Giora Kimmel

Quantitative X-Ray Diffractometry

1 Introduction.- 1.1 Phase analysis-when and why.- 1.2 Phase analysis as an analytical method.- 1.2.1 Direct methods of phase analysis.- 1.2.2 Indirect methods of phase analysis.- 1.2.3 General approach to phase quantification.- 1.3 History of quantitative X-ray phase analysis.- 1.3.1 Quantification techniques.- 1.3.2 Instrumentation.- 2 Physical basis.- 2.1 Interaction of X-rays with material.- 2.1.1 Scattering of X-rays.- 2.1.2 Absorption of X-rays.- 2.1.3 Various forms of absorption coefficients.- 2.2 Intensity in powder diffraction.- 2.2.1 General expression derived from the kinematic theory of diffraction.- 2.2.2 Polarization factor in X-ray diffractometry.- 2.2.3 Extinction of X-rays.- 2.3 Background-angle variation and intensity.- 2.3.1 Introduction.- 2.3.2 Scattering of continuous radiation.- 2.3.3 Scattering of characteristic radiation.- 2.4 X-ray diffraction by nonhomogeneous polycrystalline materials.- 2.4.1 Introduction.- 2.4.2 Two extreme cases: homogeneous and nonhomogeneous specimens.- 2.4.3 Particle absorption factor.- 2.4.4 Absorption by a nonhomogeneous system.- 2.4.5 Intensity correction for nonhomogeneous specimens.- 2.4.6 Application of the theory.- 2.4.7 Surface roughness.- 2.5 Orientation of reflecting particles.- 3 Geometric aspects of X-ray diffractometry.- 3.1 Geometric schemes in X-ray diffractometry.- 3.2 Diffractometers with Bragg-Brentano reflection focusing.- 3.2.1 General geometric features.- 3.2.2 Absorption correction.- 3.2.3 Real irradiated volume in the Bragg-Brentano scheme.- 3.2.4 Instrumental aberrations.- 3.2.5 Diffraction by a thin-layer specimen.- 3.3 Diffractometers with Seeman-Bohlin reflection focusing.- 3.3.1 Absorption correction.- 3.3.2 Instrumental aberrations.- 3.3.3 Comparison with the Bragg-Brentano scheme.- 3.4 Transmission technique with constant specimen-detector distance (Bragg-Brentano transmission analog).- 3.4.1 Geometric scheme.- 3.4.2 Absorption correction.- 3.4.3 Instrumental aberrations.- 3.4.4 Comparison between reflection and transmission Bragg-Brentano geometries.- 3.5 Transmission technique with an invariant focusing circle (Guinier diffractometer or the Seeman-Bohlin transmission analog).- 3.5.1 General description.- 3.5.2 Absorption correction.- 3.5.3 Chromatic aberration.- 3.5.4 Comparison of symmetric and asymmetric transmission geometries.- 3.6 Debye-Sherrer geometry.- 3.6.1 General view.- 3.6.2 Absorption correction.- 3.6.3 Comparison with former methods.- 3.7 Powder diffractometry with synchrotron radiation.- 3.7.1 General description.- 3.7.2 Instrumental aberrations.- 3.7.3 Diffractometric modes with synchrotron radiation.- 3.8 Position-sensitive detectors in powder diffractometry.- 4 Methodology of quantitative phase analysis.- 4.1 Introduction.- 4.2 Analysis of samples with a known mass absorption coefficient (diffraction-absorption technique).- 4.2.1 Multiphase system with a constant absorption coefficient.- 4.2.2 Two-phase system with a variable absorption coefficient.- 4.2.3 General case: multiphase systems with a variable absorption coefficient.- 4.2.4 Examples.- 4.3 Internal standard method.- 4.3.1 Basic principles.- 4.3.2 Evaluation of calibration constants.- 4.3.3 Precision of the internal standard method.- 4.3.4 Comparison of the internal standard method with the diffraction-absorption technique.- 4.3.5 Internal standard-materials and optimal amount.- 4.3.6 Application of the internal standard method.- 4.4 Doping method in quantitative X-ray diffractometry.- 4.4.1 Introduction.- 4.4.2 Constant absorption approach.- 4.4.3 General case.- 4.4.4 Two-phase approach.- 4.4.5 Precision of the analysis and optimal doping.- 4.4.6 Implementation of the doping method.- 4.5 Dilution Method.- 4.5.1 Basic aspects.- 4.5.2 Optimal dilution.- 4.5.3 Potential diluents.- 4.5.4 Use of a heavy absorber-constant-absorption approach.- 4.5.5 Implementation of the dilution method.- 4.6 Full-phase analysis of the n-phase sample.- 4.6.1 Basic equations.- 4.6.2 Application of the method to two-phase mixtures.- 4.6.3 Evaluation of the calibration coefficient ?rj.- 4.6.4 Presence of undetected phases in the analytical sample.- 4.6.5 Comparison of equations (4.62) and (4.77).- 4.6.6 Precision of the analysis.- 4.6.7 Invariance of ?rj values.- 4.6.8 Examples.- 4.7 Reference intensity ratios in quantitative analysis.- 4.7.1 Introduction.- 4.7.2 Definition and acquisition of reference intensity ratios.- 4.7.3 Implementation of reference intensity ratios.- 4.7.4 Invariance of reference intensity ratios.- 4.8 Diffraction patterns with overlapping peaks-full diffraction pattern approach.- 4.8.1 Introduction.