Prof. Dr. Jürgen Schreuer

Institute of Geology, Mineralogy and Geophysics
Ruhr-Universität Bochum

Author IDs

  • Effects of Cr/Ni ratio on physical properties of Cr-Mn-Fe-Co-Ni high-entropy alloys
    Wagner, C. and Ferrari, A. and Schreuer, J. and Couzinié, J.-P. and Ikeda, Y. and Körmann, F. and Eggeler, G. and George, E.P. and Laplanche, G.
    Acta Materialia 227 (2022)
    Physical properties of ten single-phase FCC CrxMn20Fe20Co20Ni40-x high-entropy alloys (HEAs) were investigated for 0 ≤ x ≤ 26 at%. The lattice parameters of these alloys were nearly independent of composition while solidus temperatures increased linearly by ∼30 K as x increased from 0 to 26 at.%. For x ≥ 10 at.%, the alloys are not ferromagnetic between 100 and 673 K and the temperature dependencies of their coefficients of thermal expansion and elastic moduli are independent of composition. Magnetic transitions and associated magnetostriction were detected below ∼200 K and ∼440 K in Cr5Mn20Fe20Co20Ni35 and Mn20Fe20Co20Ni40, respectively. These composition and temperature dependencies could be qualitatively reproduced by ab initio simulations that took into account a ferrimagnetic ↔ paramagnetic transition. Transmission electron microscopy revealed that plastic deformation occurs initially by the glide of perfect dislocations dissociated into Shockley partials on {111} planes. From their separations, the stacking fault energy (SFE) was determined, which decreases linearly from 69 to 23 mJ·m−2 as x increases from 14 to 26 at.%. Ab initio simulations were performed to calculate stable and unstable SFEs and estimate the partial separation distances using the Peierls-Nabarro model. While the compositional trends were reasonably well reproduced, the calculated intrinsic SFEs were systematically lower than the experimental ones. Our ab initio simulations show that, individually, atomic relaxations, finite temperatures, and magnetism strongly increase the intrinsic SFE. If these factors can be simultaneously included in future computations, calculated SFEs will likely better match experimentally determined SFEs. © 2022
    view abstract10.1016/j.actamat.2022.117693
  • Influence of non-convergent cation ordering on thermal expansion of rare-earth oxoborates RCa4O(BO3)3 (R = Er, Y, Dy, Gd, Sm, Nd, La)
    Münchhalfen, M. and Schreuer, J. and Reuther, C. and Stöcker, H.
    Materialia 26 (2022)
    The tensors of thermal expansion of monoclinic RCa4O(BO3)3 with R = Er, Y, Dy, Gd, Sm, Nd, La were studied in the temperature range from 100 K to 1373 K using high-resolution dilatometry. Reproducible anomalies, characterized by an excess strain at high temperatures, occur at different temperatures depending on the type of the R3+ cation. Additional single-crystal diffraction experiments on quenched samples and heat capacity measurements indicate that non-convergent cation ordering processes involving Ca2+ and R3+ play an essential role here. The cation distribution on the specific structural sites and the evolution of disorder with temperature are mainly influenced by the size of the trivalent cation, with the minimization of internal stresses being the driving force. The onset temperatures and the specific anisotropy of the anomalies in the thermal expansion are directly related to these processes. © 2022 The Authors
    view abstract10.1016/j.mtla.2022.101561
  • Revisiting the Growth of Large (Mg,Zr):SrGa12O19Single Crystals: Core Formation and Its Impact on Structural Homogeneity Revealed by Correlative X-ray Imaging
    Guguschev, C. and Richter, C. and Brützam, M. and Dadzis, K. and Hirschle, C. and Gesing, T.M. and Schulze, M. and Kwasniewski, A. and Schreuer, J. and Schlom, D.G.
    Crystal Growth and Design 22 (2022)
    We demonstrate the growth of large (Mg,Zr):SrGa12O19(SGMZ) single crystals and use a combination of X-ray imaging techniques to analyze their structural and chemical homogeneity. Single-crystal cylinders with lengths and diameters up to about 2.5 cm are achieved. Our characterization of polished sections reveals a localized (0001) facet that is typically formed at the center of the growth interface. Such facets are seen as the key factor limiting the growth of large-area crystals with excellent structural quality due to local deviations in the segregation behavior of the dopants. We developed a lab-based X-ray diffraction imaging technique with high sensitivity that exposes subtle variations in lattice parameters and lattice tilts, which are attributed to changes in the chemical composition and the resulting elastic deformation. The relationship between unit-cell dimensions and composition is verified by micro X-ray fluorescence mapping. In this way, we find a Ga-rich center region with a reduced unit-cell volume that is surrounded by a ring of increased tilt and elastic strain. Furthermore, we observe a 6-fold in-plane anisotropy of dopant incorporation and tree-ring-shaped structures caused by macrosteps. With rocking curve widths below 23 arcsec in ∼90% of the crystal, SGMZ crystals are largely homogeneous and hence suitable for the preparation of high-quality substrates. For most applications, the substantially enhanced crystal size enabled by very high Mg and Zr codoping levels outweighs the issues related to concentration variations arising from their addition. © 2022 American Chemical Society. All rights reserved.
    view abstract10.1021/acs.cgd.2c00030
  • A High-Pressure High-Temperature Column for the Simulation of Hydrothermal Water Circulation at Laboratory Scale
    Frank, S. and Zuber, P. and Pollak, S. and Heinze, T. and Schreuer, J. and Wohnlich, S.
    Geotechnical Testing Journal 44 (2021)
    Modeling the geothermal energy production cycle of a deep geothermal system at laboratory scale is challenging because of high-temperature and pressure conditions. In this work, a high-pressure high-temperature column to simulate production, heat transfer, and reinjection of a geothermal fluid in a fractured rock system is presented. The column includes two independently heated pressure vessels, a heat exchanger, and sensors for temperatures, pressures, flow rate, electric conductivity, and pH value of the circulating fluid at different locations. The presented column enables the quantitative analysis of coupled hydro-thermo-chemical processes in fractured rock cores close to in situ geothermal conditions. Heat extraction and reinjection of geothermal fluids into fractured reservoirs can be reproduced because of the possibility of heating and cooling of the circulating fluid. Further, it is possible to inject a second fluid phase into the column to investigate additional processes, such as mineral precipitation during reinjection. In this work, we present the experimental setup of the column and first results showing the capability of the system. © 2021 ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959.
    view abstract10.1520/GTJ20200020
  • Characterisation of an artesian groundwater system in the Valle de Iglesia in the Central Andes of Argentina
    Hinzer, I. and Altherr, M. and Christiansen, R. and Schreuer, J. and Wohnlich, S.
    International Journal of Earth Sciences (2021)
    Despite its location in the “Arid Diagonal” of South America, the Valle de Iglesia contains a number of artesian springs, the most important of which are the Baños Pismanta thermal springs, which release water at ~ 45 °C. Despite the scarcity of water resources in the Valle de Iglesia, there have been few attempts to study these springs in any detail. In this study, > 50 springs are described, each characterised by small volcano-like mud structures up to 15 m tall. Hydrogeological and hydrochemical analyses of the groundwater system in the Valle de Iglesia were performed to improve our understanding of the subsurface water flow and of the connections between the subsurface water and the associated systems of faults and springs. Site measurements were made, and the concentrations of the main ions and trace elements were also determined by laboratory analysis of water samples. The samples obtained from the spring were rich in Na–HCO3–SO4 and Na–SO4–HCO3, but the surface water samples from the Agua Negra River were rich in Ca–SO4–HCO3. The temperature of the springs was in the range 20–45 °C. Both the temperatures and the ionic ratios are compatible with the presence of a deep hydraulic circulation system. The oxidation of sulphide minerals nearby the magmatic rocks and volcanic edifices causes the mobilisation of arsenic, which accumulates in the groundwater due to the low annual rainfall. The concentrations of arsenic in the spring water samples were therefore higher than the current limit set by the World Health Organisation, meaning that the water is not suitable for human consumption. © 2021, The Author(s).
    view abstract10.1007/s00531-021-02058-0
  • Design of a Co–Al–W–Ta Alloy Series with Varying γ′ Volume Fraction and Their Thermophysical Properties
    Volz, N. and Xue, F. and Bezold, A. and Zenk, C.H. and Fries, S.G. and Schreuer, J. and Neumeier, S. and Göken, M.
    Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science 52 (2021)
    The γ′ volume fraction is a key parameter in precipitation-strengthened Co- and Ni-base superalloys and mainly determines the alloys’ properties. However, systematic studies with varying γ′ volume fractions are rare and the influence on thermal expansion has not been studied in detail. Therefore, a series of six Ta-containing Co-based alloys was designed with compositions on a γ–γ′ tie-line, where the γ′ volume fraction changes systematically. During solidification, Laves (C14-type) and µ (D85-type) phases formed in alloys with high levels of W and Ta. Single-phase γ or two-phase γ/γ′ microstructures were obtained in four experimental alloys after heat treatment as designed, whereas secondary precipitates, such as χ (D019-type), Laves, and μ, existed in alloys containing high levels of γ′-forming elements. However, long-term heat treatments for 1000 hours revealed the formation of the χ phase also in the former χ-free alloys. The investigation of the thermal expansion behavior revealed a significant anomaly related to the dissolution of γ′, which can be used to determine the γ′ solvus temperature with high accuracy. Compared to thermodynamic calculations, differential scanning calorimetry (DSC) and thermal expansion analysis revealed a larger increase of the γ′ solvus temperatures and a lesser decline of the solidus temperatures when the alloy composition approached the composition of the pure γ′ phase. © 2021, The Author(s).
    view abstract10.1007/s11661-021-06353-y
  • Elastic, piezoelectric, and dielectric properties of rare-earth calcium oxoborates RCa4O(BO3)3(R = Er, Y, Dy, Gd, Sm, Nd, La)
    Münchhalfen, M. and Schreuer, J. and Reuther, C. and Mehner, E. and Stöcker, H.
    Journal of Applied Physics 130 (2021)
    Large single crystals of rare-earth calcium oxoborates RCa4O (BO3)3 with R = Er, Y, Dy, Gd, Sm, Nd, La (RCOB) were grown by the Czochralski method. Complete sets of dielectric, piezoelectric stress, and elastic stiffness coefficients of the R C O B crystal species were determined at ambient conditions using a combination of resonant ultrasound spectroscopy and the substitution method. The results are inherently consistent and reveal clear crystal chemical trends, with the size of the trivalent cation playing an important role. In particular, the longitudinal and shear aggregate elastic stiffnesses, c11iso and c44iso, decrease from about 165 to 154 GPa and, respectively, 45 to 41 GPa from the smallest to the largest R3+ cation of the investigated crystal species, while the dielectric coefficients ∈22 and ∈22 increase. However, the maximum longitudinal piezoelectric effect peaks with 8.6 pCN-1 at NdCOB, the species where the radius of R3+ best matches the one of Ca2+. Increasing differences in the size of R3+ and Ca2+ lead to anisotropic stresses in the crystal lattice, which are partially relaxed by an increasing degree of cation disorder. © 2021 Author(s).
    view abstract10.1063/5.0061747
  • On the relation of structural disorder and thermoelastic properties in ZnGa2O4 and Zn1−xMgxGa2O4 (x ≈ 0.33)
    Hirschle, C. and Schreuer, J. and Galazka, Z. and Ritter, C.
    Journal of Alloys and Compounds 886 (2021)
    The cation distribution at room temperature, as well as elastic properties and thermal expansion of single crystal ZnGa2O4 (ZGO) and Zn1−xMgxGa2O4 (x ≈ 0.33; ZMGO) with spinel-type structure were studied in a wide temperature range using single crystal X-ray diffraction, neutron powder diffraction, inductive gauge dilatometry and resonant ultrasound spectroscopy. ZGO adopts an almost normal spinel structure, whereas ZMGO is significantly disordered. At room temperature, the elastic properties of ZMGO mostly fall between those of ZGO and MgGa2O4 (MGO). The temperature dependences of the thermoelastic properties of ZGO and ZMGO, as well as thermal expansion of ZGO reveal distinct signatures of glass-like transitions, which separate states in which the cation dynamics are fast enough to relax the cation order in response to temperature change in laboratory timescales from those in which they are not. In equilibrium, thermal expansion is increased in ZMGO, whereas the thermoelastic coefficients are decreased in both ZGO and ZMGO. The temperature range of the transition is significantly larger in ZGO compared to ZMGO and MGO. Trends within the elastic properties, thermoelastic properties, thermal expansion and the glass-like transition in the (Zn,Mg)Ga2O4 solid solution series are discussed based on the impact of inversion, structural disorder, bond character and in comparison to other spinels. © 2021 Elsevier B.V.
    view abstract10.1016/j.jallcom.2021.161214
  • Thermoelastic properties and γ’-solvus temperatures of single-crystal Ni-base superalloys
    Horst, O.M. and Schmitz, D. and Schreuer, J. and Git, P. and Wang, H. and Körner, C. and Eggeler, G.
    Journal of Materials Science 56 (2021)
    Abstract: The present work shows that thermal expansion experiments can be used to measure the γʼ-solvus temperatures of four Ni-base single-crystal superalloys (SX), one with Re and three Re-free variants. In the case of CMSX-4, experimental results are in good agreement with numerical thermodynamic results obtained using ThermoCalc. For three experimental Re-free alloys, the experimental and calculated results are close. Transmission electron microscopy shows that the chemical compositions of the γ- and the γʼ-phases can be reasonably well predicted. We also use resonant ultrasound spectroscopy (RUS) to show how elastic coefficients depend on chemical composition and temperature. The results are discussed in the light of previous results reported in the literature. Areas in need of further work are highlighted. Graphical abstract: [Figure not available: see fulltext.] © 2021, The Author(s).
    view abstract10.1007/s10853-020-05628-w
  • Elastic properties of single crystal Bi12SiO20 as a function of pressure and temperature and acoustic attenuation effects in Bi12 MO20 (M = Si, Ge and Ti)
    Haussühl, E. and Reichmann, H.J. and Schreuer, J. and Friedrich, A. and Hirschle, C. and Bayarjargal, L. and Winkler, B. and Alencar, I. and Wiehl, L. and Ganschow, S.
    Materials Research Express 7 (2020)
    A comprehensive study of sillenite Bi12SiO20 single-crystal properties, including elastic stiffness and piezoelectric coefficients, dielectric permittivity, thermal expansion and molar heat capacity, is presented. Brillouin-interferometry measurements (up to 27 GPa), which were performed at high pressures for the first time, and ab initio calculations based on density functional theory (up to 50 GPa) show the stability of the sillenite structure in the investigated pressure range, in agreement with previous studies. Elastic stiffness coefficients c 11 and c 12 are found to increase continuously with pressure while c 44 increases slightly for lower pressures and remains nearly constant above 15 GPa. Heat-capacity measurements were performed with a quasi-adiabatic calorimeter employing the relaxation method between 2 K and 395 K. No phase transition could be observed in this temperature interval. Standard molar entropy, enthalpy change and Debye temperature are extracted from the data. The results are found to be roughly half of the previous values reported in the literature. The discrepancy is attributed to the overestimation of the Debye temperature which was extracted from high-temperature data. Additionally, Debye temperatures obtained from mean sound velocities derived by Voigt-Reuss averaging are in agreement with our heat-capacity results. Finally, a complete set of electromechanical coefficients was deduced from the application of resonant ultrasound spectroscopy between 103 K and 733 K. No discontinuities in the temperature dependence of the coefficients are observed. High-temperature (up to 1100 K) resonant ultrasound spectra recorded for Bi12 MO20 crystals revealed strong and reversible acoustic dissipation effects at 870 K, 960 K and 550 K for M = Si, Ge and Ti, respectively. Resonances with small contributions from the elastic shear stiffness c 44 and the piezoelectric stress coefficient e 123 are almost unaffected by this dissipation. © 2020 The Author(s). Published by IOP Publishing Ltd.
    view abstract10.1088/2053-1591/ab6ad6
  • Processing of a single-crystalline CrCoNi medium-entropy alloy and evolution of its thermal expansion and elastic stiffness coefficients with temperature
    Laplanche, G. and Schneider, M. and Scholz, F. and Frenzel, J. and Eggeler, G. and Schreuer, J.
    Scripta Materialia 177 (2020)
    The equiatomic CrCoNi alloy is regarded as a model single-phase face-centered cubic medium-entropy alloy. A CrCoNi single crystal was grown by a Bridgman technique using a Ni-base superalloy seed. The elastic stiffnesses and thermal expansion coefficient were determined between 100 K and 673 K employing resonant ultrasound spectroscopy and dilatometry, respectively. All data were found to be in excellent agreement with those reported for polycrystalline CrCoNi. A comparison of the normalized Cauchy pressure of CrCoNi with those of other alloys indicates that interatomic bonds become more directional with increasing Cr-concentration while Co and Ni promote a metallic character. © 2019 Acta Materialia Inc.
    view abstract10.1016/j.scriptamat.2019.09.020
  • Thermoelastic anisotropy in NdScO3 and NdGaO3 perovskites
    Hirschle, C. and Schreuer, J. and Ganschow, S. and Peters, L.
