A scanning range over Bragg angles from −163 to +163° 2θ is obtained by combining a diffractometer capable of scanning both sides of the primary X-ray beam with a very short (3-in.) high-power focused X-ray tube. The ability to scan the included angle 4θ between respective diffraction profiles on either side of the primary beam over the entire range of Bragg angles, provides a direct method of eliminating errors caused by a displacement of the specimen surface from the axis of the goniometer. The method is demonstrated by determining the lattice parameters of standard specimens used in the I.U.Cr. Precision Lattice Parameter Project.

A technique is described for determining lattice constants of polycrystalline monoclinic materials and partition of observed experimental error among the several constants. The technique is illustrated for uranium tetrafluoride. Precision of the method is typically ±0.01 to ±0.02 Å on the unit cell lengths, and ±4 to ±8 min on the angle between axes. This is of the order expected, were single-crystal techniques limited to the range of Bragg angles available.

The principles of measuring surface stresses in metals by X-ray diffraction with commercially available equipment are well known. Two techniques of making stress measurement by X-ray diffraction now in general use are (1) X-ray diffractometer with electronic control panel and (2) back-reflection film camera.

The X-ray diffractometer technique has a number of important advantages over the film method, the major ones being accuracy and speed, but serious size and shape limitations are imposed on the specimen by the equipment: Because of its bulk and weight, specimens must be brought to it. The Airplane Division of The Boeing Company has capitalized on the advantages offered by the mobile backreflection film technique, especially with regard to specimen sizes and shapes. Results and techniques used, at Boeing for stress measurements in alloys of aluminum, titanium, and steel are presented. Experimental difficulties are discussed, and comparisons are made between results from the dirfractometer and backreflection camera, A portable darkroom and electropolishing unit are also presented which, with the X-ray unit, comprise a completely mobile stress-measuring facility.

Quite recently there has been commercially developed a series of high-alloy steels, on new compositional bases, which possess 3 very desirable combination of unusually high strength, good ductility, and toughness even at comparatively low temperatures. At the same time, research with mechanical working procedures, combined with optimum heat-treat considerations, have produced with several older, more conventional steels, strength levels of high orders of magnitude. Each of the considered materials is capable of yield strengths approaching or exceeding 300,000 psi, corresponding to elastic strains of about 1%.

This paper is concerned with the development and evaluation of workable X-ray stress analysis procedures to be employed to measure, with a good degree of accuracy, high elastic strains. The materials selected include maraging steels, ausformed steels, and cold-drawn A.I.S.I. 4340 steels.

Of the various possible X-ray techniques which were considered, very satisfactory results were obtained by the use of the two-exposure method. A special fixture was designed and constructed to allow uniaxial straining of test specimens while in the X-ray unit. Imposed strains were measured directly by strain gauges mounted on tbe specimen. Simultaneously, strains were measured by the use of chromium radiation filtered with vanadium foil. The peak resolution obtained was very satisfactory with a peak to background ratio of approximately 4:1 for the {211–121} martensite doublet used to measure the shift in peak location between the normal and oblique exposures. Because of the widths of the peaks involved, it is impossible to precisely specify the angular position of a given peak by inspection of the usual recorded trace. A counting technique, combined with a least-squares curve-fitting procedure involving five points, was very satisfactory for precisely locating positions of maximum intensity, Superior results were obtained when a multiplicative correction factor proposed by Koistinen and Marburger was applied.

In order to study the effects of processing variables on the defect contents of silicon wafers, an X-ray extinction contrast camera was designed and constructed to fit on the standard GE XRD-5 table. The camera, in its normal operating position, can be routinely used without interfering with the emission or diffraction instrumentation of the unit, and also can be mounted on the diffractometer stage for diffraction line breadth analysis. Routine laboratory procedures including sample preparation and mounting, film types, and film exposure and development are outlined.