- 4.8.2 Basic principles.- 4.8.3 Evaluation of phase abundances.- 4.8.4 Evaluation of the constants ?ij.- 4.8.5 Precision of the analysis.- 4.8.6 Internal standard technique in the case of overlapping peaks.- 4.8.7 Continuous pattern approach.- 4.8.8 Examples.- 4.9 Implementation of calculated powder patterns in QXRD.- 4.9.1 Introduction.- 4.9.2 Calculation of calibration constants.- 4.9.3 Full-pattern approach.- 4.9.4 Simultaneous QXRD and structure refinement by the pattern-fitting method.- 4.9.5 Sources of structural data.- 4.9.6 Quality of structural data.- 4.9.7 Comparison of calculated and experimental powder data.- 4.9.8 Summary.- 4.10 Standardless Methods.- 4.10.1 Introduction.- 4.10.2 Derivation of phase abundances and calibration constants.- 4.10.3 Full pattern approach.- 4.10.4 Number of phases in analyzed samples.- 4.10.5 Precision of the standardless techniques-optimal sample set.- 4.11 Combination of X-ray diffraction and chemical data.- 4.11.1 Phase analysis based on pure chemical data.- 4.11.2 Auxiliary X-ray diffraction data.- 4.11.3 Basic application of X-ray diffraction.- 4.12 Crystallinity of polymers.- 4.13 Analysis of low-mass samples.- 4.13.1 Critical sample masses.- 4.13.2 Analytical equations.- 4.13.3 Analytical techniques.- 5 Practical aspects of quantitative phase analysis.- 5.1 Introduction.- 5.2 Instrumentation.- 5.2.1 Introduction to instrumentation.- 5.2.2 Geometric alignment of the diffractometer.- 5.2.3 Geometric aberrations.- 5.2.4 Variable instrument parameters.- 5.2.5 Detectors and monochromators.- 5.2.6 Fixed divergence versus fixed irradiated area geometries.- 5.3 Specimen preparation.- 5.3.1 Preparation of bulk specimens.- 5.3.2 Sampling of powders.- 5.3.3 Fine grinding of powders.- 5.3.4 Powder aggregation and mixing.- 5.3.5 Powder mounts.- 5.3.6 Pressing.- 5.3.7 Dusting of loose powder on a plate.- 5.3.8 Powder deposition on a membrane filter.- 5.3.9 Preparation of oriented mounts.- 5.3.10 Handling of reactive samples.- 5.3.11 Handling of low-mass samples.- 5.4 Analytical standards.- 5.4.1 Effects of solid solution on diffracted intensity.- 5.4.2 Linear and planar structural imperfections.- 5.4.3 Particle morphology.- 5.4.4 Selection of analytical standards.- 5.5 Intensity measurements.- 5.5.1 Counting statistics.- 5.5.2 Difference and sum of intensities-counting strategy.- 5.5.3 Ratio of intensities.- 5.6 Definition and subtraction of background.- 5.6.1 Definition and subtraction of the background for a single diffraction peak.- 5.6.2 Full-pattern approach.- 5.6.3 Subtraction of incoherent scattering.- 5.7 Determination of sample absorption.- 5.7.1 Calculation of mass absorption.- 5.7.2 Measurements of absorption coefficients by transmission methods.- 5.7.3 Attenuation of reflection from a crystalline substrate.- 5.7.4 Determination of the absorption coefficient by diffraction techniques.- 5.7.5 Determination of the mass absorption coefficient by means of Compton scattering.- 5.8 Pattern decomposition and simulation.- 5.8.1 Introduction.- 5.8.2 Profile-fitting functions.- 5.8.3 Fitting of asymmetrical profiles.- 5.8.4 Adjustable parameters and constraints.- 5.8.5 Number of separated peaks and angular resolution.- 5.9 Methodology of corrections for preferred orientation.- 5.9.1 Introduction.- 5.9.2 Presentation of the pole distribution.- 5.9.3 Orientation distribution function.- 5.9.4 Determination of the orientation distribution function W(?, ?).- 5.9.5 Crystallite orientation distribution-the general case of axial texture.- 5.9.6 Approximation of the orientation distribution function W(?,?).- 5.9.7 W(?) of diffraction peaks not dependent on preferred orientation.- 5.10 Estimation of analysis errors.- 5.10.1 Introduction.- 5.10.2 Calculation of reproducibility.- 5.10.3 Scattering range of results.- 5.10.4 Comparison of observed and known phase abundances.- 5.10.5 Inter- and intralaboratory precision.- 5.10.6 Parameters of the calibration graph-estimation of standard deviation.- 5.11 Detection limit.- 5.11.1 Basic formulation.- 5.11.2 Reduction of the detection limit.- 5.11.3 Detection limit in the sample mass approach.- 5.12 Crystallite statistics.- 5.12.1 Intensity error.- 5.12.2 Methods of decreasing intensity fluctuations other than sample diminution.- 6 Industrial applications.- 6.1 Ceramics and glass ceramics.- 6.2 Naturally occurring (geologic) samples.- 6.2.1 Modal analysis of geologic samples.- 6.2.2 Analysis of bauxites.- 6.2.3 Mineralogical analysis of coal and coal ash.- 6.3 Analysis of Portland cement.- 6.4 Metallurgy.- 6.5 Thin films and coatings.- 6.6 Air pollution (aerosols and airborne dusts).- 6.7 Pharmaceuticals.- References.