    Materials Chemistry and Physics 254 (2020)
    Single crystal thermal expansion and elastic stiffness of NdGaO3 and NdScO3 were investigated by inductive gauge dilatometry and resonant ultrasound spectroscopy between 103K and 1673K, as they are used extensively as perovskite-type substrates for epitaxial crystal growth. Thermal expansion of NdGaO3 is in agreement with literature data and has very similar magnitude and anisotropy compared to NdScO3. The anisotropy of the elastic stiffness of NdGaO3 is more pronounced and qualitatively different from what is found for NdScO3. It is explained in terms of structural instabilities, which lead to known phase transitions in other perovskites. The anisotropy of the elastic stiffness of NdGaO3 is compatible with what is found for other orthorhombic perovskites that undergo a transition to a rhombohedral structure at high temperatures. The elastic properties of NdScO3 directly follow from the properties of other REScO3. The samples were characterized with regards to their compositions and lattice parameters using electron probe microanalysis and X-ray powder diffraction. © 2020 Elsevier B.V.
    view abstract10.1016/j.matchemphys.2020.123528
  • Ni-base superalloy single crystal (SX) mosaicity characterized by the Rotation Vector Base Line Electron Back Scatter Diffraction (RVB-EBSD) method
    Thome, P. and Medghalchi, S. and Frenzel, J. and Schreuer, J. and Eggeler, G.
    Ultramicroscopy 206 (2019)
    In the present work we present the Rotation Vector Base Line Electron Back Scatter Diffraction (RVB-EBSD) method, a new correlative orientation imaging method for scanning electron microscopy (OIM/SEM). The RVB-EBSD method was developed to study crystal mosaicity in as-cast Ni-base superalloy single crystals (SX). The technique allows to quantify small crystallographic deviation angles between individual dendrites and to interpret associated accommodation processes in terms of geometrically necessary dislocations (GNDs). The RVB-EBSD method was inspired by previous seminal approaches which use cross correlation EBSD procedures. It applies Gaussian band pass filtering to improve the quality of more than 500 000 experimental patterns. A rotation vector approximation and a correction procedure, which relies on a base line function, are used. The method moreover features a novel way of intuitive color coding which allows to easily appreciate essential features of crystal mosaicity. The present work describes the key elements of the method and shows examples which demonstrate its potential. © 2019 Elsevier B.V.
    view abstract10.1016/j.ultramic.2019.112817
  • Order/disorder processes and electromechanical properties of monoclinic GdCa4O(BO3)3
    Münchhalfen, M. and Schreuer, J. and Reuther, C. and Möckel, R. and Götze, J. and Mehner, E. and Stöcker, H. and Meyer, D.
    Zeitschrift fur Kristallographie - Crystalline Materials (2019)
    Large single crystals of GdCa4O(BO3)3 (space group Cm) were grown by the Czochralski method. Dielectric, piezoelectric and elastic coefficients at room temperature as well as specific heat capacity, thermal expansion and cation disorder were studied employing a variety of methods including resonant ultrasound spectroscopy, differential scanning calorimetry, dilatometry and X-ray diffraction techniques. The electromechanical parameters (4 dielectric, 10 piezoelectric and 13 elastic stiffness coefficients) obtained on different samples are in excellent agreement indicating high internal consistency of our approach, whereas the values reported in literature differ significantly. The elastic behaviour of GdCa4O(BO3)3 resembles the one of structurally related fluorapatite, i.e. the elastic anisotropy is relatively small and the longitudinal effect of the deviations from Cauchy-relations exhibit a pronounced minimum along the direction of the dominating chains of cation polyhedra. GdCa4O(BO3)3 exhibits a maximum longitudinal piezoelectric effect of 7.67 × 10-12 CN-10, a value in the order of that of langasite-type materials. Significant changes of the calcium/gadolinium distribution on the 3 independent cation sites accompanied by characteristic anomalies of heat capacity and thermal expansion suggest processes of nonconvergent cation ordering above about 900 K in GdCa4O(BO3)3. © 2019 Walter de Gruyter GmbH, Berlin/Boston.
    view abstract10.1515/zkri-2019-0026
  • Thermo-mechanical properties of mullite ceramics: New data
    Krenzel, T.F. and Schreuer, J. and Laubner, D. and Cichocki, M. and Schneider, H.
    Journal of the American Ceramic Society 102 (2019)
    Coefficients of elastic stiffnesses and thermal expansion of hot isostatically pressed, reaction-sintered and technical fused-mullite ceramics were measured between 100 and 1673 K in comparison with single crystal mullite employing resonant ultrasound spectroscopy and dilatometry, respectively. Additionally, chemical and phase compositions and the microstructure of the ceramics were studied using X-ray diffraction techniques and scanning electron microscopy. Our studies revealed that despite polycrystallinity and slight porosity of up to 1.6%, the elastic behavior of the hot isostatically pressed ceramics is near to ideal aggregate elastic properties of mullite single crystal, for example, their bulk moduli fit within 0.7% to B = 170.0 GPa of single crystal mullite. On the other hand, with B = 155 GPa, the reaction-sintered mullite behaves significantly softer. The difference can be explained with more tight grain to grain contacts in hot isostatically pressed ceramics as compared to reaction-sintered materials. The thermal expansion of both types of ceramics almost coincides with the corresponding averaged behavior of single crystal mullite. For example, between 573 and 1273 K, the volume expansion coefficients of all these materials are (18.0 ± 0.3)·10−6 K−1. Obviously, the microstructural features are less important for the macroscopic thermal expansion. Due to heterogeneous microstructure and high α-alumina and zirconia contents, the corresponding properties of fused-mullite refractory deviate strongly from those of the other mullite materials. © 2018 The American Ceramic Society
    view abstract10.1111/jace.15925
  • Thermoelastic properties of rare-earth scandates SmScO3, TbScO3 and DyScO3
    Hirschle, C. and Schreuer, J. and Ganschow, S. and Schulze-Jonack, I.
    Journal of Applied Physics 126 (2019)
    The elastic properties of rare-earth scandates were only reported at room temperature based on simulations and experimental measurements with poor agreement thus far. Using resonant ultrasound spectroscopy and inductive gauge dilatometry, we determined the elastic stiffnesses, their temperature dependence, and thermal expansion coefficients of SmScO 3, TbScO 3, and DyScO 3 between 103 K and 1673 K. Our set of elastic stiffnesses shows high internal consistency, e.g., the relations c 11 > - > c 33 > - > c 22, c 66 > - > c 44 > - > c 55, and c 13 ≥ c 12 > - > c 23 hold for all crystal species at room temperature. The structures become overall stiffer with decreasing R E-radius and increased charge density. The behavior of c 44 at low temperatures indicates in all R EScO 3 a structural instability that might lead to an orthorhombic →monoclinic transition involving shear of the (100)-plane upon increasing pressure. The transition seems to be promoted by a decreasing R E-radius. Anomalies in two mixed resistances of TbScO 3 below room temperature are indicative of at least one more structural instability that may also cause a phase transition where the structure is sheared. So far, only magnetic phase transitions at about 3 K have been observed in R EScO 3 in literature. The thermoelastic properties in [100] and [001] directions of all materials become increasingly isotropic at high temperatures, suggesting decreased structural tilt. (100) or (010) crystal cuts should be chosen for applications of a R EScO 3 as a substrate material, when mostly isotropic thermal expansion or longitudinal stiffness in-plane is desired, respectively. © 2019 Author(s).
    view abstract10.1063/1.5108584
  • A phenomenological creep model for nickel-base single crystal superalloys at intermediate temperatures
    Gao, S. and Wollgramm, P. and Eggeler, G. and Ma, A. and Schreuer, J. and Hartmaier, A.
    Modelling and Simulation in Materials Science and Engineering 26 (2018)
    For the purpose of good reproduction and prediction of creep deformation of nickel-base single crystal superalloys at intermediate temperatures, a phenomenological creep model is developed, which accounts for the typical γ/γ′ microstructure and the individual thermally activated elementary deformation processes in different phases. The internal stresses from γ/γ′ lattice mismatch and deformation heterogeneity are introduced through an efficient method. The strain hardening, the Orowan stress, the softening effect due to dislocation climb along γ/γ′ interfaces and the formation of dislocation ribbons, and the Kear-Wilsdorf-lock effect as key factors in the main flow rules are formulated properly. By taking the cube slip in slip systems and twinning mechanisms into account, the creep behavior for [110] and [111] loading directions are well captured. Without specific interaction and evolution of dislocations, the simulations of this model achieve a good agreement with experimental creep results and reproduce temperature, stress and crystallographic orientation dependences. It can also be used as the constitutive relation at material points in finite element calculations with complex boundary conditions in various components of superalloys to predict creep behavior and local stress distributions. © 2018 IOP Publishing Ltd.
    view abstract10.1088/1361-651X/aabdbe
  • Elastic moduli and thermal expansion coefficients of medium-entropy subsystems of the CrMnFeCoNi high-entropy alloy
    Laplanche, G. and Gadaud, P. and Bärsch, C. and Demtröder, K. and Reinhart, C. and Schreuer, J. and George, E.P.
