金属玻璃流变的扩展弹性模型

玻璃-液体转变现象,简称玻璃转变,被诺贝尔物理学奖获得者安德森教授评为最深奥与重要的凝聚态物理问题之一.金属玻璃作为典型的非晶态物质,具有与液体相似的无序原子结构,因此又称为冻结了的液态金属,是研究玻璃转变问题的理想模型材料.当加热至玻璃转变温度,或者加载到力学屈服点附近时,金属玻璃将会发生流动.由于热或应力导致的流动现象对金属玻璃的应用具有重要意义.本文简要回顾了金属玻璃流变现象,综述了流变扩展弹性模型的研究进展和未来发展趋势.     

Low-frequency elastic properties,domain dynamics,and spontaneous twisting of SrTiO<Subscript>3</Subscript> near the ferroelastic phase transition

The low-frequency elastic properties of strontium titanate near the ferroelastic phase transition were studied by the torsional-vibration technique. Domain wall motion was shown to contribute noticeably to the anomalies in the shear modulus and internal friction. It was established that the wall motion under varying elastic stresses is an unactivated process corresponding to viscous flow with a relaxation time inversely proportional to temperature. Spontaneous twisting of samples at the phase transition was revealed, and a model is proposed to account for the sample chirality and the spontaneous twisting effect.     

Tribological system in the boundary friction mode under a periodic external action

A mechanical analog of a tribological system in the boundary friction mode is studied. A thermodynamic model is used to analyze the first-order phase transition between liquidlike and solidlike structures of a lubricant. The time dependences of the friction force, the relative velocity of the interacting surfaces, and the elastic component of the shear stresses appearing in the lubricant are obtained. It is shown that, in the liquidlike state, the shear modulus of the lubricant and the elastic stresses become zero. The intermittent (stick-slip) friction mode detected experimentally is described. It is shown that, as the lubricant temperature increases, the frequency of phase transitions between the lubricant structural states decreases and the total friction force and elastic stress amplitudes lower. When the temperature or the elastic strain exceeds the corresponding critical value, the lubricant melts and a kinetic slip mode in which the elastic component of the friction force is zero takes place.     

Phenomenological equations of the glass transition in liquids

The paper presents a theoretical analysis of the glass transition. It is demonstrated that the kinetics of glass transition is described by the following equations: the Maxwell equation of a viscoelastic medium; the equation of elastic relaxation, which, in addition to the usual Debye term, involves a nonlinear term due to the positive feedback between the strain field and temperature; and the equation of specific heat continuity, in which the entropy term includes the contribution of elastic fields and the heat flux contains a term related to external cooling. These equations are analogous to the Lorenz synergetic system, in which the strain plays the role of an order parameter, the conjugate field reduces to elastic stresses, and the temperature is a controlling parameter.     

Alpha-plutonium's polycrystalline elastic moduli over its full temperature range

alpha-plutonium's volume-corrected polycrystal elastic moduli were measured between 18 K and the upper limit of its occurrence, near 400 K. The two independent moduli for a polycrystal-bulk and shear-behave smoothly, indicating no phase transition. Both moduli show the same 50% increase on cooling, an order of magnitude larger than in other metals. The Debye temperature obtained from low-temperature elastic moduli, 207 K, significantly exceeds most previous estimates. The Gruneisen parameter gamma=5.3, obtained from the temperature dependence of the bulk modulus, is intermediate among previous estimates using other approaches, alpha-plutonium's Poisson ratio nu is low: 0.18, nearly temperature independent, and its small decrease on warming opposes usual behavior. The high gamma, large but equal bulk modulus and shear modulus fractional stiffening on cooling, and near-temperature-invariant nu are attributed to a single mechanism: 5-f electron localization-delocalization.     

Nonlinear surface waves in soft, weakly compressible elastic media

Nonlinear surface waves in soft, weakly compressible elastic media are investigated theoretically, with a focus on propagation in tissue-like media. The model is obtained as a limiting case of the theory developed by Zabolotskaya [J. Acoust. Soc. Am. 91, 2569-2575 (1992)] for nonlinear surface waves in arbitrary isotropic elastic media, and it is consistent with the results obtained by Fu and Devenish [Q. J. Mech. Appl. Math. 49, 65-80 (1996)] for incompressible isotropic elastic media. In particular, the quadratic nonlinearity is found to be independent of the third-order elastic constants of the medium, and it is inversely proportional to the shear modulus. The Gol'dberg number characterizing the degree of waveform distortion due to quadratic nonlinearity is proportional to the square root of the shear modulus and inversely proportional to the shear viscosity. Simulations are presented for propagation in tissue-like media.     

