The direct derivation (DD) method is a technique for quantitative phase analysis (QPA). It can be characterized by the use of the total sums of scattered/diffracted intensities from individual components as the observed data. The crystal structure parameters are required when we calculate the intensities of reflections or diffraction patterns. Intensity can, however, be calculated only with the chemical composition data if it is not of individual reflections but of a total sum of diffracted/scattered intensities for that material. Furthermore, it can be given in a form of the scattered intensity per unit weight. Therefore, we can calculate the weight proportion of a component material by dividing the total sum of observed scattered/diffracted intensities by the scattered intensity per unit weight. The chemical composition data of samples under investigation are known in almost all cases at the stage of QPA. Thus, a technical problem is how to separate the observed diffraction pattern of a mixture into individual component patterns. Various pattern decomposition techniques currently available can be used for separating the pattern of a mixture. In this report, the theoretical background of the DD method and various techniques for pattern decompositions are reviewed along with the examples of applications.

Existing theories of X-ray absorption-edge fine structure do not adequately explain details of spectra observed for solids. However, the possibility that X-ray absorption spectra might eventually be used as tools for the characterizatiori of new insulator materials has prompted the study of an extensive selection of simple oxides of known chemistry and structure. The complete K absorption fine structure has been measured for some forty simple oxides of six elements of the fourth period. The L absorption-edge spectra have been measured for metallic lead and several lead oxides. The several isostructurat and polymorphic sets included among these oxides, as well as the Magnéli phases for three of the elements, have made it possible to study the effects of valence, coordination number, electron configuration, and crystal structure. The applicability of current theories of the fine structures are discussed in the light of these findings. An automated single-crystal spectrometer is described.

X-ray diffraction observation of the material internal structure beneath fracture surfaces provide fracture analysists with useful information to investigate the conditions and mechanisms of fracture. X-ray fractography is a generic name given to this technique. In the present study, the residual stress on the fracture surface of the compact tension specimens for toughness tests was measured by X-ray diffraction. The effects of notch-tip radius and tempering temperature on the fracture toughness are discussed based on the results of X-ray fractography and fracture micromechanisms.

Strontium appears in the earth's crust at a concentration of about 400 ppm and in sea water about 8,1 ppm. Consequently, all living forms have evolved in the presence of this alkaline earth and have incorporated it in their tissues. The exact role of Sr in the human body remains ambiguous (1), even though Sr has been extensively studied with reference to the radiation hazard from 90Sr (2).

Metabolic behavior of Sr, in some aspects, is similar to that of Ca (3), but substantial dissimilarities between these two are also well recognized (1,4). It has been suggested that Sr stimulates the formation of bone matrix. At higher concentrations, however, it interferes with calcification mechanism of the bone matrix (5).

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.

An effective technique using grazing-incidence X-rays and asymmetric-Bragg diffraction (GIABD) for the characterization of crystalline phases on surfaces and structural depth-profiles in thin films is described. The application of the GIABD using both X-ray and synchrotron radiation sources for the analysis of an iron-oxide magnetic thin film previously reported to have an unexpected magnetically-dead layer is discussed. The X-ray diffraction analysis using the GIABD and the conventional θ-2θ scanning techniques detected an anti-ferromagnetic hexagonal α-Fe2O3 on the surface and a ferromagnetic tetragonal γ-Fe2O3 in the bulk of the film, respectively. The synchrotron diffraction analysis using incident angles below and above the critical angle of total reflection quantitatively determined the structural depth-profiles of α-Fe2O3 and γ-Fe2O3 in the film.

The plasma focus device, a form of linear pinch discharge, produces an intense x-ray and neutron (D2) burst from a magnetically heated dense plasma. Rapidly changing magnetic fields at pinch time generate large axial electric fields which accelerate electrons and ions. In the experiments reported here the x-ray production during the plasma pinch of a 96 kilojoule (at 20 kV) plasma focus device was measured.

The purpose of these experiments was to evaluate the energy in accelerated electrons in the plasma focus device and to learn how to enhance these electron hursts. Well focused, megampere electron beams at a few hundred kilovolts, lasting less than 10 nanoseconds have applications in fusionable pellet heating experiments. (1) X-rays were monitored to evaluate these electron bursts using a defocusing bent crystal spectrometer, doubly diffused silicon (PIN) detectors, with Ross filters, thermoluminescent dosimeters (TLDs) with filters, and x-ray pinhole photography.

