Precision X-ray reflectivity data were obtained with a high-resolution reflectometer equipped with a rotating anode X-ray source and Ge 220 channel monochromators (one placed before and the other after the specimen). The surfaces and buried interfaces of thin films were characterized by ieast-squares refinement of experimental data. Values of thickness, density, and/or roughness of Pt “single-layer” and Pt/Co based multiple-layer films were determined.

Dislocations, Inclusions, and Precipitates. Impurity precipitated after growth and foreign particles accidentally included during growth both produce intense local strain fields which give rise to diffraction contrast effects resembling those seen in electron microscope images of precipitates. The relationship between the dislocation configuration and these localized strain centers can show whether the latter arise from inclusions or precipitates. Precipitates will generally be found strung along the grown-in dislocations, decorating them. On the other hand, inclusions often generate dislocations by lattice closure errors; such dislocations then fan out from the inclusion in the general direction of advance of the growth interface.

Twin Boundaries and Fault Surfaces. The cases when the twins have parallel lattices, such as in Brazilian and Dauphiné twinning in quartz, are interesting. When the crystals on either side of the twin boundary are both Bragg reflecting, the twin boundary may exhibit ‘stacking fault’ type fringes. From an analysis of the variation of visibility of these fringes in different reflections, the fault vector at the twin boundary and its variation with boundary orientation may be found. In quartz, other types of fault surfaces producing fringe contrast may lie parallel to growth horizons or they may mark growth sector boundaries. In synthetic quartz, they can also mark cell boundaries under conditions of cellular growth.

Internal Magnetic Domain Structures. In plates of Fe + 3% Si roughly parallel to (110), a variety of previously undetected domain structures has been discovered and analyzed. Diffraction contrast is produced by 90° domain walls but not by 180° walls. The 90° walls produce strong diffraction contrast even though the magnetostriction of silicon-iron is only about 10−5. In plates parallel to (112), the main lamination pattern below the complex pattern of surface closures can be revealed and, in favorable cases, interpreted.

X-ray Moiré Patterns. The most direct method of observing X-ray moiré patterns—by topography of one crystal closely superimposed upon another—involves considerable theoretical complexities and produces a variety of curious diffraction patterns. However, it shows promise of providing a means for the comparison of lattice spacings to about one part in 107 and for mapping strain fields very sensitively.

Crystal structure determination on the basis of powder diffraction data frequently involves the question how the given diffraction data with some appreciably hkl-dependent line broadening should be interpreted. In many cases, such line broadening may either: (i) reasonably well be reconciled with a certain high-symmetry structure model or (ii) with a variant of the former with lower symmetry crystal family, which frequently will give a somewhat better fit in Rietveld refinement. In this work, it is shown mathematically that symmetry reduction induced reflection spitting masked by other line broadening contributions, thus leading to some reflection splitting-induced line broadening, shows a similar hkl dependence as typically adopted for anisotropic microstrain broadening with respect to the high-symmetry structure. This implies that Rietveld refinement on the basis of the low-symmetry model (including typically isotropic line broadening) and on the basis of the high-symmetry model with anisotropic microstrain broadening can both lead to similar qualities of the fit. Hence, the refinement results for both possibilities should be carefully considered in combination with possibly available additional information (e.g. results of first-principles calculations) to arrive at adequate conclusions concerning the true symmetry of the material under investigation.

Chitin is a natural polysaccharide found in many diverse phyla and almost always occurs in association with protein. In this study the chitin polymer is characterized by X-ray diffraction from its naturally occurring unprocessed state through various steps used in the purification procedure. In addition, the effect of different treatments on the final product is examined. These studies show that native chitin has a characteristic diffraction pattern that is not altered by the mild treatments used to isolate relatively pure chitin. Chitins prepared from different sources exhibit the same characteristic diffraction pattern. In addition, chitin films prepared using non-degrading solvents retain most of the characteristic patterns. De-acylation of chitin to produce chitosan results in large changes to the diffraction pattern. To a very limited extent features present in the diffraction pattern of native chitin can be recovered by re-acylation of chitosan.

