Profile Refinement Research Articles

X-ray powder diffraction and vibrational spectroscopic investigation of the LaO(Cl1−xBrx) solid solutions

The formation of the anion solid solutions in the LaO(Cl1−xBrx) (0≤xBr≤1 ΔxBr=0.2) series was studied by the vibrational (FT-Raman) spectroscopic and X-ray powder diffraction (XPD) techniques. The Raman spectra were successfully analyzed by using the factor group analysis. The crystal structures for all members of the system were resolved from the X-ray diffraction data by using the Rietveld profile refinement method. The LaO(Cl1−xBrx) system appears to retain the tetragonal structure throughout the whole series. However, there exists two regions of the tetragonal LaOX (X=C1 or Br) phases: the chloride- and bromide-rich regions between 0≤xBr≤0.4 and 0.4≤xBr≤1, respectively. Only insignificant formation of solid solutions could be observed since the lattice parameter a and c values changed only slightly from those for the pure LaOCl and LaOBr in these two regions. Despite the absence of the solid solubility, no phase separation occurred as predicted by the Vegard's rule since the difference in the ionic radius of the Cl− and Br-ions is only about 8%. The FT-Raman studies yielded practically constant number and energies of the vibrations throughout the whole LaO(Cl1−xBrx) series resulting in similar conclusions.

A high temperature, high pressure cell for time-of-flight neutron scattering

A high temperature, high pressure cell for neutron scattering studies and capable of achieving 1100 K and 1.2 GPa is described. This cell is a modification of the McWhan clamped cell design (D.B. McWhan et al., Rev. Sci. Instr. 45 (1974) 643), adapted to incorporate a graphite heating element and optimised for time-of-flight (fixed geometry) neutron scattering techniques. Preliminary measurements are shown using standard samples for calibration as well as a profile refinement of data from an α-PbF 2 sample within the cell at ambient temperature and pressure to confirm the effectiveness of cell absorption corrections. This refinement produced reliable structural parameters which were consistent with those obtained under optimal conditions. A further measurement from a high pressure high temperature disordered phase of CuCl with clear diffuse scattering is also shown.

Stoichiometry of Li2MnO3and LiMn2O4Coexisting Phases: XRD and EPR Characterization

The coexistence of LiMn2O4and Li2MnO3phases from MnO/Li2CO3mixtures with lithium cationic fraction 0.33≤x≤0.53 was studied by X-ray diffraction (XRD) and electron paramagnetic resonance (EPR) measurements. XRD quantitative phase analysis was carried out using the Rietveld profile refinement procedure, while the Li2MnO3percentage was determined directly by comparing the EPR intensities with the intensity of the pure Li2MnO3spectrum. The experimental results show the presence of an Li-rich spinel phase and allow an estimation of the lithium excess, since the structural analysis of pure Li2MnO3samples evidenced a nearly stoichiometric composition (x=0.663) with very limited cationic disorder.

Thermoelastic equation of state of jadeite NaAlSi2O6: An energy‐dispersive Reitveld Refinement Study of low symmetry and multiple phases diffraction

We report the first measurement of a complete set of thermoelastic equation of state of a clinopyroxene mineral. We have conducted an in situ synchrotron x‐ray diffraction study of jadeite at simultaneous high pressures and high temperatures. A modified Rietveld profile refinement program has been applied to refine the diffraction spectra of low symmetry and multiple phases observed in energy dispersive mode. Unit cell volumes, measured up to 8.2 GPa and 1280 K, are fitted to a modified high‐temperature Birch‐Murnaghan equation of state. The derived thermoelastic parameters of the jadeite are: bulk modulus K=125 GPa with assumed pressure derivative of bulk modulus K′ = ∂K/∂P = 5.0, temperature derivative of bulk modulus , and volumetric thermal expansivity α = a + bT with values of a=2.56×10−5K−1 and b=0.26x10−8 K−2. We also derived thermal Grüneisen parameter γth=1.06 for ambient conditions; Anderson‐Grüneisen parameter δTo=5.02, and pressure derivative of thermal expansion ∂α/∂P = −1.06×10−6 K−1 GPa−1. From the P‐V‐T data and the thermoelastic equation of state, thermal expansions at five constant pressures of 1.0, 2.5, 4.0, 5.5, and 7.5 GPa are calculated. The derived pressure dependence of thermal expansion is: Δα/ΔP = −0.97×10−6K−1GPa−1, in good agreement with the thermodynamic relations.