Growth and structure control of HfO2−x films with cubic and tetragonal structures obtained by ion beam assisted deposition

Hafnium oxide films were grown by ion beam assisted deposition on water-cooled Si (100) substrates, under conditions of oxygen starvation, using hafnium vapor and an oxygen ion beam. The transport ratio (TR), i.e., the ratio between the arrival rate of hafnium to that of oxygen, was varied between 0.5 and 10, and ion energy was varied between 1 and 20 keV. The films were analyzed using x-ray diffraction and x-ray photoelectron spectroscopy. Films having the CaF2 cubic structure with a lattice parameter of about 0.512 nm were repeatedly obtained. In addition, at 20 keV ion energy and TR values of 4 and above, films with a tetragonal structure were obtained. The latter structure, believed to be a distortion of the cubic structure, has a c/a ratio of 1.01 and its space group is considered to be different from the high temperature tetragonal HfO2 structure. The new tetragonal structure also presents high Knoop hardness, with values between 15 and 25 GPa. Substrate rotation speed was found to affect the struct...

Ultrasonic cavitation of molten gallium: Formation of micro- and nano-spheres

Pure gallium has a low melting point (29.8°C) and can be melted in warm water or organic liquids, thus forming two immiscible liquid phases. Irradiation of this system with ultrasonic energy causes cavitation and dispersion of the molten gallium as microscopic spheres. The resultant spheres were found to have radii range of 0.2-5 μm and they do not coalesce upon cessation of irradiation, although the ambient temperature is well above the m.p. of gallium. It was found that the spheres formed in water are covered with crystallites of GaO(OH), whereas those formed in organic liquids (hexane and n-dodecane) are smooth, lacking such crystallites. However, Raman spectroscopy revealed that the spheres formed in organic liquids are coated with a carbon film. The latter may be the factor preventing their coalescence at temperatures above the m.p. of gallium.

Pressure‐induced effects and phase relations in Mg2NiH4

The low‐temperature (<210 °C) crystallographic structure, electrical conductivity, and thermal stability of Mg2NiH4 powders compacted under isostatic pressures of up to 10 kbar were studied. A comparison is made with the corresponding properties of the noncompressed material. It has been concluded that under stress‐free hydriding conditions performed below 210 °C, a two‐phase hydride mixture is formed. Each of the hydride particles consists of an inner core composed of an hydrogen‐deficient monoclinic phase coated by a layer of a stoichiometric orthorhombic phase. The monoclinic phase has a metalliclike electrical conductivity while the orthorhombic phase is insulating. High compaction pressures cause the transformation of the orthorhombic structure into the monoclinic one, thereby resulting in a pressure‐induced insulator‐to‐conductor transition. Reduced decomposition temperatures are obtained for the compressed hydrides. This reduction is attributed to kinetic factors rather than to a reduced thermodyna...

