Jürgen Schreuer

The Samson phase, β-Mg2Al3, revisited

Co-Authors: Michael Feuerbacher, Carsten Thomas, Julien P. A. Makongo, Stefan Hoffmann, Wilder Carrillo-Cabrera, Raul Cardoso, Yuri Grin, Guido Kreiner, Jean-Marc Joubert, Thomas Schenk, Joseph Gastaldi, Henri Nguyen-Thi, Nathalie Mangelinck-Noël, Bernard Billia, Patricia Donnadieu, Aleksandra Czyrska-Filemonowicz, Anna Zielinska-Lipiec, Beata Dubiel, Thomas Weber, Philippe Schaub, Günter Krauss, Volker Gramlich, Jeppe Christensen, Sven Lidin, Daniel Fredrickson, Marek Mihalkovic, Wieslawa Sikora, Janusz Malinowski, Stefan Brühne, Thomas Proffen, Wolf Assmus, Marc de Boissieu, Francoise Bley, Jean-Luis Chemin, Jürgen Schreuer Abstract. The Al−Mg phase diagram has been reinvestigated in the vicinity of the stability range of the Samson phase, β-Mg2Al3 (cF1168). For the composition Mg 38.5 Al 61.5, this cubic phase, space group Fd-3m (no 227), a = 28.242(1) Å, V = 22526(2) Å3, undergoes at 214 °C a first-order phase transition to rhombohedral β′-Mg2Al3(hR293), a = 19.968(1) Å, c = 48.9114(8) Å, V = 16889(2) Å3, (i.e. 22519 Å3 for the equivalent cubic unit cell) space group R3m (no 160), a subgroup of index four of Fd-3m. The structure of the β-phase has been redetermined at ambient temperature as well as in situ at 400 °C. It essentially agrees with Samsons model, even in most of the many partially occupied and split positions. The structure of β′-Mg2Al3is closely related to that of the β-phase. Its atomic sites can be derived from those of the β-phase by group-theoretical considerations. The main difference between the two structures is that all atomic sites are fully occupied in case of the β′-phase. The reciprocal space, Bragg as well as diffuse scattering, has been explored as function of temperature and the β- to β′-phase transition was studied in detail. The microstructures of both phases have been analyzed by electron microscopy and X-ray topography showing them highly defective. Finally, the thermal expansion coefficients and elastic parameters have been determined. Their values are somewhere in between those of Al and Mg.

Elastic and piezoelectric properties of La/sub 3/Ga/sub 5/SiO/sub 14/ and La/sub 3/Ga/sub 5.5/Ta/sub 0.5/O/sub 14/: an application of resonant ultrasound spectroscopy

The electromechanical properties of La/sub 3/Ga/sub 5/SiO/sub 14/ (LGS) and La/sub 3/Ga/sub 5.5/Ta/sub 0.5/O/sub 14/ (LGT) have been studied at room temperature on 25 samples using resonant ultrasound spectroscopy (RUS). The RUS method facilitates simultaneous determination of all independent elastic and piezoelectric constants of a sample within the same frequency range and yields sample parameters with high internal consistency. Consequently, the spread of the experimental results presented here is significantly lower than the scatter of literature data obtained by different experimental techniques.

Discontinuous evolution of single‐crystal elastic constants as a function of pressure through the C2/c ↔ P21/c phase transition in spodumene (LiAlSi2O6)

A Landau free energy expansion in one order parameter has been developed to describe the first-order C2/c ↔ P21/c phase transition at high pressures in spodumene (LiAlSi2O6). The complete set of elastic constants required for this model was determined at ambient conditions by resonant ultrasound spectroscopy. Other coefficients in the 246 expansion were calibrated using lattice parameter data from the literature, which had been collected by following the transition in a diamond anvil cell. The complete calibration leads to predictions of significant, abrupt changes in elastic constants at the transition point, 3.19 GPa, which have then been tested against ultrasonic data obtained in situ at high pressures in a uniaxial split cylinder apparatus. Velocities of compressional waves in three mutually perpendicular directions through single crystals of spodumene were measured and used to extract elastic constant data. The transition, indeed, causes large, abrupt changes of single-crystal elastic constants with increasing pressure. Steep increases in attenuation were also observed in the vicinity of the transition point for two directions and over a broader pressure interval in the third direction. The Landau expansion reproduces the general form of the elastic anomalies, even though it does not do as well for spontaneous strain variations. If this type of transition occurred in mantle pyroxenes (or in any other mantle phase), it would be expected to leave a distinctive signature in seismic velocity profiles of the Earths interior.