Crystal structures of (Li0.925Eu3+0.025)TaO3, (Li0.968Eu3+0.032)(Ta0.81Ti0.19)O2.937, (Li0.967Sm3+0.033)(Ta0.89Ti0.11)O2.978, and (Li0.950Sm3+0.033Mg0.017)(Ta0.89Ti0.11)O2.987 were investigated by X-ray powder diffraction. The initial structural parameters, taken from those of the isomorphous compound (Li0.977Eu3+0.023)(Ta0.89Ti0.11)O2.968 (space group R3c and Z = 6), were refined by the Rietveld method. A pattern-fitting method based on the maximum-entropy method was subsequently used to determine the three-dimensional electron-density distributions (EDDs) that are free from the structural bias. We confirmed that the EDDs are in accord with the resulting structural models, each of which was composed of the [(Ta, Ti)O6] octahedron and [(Li, Eu, Sm, Mg)O12] polyhedron. We compared these polyhedra and found that the prominent difference among these compounds was the centroid-to-(Li, Eu, Sm, Mg) distance (eccentricity) of [(Li, Eu, Sm, Mg)O12]. The high correlation was demonstrated between the magnitude of eccentricity and photoluminescence intensity under near ultraviolet excitation.

We have demonstrated that structures down to 150 nm can be visualized in X-ray projection images using nanofocus X-ray sources. Due to their unlimited depth of focus, they do not possess a limit on the specimen size. This is essential for three-dimensional tomographic imaging of samples with a diameter larger than a few microns. Further simulation studies have shown that optimization of the detector response curve and switching from a reflective X-ray target to a transmission target should allow us to reach sub-100-nm resolutions.

Fundamental-parameters calculations can be made on a laboratory microcomputer fo r automatic treatment of interelement absorption and enhancement effects in x-ray fluorescence analysis. A new software package, called XRF-11, uses an efficient combination of fundamental parameters and alpha factors to compensate for any lack of measured reference materials, while taking full advantage of whatever standards are available, even just pure elements. In many cases, one multi-element standard is enough for accurate analysis.

The new XRF-11 software uses the same data base of absorption coefficients, fluorescence yields, etc. as the big-computer program NRLXRF, and combines theory with experiment in a consis tent way that is similar to, but more efficient than, the treatment used in NRLXRF.

Crystal structures of A0.50SbFe(PO4)3(A=Mn, Cd) phases, obtained by solid state reaction at 920 °C, were determined at room temperature from X-ray powder diffraction (XRD) using the Rietveld method. The structures of the two samples are of the Nasicon-type with the R3 space group. Hexagonal cell parameters for A=Mn and Cd are: a=8.375(1) Å, c=21.597(2) Å and a=8.313(1) Å, c=21.996(2) Å, respectively. From XRD data, it is difficult to unambiguously distinguish between Cd2+ and Sb5+ ions in Cd0.50SbFe(PO4)3 and between Mn2+ and Fe3+ cations in Mn0.50SbFe(PO4)3. Nevertheless the overall set of cation–anion distances within the Nasicon framework clearly shows that the cation distribution can be illustrated by the {[A0.50]3a[◻0.50]3b}M1SbFe(PO4)3 (A=Mn, Cd) crystallographic formula. The divalent A2+ cations and vacancies are ordered within the two positions, 3a and 3b, of the M1 sites. Structure refinements show also a quasi-ordered distribution of Sb5+ and Fe3+ ions within the Nasicon framework. Thus, each A(3a)O6(A=Mn, Cd) octahedron shares two faces with two Fe3+O6 octahedra and each vacancy (◻(3b)O6) site is located between two Sb5+O6 octahedra.

The fuzzy frontiers between structure determination by powder diffractometry and crystal structure prediction are discussed. The application of a search-match program combined with a database of more than 60 000 predicted powder diffraction patterns is demonstrated. Immediate structure solution (before indexing) is shown to be possible by this method if the discrepancies between the predicted crystal structure cell parameters and the actual ones are <1%. Incomplete chemistry of the hypothetical models (missing interstitial cations, water molecules, etc.) is not necessarily a barrier to a successful identification (in spite of inducing large intensity errors), provided the search-match is made with chemical restrictions on the elements present in both the virtual and experimental compounds.

Extensive analyses of low-temperature powder x-ray diffraction data for spinel LiMn2O4 (Fd3¯m at room temperature) make it clear that two structural phase transitions occur: first around 285 K from cubic to orthorhombic, second around 65 K from orthorhombic to tetragonal. At temperatures under 285 K, superlattice peaks appear in the diffraction pattern that were successfully indexed by tripling the a and b axes of the spinel unit cell. At 250 K, the unit cell is face-centered orthorhombic, Fddd, F2dd, or Fd2d, with a=24.855(1), b=24.755(2), c=8.2014(3) Å, V=5046.1(4) Å3, Dx=4.284 g/cm3, Z=72. The unit cell at 30 K was confirmed to be body-centered tetragonal I41/amd or I41/a, with a=17.5176(3), c=8.1961(2) Å, V=2515.1(1) Å3, Dx=4.298 g/cm3, Z=36.

