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.

Improvements in sample preparation methods have resulted in increased accuracy in x-ray powder diffraction intensity measurements. This improvement has focused scrutiny on the instrument as a potential source of error. NIST Standard Reference Material, SRM, 1976 consists of a sintered α alumina, corundum, plate certified with respect to 12 relative intensity values from 25 to 145 degrees 2θ. Its function is to allow for standardization of powder diffraction intensity as a function of 2θ angle (instrument sensitivity). An increase in the accuracy of interlaboratory comparisons of diffraction intensity and related determinations will result. Utilization of the SRM requires the user to collect intensity data from the test instrument in a manner which conforms to that used in the certification. Graphical interpretation of the ratio of these data to those on the certificate will allow for appropriate judgment as to the condition of the test instrument. Discontinuities in the data indicate a malfunctioning or misaligned instrument. Systematic bias, introduced by design characteristics of the test instrument, manifests itself in terms of a pattern in the data other than a horizontal straight line with value of one. This bias may be removed with the calculation and application of a correction curve.

X–ray fractography is a new method utilizing the X–ray diffraction technique to observe the fracture surface for the analysis of the micromechanisms and mechanics of fracture.

In the present study, X–ray fractography was applied to brittle fracture of alumina ceramics. The first part deals with our new method of pre–cracking of ceramics. Pre–cracking was introduced to a singleedge notched specimen by longitudinal compression. Then the fracture toughness tests were conducted with pre–cracked specimens as well as notched ones. The effect of the notch radius on the fracture–toughness value was determined. The second part describes the result of X–ray fractography.

Pentaerythritol (PE) and neopentylglycol (NPG) are organic molecular crystals which have hydrogen-bonded lattices with layered- and chain-type structures, respectively. The PE undergoes solid-state phase transitions at 416K, from tetragonal to a cubic (γ’) structure and NPG also undergoes this transition at 317K from a monoclinic to a cubic (γ) structure. The phase transitions in binary PE-NPG solid solutions show more than one solid-solid transition in which the NPG-rich β transforms to γ at a constant temperature but the transition of the PE-rich a phase to γ’ passes through a two-phase field at a temperature that varies as a function of composition. Structural analyses by high-temperature x-ray diffractometry have revealed some new, interesting transitions. A phase diagram has been constructed for 0-30 mol% NPG in the PE-NPG system, using x-ray diffraction and differential scanning calorimetry results, and work is in progress to complete this diagram. The variation of lattice parameters as a function of temperature in the α, γ and γ’ phases for PE+20 mol% NPG are presented here, together with a discussion of phase transitions for certain compositions.

A rapid multielement analysis procedure for cement and ceramic type materials has been developed which uses pelletized powders and an exponential correction to the observed x-ray intensities. Only the more significant interactions are considered in an iterative process requiring a minimum of standards. The interaction coefficients are determined by a nonlinear multiple least squares fit of the standards. Average deviations obtained for the analysis of light elements in cement ranged from a low of 0.006% for K2O to a high of 0.13% absolute for SiO2.

The thermal expansion behavior of pure, Ge-doped and Li-doped hexagonal cordierites with respective compositions: 2MgO 2Al2O3 5Si02 2Mg0 2Al2O3 4Si02 Ge02) and 2MgO (2+x)AL203 (5-2x)Si02 xLi20 with x = .174, was investigated using time-of-flight neutron powder diffraction at temperatures from 22 to 750°C in vacuum. The data were refined in space group P6/mcc using the Rietveld method. The lattice thermal expansion curves of all 3 samples were quite similar. The negative axis expansion is associated with (1)displacement of the T2 cations generally toward the axis channels and (2) changes in the distortion of the coupled T1/M tetrahedra/octahedra in the structure. Both contributions were present in all 3 samples but the first was more dominant in the Ge doped sample. The nature and origin of the distortions in T1 and M are discussed.

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.

Performing highly automated, computerized X-ray spectrometric analysis ‘without standards’ calls for accurate matrix correction programs which can be based, essentially, on either the ‘fundamental parameter’ method or improved influence coefficient procedures. The coefficient scheme discussed in this paper was devised to strictly comply with the theoretical relationships for X-ray fluorescence emission, thus connecting, in a way, both approaches. This result is achieved by accurately making allowance for the two complicating factors affecting fluorescent intensities i.e. : (1) the mobility of coefficients, and (2) the occurrence of fluorescence crossed effects. The corresponding algorithm, for practical use, writes

where the (aij + bij ci) terms account for the individual influence coefficients and their variation, and ϵi refers to the overall crossed effect. The essential problem of calibration is then considered, with special emphasis being laid on : (a) experimental coefficient determination, and (b) experimental crossed effect evaluation. Current coefficient methods are briefly surveyed in relation to the present theory.