Thermal expansion and elastic properties of mullite-type Bi2Ga4O9 and Bi2Fe4O9 single crystals

Abstract Resonant ultrasound spectroscopy was used to characterize the elastic properties of single crystal orthorhombic Bi2Ga4O9 and Bi2Fe4O9 between room temperature and about 1200 K. Additionally, the coefficients of thermal expansion were studied in the range 100 K to 1280 K using high-resolution dilatometry and X-ray powder diffraction. The elastic constants at 295 K are in GPa c11 = 143.4(1), c22 = 161.9(1), c33 = 224.5(1), c44 = 68.4(1), c55 = 49.3(1), c66 = 76.6(1), c12 = 74.2(1), c13 = 62.2(1), c23 = 70.5(1) for Bi2Ga4O9, and c11 = 106.7(1), c22 = 141.2(1), c33 = 183.7(2), c44 = 53.7(1), c55 = 41.9(1), c66 = 63.8(1), c12 = 63.5(1), c13 = 59.8(1), c23 = 63.4(2) for Bi2Fe4O9. In both mullite-type compounds the strong bond chains built up by edge-sharing coordination octahedra extending parallel to [001] dominate the anisotropy of their elastic and thermoelastic properties. Smaller variations of elastic anisotropy within the (001) plane can be attributed to the specific type of cross-linking of the octahedral chains. The temperature evolution of the cij shows no hint on any structural instability or glass-like transition that might be related to the suspected ion conductivity at high temperatures. However, in both crystal species characteristic anelastic relaxation phenomena occur in the ultrasonic frequency regime close to room temperature. The smallest thermal expansion is observed in the plane perpendicular to the stiffest octahedral chains. A model is discussed to explain the apparent discrepancy in terms of cross-correlations within the three-dimensional framework of edge- and corner-linked coordination polyhedra.

Incommensurate modulation of calcium barium niobate (CBN28 and Ce:CBN28)

The incommensurately modulated crystal structures of Ca(0.28)Ba(0.72)Nb(2)O(6) (CBN28) and Ce(0.02)Ca(0.25)Ba(0.72)Nb(2)O(6) (Ce:CBN28) were refined in the supercentred setting X4bm(AA0,-AA0) of the 3 + 2-dimensional superspace group P4bm(aa½,-aa½). Both compounds are isostructural with a tetragonal tungsten bronze-type structure. The modulation of CBN28 consists of a wavy distribution of Ba and Ca atoms as well as vacancies on the incompletely occupied Me2 site with 15-fold oxygen coordination. The occupational modulation is coupled with a modulation of the atomic displacement parameters and a very weak modulation of the positional parameters of Me2. The surrounding O atoms show strong displacive modulations with amplitudes up to ca 0.2 Å owing to the cooperative tilting of the rigid NbO(6) octahedra. The Me1 site with 12-fold coordination and Nb atoms are hardly affected by the modulations. Only first-order satellites were observed and the modulations are described by first-order harmonics. In Ce:CBN28 cerium appears to be located on both the Me2 and Me1 sites. Wavevectors and structural modulations are only weakly modified upon substitutional incorporation of 0.02 cerium per formula unit of calcium.

Relaxor behavior of ferroelectric Ca0.22Sr0.12Ba0.66Nb2O6

The relaxor behavior of tetragonal tungsten bronze uniaxial relaxor ferroelectric calcium strontium barium niobate (Ca0.22Sr0.12Ba0.66Nb2O6 or CSBN-22) single crystal was studied by measuring elastic constants and thermal expansion with the aid of resonant ultrasound spectroscopy and dilatometry, respectively, in the temperature range 300 K–1503 K. Thermal expansion yields evidence of the Burns temperature TB and the intermediate characteristic temperature T*, which was also supported by the temperature evolutions of the elastic constants cij. CSBN-22 was found to be ∼2%–3% elastically stiffer than CBN-28. The presented results open the perspective to understand the relaxor behavior of CSBN.

