Interfacial free energy anisotropy driven faceting of precipitates

Abstract

During solid–solid precipitation, interface free energy anisotropy is known to drive faceting of precipitates. In this paper, using a recently developed phase field formulation based on higher order tensor terms, we develop and implement a family of phase field models and indicate the parameter choices which lead to faceted precipitate morphologies. We also indicate how to choose the parameters given either the known precipitate morphology or the interfacial free energy anisotropy. Specifically, we study the faceting of precipitates in systems with cubic and hexagonal anisotropies; in 2 and 3D implementation of our phase field model, the precipitates do show facets in accordance with the Wulff plot – including cases where the Wulff plot predicts facets made up of more than one family of planes. We also indicate the possible extensions of our model to study other problems of interest.     

Effect of interface anisotropy on tilted growth of eutectics: A phase field study

Interfacial energy anisotropy plays an important role in tilted growth of eutectics. However, previous studies mainly focused on the solid—solid interface energy anisotropy, and whether the solid—liquid interface energy anisotropy can significantly affect the tilted growth of eutectics still remains unclear. In this study, a multi-phase field model is employed to investigate both the effect of solid—liquid interfacial energy anisotropy and the effect of solid—solid interfacial energy anisotropy on tilted growth of eutectics. The findings reveal that both the solid—liquid interfacial energy anisotropy and the solid—solid interfacial energy anisotropy can induce the tilted growth of eutectics. The results also demonstrate that when the rotation angle is within a range of 30°—60°, the growth of tilted eutectics is governed jointly by the solid—solid interfacial energy anisotropy and the solid—liquid interfacial energy anisotropy; otherwise, it is mainly controlled by the solid—solid interfacial energy anisotropy. Further analysis shows that the unequal pinning angle at triple point caused by the adjustment of the force balance results in different solute-diffusion rates on both sides of triple point. This will further induce an asymmetrical concentration distribution along the pulling direction near the solid—liquid interface and the tilted growth of eutectics. Our findings not only shed light on the formation mechanism of tilted eutectics but also provide theoretical guidance for controlling the microstructure evolution during eutectic solidification.     

The effect of interfacial energy anisotropy on planar interface instability in a succinonitrile alloy under a small temperature gradient

The morphological stability of a planar interface with different crystallographic orientations is studied under a small positive temperature gradient using a transparent model alloy of succinonitrile.Novel experimental apparatus is constructed to provide a temperature gradient of about 0.37 K/mm.Under this small temperature gradient,the planar interface instability depends largely on the crystallographic orientation.It is shown experimentally that the effect of interfacial energy anisotropy on planar interface stability cannot be neglected even in a small temperature gradient system.Higher interfacial energy anisotropy leads the planar interface to become more unstable,which is different from the stabilizing effect of the interfacial energy on the planar interface.The experimental results are in agreement with previous theoretical calculations and phase field simulations.     

An apodized cubic phase mask used in a wavefront coding system to extend the depth of field

The point spread function (PSF) caused by a wavefront coding system with a cubic phase mask has big side-lobes which leads to bad image restoration. This paper proposes a novel apodized cubic phase mask to suppress the side-lobes of the PSF. Simulated annealing algorithm is used to optimize the cubic and the truncation parameter of the phase mask. The system with the novel phase mask has better performance in the modulation transfer function (MTF) especially in low-and-medium spatial frequency region. The simulation results show that the restored images with the novel phase mask are superior to the one with the classic cubic phase mask in contrast and ringing effect. The experimental results show that the side-lobes of the PSF are suppressed by using the apodized cubic phase mask.     

