The effect of grain size distribution on the frequency dependence of the ultrasonic attenuation in polycrystalline materials

An expression has been derived for the effect of the grain size distribution in polycrystalline materials on the frequency dependence of the ultrasonic attenuation. It has been shown that two specimens with the same mean grain size can have significantly different ultrasonic attenuations if their grain size distributions are different and that no unique solution in terms of the grain size exists for a particular ultrasonic attenuation against frequency curve. Qualitative agreement has been found between the theory and some of the experimental data available.     

Nonequilibrium statistical mechanical formulation for grain growth

A nonequilibrium statistical mechanical theory for grain growth is presented in this paper. The fluctuation of grain growth is determined from the self similarity of grain size distribution. The grain size distribution scaled by the averaged size is derived under the condition that the volume of specimen is strictly conserved. The growth law of grain is also derived. The scaled grain size distribution are compared with the associating lognormal distribution which is usually used in the analysis of the experimental results. It has been found that the theoretical results is in good agreement with experimental results.     

Nonequilibrium statistical mechanical formulation for grain growth

A nonequilibrium statistical mechanical theory for grain growth is presented in this paper. The fluctuation of grain growth is determined from the self similarity of grain size distribution. The grain size distribution scaled by the averaged size is derived under the condition that the volume of specimen is strictly conserved. The growth law of grain is also derived. The scaled grain size distribution are compared with the associating lognormal distribution which is usually used in the analysis of the experimental results. It has been found that the theoretical results is in good agreement with experimental results.     

考虑晶粒分布的多晶体材料超声散射统一理论

现有超声散射统一理论可通过多晶体材料的微观结构和力学特性,实现全频域范围内衰减和相速度的正演建模,但其忽略晶粒尺寸分布的影响,进而降低了正演模型的计算精度.本文对不均匀介质的波动方程进行二阶Keller近似,用全频域格林函数推导介质中的平均波;以截断对数正态分布描述晶粒分布,构建加权的空间相关函数;结合材料的弹性模量协方差,建立含晶粒分布的超声散射统一理论,揭示晶粒分布对超声散射的影响规律;制备304不锈钢试块并开展超声散射实验.结果表明考虑晶粒分布特性后,纵波衰减谱和相速度谱相对于实验结果的相异性降低约49%和64%,横波衰减谱和相速度谱相对于实验结果的相异性降低约12%和4%.可见,本文的统一理论模型能有效修正晶粒分布导致的衰减谱和相速度谱偏差,为晶粒分布反演评价提供理论基础.     

Influence of grain size on the electrical properties of the double-layered LaSr2Mn2O7 manganite

The double-layered LaSr₂Mn₂O₇ manganite was synthesized by the sol–gel process. Two samples with the average grain size from ～150 nm to ～1 μm were prepared by controlling the sintering temperature. Both samples had a tetragonal structure, with a small fraction of impurity phase in the S-1250 sample. In order to investigate the probable influence of grain size on the conduction mechanism, resistivity of the samples was measured as a function of temperature, and the data obtained was analyzed by different conduction mechanisms. It was found that with increase in the grain size, resistivity decreased at all temperature ranges. The results show that the adiabatic small polaron hopping (SPH) model is probably responsible for conduction at high temperature range, and that the 3D variable range hopping (VRH) model shows a better correlation with the experimental data for low temperature range. These analyses indicate the influence of grain size on the parameters obtained from fitting the data by both models.     

The magnetostriction of Invar alloys

The principles of the theory of a phase transition into a magnetically ordered state are formulated for Invar alloys and other similar inhomogeneous ferromagnets, for which the concept of a local Curie temperature distribution corresponding to the experimentally observed broadened temperature interval of the transition into the ferromagnetic state has existed for 10 years. A method is proposed for obtaining information about the local temperature distribution from experimental data on the change in the properties of magnets in response to a change in temperature. For iron-nickel-chromium alloys it is shown how to obtain the temperature dependence of the magnetostrictional susceptibility of the paraprocess from data on the magnetic contribution to the thermal expansion coefficient. This confirms the important role of the local Curie temperature distribution, and it also indicates a need for new analysis of experimental data on temperature-broadened magnetic ordering phase transitions. Zh. éksp. Teor. Fiz. 113, 213–227 (January 1998)     

On the critical dynamics of ferromagnets

The dynamic scaling functions for ferromagnets above and below the critical temperature are determined using mode coupling theory. Below the critical temperature we study isotropic ferromagnets taking into account the exchange interaction only and give the first numerical solution of the resulting mode coupling equations. In the paramagnetic phase we examine how the critical dynamics is modified by the addition of the dipoledipole interaction. On the basis of this theory we are able to explain in a unifying fashion the results of different experimental methods; i.e.: neutron scattering, hyperfine interaction and electron-spin resonance. Predictions for new experiments are made.     