A short history of the developments of the successive dichotomy method for powder pattern indexing is presented. In the first computer powder indexing programs (P1 and P2), only high lattice symmetries, down to orthorhombic, were considered [Louër and Louër, J. Appl. Crystallogr. 5, 271–275 (1972)]. Later on, an extension to the monoclinic symmetry was reported in DICVOL, including a partition of the volume space to first search solutions with smaller unit cell volumes [Louër and Vargas, J. Appl. Crystallogr. 15, 542–545 (1982)]. However, CPU times were slow in some monoclinic examples. A thorough mathematical analysis resulted in a significant optimization of the CPU times [Boultif and Louër, J. Appl. Crystallogr. 24, 987–993 (1991)]. Simultaneously, the method is extended to triclinic lattices. The stages of development of the various versions of the DICVOL program are described, with a particular emphasis on DICVOL91 (Boultif and Louër, 1991) and DICVOL04 [Boultif and Louër, J. Appl. Crystallogr. 37, 724–731 (2004)]. This article is written to testify to and emphasize the major role played by Daniel Louër, who introduced the successive dichotomy method and continued to its evolution and optimization over almost 40 years.

My students and I have developed a LOTUS 1-2-3 spreadsheet to aid in data reduction tasks associated with preparing powder diffraction data for publication in the Powder Diffraction File (PDF) (1987) and this journal. Portions of a sample spreadsheet and the formulae in each of the computational cells are given in the Table 1. The concept of this spreadsheet should apply to any of the available computer spreadsheet programs, although the specific codes for the mathematical functions may differ.

The user enters data only into columns C, D and F-H. All other entries will be calculated from the input data. Observed 2θ angles are entered into column D. The corresponding d-spacing is calculated in column A. The Miller indices of these peaks are entered into column C. Prior to use of the spreadsheet, the observed 2θ angles and hkl's had been used to refine unit cell parameters using the Appleman and Evans (1973) least squares unit cell parameter refinement computer program implemented for the IBM PC by Garvey (1986).

An experimental X-ray diffraction (XRD) study of calcium salts of four carboxylic acids is presented. Calcium salts of propionic, butyric, valeric, and caproic acids were synthesized mixing in a mortar Ca(OH)2 with the liquid acids. Measuring the thermogravimetric analysis curves it was determined that the salts were actually monohydrates. The densities of the synthesized samples were measured using a density gradient column. The measured values for the densities were as follows: Dm(propionate)=1.38 g/cm3, Dm(butyrate)=1.30 g/cm3, Dm(valerate)=1.26 g/cm3, Dm(caproate)=1.22 g/cm3. The XRD analysis revealed that these compounds have monoclinic cells with symmetry described by the P21/a space group. Calcium propionate hydrate has cell parameters: a=2.437 51(5) nm, b=0.681 24(1) nm, c=0.591 43(1) nm, β=95.320(2)°. For calcium butyrate hydrate the cell parameters are: a=2.966 84(8) nm, b=0.680 74(2) nm, c=0.589 29(2) nm, β=95.442(3)°. The cell parameters for calcium valerate hydrate are: a=3.566 36(4) nm, b=0.682 49(1) nm, c=0.592 77(1) nm, β=107.280(1)° and for calcium caproate hydrate a=4.180 30(5) nm, b=0.682 61(1) nm, c=0.592 13(1) nm, β=110.230(1)°. The calculated density values from the XRD results, taking into account that the number of chemical formulas in the unit cell equals four, agree very well with the measured ones. It was established that the unit cell parameter a grows with the increase of the number of carbon atoms in the aliphatic chain, while parameters b and c remain almost constant. This is an indication of the stacking layer character of the structure as has been suggested for calcium stearate monohydrate. This fact points to the possibility of the refinement of the crystalline structures taking as the starting point the reported structure for calcium stearate monohydrate.