Characterization of the non-stoichiometry in lanthanum oxyfluoride by FT-IR absorption, Raman scattering, X-ray powder diffraction and thermal analysis

The FT-IR absorption, FT-Raman scattering, X-ray powder diffraction (XPD), and thermogravimetry were used to explore the non-stoichiometry in LaOF. The TGA-DTA analyses between 30 and 1500°C showed that the LaO 1 − x F 1 + 2 x phases yielded the stoichiometric LaOF as an intermediate product. The temperature of formation of the LaOF and La 2O 3 increased with increasing excess of fluoride. The room temperature XPD data in 6.5 ⩽ 2 θ ⩽ 121° range were analyzed by the Rietveld profile refinement method and subsequently by the bond valence calculations. All LaO 1 − x F 1 + 2 x phases possess the tetragonal PbFCl-type structure (space group: P4/ nmm; Z = 2) while the stoichiometric LaOF has the hexagonal SmSI-type structure (space group: R 3m; Z = 6 ). The unit cell parameters a and c as well as the global instability index (GII) values increased with increasing excess fluoride. The GII value for each LaO 1 − x F 1 + 2 x exceeded the limit ( ca 0.2) for a possible breakdown of the tetragonal structure indicating the inherent instability of these phases. The room temperature FTIR and FT-Raman spectra between 100 and 500 cm −1 and 50 and 1000 cm −1, respectively, were investigated using the factor group analysis to get more information of the local structure in LaOF. All four IR modes (2A 2u + 2E u) the for both forms and five of the six Raman modes (3A 1g + 3E g and A 1g + 2B 1g + 3E g) for the hexagonal and the tetragonal form, respectively, were observed. The Raman spectra of the tetragonal LaOCl and all LaO 1 − x F 1 + 2 x were found remarkably similar.

On Some Structural and Spectroscopic Aspects of Rare Earth Oxycompounds

The aim of this account is to present the use and the advantages of different experimental and theoretical methods in the study of the structural and spectroscopic properties of rare earth (RE) oxyfluorides. The structural characterization was carried out with the X-ray and neutron powder diffraction techniques combined with the analysis of the acquired data with the Rietveld profile refinement method. The detailed spectroscopic studies were also used by employing the optical absorption and luminescence as well as inelastic neutron scattering data. Simple spectroscopic measurements gave, however, only qualitative description of the spectroscopic properties studied. More sophisticated and quantitative means was obtained by the application of the phenomenological crystal field theory to the spectroscopic data. On the other hand, the structural data was also used as initial input to electrostatic point charge calculation in order to extract the spectroscopic information. The structural and spectroscopic studies comprised the verification of the exact crystal and energy level structures and the characterization of the different interactions modifying the spectroscopic properties of the RE 3+ ions. Finally, the results from the theoretical model were used to explain the evolution of the crystal field effect on the 4f N energy level structure of the RE3+ ion in the RE oxyfluorides series.

Effect of cobalt substitution on cationic distribution in LiNi 1 − y Co yO 2 electrode materials

A crystal chemistry study of LiNi 1 − y Co y O 2 phases, used as positive electrode in lithium batteries, is presented. These materials crystallize in the rhombohedral system (space group: R3̄m) with a layered structure. Rietveld profile refinement of the X-ray data shows that for low substitution amounts (≤ 0.20) extra-nickel ions are always present leading to the Li 1 − z Ni 1 + z − t Co tO 2 ( t = y(1 + z)) formula ( z ∗ > 0), while for y ≥ 0.30, a pure 2D structure is obtained ( z = 0). The stabilization of the 2D character of the structure by cobalt substitution in lithium nickelate leads to the improvement of the electrochemical properties.

