Surface acoustic waves and elastic constants of InN epilayers determined by Brillouin scattering

The surface acoustic wave velocity in InN has been experimentally determined by means of Brillouin scattering experiments on c ‐ and m ‐face epilayers. From simulations based on the Green's function formalism we determine the shear elastic constants c₆₆ and c₄₄ and propose a complete set of elastic constants for wurtzite InN. The analysis of the sagittal and azimuthal dependence of the surface acoustic wave velocity indicates a slightly different elastic behavior of the m ‐face sample that basically affects the c₄₄ elastic constant. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Lattice softening in K2Pt(CN)4Br0.3·3H2O

The temperature dependences of the elastic constants, c₁₁, c₃₃, c₄₄, and c₆₆, in KCP are described. In the temperature range 10–100 K softening is observed in c₄₄, while c₆₆ decreases almost linearly with decreasing temperature. These results indicate the presence of a new critical region.     

Single-crystal elasticity of SrCO3 by Brillouin spectroscopy

ABSTRACT

The elastic stiffness tensor c_ij of synthetic strontianite (SrCO₃) was determined by Brillouin spectroscopy at ambient conditions. An inversion procedure based on Christoffel’s equation was used to determine the 9 independent elastic coefficients of orthorhombic strontianite from acoustic velocities measured along 69 different crystallographic directions in 3 randomly oriented crystal platelets. The best fit values of c₁₁, c₁₂, c₁₃, c₂₂, c₂₃, c₃₃, c₄₄, c₅₅ and c₆₆ are 153(1), 52(1), 38(11), 109.6(8), 43(15), 75(1), 28.0(5), 28.6(4) and 33.2(5) GPa, respectively. The linear compressibilities of a-, b- and c-axis at ambient conditions are 3(2), 4(6) and 10(8) 10^?3 GPa^?1. The adiabatic bulk modulus of strontianite is 64(4) GPa, intermediate between aragonite (CaCO₃) and witherite (BaCO₃), thus confirming a systematic linear relationship between cation radius and bulk modulus in aragonite-type carbonates. The shear modulus of strontianite has a value of 31(1) GPa, which is about 10% smaller in comparison to aragonite.     

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     

The elastic behaviour of ferroelastic Sb5O7I polytype 2MC studied by ultrasonic experiments and Brillouin scattering

The temperature dependence of the elastic functions of the improper ferroelastic polytype 2MC-Sb₅O₇I has been investigated in the temperature range from room temperature to well above the structural phase transition atT _c=481 K. The stiffnessesc(c^*c^*),c(a,a),c ₂₂ andc(c^*a) show a considerable softening up to 20% aroundT _c whereasc ₄₄ remains unaffected by the phase transition. The experimental results are discussed considering cubic and quartic anharmonic coupling between two components of the zone boundary order parameter and elastic waves.Carried out in Laboratories RCA Ltd, Zürich, SwitzerlandCarried out in Fakultät für Physik der Universität, Regensburg, Federal Republic of Germany     

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.     

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.     

氢化硅薄膜介观力学行为及其与微结构内禀关联特性

使用等离子体增强化学气相沉积系统，在射频和直流负偏压的双重激励下制备了本征和掺杂后的氢化硅薄膜.利用拉曼谱对薄膜进行了微结构分析，用纳米压痕系统研究了薄膜的介观力学行为.研究表明：制备于玻璃衬底上的氢化硅薄膜，由于存在非晶态的过渡缓冲层，弹性模量小于相应的制备于单晶硅衬底的薄膜.对于掺杂的氢化硅薄膜，由于磷的掺入使得薄膜晶粒细化、有序度提高，薄膜的晶态比一般在40％以上.而硼的掺入，薄膜晶态比减小，一般低于40％.同时发现，掺磷、本征和掺硼的氢化硅薄膜分别在晶态比为45％，30％和15％左右处，弹性模量较 关键词： 氢化硅薄膜 拉曼谱 弹性模量 晶态比     

Mechanical properties of thin films of hydrogenated silicon and their relationship with microstructure

Thin films of hydrogenated silicon were deposited on glass and single-crystalline silicon substrates using a capacitively coupled radio-frequency plasma-enhanced vapor-deposition system with the help of direct-current bias stimulation. Micro-Raman scattering was applied to investigate the microstructure of the thin films obtained. The crystalline volume fraction, X _c, was obtained from the Raman spectra. Microscopic mechanical characterization of the thin films was carried out by nanoindentation based on the conventional depth-sensing indentation method. An analytical relation between X _c and the elastic modulus was thereby established. The elastic modulus of the film on a glass substrate was found to be lower than that of the film on a monocrystalline silicon substrate with the same X _c. The grain size of a phosphorus-doped thin film was smaller than that of the intrinsic one, with greater ordering of the grains and X _c was found to be usually above 40%. A film with boron doping was on the opposite side, with X _c usually below 40%. In the phosphorus-doped, intrinsic, and boron-doped films, the elastic moduli were lower when the X _c values were 45%, 30%, and 15%, respectively.     

Correlation betweenT c and elastic constants of (La−M)2CuO4

By an ultrasonic method, we measured the elastic constants of polycrystalline La_1.85M_0.15CuO₄ withM=Ca, Ba, Sr. These materials show zero-resistance normal-superconductive transition temperatures of 19, 28, and 36K. VersusT _c , all the elastic stiffnesses-bulk modulus, Young modulus, shear modulus-increase. Derived from the elastic constants and average atomic volume, the Debye temperature increases linearly withT _c . In conventional BCS superconductors,T _c decreases with increasing _D .     