Diffracted intensities from an X-ray diffractometer operating with fixed or variable divergence slits were compared, following a reported systematic deviation from the theoretical 1/sinθ intensity ratio between these two slit configurations. The theoretical relationship was found to hold over a wide 2θ range provided the anti-scatter slit did not obstruct the beam at higher diffraction angles as the variable slit increased beam divergence. Such obstruction was found to be a possible explanation for the reported deviation.

X-ray diffraction and scattering on a single multipurpose X-ray platform have been used to probe the structure, composition, and thermal behavior of TiO2 nanoparticles ranging in size from 1 to 10 nm. Ambient and non-ambient Bragg diffraction, small-angle X-ray scattering (SAXS), as well as total scattering and pair-distribution function (PDF) analysis are combined to obtain a comprehensive picture of the samples. At these ultrasmall particle-size dimensions, SAXS and PDF prove powerful in distinguishing the salient features of the materials, in particular the size distribution of the primary particles (SAXS) and the identification of the TiO2 polymorphs (PDF). Structural features determined by X-ray scattering techniques are corroborated by high-resolution transmission electron microscopy. The elemental make-up of the materials has been measured using X-ray fluorescence spectrometry and energy-dispersive X-ray analysis.

In epitaxial single crystal growing it happens very often that the composition of the grown film, say AxB1-x C, is not known exactly. Usually it would be possible to find out that compositions imply by determining the lattice constants of the film. The problem of such a measurement lies in the fact of internal and unknown stresses in the film. On the other side the knowledge of the state of stress σ and strain ε can also be of great importance. To calculate the stresses from X- ray measurements we need the lattice constants in the unstrained condition.

Hornstra and Bartels have shown that the lattice constant can be det ermined by X-ray measurements if the strain is isotropic in the film plane. In the following we show that the lattice constant and the full strain tensor can be calculated fromat least four X- ray measurements also in the general case.

A new method is used in measuring the linear thermal expansion coefficients in composite consisting of a substrate Gd3Ga2Ga3O12 (GGG) and its epitaxial layer Y3Fe2Fe3O12 (YIG) within the temperature range 13.88 °C–32.50 °C. The results show that the thermal expansion coefficient of GGG in composite is larger than that of the GGG in single crystal; the thermal expansion coefficient of thick film YIG is also larger than that of thin film. The results also show that the thermal expansion coefficient of a composite consisting of film and its substrate can be measured by using a new method.

An analysis of the microstructure of nanocrystalline magnesium oxide produced by thermal decomposition of magnesium oxalate, in the temperature range 500 °C–1200 °C, is described. The study is based on diffraction line broadening analysis carried out with the integral breadth (Langford) and Fourier methods, combined with the pattern decomposition technique. Additionally, the whole pattern matching method is also applied. No marked line broadening anisotropy is observed in the patterns. It is shown that the nanopowders are characterized by minimal strain and that crystallites have an average spherical shape. Volume-weighted and area-weighted apparent sizes are in the ranges 98–480 Å and 72–282 Å, respectively, within the temperature range considered. The results obtained from line broadening analysis are compared to those observed with scanning electron microscopy and surface area measurements. A satisfactory agreement is found between sizes derived from the different techniques.

A lattice metric singularity occurs when unit cells defining two (or more) lattices yield the identical set of unique calculated d-spacings. The existence of such singularities, therefore, has a practical impact on the indexing of powder patterns. For example, when experimental data from ζ-LiBO2 were indexed, two solutions (a rhombohedral and a monoclinic lattice) with approximately the same figure of merit were found. These two lattices yield the same set of unique d-spacings even though they are characterized by different reduced cells with cell volumes in the ratio 2 to 1. From the indexing point of view, both answers are correct. A singularity of this type is common and not a mathematical rarity. In fact, any rhombohedral cell of this kind has a derivative monoclinic subcell, each of which gives the same set of unique calculated d-spacings. In actual cases like this, one can run into a trap. Due to experimental error and input parameters, an indexing program may determine only one of the cells with a high figure of merit. When this happens, it is critical to recognize that another solution exists, especially if one has determined the lower symmetry lattice.

Crystal data and a representative X-ray powder diffraction pattern are reported for a series of isomorphous compounds, LnKFe(CN)6.4H2O where Ln = La, Ce, Pr and Nd. They crystallize in the hexagonal space group P63/m (176) with Z = 2. A plot of the unit cell volume (V) versus the cube of the Ln ionic radius (r3) yields linearity with a correlation coeficient of 0.9998.