Temperature effect on the elastic properties of yttrium garnet ferrite Y<Subscript>3</Subscript>Fe<Subscript>5</Subscript>O<Subscript>12</Subscript>

The Young’s moduli along the [100] and [110] crystallographic directions and the shear modulus along the [100] direction in a high-purity yttrium garnet ferrite single crystal are measured in the temperature range from 20 to 600°C. All the independent elastic constants are calculated for this temperature range. The behavior of the elastic moduli and elastic anisotropy factor is analyzed in the vicinity of the critical temperature of the magnetic phase transition.     

Evidence for strain glass in the ferroelastic-martensitic system Ti(50-x)Ni(50+x)

We report here "strain glass," a new glassy phenomenon in ferroelastic-martensitic system of Ni-rich intermetallic Ti(50-x)Ni(50+x) (x > 1), where local strain is frozen in disordered configuration below a critical temperature Tg. The ac elastic modulus shows a minimum at Tg, which exhibits logarithmic frequency dependence following Vogel-Fulcher relationship, and the corresponding internal friction shows a frequency-dependent peak located at a lower temperature. In situ high-resolution transmission electron microscopy observations reveal uncorrelated nanoclusters of martensiticlike phase, randomly frozen in the otherwise untransformed parentlike matrix. Being parallel to spin glass and relaxor, strain glass may shed new light on the fundamental physics of glass and lead to the discovery of novel properties.     

Nonlinear response and avalanche behavior in metallic glasses

The response to different stress amplitudes at temperatures below the glass transition temperature is analyzed by mechanical oscillatory excitation of Pd₄₀Ni₄₀P₂₀ metallic glass samples in single cantilever bending geometry. While low amplitude oscillatory excitations are commonly used in mechanical spectroscopy to probe the relaxation spectrum, in this work the response to comparably high amplitudes is investigated. The strain response of the material is well below the critical yield stress even for highest stress amplitudes, implying the expectation of a linear relation between stress and strain according to Hooke’s Law. However, a deviation from the linear behavior is evident, which is analyzed in terms of temperature dependence and influence of the applied stress amplitude by two different approaches of evaluation. The nonlinear approach is based on a nonlinear expansion of the stress-strain-relation, assuming an intrinsic nonlinear character of the shear or elastic modulus. The degree of nonlinearity is extracted by a period-by-period Fourier-analysis and connected to nonlinear coefficients, describing the intensity of nonlinearity at the fundamental and higher harmonic frequencies. The characteristic timescale to adapt to a significant change in stress amplitude in terms of a recovery timescale to a steady state value is connected to the structural relaxation time of the material, suggesting a connection between the observed nonlinearity and primary relaxation processes. The second approach of evaluation is termed the incremental analysis and relates the observed response behavior to avalanches, which occur due to the activation and correlation of local microstructural rearrangements. These rearrangements are connected with shear transformation zones and correspond to localized plastic events, which are superimposed on the linear response behavior of the material.     

Shearing or compressing a soft glass in 2D: time-concentration superposition

We report surface shear rheological measurements on dense insoluble monolayers of micron sized colloidal spheres at the oil/water interface and of the protein beta-lactoglobulin at the air/water surface. As expected, the elastic modulus shows a changing character in the response, from a viscous liquid towards an elastic solid as the concentration is increased, and a change from elastic to viscous as the shear frequency is increased. Surprisingly, above a critical packing fraction, the complex elastic modulus curves measured at different concentrations can be superposed to form a master curve. This provides a powerful tool for the extrapolation of the material response function outside the experimentally accessible frequency range. The results are discussed in relation to recent experiments on bulk systems, and indicate that these two-dimensional monolayers should be regarded as being close to a soft glass state.     

Elastic strain response in the modified phase-field-crystal model

To understand and develop new nanostructure materials with specific mechanical properties, a good knowledge of the elastic strain response is mandatory. Here we investigate the linear elasticity response in the modified phase-field-crystal(MPFC) model. The results show that two different propagation modes control the elastic interaction length and time, which determine whether the density waves can propagate or not. By quantitatively calculating the strain field, we find that the strain distribution is indeed extremely uniform in case of elasticity. Further, we present a detailed theoretical analysis for the orientation dependence and temperature dependence of shear modulus. The simulation results show that the shear modulus reveals strong anisotropy and the one-mode analysis provides a good guideline for determining elastic shear constants until the system temperature falls below a certain value.     