The correlation between extinction contrast topographs and optical photographs of sawed wafers is presented. Wafers were examined in the sawed, lapped, and chemically polished conditions. Subsequent to each processing step in the surface treatment of wafers, a series of topographs was made using four different crystal orientations. In this manner the three-dimensional picture of the defects is obtained, as are the Burger's vectors of all dislocations. It appears that internal defects such as dislocations are more uniformly distributed in lapped and chemically polished wafers than in sawed and chemically polished wafers. Furthermore, different doping impurities and levels cause different amounts of contrast in the dislocation images.

Small-angle X-ray scattering measurements were made on samples of CaO—MgO—SiO2 as CaO-MgO-SiO2 glass in which met astable amorphous phase separation had been induced by heat treatment. Glass rods drawn from a melt of composition 30.5% CaO, 8.0% MgO, 61.5% SiO2 (by weight) at 1400°C were heat treated for 1, 2, 10, and 15hr at 825°C. X-ray scattering intensities of heat-treated and non-heat-treated samples were measured using an apparatus based on Kratky collimation geometry and equipped with a pulse height analyzer. Particle sizes were calculated from the radii of gyration which were determined from plots of log intensity vs, θ2, according to the method of Guinier. The data show a growth with time of the dispersed spheres from 350 to 1880 Å in diameter and correspond to the growth rate for diffusion-controlled growth of a sphere. Electron micrographs of identical samples prepared concurrently are presented. Inhomogeneity sizes obtained by the two methods are in very good agreement. Results obtained using the Kratky system in conjunction with a pulse height analyzer are compared with those obtained when a slit collimation system and balanced filter monochronmtization were used to study the same sample.

Thermal analyses of samples of thorium dicarbide in equilibrium with graphite show arrests which indicate phase transitions at 1427 ± 21°C arid 1481 ± 28°C. These thermal effects have been observed on heating and cooling both in standard thermal analysis and in differential thermal analysis using graphite as a reference material. The microstructure of thorium dicarbide samples shows the characteristic “herringbone” pattern of a material which has undergone a martensitic-type transition.

A high-temperature X-ray investigation has revealed that the observed thermal arrests correspond to erystallographic transformations. The monodinic modification found at room temperature is stable to 1427°C, at which temperature a tetragonal modification with a0 = 4.235 ± 0.002Å and c0 = 5.408 ± 0.002Å is formed. At 1481°C, the tetragonal is transformed to cubic with a0 = 5.809 ± 0.002 Å. The best agreement between observed and calculated intensities has been obtained with C-C units of 1.5-Å assumed bond length in space groups P42/mmc and Pa3 for the tetragonal and cubic modifications, respectively.

A single-crystal high-temperature X-ray camera has been built with permissible operating temperatures of 2500°C. The camera is constructed to rest upon a Siemens horizontal diffractometer and may be used with either an external electronic detector or with film. The sample is supported on an externally adjustable goniometer head and is heated from the back by an ion beam. Controlled oscillation allows rotation photographs to be obtained from the sample surface not touched by the ion stream. Temperature is controlled by a thermocouple supporting the sample, the thermocouple being an intrinsic part of the goniometer. As a design limit, zero and first order layer lines with iron Kα. radiation on specimens with lattice parameters of 2.6 Å or larger may be recorded. Copper, cobalt, and molybdenum radiation allow even greater latitude. Types of samples that may be studied include powder (pellet), single crystal, wire, or rod. The camera serves equally well for single-crystal, texture, or powder studies on refractory materials.

A new group of ternary carbide phases which are formed by combination of an element of the scandium group (which is taken to include the rare-earth elements) with aluminum and carbon has been found. These phases are related to the series of T3BCx compounds discovered by Stadelmaier (T for a transition element and B for a B subgroup element). Atomic size effects are discussed which show that T3BCx phases behave in a manner similar to many ordered binary phases of AB3 stoichiometry. There is a readjustment in size of the various metallic components which results in effective radii compatible with cubic close packing. An anomaly which appears when the observed lattice parameters of T3BCx are related to the Goldschmidt radii of the component atoms is discussed in this light. Measurements of the intensities of X-ray diffraction peaks are used to show that the carbon atom in these phases occupies the octahedral hole in the center of a Cu3Au-type unit cell. This position is maintained in alloys which contain varying amounts of carbon.