Thermoluminescent dosimeters indicated maximum x-ray yields of 140 joules above 3 keV at 57.3 kilojoules stored energy (16 kV) for a conversion efficiency to x-rays of 0.2%. 40 joules are above 60 keV and 15 joules above 80 keV. The hard x-ray pulse typically rises in 3 ns and frequently has a pulse width less than 10 ns. The low energy x-ray spectrum consists almost entirely of lines from the high Z anode insert, and the high energy spectrum is characteristic of a nonthermal power law distribution with an exponent of 2.2 ± 0.8. Peak hard x-ray production is obtained at 1 torr deuterium in contrast to peak neutron production (3 x 1010) at 5 torr. The addition of argon reduces total x-ray yield and increases the relative fraction of soft x-rays.

These measurements suggest that the plasma focus produces 1200 joules of electrons with an average energy of 150 keV, in 10 nanoseconds with a stored energy of 57.3 kilojoules. This is a power of 1.2 × 1011 watts and power density of 1.5 × 1013 watts cm−2.

The back-reflect ion double-scanning diffractometer method, by which lattice parameters can be measured with a reproducibility of one part in 150,000 has been applied at liquid helium temperatures. A cryostat attachment is described which enables diffraction profiles to be scanned on both sides of the primary X-ray beam up to 163°, 2θ. Alignment errors may, thus, be eliminated by measuring the included angle 4θ between respective Bragg reflections. The method is illustrated by measuring the lattice parameters of the I.U.Cr. standard specimens of silicon and tungsten at various cryogenic temperatures.

Use of a reference crystal to condition the beam in the double-axis diffractometer permits the Bragg peak width to be reduced to the correlation of the two crystal reflecting ranges. Some recent applications of double axis diffractometry to the study of heteroepitaxial layers are discussed. The advantages of multiple reflections for beam conditioning and the four reflection DuMond monochromator are examined. Glancing incidence and exit diffractometry permits the study of very thin layers, down to a few tens of nanometres in thickness and both synchrotron radiation and skew reflections can be used to tune the glancing angle close to the critical angle. Recent applications of triple-axis diffraction, where an analyzer crystal is used after the specimen, to the study of very thin single epitaxial layers and multiquantum well structures are reviewed.

The use of target current measurements in the electron microprobe for quantitative analysis of binary samples has been proposed by several authors. However, the equations proposed for calculations as well as instrumental conditions differ considerably. The present paper relates the target current measurements made with the Applied Research Laboratories microprobe to the backscatter coefficients determined independently. Equations for analyzing binary samples as well as applications to line scans and concentration mapping are given.

We have used conventional X-ray powder diffraction to study one of the largest volume inorganic mixed oxide unit-supercell structures done so far. This necessitated some small-angle X-ray scattering-like observations at low angles from <2° 2θ to concord with electron diffraction, which had indicated an 8 × 8 × 8 huge volume supercell of a fluorite-type basic sub-cell. Emphasis is on the detection of, possibly very weak, fingerprint, low-angle/long lines/peaks which will indicate the (often unsuspected) presence of complex polytypic arrangements of simple very strong basic sub-cells and so facilitate future synthetic studies.

High-resolution powder X-ray diffraction and density functional plane wave pseudo-potential techniques have been used to obtain an optimized structural model of silver arachidate, [Ag(O2C(CH2)18CH3]2. The unit cell is triclinic, space group P-1 with cell dimensions of a = 4.1519(10) Å, b = 4.7055(10) Å, c = 53.555(4) Å, α = 89.473(15)°, β = 87.617(5)° and γ = 76.329(5)°. The structure is characterized by an 8-membered ring dimer of Ag atoms and carboxyl groups joined by four-member Ag–O rings with fully extended zigzag side chains, giving rise to one-dimensional chains along the b-axis.

A method is presented to examine consecutive in-situ X-ray diffraction (XRD) diffractograms using exploratory factor analysis. Systematic changes in the diffractograms are described numerically by score values that could be used to correlate diffraction data with other non-stationary sample properties. Phase and structure evolution in a reacting material can be studied by in-situ XRD. The consecutively collected data can be considered a time series of datasets. Time series are non-stationary data. Such non-stationary data are often hard to examine fully by conventional evaluation methods including applications of the Rietveld method. Here a method is presented to avoid shortcomings of conventional evaluation methods. The new method helps to identify and describe significant systematic changes in in-situ XRD datasets by numerical values. These systematic changes can represent structural changes as well as changes in phase composition. The method can be used to describe the development of the complex processes of compositional and structural changes. The method is demonstrated using the example of a hydrating Portland cement mortar. This hydration process involves at least 11 phases including non-crystalline phases. In the presented example factor analysis of in-situ XRD data results in three variables (factors) describing the observed changes numerically.

