In the conventional pole figure, an accurate representation can be attained by correcting the observed X-ray diffraction intensity for any change in diffraction geometry and by comparing this with the correctly established standard intensity. For the intensity corrections, ASTM has prescribed the method of Decker et al. In practice, however, the validity of the correction formula is uncertain, since the prerequisite is difficult to attain for parallelism of an incident beam of sufficient intensity. For the standard intensity, it is desirable to take the intensity obtained with the randomly oriented material of the same composition. However, in most cases an arbitrary unit has been taken because of the difficulty in getting a truly random and uniform sample. Under these circumstances, it is first necessary for an accurate representation of pole figures to make a random sample of uniform thickness for the standard. The authors have obtained satisfactory standard samples by sintering the randomly oriented iron powder made from iron chloride and made use of them to check the method of intensity correction. Satisfactory results are obtained in the randomness tests, such as the comparison of the relative intensity diffracted from the crystal planes parallel to the sample surface and the fluctuation of diffraction intensity during α rotation.

In the reflection case by the Schulz method, the (110) reflection intensity of a random sample, by Co Kα radiation, is independent of the tilting angle up to 50°. The other reflections do not give a constant intensity for the wide range of the tilting angles because of dispersion of the diffracted beam due to the wider separation of Kα doublet in the higher reflection angle and the wider irradiated area at the lower angles. In the transmission case Schulz's correction formula is in good agreement with the observed values for the various diffraction lines and the samples of various µt, while the Decker-Harker formula does not give the absorption change with α-rotation even by an incident beam of ⅙° divergence. In both cases, an accurate determination of pole densities is made by comparing the diffraction intensity of the standard sample substituted in place of the test specimen and by correcting the absorption change due to the difference of µt between the standard and test sample, which affords good coincidence in the overlapped region. The pole figure obtained by the above method furnishes an accurate prediction of plastic and elastic anisotropy in sheet metals.

Accurate measurement of the lattice misfit between the γ and γ phases in Ni-base single crystal superalloys at high temperatures has successfully been achieved using a parallel beam mode X-ray diffractometer with a high temperature specimen stage. The superalloys have γ' precipitates, an ordered FCC structure based on Ni3Al, in a γ-matrix having a disordered FCC structure (LI2). The parallel beam mode, the optics of which is made from a Ge (111) channel cut crystal, generates a superior monochromatic and parallel CuKα1 beam, which makes it possible to resolve a cluster peak in Ni-base superalloys into individual γ and γ ‘ peaks. This peak separation was almost impossible using the CuKα1+2 doublet beam from the standard type para-focusing mode, due to the very small difference in lattice parameters between the two phases.

Double crystal diffractometer measurements on silicon bombarded to a fluence >1016 ions/cm2 with 1 MeV deuterium and 2 MeV nitrogen are reported. Such measurements provide insight into radiation damage in silicon through the observation of Bragg case pendelloesung fringes and double peak rocking curves. Bragg case pendelloesung fringes are used to determine nondestructively the projected range of ions in silicon. Double peak rocking curves are used to measure changes in lattice parameter with the ion dose. Finally, a model of radiation damage in silicon is presented.

The reduction of the background in x-ray fluorescent spectra is achieved by total reflection of the primary x-rays at a plane, smooth surface of a suitable reflector material. This effect essentially reduces the background caused by scattering of the primary photons from the substrate, thus improving the lower limits of detection in x-ray fluorescence analysis (XRF). Introducing additional to the reflector-substrate another reflector in the primary beam, this affects the spectral distribution of the exciting radiation (“high energy cutoff”). The result is an improved background, where detection limits of picogram amounts or concentrations in the ppb range are attainable for medium Z elements with energy dispersive detectors.

A method has been derived and is currently being used to plot normalized pole figures by computer techniques. As the pole distribution traces, i.e., intensity of the diffracted X-ray beam, versus angular position of the specimen are not an acceptable input for the computer, the data required from such traces are entered onto IBM punch cards. Corrections for defocusing effects may be readily made as the data are transferred from the Brown recorder traces to IBM punch cards. It is possible to program other correction factors into the computer operations providing that these correction factors or curves can be established accurately. The computer translates angular position of the specimen into reactiiinear coordinates which are an identical representation of stereographic coordinates. This computer method has been used in conjunction with the Schulz reflection technique, but modification of the computer program permits its use with other quantitative X-ray techniques for determining preferred orientation.

