Two-scale micromechanics-based probabilistic modeling of domain switching in ferroelectric ceramics

A two-scale micromechanics model is developed in this paper to analyze domain switching in ferroelectric ceramics, using a probabilistic domain switching criterion based on energetic analysis. The microstructure of ferroelectric ceramics at two distinct length scales, domains and grains, has been carefully analyzed. The interaction at domain level is accounted for by energy minimization theory, while the fluctuation at grain level is analyzed using ellipsoidal two-point correlation function. The model has been implemented by Monte Carlo method, and applied to simulate the electric poling and mechanical depoling of Pb(Zr_xTi_1-x)O₃ (PZT) ceramics across morphotropic phase boundary (MPB). The drastically different switching characteristics of PZT ceramics across MPB has been captured, and good agreement with experiments has been observed. The effects of the transformation strains and spontaneous polarizations are highlighted, confirming the proposition of Li et al. [2005. Domain switching in polycrystalline ferroelectric ceramics. Nature Materials 4, 776–781] that the strain compatibility plays a dominant role in domain switching in ferroelectric ceramics.     

Experimental validation of the spectral criterion for the diagnosis of periodic rod structures using ferroelectric strain gauges

Successive impact excitation and construction of Fourier transforms of linear and nonlinear strain responses and phase portraits of undamaged or damaged vertically suspended models of a periodic welded rod structure were used to establish the dependence of the area ratio of the phase portraits of the nonlinear and linear domains of the strain response, which characterizes the stress (damage) of the model, on the impact momentum. The dynamic strain responses were recorded using ultra-wideband (10^?2–10⁸ Hz) ferroelectric microgauges based on thin Pb(Zr_0.53Ti_0.47)O₃ films 2 µm in thickness with a 0.8 mm² contact area.     

Interplay between polarization rotation and crack propagation in PMN-PT relaxor single crystals

Investigations on the interconnection between the polarization rotation and crack propagation are performed for [110]-oriented 74Pb(Mg_1/3Nb_2/3)O₃-26PbTiO₃ relaxor ferroelectric single crystal under electric loadings along [001] direction. The crystal is of predominantly monoclinic M_A phase with scatter distributed rhombohedral (R) phase under a moderate poling field of 900 V/mm in [001] direction. With magnitude of 800 V/mm, a through thickness crack is initiated near the electrode by electric cycling. Static electric loadings is then imposed to the single crystal. As the applied static electric field increases, domain switching in the monoclinic M_A phase and phase transition from M_A to R phase occur near the crack. The results indicate that the crack features a conducting one. Whether domain switching or phase transition occurs depends on the intensity of the electric field component that is perpendicular to the applied electric field.     

Asymptotic computation of the inhomogeneity energy in a body in an external stress field

We consider a problem on an ellipsoidal inhomogeneity in an infinitely extended homogeneous isotropic elastic medium. The inhomogeneity differs from the ambient body in the elastic moduli (Poisson’s ratio ν and shear modulus μ) and in that it has intrinsic strains. We use the equivalent inclusion method to write out expressions for the Helmholtz and Gibbs free energy of the inhomogeneity as quadratic forms in the intrinsic strains and strains at infinity. The general expressions for the coefficients of these quadratic forms are written out as three rank four tensors characterizing the contribution to the energy by the plastic strain (ɛ _p ²), by the strain at infinity (ɛ ₀²), and (only for the Gibbs energy) by the cross term ɛ ⁰ ɛ _p .     

On the thermodynamic framework of generalized coupled thermoelastic-viscoplastic-damage modeling

A complete potential based framework utilizing internal state variables is put forth for the derivation of reversible and irreversible constitutive equations. In this framework, the existence of the total (integrated) form of either the (Helmholtz) free energy or the (Gibbs) complementary free energy are assumed a priori. Two options for describing the flow and evolutionary equations are described, wherein option one (the fully coupled form) is shown to be over restrictive and the second option (the decoupled form) provides significant flexibility. As a consequence of the decoupled form, a new operator, that is, the compliance operator, is defined, which provides a link between the assumed Gibb's and complementary dissipation potential and ensures a number of desirable numerical features, for example, the symmetry of the resulting consistent tangent stiffness matrix. An important conclusion reached is that although many theories in the literature do not conform to the general potential framework outlined, it is still possible in some cases, by slight modifications of the employed forms, to restore the complete potential structure.     