Finally, the advantages of an experimental, accurate coefficient procedure over the fundamental parameter approach, from a practical standpoint, are emphasized.

Mercuric iodide HgI2 room temperature solid state radiation spectrometers having 4% energy resolution at 100 KeV detected the x-ray fluorescence (XRF) of the K shell of intermediate and high Z elements. The excitation of the K shells which emit XRF more energetic than 60 KeV was achieved with 7mCi collimated 57Co and for XRF less energetic than 60 KeV the excitation was done with a 10mCi 241Am source. The K shell XRF spectra of a 1:1 mixture of U and Th, and also of the single elements of Au, Tb, Ba, Ag, Mo, and Rb are shown. The results prove the feasibility of developing mercuric iodide portable XRF spectrometers which operate at room temperature and which have a wide range of geochemical and industrial applications.

A program system design which will facilitate the exchange of automated diffractometer control programs is presented. The various procedures for collecting data and finding peaks, not involving profile fitting, were programmed, tested and evaluated. The optimum strategy evolving from this work involves a decision making algorithim which locates and removes the experimental threshold from the digital diffraction data, removes the Kα2 component, smooths and locates diffraction peaks via a second derivative procedure.

Most modern instrumental methods of analysis depend on the use of known standards of composition for calibration. Newer analytical techniques, such as the solids mass spectrometer, laser probe and, especially, the electron-probe microanalyzer have reduced the amount of a sample which can be analyzed quantitatively to a range of about 0.1 to as small as 0.00005 μg. As a corollary to these microanalytical advances, homogeneity requirements have become severe to meet analytical standards. This paper describes a continuation of the National Bureau of Standards' effort to characterize more fully existing standards as to suitability for the new microanalytical techniques. An NBS cartridge brass sample in both the wrought (NBS-1102) and chill cast forms (NBS-C1102), as well as a low-alloy steel sample (NBS-463), have been investigated by means of electron-probe micreanalysis and optical metallography. Some 17 elements are contained in the brass, while 25 elements are found in the steel. Results for 10 elements in the steel and 6 elements in the brass are presented. In the steel, iron, nickel, copper, and silicon ate essentially distributed homogeneously at micron levels, while manganese, tantalum, niobium, zirconium, sulfur, and chromium are not. In the brass, copper and zinc are distributed homogeneously at micron levels while lead, sulfur, aluminum, and silicon are not. Electron-probe micreanalyzer results indicate that both NBS-1102 and NBS-C1102 brass are suitable for use as a calibration standard for electronprobe microanalysis as well as other microsnalyticat techniques, such as the solids mass spectrometer. The results for brass have been corroborated by a number of laboratories using the electron-probe analyzer.

A self-consistent scheme is proposed for the evaluation of stressfields which vary strongly within the penetration depth of the X-rays in polycrystalline specimens which are elastically isotropic and homogeneous on a macroscopic scale. Very precise diffraction experiments have to be performed for practical applications.

Residual and applied stresses (σij) are often measured via X-ray diffraction, by calculating the resultant elastic strains (ϵij) from the measured change in interplanar spacing (“d”). This method is non-destructive, reasonably reproducible (typically ±14 MPa), can be carried out in the field, and is readily automated to give values to an operator-specified precision , Let Li represent the axes of the measuring system with L3 normal to the diffracting planes, and Pi represent the sample axes. These axes are illustrated in Figure 1. In what follows, primed stresses and strains are in the laboratory system, while unprimed values are in the sample system.

An ultrasoft X-ray spectrograph employing a demountable, water-cooled, cleanable X-ray target will be described. The effects of the spectra emanating from various target materials, operated under several conditions, on the efficiency of excitation of C K radiation will be discussed.