The influence of a wieghardt type elastic foundation on the stability of some beams subjected to distributed tangential forces

In this investigation, the influence of a Wieghardt type elastic foundation on the stability of cantilever and clamped-hinged beams subjected to either a uniformly or a linearly distributed tangential force is considered. In addition to the usual transverse foundation modulus, the Wieghardt model includes the effects of inertia and shear deformation in the foundation. Approximate solutions of the Ritz type are obtained for the pertinent eigenvalue problems, and numerical calculations are reported for various combinations of the internal damping, inertia, transverse foundation modulus and shear foundation modulus parameters. The numerical results reveal that, in general, for a fixed value of the transverse foundation modulus parameter κ, an increase in the shear foundation modulus increases the critical load, whereas an increase in the foundation inertia parameter tends to decrease the critical load. The system consisting of a clamped-hinged beam subjected to a uniformly distributed tangential force loses stability through divergence, provided that the value of κ is sufficiently small. However, when κ becomes large enough, stability will be lost through flutter. In this case, the critical load considered as a function of κ possesses a discontinuity at the transition between divergence and flutter, and its value will either increase or decrease, depending upon the degree of damping in the system.     

Ab initio study of structural,elastic, and high-pressure properties of rubidium halides RbX (X = F,Cl, Br and I)

We present first-principle calculations on the structural, elastic, and high-pressure properties of rubidium halides compounds, using the pseudo-potential plane-waves approach based on density functional theory, within the generalized gradient approximation. Results are given for lattice constant, bulk modulus and its pressure derivative. The pressure transition at which these compounds undergo structural phase transition from NaCl-type to CsCl-type structure are calculated and compared with previous calculations and available experimental data. The elastic constants and their pressure dependence are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young's modulus and Poisson's ratio for ideal polycrystalline RbF, RbCl, RbBr, and RbI aggregates. We estimated the Debye temperature of these compounds from the average sound velocity.     

Elastic interaction of two atoms adsorbed on a solid surface

The long-range interaction of two adsorbed atoms mediated by the elastic distortion of the substrate is calculated classically for an elastically isotropic substrate. For identical atoms, the interaction is repulsive; for different atoms, it can be repulsive or attractive. It varies as ρ^?3 with the distance ρ between the two adsorbed atoms. This is the same spatial dependence as for the dipole - dipole interaction between two adsorbed atoms. For two xenon atoms adsorbed on gold, the elastic interaction is somewhat smaller than the dipole-dipole interaction. The interaction energy is inversely proportional to the shear modulus of the substrate, so that it may become quite large near a distortive phase transition.     

The ferroelastic transition of betaine borate

The ferroelastic transition of betaine borate at about 142 K and the nonlinear temperature dependence of the corresponding critical elastic modulus are related to the softening of optical phonons. The transition has to be considered a ferroelastic one of the optic type, i.e. pseudoproper one, therefore. It is shown by Raman spectroscopic results that the transition is induced by a strong bilinear coupling between a homogeneous strain and at least two optic lattice modes which are of the same symmetry as the strain. Optic and dielectric, investigations support the second-order character of and the classical behaviour at this transition, which have been reported in the literature. Differences and similarities to the ferroelastic transition of betaine fumarate are discussed.     

The ferroelastic transition of betaine borate

The ferroelastic transition of betaine borate at about 142 K and the nonlinear temperature dependence of the corresponding critical elastic modulus are related to the softening of optical phonons. The transition has to be considered a ferroelastic one of the optic type, i.e. pseudoproper one, therefore. It is shown by Raman spectroscopic results that the transition is induced by a strong bilinear coupling between a homogeneous strain and at least two optic lattice modes which are of the same symmetry as the strain. Optic and dielectric, investigations support the second-order character of and the classical behaviour at this transition, which have been reported in the literature. Differences and similarities to the ferroelastic transition of betaine fumarate are discussed.     