Ti3SiC2、不锈钢和NiCr合金在人工海水中的摩擦学性能

在SRV-1型摩擦磨损试验机上考察了Ti3SiC2、NiCr合金和不锈钢在干摩擦、蒸馏水和人工海水中的摩擦磨损性能,并用扫描电镜(SEM-EDS)及光电子能谱(XPS)对磨痕形貌及成分进行分析.结果表明:Ti3SiC2/Al2O3摩擦副的摩擦系数对摩擦条件变化不敏感,在液体介质中磨损稍有降低.3种摩擦条件下存在机械磨损和摩擦氧化磨损竞争,但机械磨损始终为主要磨损机制,因此摩擦和磨损较大.不锈钢/Al2O3和NiCr合金/Al2O3两摩擦副对摩擦条件变化较敏感,摩擦系数和磨损率在于摩擦、蒸馏水和海水中依次降低,其中NiCr合金降低幅度最大.干摩擦条件下两者以机械磨损为主要磨损机制,表现为黏着磨损和材料转移;蒸馏水中机械磨损和摩擦氧化磨损并存;海水中以腐蚀磨损为主导,腐蚀产物FeCl2、CrCl3或CrO22-或CrO2-等具有减摩抗磨作用.     

On thermodynamic potentials in linear thermoelasticity

The four thermodynamic potentials, the internal energy u=u(ε_ij,s), the Helmholtz free energy f=f(ε_ij,T), the Gibbs energy g=g(σ_ij,T) and the enthalpy h=h(σ_ij,s) are derived, independently of each other, by using the Duhamel–Neumann extension of Hooke's law and an assumed linear dependence of the specific heat on temperature. A systematic procedure is then presented to express all thermodynamic potentials in terms of four possible pairs of independent state variables. This procedure circumvents a tedious transition from one potential to another, based on the formal change of variables, and inversions of the stress–strain and entropy–temperature relations. The general results are applied to uniaxial loading paths under isothermal, adiabatic, constant stress, and constant strain conditions. An interplay of adiabatic and isothermal elastic constants in the expressions for exchanged heat along certain thermodynamic paths is indicated.     

Influence of mass ratio and calcination temperature on physical and photoelectrochemical properties of ZnFe-layered double oxide/cobalt oxide heterojunction semiconductor for dye degradation applications

A visible light-active photoelectrocatalyst, ZnFe-layered double oxide (LDO)/cobalt(II,III) oxide (Co₃O₄) composites were obtained by calcining the Co loaded ZnFe-layered double hydroxide (LDH) prepared by a hydrothermal and microwave hydrothermal method. The morphological studies revealed that the ZnFe-LDO/Co₃O₄ composites exhibited a flower-like structure comprising Co₃O₄ nanowires and ZnFe-LDO nanosheets. Further, when the mass ratio of Co(NO₃)₂·6H₂O/LDH was 1:1.8 and the calcination temperature was 550 °C, the ZnFe-LDO/Co₃O₄ composite exhibited 93.3% degradation efficiency for methylene blue (MB) at the applied voltage of 1.0 V under visible light after 3 h. Furthermore, the Mott-Schottky model experiments showed that the formation of a p-n heterojunction between ZnFe-LDO and Co₃O₄ could effectively inhibit the recombination of electrons and holes in the photoelectrocatalytic process. Meanwhile, free radical scavenging experiments showed that the active radicals of ⋅OH played an important role in the degradation of MB. Therefore, the photoelectrocatalytic effect of ZnFe-LDO/Co₃O₄ provides a simple and effective strategy for the removal of organic pollutants.     

Synthesis and phase evolution of LiNb0.6Ti0.5O3 powder via a sol–gel method

A simple sol–gel route was demonstrated for the synthesis of LiNb_0.6Ti_0.5O₃ (M-phase) powder, using cheap and manageable starting materials at a relatively low temperature. The phase transitions in both chemical and solid-state processes were studied by X-ray diffraction (XRD) in detail. The results showed that in the sol–gel process the anatase TiO₂ phase first appeared at 400 °C and then LiNbO₃ solid solution (LiNbO₃ ss) emerged at 500 °C. When calcined to 600 °C, the M-phase started to appear along with the decrease of TiO₂ and LiNbO₃ ss. Single M-phase could be formed at 700 °C, which is 300 °C lower than that by the traditional solid-state method. A plausible evolution mechanism of the as-synthesized powder in calcination was proposed. The produced powder has potential applications in microelectronics systems.     

Ti_3SiC_2的加入对Ag-MoS_2-graphite复合材料力学及摩擦磨损性能的影响

采用热压烧结技术制备了Ag-Mo S2-graphite和Ag-Mo S2-graphite-Ti3Si C2两种银基自润滑复合材料,考察了两种材料的致密度、硬度、弯曲强度及其在不同环境(大气和低真空)中的摩擦磨损性能.结果表明:低润湿性使得Ti3Si C2与基体界面处的孔隙增多,降低了致密度和弯曲强度,但对硬度影响不明显;摩擦过程中Ti3Si C2颗粒易于从基体材料表面剥落,阻碍了润滑膜的形成,造成Ag-Mo S2-graphite-Ti3Si C2复合材料的摩擦系数高于Ag-Mo S2-graphite复合材料;但Ti3Si C2的添加能够明显提高复合材料在大气中的耐磨性能,这主要与摩擦过程中的材料转移和摩擦化学反应有关.     