Elastic and piezoelectric constants of tourmaline single crystals at non-ambient temperatures determined by resonant ultrasound spectroscopy

The full sets of elastic constants (considering piezoelectric effect, i.e., taking into account piezoelectric coupling effects) and piezoelectric stress constants of five natural tourmaline single crystals of different chemical composition have been determined from room temperature up to ∼900 K employing resonant ultrasound spectroscopy. Further, the coefficients of thermal expansion were studied in a wide temperature range from 100 K to 950 K. Electron microprobe analysis showed that the chemical composition of investigated samples varied over a wide range, which allows to study the compositional dependence of thermal, elastic, and piezoelectric properties of tourmalines. At room temperature, the piezoelectric constants of tourmalines were found at-least 1.5 times higher than that for α-quartz. Importantly, we find that the application of tourmaline at temperatures up to its decomposition temperature is not limited by phase transitionsor any ultrasound dissipation effects.

High temperature elastic properties of Mg-cordierite: experimental studies and atomistic simulations

Abstract The temperature dependence of the elastic stiffness coefficients of natural orthorhombic Mg-cordierite was studied between 295 K and 1573 K using resonant ultrasound spectroscopy. The measurements revealed a continuous decrease of all the elastic constants with increasing temperature. The bulk modulus softens from about 129(2) GPa at 295 K to 110(2) GPa at 1473 K. Irreversible anomalies in the temperature evolution of the resonance frequencies of certain eigenmodes were observed above 920 K due to the escape of volatiles and the occurrence of microcracks. However, the dehydrated samples still showed integrity on the macroscopic scale. Therefore, despite the occurence of the micro-cracks, a reasonable quantitative analysis of the high-temperature RUS data of cordierite samples was still feasible. The thermal expansion was studied between 100 K and 1570 K using dilatometry. The new data are consistent with earlier experimental results and confirm the expansion of the a and b unit cell parameters and the contraction of the c parameter with increasing temperature. Posäsible contributions of the Al/Si disorder to the elastic properties of Mg-cordierite were estimated on the basis of force-field and quantum mechanical calculations. The behaviour of individual elastic stiffness coefficients was followed across the order/disorder transition by Monte Carlo simulations. The simulations predicted a decrease in the bulk modulus with increasing Al/Si disorder. However, this effect is much smaller than that observed experimentally. The measured decrease in the elastic stiffness coefficients is mainly due to phonon softening effects.

Anomalous elastic behavior of relaxor ferroelectric Ca0.28Ba0.72Nb2O6:Ce studied by resonant ultrasound spectroscopy

Elastic behavior of tetragonal tungsten bronze uniaxial relaxor ferroelectric cerium doped Ca0.28Ba0.72Nb2O6 single crystal was investigated employing resonant ultrasound spectroscopy in the temperature range from room temperature up to 1323 K. Doping of cerium lowers the phase transition temperature Tc and Burns temperature Tb significantly, however, intermediate characteristic temperature T* (between the Burns temperature Tb and the temperature of maximum dielectric permittivity Tm) remains same as for pure Ca0.28Ba0.72Nb2O6. All independent elastic constants evolved differently with temperature, reflecting their coupling to different types of the reorientational motion of the polar nanoregions through their interaction with the acoustic waves.

Correlation between dielectric properties and chemical composition of the tourmaline single crystals

Dielectric responses were studied on piezoelectric tourmaline single crystals of widely varying chemical composition from different geological origins. The dielectric constants at constants stress, and dissipation factor were measured as a function of frequency (100-1000 kHz) using method of substitution. A correlation between two independent dielectric constants (along and perpendicular to crystallographic c-axis) is observed, and dependence of dielectric constants on chemical composition is presented.