Karsten Knorr

Pressure-induced structural phase transition in the IV–VI semiconductor SnS

The structural behaviour of SnS under high-pressure has been investigated by angular dispersive synchrotron powder diffraction up to 38.5 GPa. A structural phase transition from orthorhombic α-SnS to monoclinic γ-SnS was observed at 18.15 GPa. The fit of a Birch–Murnaghan equation-of-state gave the volume at zero pressure of V0 = 192.6(3) A3, the bulk modulus at zero pressure of B0 = 36.6(9) GPa and the pressure derivative of the bulk modulus for α-SnS and V0 = 160(1) A, B0 = 86.0(5) GPa and for γ-SnS. The improper ferro-elastic transition is of first-order and is accompanied by a large volume discontinuity of about 9.1%. The phase transition can be described in terms of a group/subgroup relationship. The doubling of the unit cell indicates a wavevector (1/2,0,1/2) at the U-point in the Brillouin zone.

Neutron imaging and neutron tomography as non-destructive tools to study bulk-rock samples

Neutron imaging and neutron tomography can be used as non-destructive tools for the analysis of bulk-rock samples. Here, we establish the spatial resolution currently available, and discuss applications such as phase analysis and the observation of dynamic processes.

The high-pressure α/β phase transition in lead sulphide (PbS) - X-ray powder diffraction and quantum mechanical calculations

The high-pressure behaviour of PbS was investigated by angular dispersive X-ray powder diffraction up to pressures of 6.8 GPa. Experiments were accompanied by first principles calculations at the density functional theory level. By combining both methods reliable data for the elastic properties of rock-salt type alpha- and high-pressure beta-PbS could be obtained. beta-PbS could be determined to crystallise in the CrB-type (B33), with space group Cmcm. The reversible ferro-elastic alpha/beta transition is of first order. It is accompanied by a large volume discontinuity of about 5% and a coexistence region of the two phases. A gliding mechanism of {001} bilayers along one of the cubic -directions governs the phase transition which can be described in terms of group/subgroup relationships via a common subgroup, despite its reconstructive character. The quadrupling of the primitive unit cell indicates a wave vector (0,0,pi/a) on the Delta-line of the Brillouin zone.

Prediction of the structure of LaF3 at high pressures

Abstract The structure of a high pressure polymorph of LaF 3 , which is stable at pressures above 20 GPa, has been predicted by quantum mechanical calculations. While the transition pressure is in very good agreement with an experimentally observed transition pressure, the lattice constants and space group symmetry of the current calculations are in disagreement with the interpretation of the experimental data. Also, the computed compressibility differs significantly from the experimental values obtained from the compression experiments and is in much better agreement with a bulk modulus derived from elastic constant measurements. As the model used here is known to be very reliable, a reevaluation of the high pressure data seems to be warranted.

Estimating intensity errors of powder diffraction data from area detectors

Abstract It is shown how error estimates for intensities derived from area detector data in powder diffraction experiments should be calculated. It is demonstrated that the uncritical application of standard weighting schemes to the derived one dimensional data in subsequent least-squares refinements results in meaningless goodness of fit values less than unity that prohibit the evaluation of the quality of the fit. Moreover, it is shown that the calculated estimated standard deviations of the fitted parameters can only be calculated correctly when the true uncertainties of the measured intensities are known.

Coupled Al/Si and O/N order/disorder in BaYb[Si4- xAlxOxN7- x] sialon : neutron powder diffraction and Monte Carlo simulations

The fractions of aluminium, [Al]/[Al + Si], and oxygen, [O]/[O + N], in crystallographically distinct sites of BaYb[Si4–xAlxOxN7–x] oxonitridoaluminosilicate (space group P63mc, No. 186) were refined based on the results of neutron powder diffraction for a synthetic sample with the composition of x = 2.2(2) and simulated as functions of temperature for the compositions x = 2 and x = 2.3 using a combination of static lattice energy calculations (SLEC) and Monte Carlo simulations. The SLEC calcu lations have been performed on a set of 800 structures differing in the distribution of Al/Si and O/N within the 2 × 2 × 2 supercell containing 36 formula units of BaYb[Si4–xAlxOxN7–x]. The SLEC were based on a transferable set of empirical interatomic potentials developed within the present study. The static lattice energies of these structures have been expanded in the basis set of pair-wise ordering energies and on-site chemical potentials. The ordering energies and the chemical potentials have been used to calculate the configuration energies of the oxonitridoaluminosilicates (so-called sialons) using a Monte Carlo algorithm. The simulations suggest that Al and O are distributed unevenly over two non-equivalent T(Si/Al) and three L(N/O) sites, respectively, and the distribution shows strong dependence both on the temperature and the composition. Both simulated samples exhibit order/disorder transitions in the temperature range 500–1000 K to phases with partial long-range order below these temperatures. Above the transition temperatures the Si/Al and N/O distributions are affected by short-range ordering. The predicted site occupancies are in a qualitative agreement with the neutron diffraction results.