Neutron diffraction texture study of deformed uranium plates

The texture of two depleted uranium (DU) samples, labelled DUWR and DUWR2, were studied by neutron diffraction. DUWR was prepared by warm rolling of a cast ingot, and DUWR2 was prepared by adding 20% tensile strain to the warm-rolled DUWR. Complete three-dimensional orientation distribution functions were determined using four neutron pole figures for the DUWR, and using six neutron pole figures for the DUWR2 sample, by the WIMV method of the program popLA. The textures of the two samples were essentially identical to each other. They could be described by a twisted helical density tube spiralling continuously along the ψ-axis of the Euler space. The projection of the backbone of the density tube along the θ-axis cast a linear shadow running parallel to the diagonal of the φ-ψ plane, which could be defined by a φ=ψ+90° (and φ=ψ+270°) relation. The helical tube was confined within narrow θ-angle limits, from 14° to 30° with the peak orientation at (103) 〈0 10〉. The diffraction patterns of the DUWR2 sample were measured from the normal direction to the rolling surface of the sample, up to the scattering angle of 108° using a 0.15 nm neutron beam. The Rietveld profile refinement using the textured diffraction pattern was quite satisfactory when the texture effect to the entire diffraction profile was corrected for by the corresponding pole density from the inverse pole figure.

X-ray powder diffraction study of the stability of solid solutions in (La1−xGdx)OCl

The formation of the solid solutions in the (La1−xGdx)OCl series was studied by X-ray powder diffraction (XPD) at room temperature in the 2θ region between 6.5 and 120°. The Rietveld profile refinement analyses of the XPD patterns were carried out with the background, unit cell, atomic position, isotropic temperature, and Gaussian profile form parameters refined freely. All (La1−xGdx)OCl samples possessed the tetragonal PbFCl-type structure with P4/nmm as the space group (Z=2). The unit cell parameters a and c evolve smoothly through the series and no clustering of the Gd3+ ions was observed according to Vegard's law. The solid solubility exists throughout the whole series. The valence bond model was used to estimate the relative stabilities of the different (La1−xGdx)OCl solid solutions. The global instability index (GII) which equals to the deviation between the formal valence and the sum of the calculated valence bonds of each atom in the asymmetric unit was used as a tool in the assessment. In the (La1−xGdx)OCl series, GII increases both from the end and the beginning of the series toward the middle indicating diminishing stability. No breakdown of the La–Gd solid solution could be verified experimentally although the GII value for the (La0.4Gd0.6)OCl composition exceeds the limit of 0.2 which should mean the collapse of the structure. However, the diffraction reflections were found somewhat broader in the middle of the series indicating possible local distortion or disorder.

Neutron powder diffraction study of the scintillator material ZnWO4

With a view to the technological applications of ZnWO4 crystals, we have performed Rietveld profile refinement of medium-resolution, time-of-flight, neutron powder diffraction data of synthetic ZnWO4 to improve the quality of the current crystal structure derived from single crystal X-ray techniques that produced a final solution with an R factorof only 10%. The new structural data for ZnWO4, monoclinic space group P2/c, lattice parameters of 0.469263(5), 0.572129(7), 0.492805(5) nm for a, b and c respectively, and a β angle of 90.6321(9) ° with two formula units per unit cell. The ZnO6 octahedra contain 3 pairs of Zn-O bonds of 0.2026(2), 0.2090(2) and 0.2227(3) nm and the WO6 octahedra contain 3 pairs of W-O bonds 0.1789(2), 0.1914(2) and 0.2133(3) nm. These new data confirm the basic structure of ZnWO4 and provide accurate off-centring magnitudes for the Zn and W cations.

Structural and Defect Study of LiMn2O4 Formation

Abstract The LiMn2O4 formation from MnO and Li2CO3 mixtures with lithium cationic fraction 0.31 <̲ x <̲ 0.40 was studied by structural profile refinement from X-ray data, thermal (TGA and DSC) measurements and scanning electron microscopy (SEM) observations. Quantitative phase analysis, structural and microstructural parameters and composition of the coexisting phases were obtained. Different behaviours were observed in the composition ranges 0.33 <̲ x <̲ 0.35 and x >̲ 0.37. In the former range only the stoichiometric spinel phase was obtained, in the latter, in addition to the Li2MnO3 compound, two spinel phases could be considered: I) LiMn2O4 stoichiometric spinel; II) Li1 + yMn2-yO4 (0.11 <̲ y <̲ 0.23), a non-stoichiometric phase whose small particle size resulted practically independent of the initial composition and annealing temperature. Such a conclusion was supported also by SEM observations. The relative abundance of phase II increased with increasing lithium content and with decreasing temperature.