晶体相场法研究预变形对熔点附近六角相/正方相相变的影响

应用双模晶体相场模型计算二维相图,并模拟了在熔点附近预变形和保温温度对六角相晶界演化以及六角相/正方相相变的影响.研究发现:在相变初期,当预变形为零、保温温度离熔点很近时在晶界发生缺陷诱发预熔;增大预变形,变形与缺陷的交互作用在熔点附近诱发预熔;随着预变形的进一步增大,变形在畸变处同时诱发液相和正方相,且预变形越大、保温温度越接近熔点,液相生长越明显,反之正方相生长明显.持续保温使得畸变能释放,晶粒最终完全转变为平衡正方相.模拟结果表明:预变形六角相在熔点附近保温时,由于晶界固有缺陷和预变形双重作用使得原子无序度增加,从而在晶界或其他缺陷处产生液相,待能量释放后晶粒再转变成平衡正方相,进而延缓了六角相/正方相相变时间.     

Determination of the in-plane anisotropy field in hexagonal systems via rotational magnetization: Theoretical model and Monte Carlo simulations

The magnetic anisotropy field in thin films with in-plane uniaxial anisotropy can be deduced from the VSM magnetization curves measured in magnetic fields of constant magnitudes. This offers a new possibility of applying rotational magnetization curves to determine the first- and second-order anisotropy constant in these films. In this paper we report a theoretical derivation of rotational magnetization curve in hexagonal crystal system with easy-plane anisotropy based on the principle of the minimum total energy. This model is applied to calculate and analyze the rotational magnetization process for magnetic spherical particles with hexagonal easy-plane anisotropy when rotating the external magnetic field in the basal plane. The theoretical calculations are consistent with Monte Carlo simulation results. It is found that to well reproduce experimental curves, the effect of coercive force on the magnetization reversal process should be fully considered when the intensity of the external field is much weaker than that of the anisotropy field. Our research proves that the rotational magnetization curve from VSM measurement provides an effective access to analyze the in-plane anisotropy constant K ₃ in hexagonal compounds, and the suitable experimental condition to measure K ₃ is met when the ratio of the magnitude of the external field to that of the anisotropy field is around 0.2. Supported by the National Natural Science Foundation of China (Grant Nos. 90505007 and 10774061) Recommended by LI FaShen     

Higher order terms in the inflaton potential and the lower bound on the tensor to scalar ratio r

The MCMC analysis of the CMB + LSS data in the context of the Ginsburg–Landau approach to inflation indicated that the fourth degree double-well inflaton potential in new inflation gives an excellent fit of the present CMB and LSS data. This provided a lower bound for the ratio r of the tensor to scalar fluctuations and as most probable value r ? 0.05, within reach of the forthcoming CMB observations. In this paper we systematically analyze the effects of arbitrarily higher order terms in the inflaton potential on the CMB observables: spectral index n_s and ratio r. Furthermore, we compute in close form the inflaton potential dynamically generated when the inflaton field is a fermion condensate in the inflationary universe. This inflaton potential turns out to belong to the Ginsburg–Landau class too. The theoretical values in the (n_s, r) plane for all double well inflaton potentials in the Ginsburg–Landau approach (including the potential generated by fermions) fall inside a universal banana-shaped region B. The upper border of the banana-shaped region B is given by the fourth order double-well potential and provides an upper bound for the ratio r. The lower border of B is defined by the quadratic plus an infinite barrier inflaton potential and provides a lower bound for the ratio r. For example, the current best value of the spectral index n_s = 0.964, implies r is in the interval: 0.021 < r < 0.053. Interestingly enough, this range is within reach of forthcoming CMB observations.     

Influence of the mode of deformation on recrystallisation kinetics in Nickel through experiments,theory and phase field model