High-pressure phase transition of the oxonitridosilicate chloride Ce4[Si4O3+xN7-x]Cl1-xOx with x = 0.12 and 0.18

Abstract The high-pressure behaviour of the oxonitridosilicate chlorides Ce4[Si4O3+xN7–x]Cl1–xOx, x = 0.12 and 0.18, is investigated by in situ powder synchrotron X-ray diffraction. Pressures up to 28 GPa are generated using the diamond-anvil cell technique. A reversible phase transition of first order occurs at pressures between 8 and 10 GPa. Within this pressure range the high- and the low-pressure phases are observed concomitantly. At the phase transition the unit cell volume is reduced by about 5%, and the cubic symmetry (space group P213) is reduced to orthorhombic (space group P212121) following a translationengleiche group-subgroup relationship of index 3. A fit of a third-order Birch-Murnaghan equation of state to the p–V data results in a bulk modulus B0 = 124(5) GPa with its pressure derivative B′ = 5(1) at V0 = 1134.3(4) Å3 for the low-pressure phase and in B0 = 153(10) GPa with B′ = 3.0(6) at V0 = 1071(3) Å3 for the high-pressure phase. The orthorhombic phase shows an anisotropic axial compression with the a axis (which is the shortest axis) being more compressible (k(a) = 0.0143(4) 1/GPa) than the b and c axes (k(b) = 0.0045(2), k(c) = 0.0058(2) 1/GPa). The experimental results confirm an earlier prediction of the pressure-induced instability of isotypic Ce4[Si4O4N6]O, and also show that the bulk modulus was predicted reasonably well.

Structural variations in the solid solution series of sodalite-type |(EuxCa2-x)4(OH)8|[(Al2+xSi1-x)4O24]-SOD with 0 <x < 1, determined by X-ray powder diffraction and 27Al MAS NMR spectroscopy

Abstract The mineral bicchulite, |Ca8(OH)8|[Al8Si4O24]-SOD, has sodalite-(SOD)-type structure. It is one of the few minerals contradicting Loewenstein’s rule, as it contains twice as much Al as Si at the topologically unique tetrahedrally coordinated position, with both species being randomly distributed. The solid solution series |(EuxCa2–x)4(OH)8|[(Al2+xSi1–x)4O24]-SOD with 0 ≤ x ≤ 1 and Δx = 0.125, was synthesized in order to clarify, whether the continuous violation of Loewensteins rule is possible in an aluminosilicate framework structure like SOD, or whether the reported examples of SOD-type compounds with an Al : Si-stoichiometry of 2 : 1 represent a preferred composition on the tetrahedrally coordinated site of the structure. Here, we report on the variation of the lattice parameter and of some structural parameters in the series, determined by X-ray powder diffraction and results of 27Al MAS NMR spectroscopy. We found Loewensteins rule to be systematically and continuously violated in this series. The observed structural variations mainly reflect stronger electrostatic interactions between the cage cations and the sodalite framework with increasing (Al + Eu)-content. While the evaluation of the X-ray diffraction data indicate a global adaptation of the sodalite framework to the cage guest size, the significant line-broadening of the NMR spectra with increasing (Al + Eu)-content points towards local adaptations of the framework to the shape of the cage guests.

The transformation mechanism of the sodalite- to the melilite-topology : Thermal expansion and decomposition of bicchulite-type to melilite-type compounds

Abstract The mineral bicchulite, |Ca8(OH)8|[Al8Si4O24]-SOD, has the sodalite-(SOD-)type structure. At elevated temperatures it decomposes into gehlenite, Ca2Al2SiO7 (melilite-type structure), and water (vapour). We report on the thermal expansion of two bicchulite-type compounds, the mineral bicchulite up to T = 740 K and |Ca6Eu2(OH)8|[Al10Si2O24]-SOD up to T = 1025 K. The expansion mechanism is described. Insitu X-ray powder diffraction experiments were performed to evaluate the thermal decomposition of |Ca6Eu2(OH)8|[Al10Si2O24]-SOD into 4 (Ca1.5Eu0.5)T1[T22O7] and 4 H2O, with Ti = Al or Si in a ratio of 5 : 1. A structural mechanism for the transformation from the sodalite to the melilite topology is proposed, based on geometrical considerations.

Crystal chemistry of molybdenum phosphides from density functional theory calculations

Abstract The structures, bonding and relative thermodynamic stabilities of the crystalline molybdenum phosphides Mo 3 P, Mo 8 P 5 , Mo 4 P 3 , MoP, MoP 2 , MoP 4 , have been investigated by density functional theory calculations. The elastic stiffness coefficients for MoP and MoP 2 have been predicted.