Quasi-Classical and Classical Cross Sections for the Scattering of Electrons on the Coulomb Cut-Off Potential

The elastic scattering of electrons on the cut-off Coulomb potential U_c(r) = ?1/r + 1/r_c, for r ≦ r_c and U_c(r) = 0, for r > r_c, has been considered. It has been shown that for ε > 0.5/r_c (ε is the energy of free electrons in atomic units) the analytical quasi-classical expressions describe quite well the behaviour of transport, differential and total cross sections for elastic scattering. It has been shown moreover, that in the energy range considered, transport cross section could be determined with practically the same accuracy already by means of classical, analytical expressions. Born approximations show larger deviations from exact quantum calculations.     

锌的X射线热漫散衍射及弹性系数

提出使用逐步逼近方法进行X射线热漫散衍射强度的水平与垂直发散修正。从测量的热漫散衍射强度经过各种修正之后,得到锌的弹性系数与超声方法得到的结果相符,分别为(以10¹²达因/厘米²为单位):c₁₁=1.6₉,c₁₂=0.39₄,c₁₃=0.54₉,c₃₃=0.68₂,c₄₄=0.42₉,c₆₆=(1/2c₁₁-1/2c₁₂=0.64₈。     

Brillouin spectrum of Ca(OH)2

Brillouin spectrum of several directions, such as [0,0,1], [0,1,1]/?2, [0,1,0] and [1,/?2,1/2,1/2] of Ca(OH)₂ crystals were measured. The elastic stiffness coefficients c₁₁, c₃₃, c₄₄, c₆₆ and c₁₃ are estimated to be (in N/m² × 10¹⁰): 9.928±0.15, 3.260±0.2, 0.985±0.2, 3.155±0.15 and 2.965±1.5, respectively. Large dispersion of ultrasonic and hypersonic longitudinal velocities is noted.     

Ferroelastic phase transition in crystalline K<Subscript>3</Subscript>Na(CrO<Subscript>4</Subscript>)<Subscript>2</Subscript>: Acoustic studies

Ultrasonic studies of the temperature behavior of the velocity and damping of sound for the xx and zz longitudinal and yx and zx transverse waves in K₃Na(CrO₄)₂ have been carried out in the temperature interval 185–295 K, which includes the region of the ferroelastic phase transition. The acoustic parameters for both shear and longitudinal waves were found to have anomalies in the region of the phase transition with a Curie temperature of 235.5 K. A theoretical analysis of the softening of the elastic moduli c₄₄ and c₆₆ was performed on the basis of the Landau expansion in terms of the strain tensor components ?₄ and (?₂-?₁)/2 considered as the linearly coupled primary and secondary order parameter, respectively. The absolute values of the elastic moduli c₁₁, c₃₃, c₄₄, c₆₆, c₁₂, and c₁₄ at 295 K were calculated.     

Potential ultra-incompressible material ReN: First-principles prediction

The structural, elastic and electronic properties of ReN are investigated by first-principles calculations based on density functional theory (DFT). The most stable structure of ReN is a NiAs-like structure, belonging to space group P6₃/mmc with a=2.7472 and c=5.8180 Å. ReN is a metallic ultra-incompressible solid and it exhibits low elastic anisotropy. Its linear incompressibility along the c-axis exceeds that of diamond. Its ultra-incompressibility is attributed to the high valence electron density and strong covalence bondings. Our results indicate that ReN can be used as a potential ultra-incompressible conductor. In particular, a superconducting transition temperature is predicted as T_c≈4.8 K for NiAs-like ReN, which agrees well with the available experimental value.     

Anomalously low elastic stability of NaCl-H<Subscript>2</Subscript>O ice at low temperatures

Water-NaCl solid solutions with the salt weight fraction p = 0.0001–0.1000 subjected to high uniaxial compression exhibit elastic instability (similar to the Bridgman explosive effect) in the temperature range 100–260 K. At temperatures from 225 to 260 K, stability threshold P _c (or a critical pressure at which the explosive instability occurs) of these solutions is equal to, or higher than, P _c for pure water ice. However, in the temperature interval 100–225 K, thresholds P _c for the NaCl-water solid solutions with p ≥ 0.001 are anomalously low. The largest drop of P _c (by 15 to 30 times relative to P _c for pure water ice) is observed for low p, 0.001 ≤ p ≤ 0.010. The possible structure of the solid ice solutions in all the temperature ranges mentioned above is analyzed in terms of the percolation theory as applied to elastic networks.     

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     

氦泡对铝的弹性性质的影响

主要利用分子动力学方法模拟计算了含氦泡的铝的弹性性质,首先,应用第一性原理的方法计算了Al-He的相互作用势.其次,从两个不同的方面研究了氦泡对铝弹性常数的影响,一是不同的氦泡尺寸(直径分别是16, 20, 25, 30和3.5nm),二是不同的氦泡压力(即固定氦泡大小,氦泡内氦原子的个数与空位的比分别大约是5％,15％,45％ 和85％).结果表明弹性常数随着氦泡半径的增大而减小,对于固定大小的氦泡,随着氦泡内的压力变化弹性常数基本保持恒定.最后通过建立弹性复合体模型,得到的解析解定性上解释了氦泡的大小以及内压对铝的弹性常数的影响,与分子动力学模拟结果吻合. 关键词： 辐照损伤 氦泡 分子动力学 弹性常数     

First-principles calculations on elasticity of under pressure

First-principles calculations of the crystal structure and the elastic properties of OsN₂ have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as with some of the existing model calculations. The dependence of the elastic constants c_ij, the aggregate elastic moduli (B,G,E), Poisson’s ratio, and the elastic anisotropy on pressure has been investigated. Moreover, the variation of the Debye temperature and the compressional and shear elastic wave velocities with pressure P up to 60 GPa at 0 K have been investigated for the first time.