Isothermal kinetics and relaxation recovery of high-frequency shear modulus in the course of structural relaxation of Pd<Subscript>40</Subscript>Cu<Subscript>30</Subscript>Ni<Subscript>10</Subscript>P<Subscript>20</Subscript> bulk glass

Isothermal kinetics of relaxation of the high-frequency (1.4 MHz) shear modulus during structural relaxation of Pd₄₀Cu₃₀Ni₁₀P₂₀ bulk metallic glass below the glass transition temperature is studied by an in situ method of contactless electromagnetic acoustic transformation. The kinetic law of relaxation is established. It is shown that quenching of aged samples from the supercooled liquid state leads to a decrease in the absolute value of shear modulus to below the initial value; the degree of subsequent isothermal relaxation of the modulus may be several times higher than the initial value. Possible reasons for relaxation and recovery of the shear modulus are considered.     

高压下RhB的相变、弹性性质、电子结构及硬度的第一性原理计算

采用密度泛函理论中的赝势平面波方法系统地研究了高压下RhB的结构相变、弹性性质、电子结构和硬度.分析表明,RhB在25.3 GPa时从anti-NiAs结构相变到FeB结构,这两种结构的弹性常数、体弹模量、剪切模量、杨氏模量和弹性各向异性因子的外压力效应明显.电子态密度的计算结果显示,这两种结构是金属性的,且费米能级附近的峰随着压强的增大向两侧移动,赝能隙变宽,轨道杂化增强,共价性增强,非局域化更加明显.此外,硬度计算结果显示,anti-NiAs-RhB的金属性比较弱,有着较高的硬度,属于硬质材料.     

A Comprehensive Numerical Investigation on the Mechanical Properties of Hetero-Junction Carbon Nanotubes

A set of forty-three hetero-junction CNTs, made of forty-four homogeneous carbon nanotubes of different chiralities and configurations with all possible hetero-connection types, were numerically simulated, based on the finite element method in a commercial finite element software and their Young's and shear moduli, and critical buckling loads were obtained and evaluated under the tensile, torsional and buckling loads with an assumption of linear elastic deformation and also compared with each other. The comparison of the linear elastic behavior of hetero-junction CNTs and their corresponding fundamental tubes revealed that the size, type of the connection, and the bending angle in the structure of hetero-junction CNTs considerably influences the mechanical properties of these hetero-structures. It was also discovered that the Stone-Wales defect leads to lower elastic and torsional strength of hetero-junction CNTs when compared to homogeneous CNTs. However, the buckling strength of the hetero-junction CNTs was found to lie in the range of the buckling strength of their corresponding fundamental tubes. It was also determined that the shear modulus of hetero-junction carbon nanotubes generally tends to be closer to the shear modulus of their wider fundamental tubes while critical buckling loads of these heterostructures seem to be closer to critical buckling loads of their thinner fundamental tubes. The evaluation of the elastic properties of hetero-junction carbon nanotubes showed that among the hetero-junction models, those with armchair-armchair and zigzag-zigzag kinks have the highest elastic modulus while the models with armchair-zigzag connections show the lowest elastic stiffness. The results from torsion tests also revealed the fact that zigzag-zigzag and armchair-zigzag hetero-junction carbon nanotubes have the highest and the lowest shear modulus, respectively. Finally, it was observed that the highest critical buckling loads belong to armchair-armchair hetero-junction carbon nanotubes and the lowest buckling strength was found with the hetero-junction models with armchair-zigzag connection.     

Elastic properties and spectroscopic studies of lithium lead borate glasses

Elastic properties of xLi₂O — 20PbO — (80-x)B₂O₃ glasses have been measured at a frequency of 10 MHz using X-cut and Y-cut quartz transducers. The trends in the variation of elastic moduli, Poisson’s ratio and Debye temperature have been studied. The elastic moduli namely longitudinal and young’s modulus show strong linear dependence while bulk and shear modulus vary marginally as a function of Li₂O concentration. The Poisson’s ratio is found to be almost constant and Debye temperature increases with the increase of Li₂O concentration. IR, MAS-NMR and glass transition temperature studies have been also carried out. Glass transition temperature is found to increase with increase of Li₂O concentration. IR and MAS-NMR spectra show characteristic features of borate network and systematic change as a function of Li₂O concentration. The variation in the elastic properties and structural features of IR and MAS-NMR indicate that Pb²⁺ ions are likely to occupy network forming positions in this glass system. Paper presented at the 2nd International Conference on Ionic Devices, Anna University, Chennai, India, Nov. 28–30, 2003.