texture in rolled cubic materials. The augmented Jacobi polynomials, which are the basis of the generalized spherical harmonics, have been derived for cubic crystallographic symmetry and orthotopic physical symmetry through the sixteenth order. Truncation of the series expansions at the sixteenth order should permit treatment of textures having a maximum of 17 times random and a minimum angular width at half maximum of 34°. A numerical technique has been developed which permits approximate evaluation of the integral equations from a finite array of data points. The method is illustrated for commercial steels and is used to elucidate the primary recrystalization texture of a decarburized Fe-3%Si alloy.