Analysis of the optical spectra and paramagnetic susceptibility of DyOF

The optical absorption spectra of the rhombohedral DyOF were measured at selected temperatures between 9 and 300 K. The emission spectra of the ion in the LaOF and GdOF matrices were obtained at 77 K and room temperature. The energy level scheme of ( electron configuration) was simulated with a Hamiltonian of 20 parameters. The diagonalization of the energy matrices including simultaneously the free ion and crystal field (c.f.) interactions was carried out for the point symmetry of the site. Good correlation with an rms deviation of was obtained between the experimental and calculated energy level schemes of 153 Kramers doublets. The c.f. parameters show only slight distortion from symmetry. A comparison to , , , , and electron configuration) in other REOF matrices showed smooth evolution of the c.f. effect which was discussed in terms of the possible interactions involved. The x-ray powder diffraction pattern of DyOF between was analysed by the Rietveld profile refinement method. The structural data were used to calculate the c.f. parameters by the modified electrostatic point charge model yielding , and values close to the experimental ones, whereas the , , and values were too large. Using the experimental free ion and c.f. wave functions, the paramagnetic susceptibility of DyOF as a function of temperature was simulated. Above the Néel temperature (3.6 K), good agreement was obtained between the calculated and experimental susceptibilities in the paramagnetic range.

Coordination chemistry in the solid state

Salts, e.g. LiPF 6 , may be dissolved in solid polymers, e.g. (CH 2 —CH 2 —O) n . Dissolution is driven by the complexation of the cations by the donor groups on the polymer chains. The resulting solids are coordination compounds with infinite ligands. They form a vital bridge between coordination chemistry in solution and more classical solid-state chemistry. The solid coordination compounds are often referred to as polymer electrolytes. In this paper I present a view of the coordination chemistry of these fascinating compounds which yield elegant structures as well as forming the basis of high technology devices for the 21st century. Topics covered include: the forces driving complexation; the major ligands and complexes; the structures of several model systems; and the physical properties and applications of the materials.

Studies on crystallization of electroless NiP deposits

Electroless Nickel-Phosphorus deposits with phosphorus content of 4.35, 5.45, 6.80, 8.10 and 9.12 Wt.% P were made, on mild steel substrates. The deposits were annealed at 60, 100, 200, 300, 330, 360, 400 and 600°C for 2 hours. The crystallization process of these deposits was studied using X-ray line profile analysis, differential scanning calorimetry and microhardness. The X-ray diffraction pattern of all the deposits indicated the presence of crystalline and amorphous phases coexisting in the as deposited condition. The lattice disorder in the crystalline phase increased with increasing phosphorus content. Profile refinement techniques have been used to separate the crystalline nickel (111) reflection from the amorphous profile. The separated (111) and (222) profiles of nickel were used for crystallite size and microstrain analysis. The crystallite size of nickel was found to vary from 50Å in the as deposited condition to about 600Å in the fully annealed state (400°C). The crystallite size increased sharply above 300°C, indicating the onset of precipitation. The microhardness values showed typical precipitation hardening type of behavior, increasing from an initial value of about 450 VHN in the as deposited state to the peak hardness of about 825 to 950 VHN, corresponding to a temperature range of 360 to 400°C. Differential scanning calorimetry of these deposits, indicated only one major reaction between 325 to 375°C. Ni 3P has been identified as the final stable precipitate at 600°C.

Crystal Structure Determination from Powder Diffraction Data

A wide range of important crystalline solids cannot be prepared in the form of single crystals of suitable size and quality for structural characterization by conventional single-crystal X-ray diffraction methods. The development of techniques for crystal structure determination from powder diffraction data is clearly important for allowing the structural characterization of such materials. Although the structure refinement stage of the structure determination process can now be carried out fairly routinely using the Rietveld profile refinement technique, structure solution directly from powder diffraction data is associated with several intrinsic difficulties. The article surveys the field of crystal structure determination from powder diffraction data. Particular emphasis is given to the challenging structure solution stage of the structure determination process, with illustrative case studies highlighting the features of each of the main methods that are currently used for structure solution from powde...

