Ultrasound studies of single crystal thulium in an applied magnetic field

The paper reports the first measurements of the single crystal elastic constants of the heavy rare earth metal thulium as a function of temperature and magnetic field. The constants were obtained from ultrasonic velocity measurements over a temperature range of 4.2–296 K and in applied magnetic fields of up to 5 T. The elastic constants; C₁₁, C₃₃, C₄₄ and C₆₆=(C₁₁–C₁₂)/2 were determined from the ultrasonic velocities. Anomalies in the elastic constants were observed at 58 K from the c-axis propagated shear wave measurements and at 55 K from the c-axis propagated longitudinal wave measurements. Significant softening of the elastic constants C₃₃ and C₄₄ was observed close to T_N. Application of a magnetic field (>2 T) along the c-axis direction induced further softening of the material. Electromagnetic acoustic transducers (EMATs) were also employed in addition to conventional piezoelectric quartz transducers. A marked increase in the EMATs acoustic coupling efficiency (generation and detection efficiency) occurred close to T_N.     

Ultrasonic wave propagation in IIIrd group nitrides

The ultrasonic attenuation in hexagonal structured (wurtzite) third group nitrides (GaN, AlN and InN) has been evaluated at 300 K for an ultrasonic wave propagating along the unique axis of the crystal. Higher order elastic constants of these materials are calculated using the Lennard-Jones potential for the determination of ultrasonic attenuation. The ultrasonic velocity, Debye average velocity, thermal relaxation time and acoustic coupling constant are evaluated along the z-axis of the crystal using the second order elastic constants and other related parameters. The contributions of the elastic constants, thermal conductivity, thermal energy density, ultrasonic velocity and acoustic coupling constant to the total attenuation are studied. On the basis of the ultrasonic attenuation, it can be concluded that the AlN is more ductile than either GaN or InN at 300 K. Orientation dependent characterization has been achieved by calculation of the orientation dependent ultrasonic velocity, Debye average velocity and thermal relaxation time for the materials.     

Temperature-dependent Brillouin scattering studies of surface acoustic modes in Nd0.5Sr0.5MnO3

Brillouin scattering experiments are carried out to study the surface acoustic waves in Nd_0.5Sr_0.5MnO₃ as a function of temperature in the range of 40-300 K covering the metal-insulator and charge-ordering phase transitions. The surface modes include surface Rayleigh wave, pseudo-surface acoustic wave (PSAW) and high velocity PSAW. The observed softening of the sound velocities for the surface modes below paramagnetic to ferromagnetic transition, T_c is related to the softening of the C₄₄ elastic constant. The subsequent hardening of the sound velocity below the charge ordering transition temperature T_co is attributed to the coupling of the acoustic phonon to the charge ordered state via long range ordering of the strong Jahn-Teller (JT) distortion.     

Elastic constants in RbI,determined by inelastic neutron scattering

Long-wavelength acoustic phonons have been studied in the whole (100)-plane of RbI at 295 K by means of inelastic neutron scattering. The raw data have been corrected for resolution effects taking into account the curvature of the dispersion surface and variations of the mode eigenvectors. The shifts of the neutron groups due to these resolution effects are discussed in detail. The analysis of the experimental results gives for the zero sound elastic constantsc ₁₁=28.15±0.5,c ₁₂=3.7±0.5 andc ₄₄=2.85±0.1 10¹⁰ dyn/cm². A comparison with first sound elastic constants taken from ultrasonic measurements yields significant differences between the high and low frequency elastic constantsc ₁₁ andc=(c ₁₁–c ₁₂)/2. The differences calculated from recent theories are in agreement with the experimental results for the elastic constantsc ₁₁,c ₄₄ andc, but not forc ₁₂. The dispersion surface in the (100)-plane is also shown for some out-of-symmetry data and compared with ultrasonic data as well as with theoretical results.Research supported by BMFT     

Acoustic properties of proton exchanged LiNbO3 investigated by Brillouin scattering

The propagation of surface acoustic waves at microwave frequencies (10¹⁰ Hz) was studied on proton exchanged LiNbO₃ crystals by means of Brillouin scattering. The proton exchange causes a large velocity reduction for surface acoustic waves propagating in the x–y plane of ay-cut crystal as well as for longitudinal bulk acoustic waves travelling in the proton exchanged sub-surface region. The velocity reduction amounts to about 20% for both types of waves. The corresponding elastic constants are reduced even by about 40% since the density remains almost constant. This softening seems to involve both the shear and compressional elastic constants, but in an anisotropic way.Thus by proton exchange it is possible to build acoustic waveguides adjacent to the surface, similar to the construction of optical waveguides. By a lateral control of the proton exchange rate optical elements for ultrasonic waves, for example, acoustic lenses can be produced without deformation of the flat surface.The absorption of surface acoustic waves on proton exchanged surfaces is stronger than on pure LiNbO₃ indicating a novel absorption mechanism becoming active in the proton exchanged material.     