    Journal of Alloys and Compounds 746 (2018)
    Elastic moduli of a set of equiatomic alloys (CrFeCoNi, CrCoNi, CrFeNi, FeCoNi, MnCoNi, MnFeNi, and CoNi), which are medium-entropy subsystems of the CrMnFeCoNi high-entropy alloy were determined as a function of temperature over the range 293 K–1000 K. Thermal expansion coefficients were determined for these alloys over the temperature range 100 K–673 K. All alloys were single-phase and had the face-centered cubic (FCC) crystal structure, except CrFeNi which is a two-phase alloy containing a small amount of body-centered cubic (BCC) precipitates in a FCC matrix. The temperature dependences of thermal expansion coefficients and elastic moduli obtained here are useful for quantifying fundamental aspects such as solid solution strengthening, and for structural analysis/design. Using the above results, the yield strengths reported in literature for these alloys were normalized by their shear moduli to reveal the influence of shear modulus on solid solution strengthening. © 2018 The Author(s)
    view abstract10.1016/j.jallcom.2018.02.251
  • High-temperature ultrasound attenuation in langasite and langatate
    Hirschle, C. and Schreuer, J.
    IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 65 (2018)
    The ultrasound attenuation in langasite crystals increases rapidly at about 800 K with increasing temperature for reasons that are not well understood. In this paper, the attenuation quantified as Q-1 of the langasite-type materials La3Ga5SiO14 (LGS) and La3Ta0.5Ga5.5O14 (LGT) was studied from room temperature to 1653 and 1608 K, respectively, using resonant ultrasound spectroscopy. Two to three attenuation peaks can be seen. A change of the magnitudes of the largest two attenuation peaks in LGT was correlated with the changing color of an LGT sample, which is related to its oxygen vacancy concentration. Thus, the attenuation likely involves oxygen vacancies. The observed Q-1 can be explained well by a model based on the anelastic relaxation of two to three noninteracting point defects causing Debye peak-like attenuation maxima. The activation energies of the largest two relaxation peaks match the activation energies for different conductivity mechanisms in LGS and LGT. Thus, the oxygen movement-based conductivity and the relaxation processes seem to involve the exchange of ions and vacancies on the same positions. The largest two attenuation peaks are probably caused by the movement of ions induced by two different phenomena, the deformation of the lattice (point-defect relaxation) on the one hand and the electric field via the piezoelectric effect (piezoelectric/carrier relaxation) on the other hand. © 1986-2012 IEEE.
    view abstract10.1109/TUFFC.2018.2836434
  • Interplay of cation ordering and thermoelastic properties of spinel structure MgGa2O4
    Hirschle, C. and Schreuer, J. and Galazka, Z.
    Journal of Applied Physics 124 (2018)
    The coefficient of thermal expansion and elastic stiffnesses of spinel structure MgGa2O4 were determined from 103 K to 1673 K using dilatometry and resonant ultrasound spectroscopy. The state of cation order was investigated on specimens quenched from temperatures up to 1473 K via single-crystal X-ray diffraction. Even at room-temperature, the material is stiffer than what was expected from DFT simulations at 0 K, however, the stiffness falls within the predicted range based on the stiffness of the constituent oxides of MgGa2O4. The anisotropy of its longitudinal elastic stiffness is low, whereas there is a high anisotropy of the shear resistance compared to other cubic materials. At about 820 K-860 K, the temperature dependences of both thermal expansion and elastic properties change rapidly. Cation reordering also starts in this temperature range; the state of order is static at lower temperatures. Thus, MgGa2O4 undergoes a glass-like transition when heated above 820 K-860 K, where the state of cation order starts relaxing towards equilibrium in laboratory timescales. Landau-theory for nonconvergent cation ordering can describe the observed cation order at elevated temperatures well. © 2018 Author(s).
    view abstract10.1063/1.5037786
  • On Shear Testing of Single Crystal Ni-Base Superalloys
    Eggeler, G. and Wieczorek, N. and Fox, F. and Berglund, S. and Bürger, D. and Dlouhy, A. and Wollgramm, P. and Neuking, K. and Schreuer, J. and Agudo Jácome, L. and Gao, S. and Hartmaier, A. and Laplanche, G.
    Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science (2018)
    Shear testing can contribute to a better understanding of the plastic deformation of Ni-base superalloy single crystals. In the present study, shear testing is discussed with special emphasis placed on its strengths and weaknesses. Key mechanical and microstructural results which were obtained for the high-temperature (T ≈ 1000 °C) and low-stress (τ ≈ 200 MPa) creep regime are briefly reviewed. New 3D stereo STEM images of dislocation substructures which form during shear creep deformation in this regime are presented. It is then shown which new aspects need to be considered when performing double shear creep testing at lower temperatures (T < 800 °C) and higher stresses (τ > 600 MPa). In this creep regime, the macroscopic crystallographic [11−2](111) shear system deforms significantly faster than the [01−1](111) system. This represents direct mechanical evidence for a new planar fault nucleation scenario, which was recently suggested (Wu et al. in Acta Mater 144:642–655, 2018). The double shear creep specimen geometry inspired a micro-mechanical in-situ shear test specimen. Moreover, the in-situ SEM shear specimen can be FIB micro-machined from prior dendritic and interdendritic regions. Dendritic regions, which have a lower γ′ volume fraction, show a lower critical resolved shear stress. © 2018 The Author(s)
    view abstract10.1007/s11661-018-4726-9
  • Thermophysical and Mechanical Properties of Advanced Single Crystalline Co-base Superalloys
    Volz, N. and Zenk, C.H. and Cherukuri, R. and Kalfhaus, T. and Weiser, M. and Makineni, S.K. and Betzing, C. and Lenz, M. and Gault, B. and Fries, S.G. and Schreuer, J. and Vaßen, R. and Virtanen, S. and Raabe, D. and Spiecker, E. and Neumeier, S. and Göken, M.
    Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science 49 (2018)
    A set of advanced single crystalline γ′ strengthened Co-base superalloys with at least nine alloying elements (Co, Ni, Al, W, Ti, Ta, Cr, Si, Hf, Re) has been developed and investigated. The objective was to generate multinary Co-base superalloys with significantly improved properties compared to the original Co-Al-W-based alloys. All alloys show the typical γ/γ′ two-phase microstructure. A γ′ solvus temperature up to 1174 °C and γ′ volume fractions between 40 and 60 pct at 1050 °C could be achieved, which is significantly higher compared to most other Co-Al-W-based superalloys. However, higher contents of Ti, Ta, and the addition of Re decrease the long-term stability. Atom probe tomography revealed that Re does not partition to the γ phase as strongly as in Ni-base superalloys. Compression creep properties were investigated at 1050 °C and 125 MPa in 〈001〉 direction. The creep resistance is close to that of first generation Ni-base superalloys. The creep mechanisms of the Re-containing alloy was further investigated and it was found that the deformation is located preferentially in the γ channels although some precipitates are sheared during early stages of creep. The addition of Re did not improve the mechanical properties and is therefore not considered as a crucial element in the design of future Co-base superalloys for high temperature applications. Thermodynamic calculations describe well how the alloying elements influence the transformation temperatures although there is still an offset in the actual values. Furthermore, a full set of elastic constants of one of the multinary alloys is presented, showing increased elastic stiffness leading to a higher Young’s modulus for the investigated alloy, compared to conventional Ni-base superalloys. The oxidation resistance is significantly improved compared to the ternary Co-Al-W compound. A complete thermal barrier coating system was applied successfully. © 2018, The Minerals, Metals & Materials Society and ASM International.
    view abstract10.1007/s11661-018-4705-1
  • Numerical modelling of the czochralski growth of β-Ga2O3
    Miller, W. and Böttcher, K. and Galazka, Z. and Schreuer, J.
    Crystals 7 (2017)
    Our numerical modelling of the Czochralski growth of single crystalline β-Ga2O3 crystals (monoclinic symmetry) starts at the 2D heat transport analysis within the crystal growth furnace, proceeds with the 3D heat transport and fluid flow analysis in the crystal-melt-crucible arrangement and targets the 3D thermal stress analysis within the β-Ga2O3 crystal. In order to perform the stress analysis, we measured the thermal expansion coefficients and the elastic stiffness coefficients in two samples of a β-Ga2O3 crystal grown at IKZ. Additionally, we analyse published data of β-Ga2O3 material properties and use data from literature for comparative calculations. The computations were performed by the software packages CrysMAS, CGsim, Ansys-cfx and comsol Multiphysics. By the hand of two different thermal expansion data sets and two different crystal orientations, we analyse the elastic stresses in terms of the von-Mises stress. © 2016 by the authors; licensee MDPI, Basel, Switzerland.
    view abstract10.3390/cryst7010026
  • Advanced scale bridging microstructure analysis of single crystal Ni-base superalloys
    Parsa, A.B. and Wollgramm, P. and Buck, H. and Somsen, C. and Kostka, A. and Povstugar, I. and Choi, P.-P. and Raabe, D. and Dlouhy, A. and Müller, J. and Spiecker, E. and Demtroder, K. and Schreuer, J. and Neuking, K. and Eggeler, G.