The identification of non-metallic phases occurring in a metallic matrix cannot always be accomplished by standard methods of X-ray diffraction analysis. Separation of the nonmetallic phases from the matrix by chemical extraction, with subsequent X-ray diffraction analysis allows identification of the nonmetallic phases without the problems associated with X-ray analysis of bulk samples.

In one study of alloy carbide dispersions in columbium, X-ray diffraction of the bulk samples could adequately identify the carbides present, but it was only by studying the chemically extracted residues that an important oxygen gettering effect of one of the alloy additions was discovered. In another study, X-ray diffraction work on extraction residues of Cb-Zr alloys showed evidence of a double oxygen gettering effect producing two distinct oxides. In the built sample, some of the diffraction lines produced by one of these oxides were masked by the tines of the columbiurn matrix. Therefore, only by use of an extraction technique were these two oxides identifiable by X-ray diffraction. In a Cb–10Ti–10Mo alloy, X-ray diffraction was used to study the nature of the sub scale formed during oxidation of the alloy. At least two nonmetallic phases were found. By using chemical extraction techniques, the phase responsible for the formation of the subscale was identified as TiO.

These studies demonstrate some of the advantages of the chemical extraction techniques for obtaining samples of nonmetallic phases for study by X-ray diffraction.

Escape peaks occur when the incident X-ray quantum, energy exceeds the absorption edge energy of the detector element and the resulting X-ray fluorescence is lost from the detector. The most common escape peaks result from 1 K-fluorescence in NaI-scintillation counters and Xe K-, Xe L-, and Kr K-fluorescence in proportional counters. The average pulse amplitude of the escape peak is proportional to the difference of the Energies of the incident and fluorescent X-rays. If the intensity of the escape peak is high as in the case of Mo Kα and a kryptoopreportional counter, and the lower level of the pulse height analyzer is raised to reject the escape peak, the quantum counting efficiency may be reduced by a factor of two. When the pulse height analyzer is set for characteristic incident radiation, escape peaks appear in powder patterns at small diffraction angles. These broad low-intensity peaks are often mistakenly identified as resulting from misalignment, scattering, etc. Each powder reflection can produce its own escape peak which occurs at an angle slightly smaller than the absorption edge of the detector element. In a silicon powder pattern the three strongest reflections produce three resolved escape peaks whose peak intensities are about 4% of their corresponding Cu Kα peaks when the X-ray tube is operated at 50 kV. The escape peak intensities decrease with decreasing X-ray tube voltage and disappear when the voltage is lower than the absorption edge energy of the detector element. Absorption edge peaks observed without the upper level of the pulse height analyzer are similar in appearance, intensity, and diffraction angle to the escape peaks. In complex powder patterns the escape peak pattern is unresolved and may produce a number of very broad peaks.

An IBM 7090 computer program has been written to determine precise lattice parameters for cubic, tetragonal, orthorhombic, and hexagonal systems. Leastsquares analysis is made with data fitted to the equation

where E is the eccentricity and A. is the absorption-divergence error. The computer program will make the least-squares analysis with neither, either, or both of the error(s) included. Data can then be reprocessed for other combinations of errors. After having determined the lattice parameter(s), on request, the computer program will predict the interplanar spacings, including the errors, so that observed data in the high-angle region may be indexed by comparison. Use of the program indicates that the most consistently reproducible parameters are obtained using only A, the absorption—divergence error.

The phase and elemental distributions on zirconium alloys containing 5, 10, 25, 35, and 50 at.%. yttrium, oxidized in dry air at 1200 and 1600°C, have been studied by X-ray diffraction, fluorescence, and electron-microprobe techniques. Zirconium-yttrium alloys, which are entirely solid at 1200°C, and zirconium 5 and 25 at.% yttrium alloys, which aire two-phase solid plus liquid at 1600°C, form a multiphase scale of ZrO2, Y2O3, and ZrN. The phase distribution varies with yttrium content, while the average metal composition remains constant throughout the oxide scale and base metal. In contrast, zirconium 35 and 50 at.% yttrium alloys, which are entirely liquid at 1600°C, form a single-phase Y2O3 layer.