Rietveld profile refinements using high-resolution pulsed neutron povder diffraction data, collected at IPNS, often reveal broad intensity contributions from sources other than the crystalline materials being studied. Such non-crystalline intensity hampers standard Rietveld refinement, and its removal and/or identification is imperative for successful refinement of the crystalline structure. A Fourier-filtering technique allows removal of the non-crystalline scattering contributions to the overall scattering pattern and yields information about the noncrystalline material. In particular, Fourier transformation of residual intensities not accounted for by the Rietveld procedure results in a real-space correlation function similar to a radial distribution function (RDF). From the inverse Fourier transform of the correlation function a Fourier-filtered fit to the diffuse scattering is obtained. This mathematical technique was applied to data for crystalline quartz, amorphous silica, and to a simulated diffraction pattern for a mixture of the two phases.

REX is a Fortran program for analysis of spectra obtained in PIXE analysis. The underlying model is still under development; however, one year of experience has demonstrated REX's capability to be a fast reliable tool. The modeling of the different components and effects of the physical model is briefly discussed. Evidence is shown that secondary effects mostly due to Compton-scattering in and around the detector are important factors. In order to assure that heavy elements are recorded with sufficient sensitivity during short bombardment times, low energy X-rays are suppressed but not completely absorbed by use of a Mylar absorber with a hole. Such an absorber sometimes introduces severe problems for other techniques of spectrum analysis. However, to REX there is only the job to find the transmission curve of the absorber.

The wall effect present in the gas-filled proportional counters and the low-energy background caused by it are well-known disadvantages. In this paper a method is presented to define the radial position of a single X-ray absorption in ordinary proportional counters. The method utilizes the variation in detector pulse collection times due to the electron diffusion. This variation can be determined with a specially constructed risetime analyzer which effectively forms a dead zone of cylindrical shape inside the detector. The properties and performance of the method are demonstrated. In the experiment performed the signal to background ratio was improved by a factor of twenty.

Since the method of X-ray multiaxial stress analysis (ψ-splitting problem) was proposed by Dolle and Hauk, their method is often utilized for residual stress evaluation on a processed surface. However, as pointed out by thanselves, a theoretical problem still remains on the assumption of the stress state. Namely, the effect of ψ-splitting is impossible unless stress gradients with respect to the direction of the depth in σ13 or σ23 are present, because these components and σ33 have to vanish at the outer surface. Actually, we often find the 2θ vs. sin2ψ relations which do not agree with their theory. In this paper, we proposed a new method for X-ray multiaxial stress analysis in which the effect of stress gradient was considered. The basic equation of this method was solved by means of the integral method proposed by Lode and Peiter. The validity of the present method was proved through a numerical simulation and an experiment.

Modern (>1950) data analysis techniques are commonly applied in many scientific fields but their careful application in other fields, including X-Ray diffraction, has been notably lacking or generally confined to the environment of university research. Perhaps this lack of widespread application in XRD can be blamed on the absence of sophisticated computer controlled instrumentation, and, if this is so, the situation should change rapidly, since today's automated diffractometers are driven by very powerful minicomputers with large firm disks and sophisticated operating systems. In such an environment it is entirely practical to implement, on-line, state-of- the-art data analysis techniques, and in this paper we present one such example.

A Monte Carlo model that predicts the entire photon, spectrum for energy-dispersive X-ray fluorescence (EDXRF) analyzers excited by radio-isotope sources from multielement homogeneous samples is developed and demonstrated. The components of the photon spectrum include: (1) the and Kα and Kβ characteristic primary, secondary and tertiary X rays from both the unscattered and scattered source photons, (2) the characteristic X rays excited by other characteristic X rays that have been scattered, and (3) the scattered source photons from single, double, and multiple scatters in the sample.

The computer code NCSMCXF based on this model has been developed. It is capable of handling up to 20 elements per sample and provides a detailed account of the intensities of the X rays and backscattered source photons per unit source decay as well as a summary of the relative intensities from all elements present in the sample. Cubic splines are used within the code for photoelectric and total scattering cross sections and two-variable cubic splines for angular coherent and incoherent scattering distributions for efficiency in both computation time and storage. The code also provides the pulse-height spectrum of the sample by using the appropriate Si(Li) detector response function. The Monte Carlo predictions for benchmark experimental results on two alloy samples of known composition indicate that the model is very accurate. This approach is capable of replacing most of the experimental work presently required in EDXRF quantitative analysis.

A previous Monte Carlo model that uses the simple assumption of spherical homogeneous particles to approximate sample heterogeneities has been modified to improve the computer execution time requirements for the heterogeneous sample case. A new technique for photon tracking in this medium is used and reduces the computation time requirement by half.