Roles of nonequilibrium conduction electrons on the magnetization dynamics of ferromagnets

The mutual dependence of spin-dependent conduction and magnetization dynamics of ferromagnets provides the key mechanisms in various spin-dependent phenomena. We compute the response of the conduction electron spins in a spatial and time varying magnetization M(r,t) in the time-dependent semiclassical transport theory. We show that the induced nonequilibrium conduction spin density in turn generates four spin torques acting on the magnetization-with each torque playing a different role in magnetization dynamics. By comparing with recent theoretical models, we find that one of these torques which has not been previously identified is crucial to consistently interpreting experimental data on domain wall motion.     

Modelling of austenite grain growth kinetics in a microalloyed steel (30MSV6) in the presence of carbonitride precipitates

Austenite grain growth kinetics in the presence of secondary precipitates of a microalloyed steel (30MSV6) was studied employing quantitative metallographic techniques. Austenitizing experiments were carried out at 1,000, 1,100 and 1,200?°C. According to the experimental data, abnormal grain growth behaviour is observed at 1,100?°C while it is normal at 1,000 and 1,200?°C. TEM observation represents multicomponent carbonitride precipitate, (Ti,V)(C,N), in the as-received steel with a mean radius of 35?nm. A mathematical model is proposed considering austenite grain growth along with dissolution and coarsening kinetics of the multicomponent precipitates. The austenite grain growth model for short-term non-isothermal and subsequent long-term isothermal heating stages was developed using a statistical approach. The model includes an algorithm to estimate the size distribution of austenite grains. Precipitate mean field dissolution and Lifshitz–Slyozov–Wagner coarsening models were integrated in the proposed model to calculate the pinning pressure retarding the grain boundary movement. The mean austenite grain size and the grain size distribution (normal and abnormal) calculated by the model are in good agreement with experimental data.     

Grain boundary curvature and grain growth kinetics with particle pinning

Second-phase particles are used extensively in design of polycrystalline materials to control the grain size. According to Zener’s theory, a distribution of particles creates a pinning pressure on a moving grain boundary. As a result, a limiting grain size is observed, but the effect of pinning on the detail of grain growth kinetics is less known. The influence of the particles on the microstructure occurs in multiple length scales, established by particle radius and the grain size. In this article, we use a meso-scale phase-field model that simulates grain growth in the presence of a uniform pinning pressure. The curvature of the grain boundary network is measured to determine the driving pressure of grain growth in 2D and 3D systems. It was observed that the grain growth continues, even under conditions where the average driving pressure is smaller than the pinning pressure. The limiting grain size is reached when the maximum of driving pressure distribution in the structure is equal to the pinning pressure. This results in a limiting grain size, larger than the one predicted by conventional models, and further analysis shows consistency with experimental observations. A physical model is proposed for the kinetics of grain growth using parameters based on the curvature analysis of the grain boundaries. This model can describe the simulated grain growth kinetics.     

Formation of inhomogeneous magnetic structures in weak ferromagnets with rhombohedral symmetry

A model of formation of inhomogeneous magnetic structures in weak ferromagnets with rhombohedral symmetry is proposed. This model is based on the general theory of ferromagnetism in these compounds. The quantitative calculations of the dependence of the period of magnetic inhomogeneities on the parameters of the samples are presented and compared with experimental data.     

Inhomogeneous magnetic structures in rhombohedral weak ferromagnets

A model of formation of inhomogeneous magnetic structures in weak ferromagnets of rhombohedral symmetry is presented, which is based on the general theory of ferromagnetism in such compounds. The dependence of the period of magnetic inhomogeneities on the parameters of samples is qualitatively calculated. A comparison with experimental data is given.     

Parametric excitation of phonons in iron borate (FeBO3)

The nonlinear relaxation of the ferromagnetic resonance into short-wavelength phonons is investigated theoretically for weak ferromagnets. A generalized theory of firstorder Suhl instabilities is elaborated showing that the decisive nonlinear term results from the magnetoelastic interaction. Nonlinearities of the dipole-dipole-interaction, generally predominating parametric effects in ferro- and ferrimagnetic materials, can be neglected. The results fit in satisfactorily with the experimental data obtained for FeBO₃.     

On the annealing of junction disclinations in deformed polycrystals

The kinetics of relaxation of disclination quadrupoles formed within triple junctions of grains during plastic deformation are studied. The calculations are made using the discrete dislocation model for disclinations by simulating the climb of dislocations. Exponential relationships are obtained for the relaxation of the strength and elastic energy of disclination quadrupoles with a characteristic time proportional to the cube of grain size. The distribution of vacancy fluxes along grain boundaries (GBs) during the relaxation of a disclination quadrupole is studied in detail. The relation between continuum and discrete dislocation approaches to a study of the GB recovery process is considered. Characteristics of each relaxation stage are studied. A hierarchy of characteristic relaxation times for dimerent grain size ranges is constructed and it is show that in nanocrystalline materials the spreading time of trapped lattice dislocations can depend on the grain size.     