Transport coefficients for a partially ionized two-temperature plasma with ions and neutral particles having different masses

The viscosity, heat-conduction, and diffusion coefficients are calculated for a two-temperature three-component plasma composed of ions, neutral particles and electrons when the masses of the ions m_i and neutral particles m_a are different. Similar transport coefficients for m_i=m_a were calculated in [1–3]. The numerical values obtained for the transport coefficients are compared with the values calculated from the formulas of [1–3]. Numerical calculations are carried out for helium with a cesium additive (m_i>m_a) and for krypton with a lithium additive (m_ia).Finally, the author is grateful to V. V. Gogosov, under whose direction this work was carried out.     

Ab initio LDA+U prediction of the tensile properties of chromia across multiple length scales

Periodic density functional theory (DFT) and DFT+U calculations are used to evaluate various mechanical properties associated with the fracture of chromia (Cr₂O₃) along the [0 0 0 1] and directions. The properties investigated include the tensile strength, elastic constants, and surface energies. The tensile strengths are evaluated using an ideal tensile test, which provides the theoretical tensile strength, and by fitting the calculated data to universal binding energy relationships (UBER), which permit the extrapolation of the calculated results to arbitrary length scales. The results demonstrate the ability of the UBER to yield a realistic estimate of the tensile strength of a 10-μm-thick sample of Cr₂O₃ using data obtained through calculations on nanoscopic systems. We predict that Cr₂O₃ will fracture most easily in the direction, with a best estimate for the tensile strength of 386 MPa for a 10 μm grain, consistent with flexural strength measurements for chromia. The grain becomes considerably stronger at the nanoscale, where we predict a tensile strength along the same direction of 32.1 GPa for 1.45 nm crystallite. The results also provide insight into the origin of the direction dependence of the mechanical properties of Cr₂O₃, with the differences in the behavior along different directions being related to the number of Cr-O bonds supporting the applied tensile load. Additionally, the results shed light on various practical aspects of modeling the mechanical properties of materials with DFT+U calculations and in using UBERs to estimate the mechanical properties of materials across disparate length scales.     

激光熔覆原位制备Ti3Al金属间化合物涂层结构及摩擦学性能

利用激光熔覆原位合成技术在纯钛表面制备了Ti3Al金属间化合物涂层.用X射线衍射仪、扫描电镜和高分辨透射电镜分析了涂层的组成和组织结构.在UMT-2MT摩擦磨损试验机上对Ti3Al金属间化合物涂层在不同载荷和不同滑动速度下的摩擦磨损性能进行了测试.结果表明:Ti3Al金属间化合物涂层的主要组成物相为Ti3Al,涂层与基材冶金结合,涂层显微组织结构主要为树枝状晶,涂层的平均显微硬度约为HV0.2530,涂层的摩擦系数随载荷和滑动速度的增加而减小,磨损体积随载荷和滑动速度的增加而增加.Ti3Al金属间化合物涂层相对于钛基材耐磨性能显著提高.     

A Helmholtz free-energy function for a Cu–Al–Ni shape memory alloy

In this paper we develop a free energy function for a Cu–Al–Ni alloy undergoing cubic–orthorhombic phase transitions. We use the irreducible Lagrangian strain polynomial invariants of the cubic austenite parent phase to construct a polynomial expansion for the Helmholtz free energy. Our expansion retains quartic terms of the strain components in order to describe the two-phase material—the cubic austenite phase and six variants of the orthorhombic martensite phase. The coefficients of the free energy polynomial function are temperature dependent and are fitted to appropriate experimental data for austenite and martensite phases from literature. The resulting Helmholtz free energy function is given by (3.20), (4.11). We examine the response predicted by the model for shear in the twinning directions.     