Second-order and third-order elastic constants of B4C ceramics

The linear and nonlinear elastic properties of B₄C boron carbide ceramics have been studied. The second-order elastic constants and other parameters of the theory of elasticity in the linear approximation have been calculated based on the experimentally measured density and velocity values of longitudinal and shear bulk acoustic waves in the samples. The Thurston-Brugger method has been used to determine the third-order elastic constants of B₄C. To achieve this, we have measured the relative changes of the longitudinal and shear bulk acoustic wave velocities depending on the uniaxial compression applied to the sample.     

Photoluminescence properties of selectively grown InN microcrystals

We investigated the photoluminescence (PL) properties of regularly arranged N‐polar InN microcrystals with m ‐plane sidewall facets. We observed narrow PL emission at 0.678 eV with a linewidth of ～14 meV at 4 K and a clear band‐filling effect with increasing excitation power. We also observed a normal red shift of the PL peak energy as large as 51 meV (～150 nm) with increasing temperature from 4 to 300 K, similar to that observed for non‐degenerated semiconductors. The integrated PL intensity ratio I_300K/I_4K was measured to be 6.1%. These results indicate that InN microcrystals have a low residual carrier density and excellent optical properties without being adversely affected by surface electron accumulation, despite their relatively high surface area. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

α-Ti2Zr高压物性的第一性原理计算研究

基于密度泛函理论的第一性原理计算获得了α-Ti₂Zr的晶体结构、弹性常数、德拜温度和电子分布情况, 研究了它们与压力的关系. 计算得到的晶体结构参数与实验值一致. 运用有限应变方法计算得到了α-Ti₂Zr的体积模量B、剪切模量G、杨氏模量E和泊松比σ. B和E的零压值分别为101.2和35.6 GPa. G/B的值较小, 并且随着压力的增加而减小, 表明α-Ti₂Zr具有优异的延展性. 基于弹性常数得到平均声速, 从而获得了德拜温度Θ=321.7 K. 通过解Christoffel方程获得的压缩波和剪切波数据揭示α-Ti₂Zr具有较强的各向异性. 此外, 压力诱导电子从s轨道到d轨道的转移说明在一定压力下α-Ti₂Zr将转变为β相. 关键词： 第一性原理 α-Ti₂Zr')" href="#">α-Ti₂Zr 物性 高压     

Acoustic symmetry and the third order elastic constants of tetragonal TII (4/m) crystals

The mode equations which relate the measured hydrostatic and uniaxial pressure derivatives of the “natural” ultrasonic velocity to the second and third order elastic constants for the tetragonal TII (4/m) Laue group have been transformed from the crystallographic (XYZ) axial frame to a reference frame (k, k + π/2, Z) comprised of two acoustic symmetry axes and the fourfold axis. It is found that, if the acoustic symmetry axes do not shift appreciably with pressure, the mode equations for TII crystals in this reference frame are much simpler than those in the crystallographie axial frame (XYZ), having the same form as those for the higher symmetry TI Laue group. Hence 12 transformed third order elastic constants can be obtained experimentally for TII crystals by making measurements of the hydrostatic and uniaxial pressure derivatives of ultrasonic wave velocity of modes propagated in the (k, k + π/2, Z) axial set with the uniaxial stresses also applied in this reference frame. The approach has been used to determine the 12 transformed third order elastic constants of scheelite (CaWO₄).     