Size effects under martensitic deformation of shape-memory alloys

The effect of the grain size and film thickness on the parameters of martensitic transitions and deformation behavior of shape-memory alloys is studied in terms of the theory of smeared martensitic transitions. Comparison of theoretical results with experimental data suggests that the transformation kinetics related to the growth mechanism and shrinkage of martensite lamellas when transformation steps (dislocations) move along their boundaries is most sensitive to the size factor.     

考虑晶粒尺寸效应的超薄(10–50 nm) Cu电阻率模型研究

结合Marom模型与实验数据, 给出了晶粒尺寸与金属薄膜厚度的关系式. 基于已有的理论模型, 针对厚度为10–50 nm Cu薄膜, 考虑到表面散射与晶界散射以及电阻率晶粒尺寸效应, 提出一种简化电阻率解析模型. 结果表明, 在10–20 nm薄膜厚度范围内, 考虑晶粒尺寸效应后的简化模型与现有实验数据符合得更好. 相对于Lim, Wang与Marom模型, 所提模型的相对标准差分别降低74.24%, 54.85%, 78.29%. 关键词： 表面散射 晶界散射 晶粒尺寸效应 平均自由程     

Mode coupling theory for the critical dynamics of dipolar ferromagnets

The critical dynamics of ferromagnets has been studied by various experimental methods sampling different regions in wave vector space. Nevertheless there seemed to be a list of contradictions between these experiments. Within a mode coupling theory including both short range exchange and long range dipolar interaction we are able to resolve the seemingly contradictory situation.     

Critical dynamics of magnets

We review our current understanding of the critical dynamics of magnets above and below the transition temperature with focus on the effects due to the dipole-dipole interaction present in all real magnets. Significant progress in our understanding of real ferromagnets in the vicinity of the critical point has been made in the last decade through improved experimental techniques and theoretical advances in taking into account realistic spin-spin interactions. We start our review with a discussion of the theoretical results for the critical dynamics based on recent renormalization group, mode coupling and spin-wave theories. A detailed comparison is made of the theory with experimental results obtained by different measuring techniques, such as neutron scattering, hyperfine interaction, muon spin resonance, electron spin resonance, and magnetic relaxation, in various materials. Furthermore we discuss the effects of dipolar interaction on the critical dynamics of three-dimensional isotropic antiferromagnets and uniaxial ferromagnets. Special attention is also paid to a discussion of the consequences of dipolar anisotropies on the existence of magnetic order and the spin-wave spectrum in two-dimensional ferromagnets and antiferromagnets. We close our review with a formulation of critical dynamics in terms of nonlinear Langevin equations.     

Optical extinction for determining the size distribution of gold nanoparticles fabricated by ultra-short pulsed laser ablation

This work presents a method, based on measurements of the optical extinction spectra, to determine the size of spherical gold nanoparticles produced using the femtosecond laser ablation process in deionized water. By using an improved theoretical model that modifies the contribution of the free electrons to the dielectric function introducing a size-dependent term, it is possible to fit the full experimental extinction spectrum considering a certain size distribution. Additionally, in order to obtain complementary measurements of the size distribution, TEM analysis was performed. The results obtained showed that the predominant nanoparticle size distribution ranges from 1 to 11 nm in terms of radii. An optical extinction measurement together with an appropriate theoretical model based on Mie’s theory represents a simple, low-cost, fast and easy method to describe a multimodal size distribution of spherical gold nanoparticles.     

Microscopic theory of non local pair correlations in metallic F/S/F trilayers

We consider a microscopic theory of F/S/F trilayers with metallic or insulating ferromagnets. The trilayer with metallic ferromagnets is controlled by the formation of non local pair correlations among the two ferromagnets which do not exist with insulating ferromagnets. The difference between the insulating and ferromagnetic models can be understood from lowest order diagrams. Metallic ferromagnets are controlled by non local pair correlations and the superconducting gap is larger if the ferromagnetic electrodes have a parallel spin orientation. Insulating ferromagnets are controlled by pair breaking and the superconducting gap is smaller if the ferromagnetic electrodes have a parallel spin orientation. The same behavior is found in the presence of disorder in the microscopic phase variables and also in the presence of a partial spin polarization of the ferromagnets. The different behaviors of the metallic and insulating trilayers may be probed in experiments. Received 4 July 2001 and Received in final form 8 November 2001