Characterization of the structure of TbD2.25 at 70 K by neutron powder diffraction

A neutron-powder-diffraction pattern of the superstoichiometric rare-earth dideuteride TbD2.25 was measured at 70 K. Profile refinements indicated that the TbD2.25 structure possesses I4/mmm symmetry with deuterium fully occupying the tetrahedral (t) interstices of the nominally fcc Tb lattice and the excess deuterium occupying one-fourth of the octahedral (o) interstices with long-range order. Ideal order corresponds to the occupation of only those o sites within every fourth (042)Cubic plane, in agreement with the results of a previous TbD2 + x study. Moreover, in line with recent LaD2.25 results, refinements indicated that the o-site deuterium (Do) ordering in TbD2.25 is accompanied by a slight tetragonal distortion, an outward expansion of the cubic ensemble of eight t-site deuterium atoms surrounding each Do atom, and a decrease in the c-directed TbDo bond distances by a displacement of the Tb atoms toward the Do atoms.

Quantitative Determination of Low-Phase Volume Fraction in Ferro-Silicon Alloys by the Rietveld Profile-Refinement Method. Neutron Diffraction Data Compared with Other Methods

Neutron diffraction data collected from ferrosilicon alloy powders have been analysed using the Rietveld profile-refinement method in order to perform a quantitative determination of the phase volume fraction. The results obtained have been compared with those determined from other methods such as imaging analysis, chemical analysis and phase-diagram calculation by a thermodynamic approach. For low phase volume fractions, the Rietveld profile refinement of the neutron-powder-diffractometer data gives results that are more accurate than those from imaging analysis and that are more representative at the ingot scale than those from chemical analysis, owing to the greater quantity of powder analysed. As concerns the thermodynamic calculations, two phase volume fraction determinations may be performed: quantitative, at equilibrium, and qualitative, out of equilibrium.

A quantitative measure for the goodness of fit in profile refinements with more than 20 degrees of freedom

A quality indicator Nσ is defined that exhibits immediately the significance level of the result of a least-squares refinement. For a refinement with v degrees of freedom, Nσ = (M − ν)/(2ν)1/2 expresses the deviation of the deviance M from its expected value v in terms of its standard deviation (2ν)1/2. The deviance M is the sum of weighted squared differences between observed and model data. For any ν > 20, |Nσ | should be as small as possible; however, it should be < 3 for a sufficiently good refinement. Thus, Nσ is a quantitative measure for the conformity of data, their weights and the model, independent of the number of the degrees of freedom.

Solid–solid phase transitions in n-alkanes C23H48 and C25H52: X-ray power diffraction study on new layer stacking in phase V

The solid–solid phase transitions and the crystal structures of odd n-alkanes, n-C23H48, and n-C25H52, were investigated by x-ray powder diffraction. The phase transitions, I→V→RI for n-C23H48 and I→V→IV→RI for n-C25H52, were observed, where phases I, V, IV are the low-temperature ordered phases, and the phase RI is the rotator phase. The crystal structure of phase V was determined by the Rietveld profile refinement method. Phase V is orthorhombic (Pbnm). New molecular layer stacking appears in phase V, while the lamellar structure and the lateral packing of molecules are same as those in phase I and phase IV. The solid–solid phase transitions below the rotator phase transition of odd n-alkanes found to be characterized by the changes in molecular layer stacking are considered to be caused by the increased disorder in the layer surface.

A synchrotron X-ray powder diffraction study of CoAl2O4and CoGa2O4by PSD diffractometer technique

X-ray powder diffraction data for the spinels CoAl2O4and CoGa2O4were measured with synchrotron radiation usingλ= 1.2033 Å, determined with Si as a standard (a= 5.4305 Å). The two blue compounds prepared hydrothermally are cubic with space groupFd3m. Profile refinements gave the results: CoAl2O4hada= 8.0968(1) Å and composition (Co0.71Al0.29]Al1.71Co0.29]O4and CoGa2O4hada= 8.3229(1) Å and composition Ga[CoGa]O4. The degree of inversion is thus 0.29 for CoAl2O4and one for CoGa2O4.