The nanostructural features of the gas-phase displacement reaction 2Mg(g)+SiO2→2MgO(s)+{Si}, where SiO2 is in the form of diatom shells were studied via X-ray diffraction and Fourier methods. Diatomaceous powder heated to 700 °C in a sealed graphite cell in the presence of Mg vapor formed MgO via a displacement reaction. Warren-Averbach analysis performed on samples reacted for different times showed an initial sharp MgO grain size distribution which broadened with time. New MgO crystallization was shown to occur until about 60 min, whereafter only MgO grain growth occurred. Median MgO crystallite size increased from 7.5 to 24.9 nm during this period, whereas microstrain decreased dramatically past 60 min annealing time.

The kalipyrochlore (K,Sr,Na,Ca,H2O)2−m(Nb,Ti)2−xO6−wY1−n, with (0<m<0.8, x∼0.2, w = 0 and 0.2<n<1) from Lueshe, Zaire is a defect pyrochlore species whose A-site weakly depleted. The measured powder diffraction is presented with a calculated figure of merit F(30) = 74.7(0.010,39). The structure has been refined by single-crystal from X-ray diffraction data collected on a Huber four-circle diffractometer and by Rietveld analysis from X-ray powder diffraction data. The slightly weathered crystal (studied by single crystal) has a cubic pyrochlore-type structure with the same atomic positions and a unit-cell parameter a = 10.603(5) Å, space group (S.G.): Fd3m. The highly weathered crystal (studied by Rietveld) has the same cubic pyrochlore-type structure except for the oxygen position. The oxygen moved from the 48f position with x, y, z equal to 0.284, 0, 0 to x = 0.308(5), y = 0.024(6) and z = –0.028(9). The cell parameter is a = 10.569(6)±0.0007 Å. These modifications of positions induce a distortion of the A-site into an hexagonal bipyramid and an elongation of the B-site along the c axis of the octahedron.

The Rietveld method can be combined with the addition method to determine the absolute quantities of the phases treated by Rietveld refinement plus the quantity of phase(s) not treated by it (amorphous or unobserved). If q is the added proportion of a defined phase already present in the sample, and a1 and a2 its relative proportions as determined by Rietveld refinement prior and after the addition, the proportion of the amorphous (untreated) phase(s) in the original sample is calculated as xo=[a2−(1−q)a1−q]/(1−q)(a2−a1). The absolute quantities of the phases treated by Rietveld refinement are then determined by a correction for the content of the amorphous phase(s), or they can be calculated directly from specific equations. The advantage of the method is that no new variables are introduced in the refinement when the added standard already is a part of the original mixture.

θ-KAlF4 is a new nanosized potassium tetrafluoroaluminate metastable polymorph (13×18×55 nm3). The crystal structure is solved ab initio from X-ray powder diffraction data in direct space [orthorhombic unit cell with a=8.3242(3) Å, b=7.2502(3) Å, c=11.8875(4) Å, V=717.44(5) Å3, Z=8, and space group Pnma]. This new structure type, unique in the whole AIMIIIF4 family, is related to the fluorite structure and consists of AlF6 octahedra linked via a common edge forming a bioctahedral motif which is trans-connected through the corner-shared fluorine, resulting in the formation of infinite ladderlike double file of octahedra ([Al2F8]2−)n running along the b axis.

A quantitative phase analysis often requires advanced numerical studies to determine the appropriate intensity values. In this paper the method of fitting analytical functions to the experimental profile is applied to X-ray powder diffraction patterns obtained with FeK radiation. In the present work, the authors examine some problems connected with numerical studies, especially the function describing the experimental profile. The usefulness of the α2 elimination procedure and the angular dependence FWHM are also examined.

Internal elastic strain (i.e., residual stress) and the diffracted X-ray intensity variation over several orientations of crystallites with respect to the specimen surface were investigated as a means of differentiating two qualities of polycrystalline nickel plating. A unique instrument based upon a position-sensitive scintillation X-ray detector was used to apply all of the techniques commonly applied to X-ray stress analysis in this investigation. It was concluded that residual stress measurements did not provide a clear distinction between the two specimens, but comparison of the relative intensities diffracted from crystallographic planes at certain orientations with the surface did provide a distinction.

CaTi1−xSnxO3 (x = 0.0–1.0) solid solutions were prepared by solid-state reaction at 1450 °C. Rietveld refinement of their powder X-ray diffraction patterns revealed that all the solid solutions crystallized in orthorhombic cells with the perovskite-type structure, the space group Pbnm. The refined unit-cell parameters linearly increased with nominal tin contents x.