Structural modifications of hafnium oxide films prepared by ion beam assisted deposition under high energy oxygen irradiation

Abstract This work deals with high-energy ion beam assisted deposition (IBAD) of HfO 2 on Si(100) substrates. Hafnium vapor was generated from a metallic hafnium target with simultaneous bombardment with oxygen ions accelerated at energies of 1–20 keV, a much higher energy regime than in other IBAD works. The transport ratio (TR), defined as the ratio between the hafnium arrival rate and the oxygen ion dose, was in the range of 0.5–10. The substrate was not heated during deposition. The films’ structure and properties were characterized using X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), electron probe micro-analysis (EPMA), and Knoop microhardness. Significant structural modifications were observed with parameter variation. Films consisting of tetragonal and cubic structure or mixtures of these with the monoclinic phase were obtained. To the authors’ knowledge this is the first report of non-monoclinic phases observed in IBAD films. Measurements of film stoichiometry show that the films are oxygen deficient; the Hf/O ratio appears to be approximately 1:1.5 despite variations in TR. At 20 keV acceleration energy the microhardness increased linearly with TR, reaching a maximum of 25 GPa at a TR value of 10. The high hardness is associated with the new tetragonal phase.

Postdeposition treatments of TiNx Part I: effects of annealing on the structure of nitrogen-rich films

Abstract This paper discusses various defects in TiN and related nitrides and their repair by heat treatments. X-ray diffractograms of TiN x films deposited on glass substrates with increasing nitrogen content in the plasma chamber show gradual changes in the structure, from normal TiN x to anomalous films having the CaF 2 structure. The differences between the diffractograms of the two types of structure are analysed in view of the increased nitrogen content in the deposition chamber. The apparent (111) orientation observed in films obtained with high amounts of nitrogen in the plasma is explained as an intrinsic feature of the CaF 2 structure with very small crystallites. Structural repair was observed in all films after heat treatment for 8 h at 500°C and the CaF 2 -type phase transformed into randomly oriented NaCl phase.

Structure of UAl4 prepared by solid state reaction

Abstract Randomly oriented polycrystalline UAl4 was obtained by arc melting of Al–66.7wt.%U alloy followed by a short-time solid state reaction. X-ray powder diffractometer (XRPD), scanning electron microscopy–energy dispersive spectroscopy (SEM–EDS) and density measurements were used in order to determine the exact deviation of stoichiometry in the UAl4 structure. Machine ball-milled powder samples were used in order to obtain high quality XRPD data, which could be refined by Rietveld method. It was confirmed that only ∼90% of the uranium sites are occupied. There is no evidence for ordering of vacancies in our samples.

Long-term amorphisation of C+ and N2+ implanted layers on a uranium surface

Abstract Ion implantation of C + or N 2 + on uranium surfaces produces crystalline compounds (uranium carbides or nitrides, respectively), which have been shown to provide excellent protection against ambient corrosion. Some long-term changes of these implanted layers were detected that even though not affecting the protection ability, still are of fundamental interest. The most prominent change is the amorphisation of the carbide or nitride layers, which takes place after a few years of air exposure. This amorphisation did not result from the oxidation of the layer (the formed oxides are much thinner than the thickness of the implanted layers), but is still assisted by air exposure (i.e., the amorphisation rates of samples kept under vacuum are much lower than those exposed to the ambient atmosphere). Some additional long-term changes in the layer compositions (transitions of UN 2 to U 2 N 3 ) and distributions (inward diffusion of the implanted ions) were also apparent. It is suggested that the presence of hydrogen in the implanted layer, originating from the dissociation of water molecules on the surface, may accelerate the amorphisation and the UN 2 to U 2 N 3 transition due to the possible increase in the diffusion constant.

Formation of particles of bismuth-based binary alloys and intermetallic compounds by ultrasonic cavitation

This work describes the interactions of molten bismuth with other low-melting point metals (Sn, In, Ga and Zn) under sonication. Binary combinations of bismuth and one of these metals were melted together in hot silicone oil and irradiated with ultrasonic energy to form micro/nano alloy particles. The morphology, composition and crystal structure of these particles were analyzed. It was found that bismuth forms metal matrix composites with tin and zinc, intermetallic compounds with indium and an alloy with gallium. We also followed the structural changes in the system by X-ray diffraction (XRD), differential scanning calorimetry (DSC), and electron microscopy.

Thermal anisotropy of tialite (Al2TiO5) by powder XRD

Abstract Tialite was synthesized from stoichiometric mixtures of commercial corundum and rutile (8–10 μm) or nanophase coprecipitated alumina and titania precursor powders. Uniaxially compressed tablets of these precursors were calcinated at a temperature in the 1,200–1,500°C range, and cooled to room temperature. One of the nanometric precursors showed appearance of tialite already at 1,300°C, while the commercial powders began to react only at 1,400°C. In all cases the synthesis was complete at 1,500°C. The X-ray diffractograms of the products showed that tialite derived from commercial precursors assumed a preferred orientation, which was probably induced by the compression of the tablet. No anisotropy was noted after adding a small amount of silica to the commercial powder, however, this led to mullite formation. Nanophase precursors yielded crystallites with random orientation.