The mechanism of air oxidation of solid zirconium-yttrium alloys, up to 50 at. % yttrium, is one of anion diffusion to the oxide-metal interface with little or no diffusion of the metallic elements. The oxidation of liquid alloys differs in that, as a result of yttrium diffusion to the oxide-liquid interface, Y2O3 is the only oxide formed. Ternary Zr-Y-O isotherms are presented to illustrate the phase distribution and mode of formation.

The practicability of using a symmetrical transmission method for accurate measurement of line positions and intensities for polymer samples was investigated. In comparison with the conventional symmetrical reflection method, the transmission method has some inherent advantages in the measurement of line positions. Very little extraneous line asymmetry is introduced by transmission, and errors due to sample misalignment can usually be corrected empirically. On the other hand, the reflection method introduces noticeable line asymmetry and a shift of the center of intensity toward smaller 2θ. Also, errors due to sample misalignment may be difficult to correct. Intensity measurements can usually be made with about the same accuracy by either method. However, the transmission method is less sensitive to misalignment errors, especially at the lower diffraction angles.

A study of two homologous series of liquid oiganosilicates showed a position change of the diffraction maximum of the halo. The first series consisted of polymeric silicic acid esters of the general formula SinOn-1(OC2H5)2n+2 with the following arrangement, where n = 1,2,3,…

For these compounds, an increase of the d-spacings was observed with increasing length of the –Si–O–Si– chain. The d-spacings observed require coiled molecules.

The second series consisted of orthoesters of silicic acid with the general formula Si(OR)4, where R is the aliphatic hydrocarbon chain. Here, an increase of the d-spacings was observed with increasing number of carbon atoms in the hydrocarbon chain. The molecules have close to spherical symmetry. The hydrocarbon chains provide a very efficient shielding of the [SiO4] tetrahedra, so that only very little intermolecular interference occurs. A similar relation exists also for the refractive indices of these compounds which increase with increasing length of the –Si–O–Si– chain in Series 1 and with increasing number of carbon atoms in Series 2. A plot of silicon concentration vs. d-values or refractive index shows both minimum values for ethyl orthosilicate.

D. B. Nash could show that for silicate glasses, the d-values increased with increasing SiO2 content. For liquid organosilicon compounds, not the silicon content but the size of the molecule (total number of atoms except hydrogen) is responsible for both the change of the d-values and the refractive indices. The size of the “ordered regions” in these liquids is related to the size of the molecules only. The interaction of molecules is minimized by the shielding effect of the organic groups,

By soaking formalinized rat-tail tendons in 2 M resorcinol, the tendon lattice is expanded equatorially from an interplanar spacing of 11.7 Å to 14.5 Å, indicating a diameter of 7.2 Å for the spiral core of collagen. Resorcinol distorts the lattice of nylon (6:6), converting the normal triclinic cell to an orthorhombic cell whose a and b axes are approximately four times those of the original nylon and whose c axis is reduced from 17.2 to 16.5 Å.

In the study of X-ray absorption fine structure, one is faced with the task of measuring sample absorbance over an extended wavelength region. For the sake of accuracy, these measurements are often carried out on a fixed-count basis. Manual collection of the data at a hundred or more spectrometer settings is a tedious and time-consuming chore. This paper describes an automated system for accumulating absorption data.

The equipment is used in conjunction with a Philips wide-range goniometer employed as a single-crystal spectrometer. It consists of: (1) a four-position sample changer, (2) a fixed-count selector for each sample position, (3) a five-digit counter and paper tape printer which register and record sample identification and counting times based on a 60-cps clock frequency, and (4) a programmer. The spectrometer advance is accomplished using the Philips step-scan arrangement. An IBM 7094 FORTRAN program for data reduction and computation will be described. The possibility of using X-ray absorption fine-structure measurements as a quantitative method for determining the various absorbing species will be discussed.