The feasibility of using computer techniques to plot inverse pole figures has been considered.

Six computer synthesized data sets, each representing a mixture, and one physical mixture were prepared and widely distributed in order to study the various search/match methods and factors which affect their success. A total of 67 returns were received representing eight countries and three search methods. The participants were primarily from industrial laboratories. The average score exceeded 90%. The Hanawalt search method yielded the best overall score. Use of the Frequently Encountered Phases subfile decreased the search time by about 40% and marginally increased the success rate. For the physical mixture the Δd/d and ΔI/I values were measured to about 2/1000 and 40% respectively. Use of an internal standard improved the d-values by a factor of 2 and resulted in better search/match performance.

The development of deformation textures of both initially disordered and ordered Cu3Au has been studied and discussed in terms of the stacking fault energies and twinning probabilities. No differences in the deforir.ation textures of the ordered and disordered materials were detected at deformations up to 40% reduction. However, at reductions of approximately 42% a marked difference was observed. This difference is attributed both to the degree of order and to the stacking fault energy of the ordered sample being conducive to deformation twinning at this stage of the rolling schedule. For samples which were reordered below the racrystallization temperature at intermediate stages of deformation (every 10% in total reduction) no differences between the ordered and initially disordered samples were observed up to 90% total reduction in thickness.

The quality and interpretation of diffraction topographic images are strongly dependent on. the detailed laboratory techniques that are used in making them. In this paper practical instructions are given for the preparation of Berg-Barrett and Lang topographs. It is hoped that these suggestions will enable the novice in the field of X-ray topography to produce high quality images and to interpret them with a minimum of learning time. The topics treated include adjustment of the critical conditions for attaining highest resolution, choice of radiation and the specific hkl planes to be used, conditions limiting the size of the image, cause and avoidance of image distortion, choice of photographic emulsions, plate processing for best contrast and resolution, photomicrographs of the original image, and plate preservation.

A procedure is described for making self absorption corrections for x-ray fluorescence analysis of ambient air aerosols which are collected in two size ranges with a dichotomous sampler. Calculations for fine particles are based on the assumption of a uniform layer of accumulated deposit which has an exponentially decreasing depth profile within a membrane filter. Coarse particles are treated as spheres with a log normal mass distribution which is subject to modification by the sampling device. An average attenuation and the associated uncertainty is deduced for coarse particles by considering a wide variety of possible chemical compositions.

X-ray diffraction patterns using continuous radiation from copper and tungsten target x-ray tubes and detected with a Si(Li) energy analysis system are presented. Errors caused by a misaligned diffractometer and x-ray penetration into the sample are shown to be more difficult to correct and larger in magnitude than errors arising from energy calibration. All these errors can be minimized by mixing a standard with the unknown sample.

The energy resolution of the detector influences the breadth of the diffraction peaks more strongly than the standard slit systems available with commercial diffractometers. Thus, to reduce the recording time and maintain the same standard deviation for the data, one should increase the sizes of the front and receiving slits including the Soller slits. X-ray energy diffraction patterns can be recorded with standard deviations less than +0.001 Å in the d spacing with only 200 sec measurement time using the standard diffractometer slit system. Copper targets are probably as useful as tungsten even though the continuous intensity is about three times.less. Copper has fewer interfering characteristic lines, and its use permits convenient conversion to normal θ scanning diffractometer operation.

A detailed study has been made of the intensities of the L, M, and N X-ray spectra for wavelengths in the region from 2-85 Å. Some of the lines of these spectra involve energy levels which are gradually being depopulated with decrease in atomic number, and this leads to a progressive simplification of the spectra as the wavelength increases. Spectra have also been obtained from several compounds involving these elements in different valence states. Differences in relative intensities have been observed for these compounds, but because of a lack of accurate information about absorption, it is impossible as yet to give such results an adequate interpretation.