High‐resolution Brillouin scattering and heat capacity studies of bis(guanidinium)zirconium bis(nitrilotriacetate)hydrate, [C(NH2)3]2Zr[N(CH2COO)3]2·H2O

High‐resolution micro‐Brillouin scattering and heat capacitiy studies of polar bis(guanidinium)zirconium bis(nitrilotriacetate)hydrate were performed in the temperature range 230–305 K. Strong anomalies in the Brillouin shift and the attenuation were observed near 290 K upon cooling for the sound waves corresponding to the c₂₂ elastic constant. For this elastic constant, the coupling between the order parameter and the elastic strains is linear quadratic. In case of the c₄₄ and c₆₆, the coupling is biquadratic, giving rise to an increase of these parameters below 290 K. The analysis of the acoustic anomalies and heat capacity results near 290 K revealed that they correspond to a second‐order, cell‐multiplying, displacive phase transition. The second phase transition leads to weak acoustic anomalies at approximately 284 K. Copyright © 2009 John Wiley & Sons, Ltd.     

Elastic properties of Nb-based alloys by using the density functional theory

A first-principles density functional approach is used to study the electronic and the elastic properties of Nb₁₅X(X = Ti, Zr, Hf, V, Ta, Cr, Mo, and W) alloys. The elastic constants c₁₁ and c₁₂, the shear modulus C', and the elastic modulus E_〈100〉 are found to exhibit similar tendencies, each as a function of valence electron number per atom (EPA), while c₄₄ seems unclear. Both c₁₁ and c₁₂ of Nb₁₅X alloys increase monotonically with the increase of EPA. The C' and E_〈100〉 also show similar tendencies. The elastic constants (except c₄₄) increase slightly when alloying with neighbours of a higher d-transition series. Our results are supported by the bonding density distribution. When solute atoms change from Ti(Zr, Hf) to V(Ta) then to Cr(Mo, W), the bonding electron density between the central solute atom and its first neighbouring Nb atoms is increased and becomes more anisotropic, which indicates the strong interaction and thus enhances the elastic properties of Nb-Cr(Mo, W) alloys. Under uniaxial 〈100〉 tensile loading, alloyed elements with less (more) valence electrons decrease (increase) the ideal tensile strength.     

Determination of elastic constants using a scanning acoustic microscope

A cubic single crystal of GaAs with two polished (100)-surfaces was examined with a scanning acoustic microscope (SAM) in transmission mode. The images of the transmitted ultrasound amplitude measured at frequencies of 350–400 MHz contain sufficient information about the acoustic anisotropy of the crystal to determine the complete set of the three elastic constants C₁₁, C₁₂, C₄₄ numerically. This was done by an interactive fitting procedure correlating simulated images with the measured one. This technique seems to be universally applicable to virtually all sorts of single crystals. Compared to plane wave investigations it saves preparatory labour since one single crystal orientation suffices for a determination of all elastic constants.     

Ferroelastic phase transition and anomalous elastic and thermal properties of betaine borate (CH3)3NCH2COO·H3BO3

The temperature and pressure derivatives of the elastic constants of orthorhombic betaine borate, (CH₃)₃NCH₂COO·H₃BO₃, have been determined by measuring temperature and stress induced shifts of resonance frequencies of thick plates at ca. 15 MHz in the range between 140 and 300 K and 0 and 3 kbar. The elastic ‘shear’ resistance c₄₄ exhibits a value as low as 0.0492×10¹⁰Nm^-2at 293 K. With decreasing temperature c₄₄ approaches zero at ca. 142.5 K, indicating an acoustic soft mode behaviour connected with a ferroelastic phase transition. The softening of c₄₄ is described in a good approximation by c₄₄(T)_p=0 =alogT/T₀ with a=0.0663×10¹⁰Nm^-2 and T₀ = 139.5 K. Further, c₄₄ decreases with increasing pressure according to the linear relation c₄₄(p)_{T=293 K} = 0.0492?0.184×10^-4p (p in bar, c₄₄ in 10¹⁰ Nm^-2). All other elastic constants show a quite normal temperature and pressure dependence. At 293 K the transition is induced by a pressure of 2.65 kbar. The transition temperature T_c depends linearly on pressure according to T_c = 142.5+0.0568 p (pinbar, T_cinK). Passing through the transition no discontinuous change of the lattice constants is observed. The three principal coefficients of thermal expansion and the pressure derivatives of the dielectric constants exhibit discontinuities at the transition. The transition is of strongly second order.     