    Advanced Engineering Materials 17 (2015)
    In the present work, we show how conventional and advanced mechanical, chemical, and microstructural methods can be used to characterize cast single crystal Ni-base superalloy (SX) plates across multiple length scales. Two types of microstructural heterogeneities are important, associated with the castmicrostructure (dendrites (D) and interdendritic (ID) regions - large scale heterogeneity) and with the well-known γ/γ′ microstructure (small scale heterogeneity). Using electron probe microanalysis (EPMA), we can showthat elements such as Re, Co, andCr partition to the dendrites while ID regions contain more Al, Ta, and Ti. Analytical transmission electron microscopy and atom probe tomography (APT) show that Al, Ta, and Ti partition to the γ′ cubes while g channels show higher concentrations of Co, Cr, Re, andW.We can combine large scale (EPMA) and small-scale analytical methods (APT) to obtain reasonable estimates for γ′ volume fractions in the dendrites and in the ID regions. The chemical and mechanical properties of the SX plates studied in the present work are homogeneous, when they are determined from volumes with dimensions, which are significantly larger than the dendrite spacing. For the SX plates (140mm x 100mm x 20mm) studied in the present work this holds for the average chemical composition as well as for elastic behavior and local creep properties. We highlight the potential of HRTEM and APT to contribute to a better understanding of the role of dislocations during coarsening of the γ′ phase and the effect of cooling rates after high temperature exposure on the microstructure. © 2014 Wiley-VCH Verlag GmbH & Co. KGaA.
    view abstract10.1002/adem.201400136
  • Influence of microstructure on macroscopic elastic properties and thermal expansion of nickel-base superalloys ERBO/1 and LEK94
    Demtröder, K. and Eggeler, G. and Schreuer, J.
    Materialwissenschaft und Werkstofftechnik 46 (2015)
    In the present work the thermal expansion and the elastic properties of second generation nickel-base superalloy single crystals ERBO/1 (CMSX-4 variation) and LEK94 have been studied between about 100 K and 1273 K using dilatometry and resonant ultrasound spectroscopy, respectively. Inhomogeneity related to the large scale microstructure of the samples can act as a potential source of scatter for the propagation of ultrasonic waves. This can be overcome by choosing samples of sufficient size so that they appear as homogeneous media at the scale of the elastic wave length. Our final results are in good agreement with data reported in literature for similar alloy systems. In particular, the elastic material properties are only weekly affected by moderate variations in chemical composition and microstructure. Taking into account literature data for other superalloys like CMSX-4, we derive general polynomial functions which describe the temperature dependence of the elastic moduli E<inf>〈100〉</inf>, E<inf>〈110〉</inf> and E<inf>〈111〉</inf> in nickel-base superalloys to within about ±3%. It was also observed that the alloys ERBO/1 and LEK94 show weak but significant anomalies in both thermal expansion and temperature coefficients of elastic constants above about 900 K. These anomalies are probably related to the gradual dissolution of the γ′-precipitates at higher temperatures. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstract10.1002/mawe.201500406
  • Influence of the Bi 6s2 lone electron pair on elastic properties of monoclinic Bi4B2O9
    Schreuer, J. and Mühlberg, M. and Burianek, M. and Wallrafen, F.
    Zeitschrift fur Kristallographie - Crystalline Materials 230 (2015)
    The coefficients of thermal expansion and the complete set of elastic stiffness coefficients of monoclinic Bi4B2O9 were determined as functions of temperature employing dilatometry and, respectively, a combination of resonant ultrasound spectroscopy and the plate resonance technique. Thermal expansion as well as elasticity of Bi4B2O9 exhibit a pronounced anisotropy, with the directions of the maximum longitudinal elastic stiffness and of the minimal longitudinal thermal expansion running almost parallel to [1¯02]. Further, between 100 K and 535 K the principal axes system of the linear thermal expansion rotates by more than 30° around the 2-fold symmetry axis. The deviations from Cauchy-relations show a similar behavior. Both, the anisotropy and the temperature induced changes of the investigated properties are mainly controlled by the stereochemically active Bi 6s2 lone electron pairs. At room temperature their Wang-Liebau vectors possess preferred components within a plane that runs almost perpendicular to [1¯02]. A systematic analysis of the elastic behavior of bismuth oxides using the quasi-additivity rule for elastic S-factor reveals a general trend: With decreasing relative amount of Bi2O3 the Bi3+ cations tend to align their stereochemically active lone electron pairs in planes or eventually in one direction. With respect to the elastic behavior of the compound the alignment of the easliy deformable lone electron pairs is unfavorable and causes an elastic softening. © 2015 by De Gruyter.
    view abstract10.1515/zkri-2015-1852
  • Mullite: Crystal Structure and Related Properties
    Schneider, H. and Fischer, R.X. and Schreuer, J.
    Journal of the American Ceramic Society 98 (2015)
    Mullite is certainly one of the most important oxide materials for both conventional and advanced ceramics. Mullite belongs to the compositional series of orthorhombic aluminosilicates with the general composition Al2(Al2+2xSi2-2x)O10-x. Main members are sillimanite (x = 0), stoichiometric 3/2-mullite (x = 0.25), 2/1-mullite (x = 0.40), and the SiO2-free phase ι-alumina (x = 1, crystal structure not known). This study gives an overview on the present state of research regarding single crystal mullite. Following a short introduction, the second part of the review focuses on the crystal structure of mullite. In particular, the characteristic mullite-type structural backbone of parallel chains consisting of edge-sharing MO6 octahedra and their specific cross-linkage by TO4 tetrahedra is explained in detail, the role of cation disorder and structural oxygen vacancies is addressed, and the possibility of cation substitution on different sites is discussed. The third part of the study deals with physical properties being relevant for technical applications of mullite and includes mechanical properties (e.g., elasticity, compressibility, strength, toughness, creep), thermal properties (e.g., thermal expansion, heat capacity, atomic diffusion, thermal conductivity), electrical conductivity, and optical properties. Special emphasis is put on structure-property relationships which allow for interpretation of corresponding experimental data and offer in turn the possibility to tailor new mullite materials with improved properties. Finally, the reported anomalies and discontinuities in the evolution of certain physical properties with temperature are summarized and critically discussed. © 2015 The American Ceramic Society.
    view abstract10.1111/jace.13817
  • Special issue: Crystal physics in Germany - The lifework of siegfried haussühl (∗25th November 1927, †07th January 2014)
    Schreuer, J.
    Zeitschrift fur Kristallographie - Crystalline Materials 230 (2015)
    view abstract10.1515/zkri-2015-5003
  • Chemically induced fracturing in alkali feldspar
    Scheidl, K.S. and Schaeffer, A.-K. and Petrishcheva, E. and Habler, G. and Fischer, F.D. and Schreuer, J. and Abart, R.
    Physics and Chemistry of Minerals 41 (2014)
    Fracturing in alkali feldspar during Na+-K+ cation exchange with a NaCl-KCl salt melt was studied experimentally. Due to a marked composition dependence of the lattice parameters of alkali feldspar, any composition gradient arising from cation exchange causes coherency stress. If this stress exceeds a critical level fracturing occurs. Experiments were performed on potassium-rich gem-quality alkali feldspars with polished (010) and (001) surfaces. When the feldspar was shifted toward more sodium-rich compositions over more than about 10 mole %, a system of parallel cracks with regular crack spacing formed. The cracks have a general (h0l) orientation and do not correspond to any of the feldspar cleavages. The cracks are rather oriented (sub)-perpendicular to the direction of maximum tensile stress. The critical stress needed to initiate fracturing is about 325 MPa. The critical stress intensity factor for the propagation of mode I cracks, KIc, is estimated as 2.30-2.72 MPa m1/2 (73-86 MPa mm1/2) from a systematic relation between characteristic crack spacing and coherency stress. An orientation mismatch of 18° between the crack normal and the direction of maximum tensile stress is ascribed to the anisotropy of the longitudinal elastic stiffness which has pronounced maxima in the crack plane and a minimum in the direction of the crack normal. © 2013 Springer-Verlag Berlin Heidelberg.
    view abstract10.1007/s00269-013-0617-1
  • Electrical conductivity of synthetic mullite single crystals
    Malki, M. and Schreuer, J. and Schneider, H.