A two-crystal spectrometer that makes full use of conventional diffractometet: or spectrometer motions has been constructed so that it can be easily attached to a commercial instrument. The requisite degree of parallelism of the two crystalrotation axes is maintained by keeping both parallel to a single ground surface. Special alignment aids have been constructed to facilitate the rapid alignment of the instrument, which can be operated manually in 1″ intervals or used for automatic scanning in steps of 0.01°. Some guide lines for comparing the relative performance of spectrometers in X-ray absorption spectroscopy are suggested.

Nanocrystalline powders of Fe and W were prepared by mechanical working in a highenergy Spex 8000 mixer/mill. The diffraction patterns were recorded with Co Kα radiation and the line profiles were subjected to a Fourier analysis. The size 〈D〉 of the coherently diffracting domains (x-ray particle size) and the root-mean square strains 〈ε2L〉1/2 were determined with the Warren-Averbach method. In addition, the integral breadths were evaluated and corrected for instrumental broadening assuming Cauchy line profiles. In order to separate particle size and strains, the corrected breadths β(s) = βcosθ/λ were plotted as a function of s = 2sinθ/λ, i.e., β(s) =(1/D) + 2ε s, where D = 〈D2/〈D〉 and ε is a strain averaged over the domain size D.

X-ray fluorescence analysis indicated that the W powders contained an iron and chromium contamination due to the abrasion of the stainless steel balls reaching a value of 24 at% Fe+Cr after 20h of milling. Since W is elastically isotropic, all available (hkl) reflections can be used in the Warren-Averbach and line breaddi analyses. After 20 h of milling, the W powder exhibited a particle size 〈D〉 = 35 Å and a strain 〈ε2〉1/2 = 0.52% at L = 30 Å. The integral breadths yielded the particle size D1 = 70 Å and the strain ε = 0.38%. in the case of Fe powder, also milled for 20 h, the (110) - (220) pair of reflections was used to calculate the particle size and strains. The Fourier analysis yielded the values 〈D〉 = 105 Å and 〈ε2〉1/2 = 0.59% at L = 30 Å. The corresponding integral breadth values are D1 = 280 Å and ε1 = 0.7%. The sum of the particle size Fourier coefficients is equal to the integral breadth particle size D1 = 125 Å, which is very close to value 〈D〉 = 105 Å indicating that the particle or domain sizes have a very narrow size distribution.

Instrumentation for soft X-ray research is briefly described. Preliminary results are shown for several dispersing systems which have been found useful in the 10 to 60 Å region. Results from single crystals of Group 1A salts of phthalic acid are discussed and intensity measurements are reported. Other organic single crystals, such as long-chain derivatives of adipic acid are evaluated, along with films of organic compounds prepared by the Blodgètt-Langmuir technique. The efficiencies of the dispersing elements mentioned above are compared with commercial crystals such as mica, gypsum, ADP, and EDDT. Performance of detectors for soft X-rays is shown for fiow-proportional and Geiger counters, a solid state silicon barrier detector, and a windowless resistance strip magnetic electron multiplier. The relative efficiencies of several photocathode materials for the latter are discussed. The design for a scintillation counter sensitive over a wide energy range is discussed and preliminary results using the counter in the region 1-15 Å are shown.

In the “double-Voigt” approach, an exact Voigt function describes both size- and strainbroadened profiles. The lattice strain is defined in terms of physically credible mean-square strain averageid over a distance in the diffracting domains. Analysis of Fourier coefficients in a harmonic approximation for strain coefficients leads to the Warren-Averbach method for the separation of size and strain contributions to diffraction line broadening. The model is introduced in the Rietveld refinement program in the foliowing way: Line widths are modeled with only four parameters in the isotropic case. Varied parameters are both surface- and volumeweighted domain sizes and root-mean-square strains averaged over two distances. Refined parameters determine the physically broadened Voigt line profile. Instrumental Voigt line profile parameters are added to obtain the observed (Voigt) line profile. To speed computation, the corresponding pseudo-Voigt function is calculated and used as a fitting function in refinement. This approach allows for both fast computer code and accurate modeling in terms of physically identifiable parameters.