Elastic and magnetoelastic effects in CeB6

Elastic constants of CeB₆ were redetermined by ultrasonic and Brillouin scattering measurements. We found all elastic constants to be positive, especiallyc ₁₂. The temperature and magnetic field dependence of the elastic modesc ₄₄ and (c ₁₁-c ₁₂)/2 is explained on the basis of the newly proposed crystalline-electric-field level scheme for CeB₆ with the ₇ level 545 K above the ₈ ground state. The deduced quadrupolar coupling constants give an antiferroquadrupolar ordering temperature of 3.3 K in agreement with experiment.Supported by the DFG, SFB65, SFB125 and SFB126     

Elastic properties of the premelting phases of the perfluoroalkanes C16F34 and C20F42

The elastic properties of the solid state of linear oligomers are closely related to their special intra-and inter-molecular interactions. This is proved for the perfluoroalkanes C₁₆F₃₄ and C₂₀F₄₂. The elastic tensors of both materials have been measured with Brillouin spectroscopy as a function of temperature. Both systmes show an extremely weak shear stiffnessc ₄₄, indicating the existence of a smectic-B like structure and an unexpected strong elastic anisotropy inversion in the premelting phase. Moreover a Curie-Weiss-law behavior was found for the stiffness constantc ₃₃ indicating the existence of a soft longitudinal acoustic phonon mode. The transition temperatureT _c is for C₂₀F₄₂ below the melting point. The elastic properties are purely static. The observations are tentatively attributed to an intermolecular premelting process.     

高压下闪锌矿InN光电性质的密度泛函研究

 采用密度泛函理论,计算了闪锌矿型InN在压力下的结构、力学性质和光学性质,结果显示,随着压强的增大晶格常数减小。给出了零压下C₁₁、C₁₂、B、C_s、C₄₄的值及至70 GPa压力下弹性常数随压强的变化关系。结果表明,C₁₁、C₁₂、B随压强增大而增大,C_s、C₄₄随压强增大而减小,计算结果与现有实验和理论结果符合较好。在价带区,InN的分态密度（PDOS）有两个带,且在费米面附近密度很小,显示其倾向于形成稳定结构并且导电性较差。对闪锌矿型InN在高压下的光学性质研究发现,导带电子向高能方向偏移,而价带电子向低能方向偏移,结果导致能带间隙增大,光吸收谱在压力的作用发生了“蓝移”。研究结果对认识高压下闪锌矿型InN的结构、电学及光学性质具有重要意义。     

Pressure dependence of elastic constants in zinc-blende GaN and InN and their influence on the pressure coefficients of the light emission in cubic InGaN/GaN quantum wells

We have studied the influence of nonlinear elastic effects on the pressure coefficients of light emission, dE_E/dP, in cubic InGaN/GaN quantum wells. By means of ab-initio calculations, we have determined the pressure dependences of the elastic constants, C₁₁, C₁₂ and C₄₄ in zinc-blende InN and GaN. Further, we show that the pressure dependence of the elastic constants results in significant reduction of dE_E/dP in cubic InGaN/GaN quantum wells and essentially improves the agreement between experimental and theoretical values.     

First-principles study of bonding,elasticity-relevant and acoustic properties of BaAlBO3F2

The band structure, density of states, charge densities, and elasticity-relevant properties of BaAlBO₃F₂ are obtained by first-principles density functional calculations within the generalized gradient approximation. Other elasticity-relevant constants, such as the the Young's modulus, Poisson ratio, velocity of acoustic waves, and the Debye temperature are also deduced from the elastic constants. Bonding analysis demonstrates that BaAlBO₃F₂ has different bonding properties between basal (ab) plane and c axis. The analyses on elasticity-relevant properties indicate BaAlBO₃F₂ is mechanically stable and anisotropic. It is also shown that BABF is an ionic crystal with brittle character. Our these results give a reasonable explanation for the experimental finding that BaAlBO₃F₂ is apt to crack along c axis. Proceeding from Christoffel equation, we discuss the propagation properties of acoustic modes in BaAlBO₃F₂ to give a theoretical guidance for measuring its elastic constants. Research shows that the calculated average velocities of longitudinal and transverse modes from Christoffel equation are in good agreement with those from classic Debye model.     

Magnetoelastic effects in La1−xCexB6

The elastic constants of La_1−xCe_xB₆ (x = 0.00, 0.01, 0.03) single crystals were determined by ultrasonic measurements. The temperature dependence of the elastic symmetry modes c₄₄ and (c₁₁ − c₁₂)/2 is explained on the basis of the crystalline-electric-field level scheme of CeB₆ by taking the magnetoelastic interaction into account. An influence of the Kondo effect on the elastic constants could not be detected.