    American Mineralogist 99 (2014)
    The electrical conductivity of 2/1-mullite (approximate composition 2Al2O3 •SiO2) was measured using plane parallel, polished plates cut perpendicular to [100], [010], and [001] from a large single crystal grown by the Czochralski method. Impedance spectra were recorded in the 1 Hz to 1 MHz frequency range at temperatures from 550 to 1400 °C in air. The conductivity vs. temperature curves display changes of their slope between 850 and 950 °C depending on the crystallographical direction. The low-temperature region (T < 850 °C) of conductivity is characterized by low-electrical conductivities (σav ≈ 5.4 × 10 -9 Ω-1cm-1, average conductivity at 550 °C) with σ[010] &gt; σ[100] &gt; σ[001] and low-activation energies (≈0.66 eV, average value). In the high-temperature region (T &gt; 950 °C) the electrical conductivity is significantly higher (σav ≈ 1.1 × 10-5 Ω-1cm-1, average conductivity at 1400 °C) with σ[001] &gt; σ[100] ≈ σ[010], and with higher activation energies (≈1.6 eV). While the conductivity in the low-temperature region essentially is electronic, ion conductivity dominates the conductivity in the high-temperature region. We believe that the ionic conductivity is essentially due to hopping of O atoms from structural sites linking the tetrahedral double chains in mullite toward adjacent oxygen vacancies especially in c-axis direction. These oxygen hoppings are associated with complex structural re-arrangements, which control and slow down the velocity of the processes. Thus the electrical conductivity of mullite at high temperature is much lower than, e.g., that of Y-doped zirconia, but is significantly higher than that of a-alumina.
    view abstract10.2138/am.2014.4442
  • Incommensurate modulations of relaxor ferroelectric Ca 0.24Ba0.76Nb2O6 (CBN24) and Ca 0.31Ba0.69Nb2O6 (CBN31)
    Graetsch, H.A. and Pandey, C.S. and Schreuer, J. and Burianek, M. and Mühlberg, M.
    Acta Crystallographica Section B: Structural Science, Crystal Engineering and Materials 70 (2014)
    CBN crystals show a one- and a two-dimensionally modulated modification. The former is isotypic with orthorhombic Ba4Na2Nb 10O30 and the latter with the tetragonal tungsten bronze type of crystal structure. The orthorhombic form irreversibly transforms to the tetragonal polymorph at the ferroelectric phase transition near 603 K. Orthorhombic and tetragonal CBN24 slightly differ in the distribution of the Ba and Ca atoms over the incompletely filled Me1 and Me2 sites. The tetragonal symmetry is further broken in orthorhombic CBN24 by different amplitudes of the positional modulations of O atoms which are symmetrically equivalent in the TTB structure. A similar orthorhombic phase of CBN31 could be obtained by quenching from 1473 K. © 2014 International Union of Crystallography.
    view abstract10.1107/S2052520614011676
  • Physicochemical characteristics of drip waters: Influence on mineralogy and crystal morphology of recent cave carbonate precipitates
    Riechelmann, S. and Schröder-Ritzrau, A. and Wassenburg, J.A. and Schreuer, J. and Richter, D.K. and Riechelmann, D.F.C. and Terente, M. and Constantin, S. and Mangini, A. and Immenhauser, A.
    Geochimica et Cosmochimica Acta 145 (2014)
    Speleothems are one of the most intensively explored continental archives for palaeoclimate variability. The parameters, however, that control speleothem petrography and its changes with time and space, specifically calcite crystal morphology and carbonate mineralogy, are still poorly understood. In order to shed light on processes and their products, precipitation experiments of recent carbonate crystals on watch glasses and glass plates were performed in seven selected caves. Drip water sites were analysed for their fluid Mg/Ca molar ratio, pH, degree of saturation for calcite and aragonite and drip rates. Corresponding precipitates were analysed with respect to their mineralogy, calcite crystal morphology and Mg/Ca molar ratio of calcite. The following results are found: High fluid Mg/Ca ratios are found only for caves situated in dolostone, thus the hostrock lithology indirectly controls the carbonate mineralogy and calcite crystal morphology of speleothems. The precipitation of aragonite in place of calcite occurred only in dolostone caves and is bound to very specific conditions. These are: high fluid Mg/Ca ratios (≥0.5), high fluid pH (&gt;8.2) and low fluid saturation indices for calcite (< 0.8). These specific conditions are induced by slow drip rates of < 0.2ml/min as often under more arid conditions, causing the precipitation of calcite/aragonite prior to reaching the stalagmite top. Due to this, fluid chemistry is altered, which in turn leads to changes in carbonate mineralogy and geochemistry on the stalagmite top. Calcite growth is inhibited at high fluid Mg/Ca ratios and hence, aragonite precipitation is kinetically stabilised. An increase of the drip water Mg/Ca ratio leads to an increased incorporation of Mg2+ into the calcite crystal lattice and thus, to a change in calcite crystal morphology. Four distinctive changes occur with increasing Mg2+ incorporation: (i) development of new forms (steeper rhombohedra and base pinacoid) at the edges and corners of the crystal seed, (ii) crystal habit tend to elongate along [001] due to slower growth of faces with high Mg2+ densities, (iii) reconstitution of crystal faces with low Mg2+ densities, and (iv) occurrence of calcite crystals with bended faces and edges due to very high Mg2+ (Mg/Ca ratios of 0.009-0.051) incorporation. Growth rates and possibly also organic compounds, however, may also affect the morphology of calcite crystals. Based on the data shown here, the relation of Mg2+ incorporation and the resulting changes in calcite crystal morphologies as well as the conditions of aragonite precipitation are now clearly better understood. Further work should aim at linking the calcite crystal morphology of watch glass precipitates with calcite crystal fabrics in speleothems in order to exploit the petrographic archive of speleothem deposits. © 2014 Elsevier Ltd.
    view abstract10.1016/j.gca.2014.09.019
  • Relaxor behavior of pure and cerium doped CaxBa 1-xNb2O6
    Pandey, C.S. and Schreuer, J. and Burianek, M. and Muehlberg, M.
    Ferroelectrics 464 (2014)
    Here we report the relaxor behavior of pure and cerium doped Czochralski grown lead free relaxor ferroelectric single crystals CaxBa 1-xNb2O6 (CBN-x) (0.18 ≤ x ≤ 0.35) using temperature dependent elastic behavior. We observed that the dynamic relaxor behavior strongly varies with the variation of Ca content as well as with doping. Evidence is found for a more pronounced relaxor behavior with increasing Ca content and doping. Characteristic temperature Tz.ast; (temperature at which static behavior of the polar nanoregions begins to appear) found to be unaffected with Ca content variation as well as doping Copyright © Taylor & Francis Group, LLC.
    view abstract10.1080/00150193.2014.893152
  • Structure-property relations of orthorhombic [(CH 3) 3 NCH 2COO ] 2(CuCl 2) 3·2 H 2O
    Haussühl, E. and Schreuer, J. and Wiehl, L. and Paulsen, N.
    Journal of Solid State Chemistry 212 (2014)
    Large single crystals of orthorhombic [(CH3)3 NCH2COO]2(CuCl2)3·2H2O with dimensions up to 40×40×30 mm3 were grown from aqueous solutions. The elastic and piezoelastic coefficients were derived from ultrasonic resonance frequencies and their shifts upon variation of pressure, respectively, using the plate-resonance technique. Additionally, the coefficients of thermal expansion were determined between 95 K and 305 K by dilatometry. The elastic behaviour at ambient conditions is dominated by the 2-dimensional network of strong hydrogen bonds within the (001) plane leading to a corresponding pseudo-tetragonal anisotropy of the longitudinal elastic stiffness. The variation of elastic properties with pressure, however, as well as the thermal expansion shows strong deviations from the pseudo-tetragonal symmetry. These deviations are probably correlated with tilts of the elongated tri-nuclear betaine-CuCl 2-water complexes. Neither the thermal expansion nor the specific heat capacity gives any hint on a phase transition in the investigated temperature range. © 2014 Elsevier Inc.
    view abstract10.1016/j.jssc.2014.01.004
  • Relaxor behavior of CaxBa1-xNb2O 6 (0.18≤x≤0.35) tuned by Ca/Ba ratio and investigated by resonant ultrasound spectroscopy
    Pandey, C.S. and Schreuer, J. and Burianek, M. and Mühlberg, M.
    Physical Review B - Condensed Matter and Materials Physics 87 (2013)
    Dependence of relaxor behavior of incompletely filled tetragonal tungsten bronze uniaxial relaxor ferroelectric calcium barium niobate (Ca xBa1-xNb2O6, CBN-x) on its composition was investigated by varying Ca/Ba ratio (0.18 ≤ x ≤ 0.35) and studying its thermal and elastic properties. Recently, we have reported the relaxor behavior CBN-28 with the evidence of the existence of the Burns temperature TB, and the intermediate characteristic temperature T*. In this work, we show that the dynamics of polar nanoregions (and hence the relaxor behavior) strongly varies with the Ca/Ba ratio. Evidence is found for a more pronounced relaxor behavior with increasing x. The Curie temperature and the Burns temperature are also very sensitive to the composition, whereas the characteristic temperature T* appears unaffected from the Ca/Ba ratio. The bonding interaction has been explained on the basis of bulk modulus, Poisson's ratio, and deviation from Cauchy relations. Presented results open the perspective to understand the variation of relaxor behavior of CBN-x (∼0.18≤x≤∼0.35) above Curie temperature. © 2013 American Physical Society.
    view abstract10.1103/PhysRevB.87.094101
  • Relaxor behavior of ferroelectric Ca0.22Sr0.12Ba 0.66Nb2O6
    Shekhar Pandey, C. and Schreuer, J. and Burianek, M. and Mühlberg, M.