Yielding and intrinsic plasticity of Ti–Zr–Ni–Cu–Be bulk metallic glass

Bulk metallic glass with composition Ti₄₀Zr₂₅Ni₈Cu₉Be₁₈ exhibits considerably high compressive yield stress, significant plasticity (with a concomitant vein-like fracture morphology) and relatively low density. Yielding and intrinsic plasticity of this alloy are discussed in terms of its thermal and elastic properties. An influence of normal stresses acting on the shear plane is evidenced by: (i) the fracture angle (<45°) and (ii) finite-element simulations of nanoindentation curves, which require the use of a specific yield criterion, sensitive to local normal stresses acting on the shear plane, to properly match the experimental data. The ratio between hardness and compressive yield strength (constraint factor) is analyzed in terms of several models and is best adjusted using a modified expanding cavity model incorporating a pressure-sensitivity index defined by the Drucker–Prager yield criterion. Furthermore, comparative results from compression tests and nanoindentation reveal that deformation also causes strain softening, a phenomenon which is accompanied with the occurrence of serrated plastic flow and results in a so-called indentation size effect (ISE). A new approach to model the ISE of this metallic glass using the free volume concept is presented.     

Thermal transport in spin ice

In order to analyse low temperature heat transport in the spin ice compound Dy₂Ti₂O₇, we derive thermodynamic field equations that are based on the kinetic theory of phonons and their interaction with localised magnetic excitations. It is shown that the solution of the derived field equations for given boundary and initial values of heat-pulse experiments well describes all measured temperature profiles recorded in the temperature range from 0.3 to 15?K and in magnetic fields up to 1.5?T. The evaluated temperature and field dependencies of both the specific heat contributions and their corresponding relaxation times indicate that the magnetic excitations above the ground-state manifold of the spin ice compound Dy₂Ti₂O₇ take the form of magnetic monopoles.     

Reflection and transmission of plane waves at an imperfectly bonded interface between piezoelectric and piezomagnetic media

The paper analyzes the reflection and transmission of plane waves at an imperfect interface between piezoelectric (PE) and piezomagnetic (PM) media. The materials are assumed to be transversely isotropic. The linear spring model is used to describe the imperfection of bonding behavior at the interface. According to this model, the properties of the interface can be characterized by the normal and tangential interfacial stiffnesses. Numerial examples are performed for BaTiO₃/CoFe₂O₄ material combination. Four cases, a perfect, slip, normal weak bonding and unbonding interfaces for the coupled quasi-pressure (QP) wave incidence from BaTiO₃ medium are compared in detail. Numerical results of the reflection and transmission coefficients (RTCs) varying with incident angle for different interfacial stiffnesses are presented. Results show that the transmitted QP/reflected QSV waves are the strongest in the perfect/unbonded cases, respectively. The scattered waves in the slip and normal weak bonding cases are between those of the perfect and unbonded cases generally. Critial angles have noticeable effect on the RTCs and energy coefficients for the coupled scattered waves of the perfect and slip cases but have a little/no effect on those of the normal weak bonding/unbonded cases. It is found that the sum of the energy carried by the transmitted/reflected QP and QSV waves is less than unit for the imperfect bonding between BaTiO₃/CoFe₂O₄ solids. These results may provide some useful reference datum for the imperfection measurment at the PE and PM interface.     

Applications of the dual integral formulation in conjunction with fast multipole method to the oblique incident wave problem

In this paper, the dual integral formulation is derived for the modified Helmholtz equation in the propagation of oblique incident wave passing a thin barrier (zero thickness) by employing the concept of fast multipole method (FMM) to accelerate the construction of an influence matrix. By adopting the addition theorem, the four kernels in the dual formulation are expanded into degenerate kernels that separate the field point and the source point. The source point matrices decomposed in the four influence matrices are similar to each other or only to some combinations. There are many zeros or the same influence coefficients in the field point matrices decomposed in the four influence matrices, which can avoid calculating the same terms repeatedly. The separable technique reduces the number of floating‐point operations from O((N)²) to O(N log^a(N)), where N is the number of elements and a is a small constant independent of N. Finally, the FMM is shown to reduce the CPU time and memory requirement, thus enabling us to apply boundary element method (BEM) to solve water scattering problems efficiently. Two‐moment FMM formulation was found to be sufficient for convergence in the singular equation. The results are compared well with those of conventional BEM and analytical solutions and show the accuracy and efficiency of the FMM. Copyright © 2008 John Wiley & Sons, Ltd.     

A micromechanics constitutive model for pure dilatant martensitic transformation of ZrO2-containing ceramics

A new micromechanics constitutive model for pure dilatant transformation plasticity of structure ceramics is proposed in this paper. Based on the thermodynamics, micromechanics and microscalet→m transformation mechanism analysis of the TZP and PSZ ZrO₂-containing ceramics, an analytic expressions of the Helmholtz and complementary free energy of the constitutive element for the case of pure dilatant transformation is derived for the first time in a self-consistent manner. By the analysis of energy dissipation in the forward and reverse transformations, the micromechanics constitutive law is derived in the framework of Hill-Rice's internal variable constitutive theory. The project is supported by the National Natural Science Foundation of China.