Uniaxial Plastic Deformation (UPD) has been known to produce anomalies in residual stress measurements based on x-ray diffraction techniques. This study was undertaken to determine the magnitude of the effects, if any, on residual stress calculations from various materials subjected to UPD. An x-ray diffraction study using the two-exposure method ( ψ = 0° and ψ = U5°) was made on several iron, aluminum, and titanium alloys (AISI 4340, 4330M, 4130; 2024-13, 7075-T611; Ti-6Al-4V) before and after these alloys were deformed plastically by bending on a U-bend test fixture. The x-ray peak shifts, Δ2θ0-ψ, were recorded and the x-ray stress factors, Ki, calculated by three different methods. The results indicate that UPD of the calibration specimens will increase or decrease Ki depending on the alloy. These results are discussed together with observations on the additivity of residual and applied stresses, and the per cent differences in the stress measurements based on stress factors calculated by three different methods.

High-temperature X-ray powder photography has proved of great value in many directions in the metallurgical field. Some of the successes achieved and problems encountered by the author and other investigators using an established-type camera (British Unicam) for temperatures up to 1400°C will be discussed. This will be by way of specific case histories, chosen both for their own scientific interest and to illustrate the techniques employed. The applications concern phase transformations and the measurement of coefficients of thermal expansion in iron and steels, as well as in some nonferrous metals and inorganic compounds.

Elastic modulus EI of crystalline regions of various high polymers in the direction parallel to the chain axis were measured using an X-ray diffraction method. The crystal deformation can be detected directly by the diffraction peak shift as a function of applied constant stress. The stress in the crystalline regions is assumed to be equal to that applied to the specimen. The validity of this assumption has been proven experimentally for polyethylene, poly(p-phenylene terephthalamide) and so on. The EI values were discussed in relation to molecular conformation and deformation mechanism of the chains.

Guided by the dispersion, surface of dynamical theory, we easily obtain evidence of the fact that in asymmetrical surface reflections (Bragg case) of X-rays at a perfect crystal, the angular widths of the incident and reflected beams are different from the same widths in the symmetrical Bragg case. The beam with the smaller glancing angle to the surface is angularly expanded, the other one, contracted (though in cross section, the former is contracted and the latter, expanded). Consequently, if the incident glancing angle is the smaller one (striping incidence, Vreftection), the angular width of the reflected beam is smaller than in the symmetric case (S-reflection), and that of the reflected section out of the primary beam is greater, and vice versa (striping emergence, if-reflection). At striping incidence, a contraction occurs, whereas at striping emergence, expansion of the angular reflection range occurs. These facts offer a number of possibilities for applying asymmetrical reflections to the well-known technique of the two crystal diffractometer—the author proposes the term “diffractometer” instead of the widely used “spectrometer”—in the (nv, −n)-position. These possibilities extend the efficiency of the double diffractometer with multiple effects, and some of them are given below: (1) Realization of rocking curves of extremely small angular width in the (nv, −nR)-position, and consequently increased sensibility of that width to lattice distortions, (2) Use of the extremely small angular width (or more strictly, the sharp θ-λ-coordination) of the beam emerging from a first crystal. This is in V-reflection for scanning the intrinsic diffraction pattern of the second crystal used in S- or V-reflection [(nv, −ns) or (nv, −nv) -position], (3) Increased steepness of the sides of the rocking curves using (nv, −nR) or (nv, −ns)-positions which allows double diffractometric topography (Bond-Andrus, Bonse-Kappler) of increased angular resolving power. (4) Repeated ^-reflections (eventually within a single crystal provided with a suitable groove) leading to further angular contraction of the resulting reflected beam and therefore further increased angular resolving power [(nv, −nv, nR, −nR)- and (nv, −nv, +nS)-positions]. Here the tails of the rocking curve are also suppressed by multiple reflection (Bonse-Hart).

A quantitative x-ray fluorescence (XRF) analytical system has been developed with the emphasis on small sample size. The system employs a two kilowatt tungsten anode x-ray tube, and an 80 mm2 lithium drifted silicon x-ray detector arranged in a compact geometry. Operation at 55 kV and 20 m A give a sensitivity of 153 counts/min/ng at Z=42 (molybdenum). A computer controlled target changer makes it capable of analyzing 32 targets automatically. The sample target is rotated during irradiation, so that the average sample position is defined to 0.2 mm. Several sets of 5 to 9 calibration targets have exhibited a standard deviation of less than 1%.