    Applied Physics Letters 102 (2013)
    The relaxor behavior of tetragonal tungsten bronze uniaxial relaxor ferroelectric calcium strontium barium niobate (Ca0.22Sr 0.12Ba0.66Nb2O6 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. © 2013 American Institute of Physics.
    view abstract10.1063/1.4775686
  • Crystal chemistry and properties of mullite-type Bi 2M 4O 9: An overview
    Schneider, H. and Fischer, R.X. and Gesing, T.M. and Schreuer, J. and Mühlberg, M.
    International Journal of Materials Research 103 (2012)
    Bi 2M 4O 9 (M = Al 3+, Ga 3+, Fe 3+) belongs to the family of mullite-type crystal structures. The phases are orthorhombic with the space group Pbam. The backbones of the isostructural phases are edge-connected, mullite-type octahedral chains. The octahedral chains are linked by dimers of M 2O 7 tetrahedral groups and by BiO polyhedra. The Bi 3+ cations in Bi 2M 4O 9 contain stereo-chemically active 6s 2 lone electron pairs (LEPs) which are essential for the stabilization of the structure. Although the octahedral chains of the closely related Bi 2Mn 4O 10 are similar to those of Bi 2M 4O 9, Bi 2 Mn 4O 10 contains dimers of edge-connected, five-fold coordinated pyramids instead of four-fold coordinated tetrahedra. Also the 6s 2 LEPs of Bi 3+ in Bi 2Mn 4O 10 are not stereo-chemically active. Complete and continuous solid solutions exist for Bi 2(Al 1-xFe x) 4O 9 and Bi 2(Ga 1-x Fe x) 4O 9 (x = 0 - 1). Things are more complex in the case of the Bi 2(Fe 1-xMn x) 4O 9+y mixed crystals, where a miscibility gap occurs between x = 0.25 - 0.75. In the Fe-rich mixed crystals most Mn atoms enter the octahedra as Mn 4+, with part of the tetrahedral dimers being replaced by fivefold coordinated polyhedra, whereas in the Mn-rich compound Fe 3+ favorably replaces Mn 3+ in the pyramids. The crystal structure of Bi 2M 4O 9 directly controls its mechanical properties. The stiffnesses of phases are highest parallel to the strongly bonded octahedral chains running parallel to the crystallographic c-axis. Perpendicular to the octahedral chains little anisotropy is observed. The temperature- induced expansion perpendicular to the octahedral chains is probably superimposed by contractions. As a result the c-axis expansion appears as relatively high and does not display its lowest value parallel to c, as could be inferred. Maximally 6% of Bi 3+ is substituted by Sr 2+ in Bi 2Al 4O 9 corresponding to a composition of (Bi 0.94Sr 0.06) 2Al 4O 8.94. Sr 2+ for Bi 3+ substitution is probably associated with formation of vacancies of oxygen atoms bridging the tetrahedral dimers. Hopping of oxygen atoms towards the vacancies should strongly enhance the oxygen conductivity. Actually the conductivity is rather low (σ = 7 . 10 -2 S m -1 at 1073 K, 800 °C). An explanation could be the low thermal stability of Sr-doped Bi 2Al 4O 9, especially in coexistence with liquid Bi 2O 3. Therefore, Bi 2Al 4O 9 single crystals and polycrystalline ceramics both with significant amounts of M2+ doping (M = Ca 2+, Sr 2+) have not been produced yet. Thus the question whether or not M 2+-doped Bi 2M 4O 9 is an oxygen conducting material is still open. © 2012 Carl Hanser Verlag.
    view abstract10.3139/146.110716
  • Elastic and piezoelectric constants of tourmaline single crystals at non-ambient temperatures determined by resonant ultrasound spectroscopy
    Shekhar Pandey, C. and Schreuer, J.
    Journal of Applied Physics 111 (2012)
    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 -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. © 2012 American Institute of Physics.
    view abstract10.1063/1.3673820
  • Incommensurate modulation of calcium barium niobate (CBN28 and Ce:CBN28)
    Graetsch, H.A. and Pandey, C.S. and Schreuer, J. and Burianek, M. and Mühlberg, M.
    Acta Crystallographica Section B: Structural Science 68 (2012)
    The incommensurately modulated crystal structures of Ca 0.28Ba 0.72Nb 2O 6 (CBN28) and Ce 0.02Ca 0.25Ba 0.72Nb 2O 6 (Ce:CBN28) were refined in the supercentred setting X4bm(AA0,-AA0) of the 3 + 2-dimensional superspace group P4bm(aa1/2,-aa). 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. © 2012 International Union of Crystallography Printed in Singapore-all rights reserved.
    view abstract10.1107/S0108768111054863
  • Single crystal growth and characterization of mullite-type Bi 2Mn 4O 10
    Burianek, M. and Krenzel, T.F. and Schmittner, M. and Schreuer, J. and Fischer, R.X. and Mühlberg, M. and Nénertd, G. and Schneider, H. and Gesing, T.M.
    International Journal of Materials Research 103 (2012)
    A part of the pseudo-binary join Bi 2O 3-Bi 2Mn 4O 10 of the ternary system Bi 2O 3 -MnO-MnO 2 was examined using thermo-analytical methods. Because Bi 2Mn 4O 10 melts incongruently single crystals of up to 20 mm in diameter were grown by the top seeded solution growth method in the temperature range from about 1223 K to 1173 K. Single crystal neutron diffraction confirmed the principles of the crystal structure of Bi 2Mn 4O 10 but revealed much smaller distortions of the cation coordination polyhedra. In contrast to the anisotropy observed in other mullite-type Bi containing compounds, the linear thermal expansion of Bi 2Mn 4O 10, as studied by means of dilatometry and X-ray powder diffraction techniques, is characterized by α 11 &gt; α;33 &gt; α22 at room temperature. The relatively large expansion along the a-axis can be attributed to the two oxygen atoms bridging two corner shared MnO 5 tetrahedral pyramids which alternate with the structural void between two adjacent Bi 3+ cations. © 2012 Carl Hanser Verlag.
    view abstract10.3139/146.110714
  • Structure-property relations and thermodynamic properties of monoclinic petalite, LiAlSi 4O 10
    Haussühl, E. and Schreuer, J. and Winkler, B. and Haussühl, S. and Bayarjargal, L. and Milman, V.
    Journal of Physics Condensed Matter 24 (2012)
    Structure-property relations of monoclinic petalite, LiAlSi 4O 10, were determined by experiment and atomistic modeling based on density functional theory. The elastic stiffness coefficients were measured between room temperature and 570K using a combination of the plate-resonance technique and resonant ultrasound spectroscopy. The thermal expansion was studied between 100 and 740K by means of dilatometry. The heat capacity between 2 and 398K has been obtained by microcalorimetry using a quasi-adiabatic calorimeter. The experimentally determined elastic stiffness coefficients were employed to benchmark the results of density functional theory based model calculations. The values in the two data sets agreed to within a few GPa and the anisotropy was very well reproduced. The atomistic model was then employed to predict electric field gradients, the lattice dynamics and thermodynamic properties. The theoretical charge density was analyzed to investigate the bonding between atoms. © 2012 IOP Publishing Ltd.
    view abstract10.1088/0953-8984/24/34/345402
  • Thermal expansion and elastic properties of mullite-type Bi 2Ga 4O 9 and Bi 2Fe 4O 9 single crystals
    Krenzel, T.F. and Schreuer, J. and Gesing, T.M. and Burianek, M. and Mühlberg, M. and Schneider, H.
    International Journal of Materials Research 103 (2012)
    Resonant ultrasound spectroscopy was used to characterize the elastic properties of single crystal orthorhombic Bi 2Ga 4O 9 and Bi 2Fe 4O 9 between room temperature and about 1200 K. Additionally, the coefficients of thermal expansion were studied in the range 100 K to 1 280 K using high-resolution dilatometry and X-ray powder diffraction. The elastic constants at 295 K are in GPa c 11 = 143.4(1), c 22 = 161.9(1), c 33 = 224.5(1), c 44 = 68.4(1), c 55 = 49.3(1), c 66 = 76.6(1), c 12 = 74.2(1), c 13 = 62.2(1), c 23 = 70.5(1) for Bi 2Ga 4O 9, and c 11 = 106.7(1), c 22 = 141.2(1), c 33 = 183.7(2), c 44 = 53.7(1), c 55 = 41.9(1), c 66 = 63.8(1), c 12 = 63.5(1), c 13 = 59.8(1), c 23 = 63.4(2) for Bi 2Fe 4O 9. 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 c ij 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. © 2012 Carl Hanser Verlag.
    view abstract10.3139/146.110718
  • Thermally induced structural changes in incommensurate calcium barium niobate Ca 0.28Ba 0.72Nb 2O 6 (CBN28)
    Graetsch, H.A. and Schreuer, J. and Burianek, M. and Mühlberg, M.
    Journal of Solid State Chemistry 196 (2012)
    The incommensurately modulated crystal structure of relaxor ferroelectric CBN28 was refined at elevated temperatures up to 330 °C in the 32 dimensional superspace group P4bm(αα1/2,-αα1/2). The structural modulations mainly consisting of cooperative tilting of NbO 6 octahedra and an occupational modulation of the large cation site Me2 persist beyond the diffuse ferroelectric transition with slightly reduced amplitudes. A change of symmetry was not observed. Both symmetrically non-equivalent NbO 6 octahedra are distorted by off center shifts of the Nb atoms in the same direction along the tetragonal c-axis. The displacements of the Nb atoms are gradually reduced with increasing temperatures until one of the Nb atoms crosses the center of its coordination polyhedron near the transition temperature T M adopting an uncompensated anti-ferroelectric configuration. This change is accompanied by enhanced thermal motions of the Nb atoms along the c-axis. Structural distortions and electric polarization do not completely vanish at T M but may persist in fluctuating polar nanodomains. © 2012 Elsevier Inc. All rights reserved.
    view abstract10.1016/j.jssc.2012.06.028
  • Anomalous elastic behavior of relaxor ferroelectric Ca 0.28Ba 0.72Nb 2O 6:Ce studied by resonant ultrasound spectroscopy
    Shekhar Pandey, C. and Schreuer, J. and Burianek, M. and Mühlberg, M.
    Applied Physics Letters 99 (2011)
    Elastic behavior of tetragonal tungsten bronze uniaxial relaxor ferroelectric cerium doped Ca 0.28Ba 0.72Nb 2O 6 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 T c and Burns temperature T b significantly, however, intermediate characteristic temperature T * (between the Burns temperature T b and the temperature of maximum dielectric permittivity T m) remains same as for pure Ca 0.28Ba 0.72Nb 2O 6. 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. © 2011 American Institute of Physics.
    view abstract10.1063/1.3670323
  • Anomalous elastic behavior of relaxor ferroelectric Ca 0.28Ba0.72Nb2O6 single crystals
    Pandey, C.S. and Schreuer, J. and Burianek, M. and Mühlberg, M.
    Physical Review B - Condensed Matter and Materials Physics 84 (2011)
    Full sets of elastic constants cij of tetragonal tungsten bronze relaxor ferroelectric Ca0.28Ba0.72Nb2O 6 (CBN-28) single crystals are measured above Curie temperature up to 1503 K employing resonant ultrasound spectroscopy. Thermal expansion measurements on as-grown unpoled CBN-28 reveal the existence of a characteristic temperature T* (∼800 K) for CBN-28 between the Burns temperature Tb (∼1100 K) and the temperature of maximum dielectric permittivity Tm (∼600 K). The influence of polar nanoregions (PNRs) on the elastic properties of CBN-28 is studied in detail. The temperature evolution of cij shows pronounced anomalies. All independent elastic constants evolved differently, with temperature reflecting their coupling to different types of the reorientational motion of PNRs through their interaction with acoustic waves. The anisotropy of longitudinal elastic stiffness coefficients and the deviation from Cauchy relations for CBN-28 are also studied, showing the evolution of material anisotropy and the nature of bonding interactions with temperature, respectively. © 2011 American Physical Society.
    view abstract10.1103/PhysRevB.84.174102
  • Correlation between dielectric properties and chemical composition of the tourmaline single crystals
    Pandey, C.S. and Jodlauk, S. and Schreuer, J.
    Applied Physics Letters 99 (2011)
    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. © 2011 American Institute of Physics.
    view abstract10.1063/1.3646912
  • High temperature elastic properties of Mg-cordierite: Experimental studies and atomistic simulations
    Haussühl, E. and Vinograd, V.L. and Krenzel, T.F. and Schreuer, J. and Wilson, D.J. and Ottinger, J.
    Zeitschrift fur Kristallographie 226 (2011)
    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 occurrence 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. Possible 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. © by Oldenbourg Wissenschaftsverlag, München.
    view abstract10.1524/zkri.2011.1307
  • Radiaxial-fibrous calcites: A new look at an old problem
    Richter, D.K. and Neuser, R.D. and Schreuer, J. and Gies, H. and Immenhauser, A.
    Sedimentary Geology 239 (2011)
    Marine radiaxial-fibrous and fascicular-optic calcites are very common but poorly understood pore-filling cements in Paleozoic and Mesozoic marine neritic and upper bathyal limestones. The main diagnostic feature of these cements is their converging or diverging crystal c-axis, respectively. The reasons for this anomalous texture are at present unknown. Another controversy is due to the relative lack of occurrences in Cenozoic strata and their apparent absence in Quaternary marine limestones. Despite these uncertainties, marine fibrous cements are thought by some to be amongst the best proxies for the geochemistry of ancient oceans because of the absence of metabolic effects during their precipitation. Applying electron backscatter diffraction analysis, we here for the first time document radiaxial-fibrous and subordinate fascicular-optic fibrous biominerals from well-preserved Jurassic and Cretaceous low-Mg calcite belemnite rostra. The finding of fibrous biogenic calcites in combination with the recent description of Holocene and modern fibrous calcites in stalagmites represents-in the view of the authors-a significant advance in carbonate research. Here, these findings are placed in their wider, processes-oriented context and the significance of biogenic and speloan fibrous calcite for their marine counterparts is assessed. Comparing the physico-chemical and organomineralic properties of different precipitation sites indicates that the diagnostic variations in the crystal c-axis orientation are not related to a specific nucleation environment or substratum. In contrast, preliminary crystallographic analyses suggest that kinetic factors during nucleation or subtle gradients in the statistical replacements of Ca2+ by Mg2+ in the crystal structure may lead to local strain resulting in converging or diverging crystal c-axes. © 2011 Elsevier B.V.
    view abstract10.1016/j.sedgeo.2011.06.003
  • Magnetoelastic and structural properties of azurite Cu3(CO 3)2(OH)2 from neutron scattering and muon spin rotation
    Gibson, M.C.R. and Rule, K.C. and Wolter, A.U.B. and Hoffmann, J.-U. and Prokhnenko, O. and Tennant, D.A. and Gerischer, S. and Kraken, M. and Litterst, F.J. and Süllow, S. and Schreuer, J. and Luetkens, H. and Brühl, A. and Wolf, B. and Lang, M.
    Physical Review B - Condensed Matter and Materials Physics 81 (2010)
    Azurite, Cu3 (CO3) 2 (OH) 2, has been considered an ideal example of a one-dimensional diamond chain antiferromagnet. Early studies of this material imply the presence of an ordered antiferromagnetic phase below T N∼1.9 K, while magnetization measurements have revealed a 1/3 magnetization plateau. To the best of our knowledge, no corroborating neutron-scattering results have been published to confirm the ordered magnetic moment structure. We present recent neutron-diffraction results which reveal the presence of commensurate magnetic order in azurite which coexists with significant magnetoelastic strain. The latter of these effects may indicate the presence of spin frustration in zero applied magnetic field. Muon spin rotation reveals an onset of short-range order below 3 K and confirms long-range order below TN. © 2010 The American Physical Society.
    view abstract10.1103/PhysRevB.81.140406
  • Ultrasonic investigation on the distorted diamond chain compound Azurite
    Cong, P.T. and Wolf, B. and Tutsch, U. and Remović-Langer, K. and Schreuer, J. and Süllow, S. and Lang, M.
    Journal of Physics: Conference Series 200 (2010)
    The natural mineral Azurite [Cu3(CO3) 2(OH)2] has been considered as a model substance for the 1D distorted antiferromagnetic diamond chain, the microscopic couplings of which, however, are still under discussion. Here we present results of the longitudinal elastic constant c22 down to 80 mK and magnetic fields up to 12 T. c22 reveals clear signatures of the magnetic energy scales involved and discloses distinct anomalies at the Néel ordering TN = 1.88 K. Based on measurement as a function of temperature and magnetic field, a detailed B-T phase diagram is mapped out which includes an additional phase boundary of unknown origin at low temperature (T < 0.5 K). Entering the new phase is accompanied by a pronounced softening of the c 22 elastic constant. These observations, together with results obtained by spectroscopic investigations reported in the literature, reflect an unusual long-range magnetically ordered state at very low temperatures. © 2010 IOP Publishing Ltd.
    view abstract10.1088/1742-6596/200/1/012226
  • crystal structure

  • crystal structure

  • ferroelectrics

  • resonant ultrasound spectroscopy

  • x-ray diffraction

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