Abstract

In this paper, we report the influence of the mode of deformation on recrystallisation kinetics through experiments, theory and a phase field model. Ni samples of 99.6% purity are subjected to torsion and rolling at two equivalent plastic strains and the recrystallisation kinetics and microstructure are compared experimentally. Due to significant differences in the distributions of the nuclei and stored energy for the same equivalent strain, large differences are observed in the recrystallisation kinetics of rolled and torsion-tested samples. Next, a multi-phase field model is developed in order to understand and predict the kinetics and microstructural evolution. The coarse-grained free energy parameters of the phase field model are taken to be a function of the stored energy. In order to account for the observed differences in recrystallisation kinetics, the phase field mobility parameter is a required constitutive input. The mobility is calculated by developing a mean field model of the recrystallisation process assuming that the strain free nuclei grow in a uniform stored energy field. The activation energy calculated from the mobilities obtained from the mean field calculation compares very well with the activation energy obtained from the kinetics of recrystallisation. The recrystallisation kinetics and microstructure as characterised by grain size distribution obtained from the phase field simulations match the experimental results to good accord. The novel combination of experiments, phase field simulations and mean field model facilitates a quantitative prediction of the microstructural evolution and kinetics.     

Energy studies of precipitation sequence in Ni_(75)Al_(10)Cr_(15) alloy based on the phase field theory

Based on the phase field theory, the phase precipitation sequence of Ni75Al10Cr15 alloy and the free energy of each phase were studied. Moreover, the interatomic potentials of L10 phase, L12 phase and DO22 phase changing with temperature and concentrations were computed through utilizing the interatomic potentials equations induced by Khachaturyan’s relational equations between the interatomic potentials and the long-range order (LRO) parameters. Results match preceding work and demonstrate that the phase p...     

正交非均匀电场中氢原子的高激发态

用数学软件Mathematica研究正交非均匀电场中氢原子两个高激发态(n=4和5)的能级和波函数.讨论能级分裂,并绘制零级近似下氢原子的电子概率角分布图.     

Quantum field theory in curved spacetime,the operator product expansion,and dark energy

To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved spacetime, the theory must be formulated in a local and covariant manner in terms of locally measurable field observables. Since a generic curved spacetime does not possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require symmetries or a preferred notion of a “vacuum state” and “particles”. We propose such a formulation of quantum field theory, wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients—and, thus, the quantum field theory. By contrast, ground/vacuum states—in spacetimes, such as Minkowski spacetime, where they may be defined—cannot vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than the natural scales of the theory. Fourth Award in the 2008 Essay Competition of the Gravity Research Foundation.     

Dynamic phase transitions and dynamic phase diagrams in the kinetic spin-5/2 Blume-Capel model in an oscillating external magnetic field: Effective-field theory and the Glauber-type stochastic dynamics approach

Using an effective field theory with correlations, we study a kinetic spin-5/2 Blume-Capel model with bilinear exchange interaction and single-ion crystal field on a square lattice. The effective-field dynamic equation is derived by employing the Glauber transition rates. First, the phases in the kinetic system are obtained by solving this dynamic equation. Then, the thermal behavior of the dynamic magnetization, the hysteresis loop area and correlation are investigated in order to characterize the nature of the dynamic transitions and to obtain dynamic phase transition temperatures. Finally, we present the phase diagrams in two planes, namely (T/zJ, h₀/zJ) and (T/zJ, D/zJ), where T absolute temperature, h₀, the amplitude of the oscillating field, D, crystal field interaction or single-ion anisotropy constant and z denotes the nearest-neighbor sites of the central site. The phase diagrams exhibit four fundamental phases and ten mixed phases which are composed of binary, ternary and tetrad combination of fundamental phases, depending on the crystal field interaction parameter. Moreover, the phase diagrams contain a dynamic tricritical point (T), a double critical end point (B), a multicritical point (A) and zero-temperature critical point (Z).     

Critical behaviours and magnetic properties of three-dimensional bond and anisotropy dilution Blume——Capel model in the presence of an applied field

This paper studies the critical behaviours and magnetic properties of three-dimensional bond and anisotropy dilution Blume--Capel model (BCM) in the presence of an applied field within the effective field theory. The trajectory of tricritical point, reentrant transitions and degenerate patterns of anisotropy are obtained both for the bond and the anisotropy dilutions. The global phase diagrams demonstrate unusually reentrant phenomena. The temperature dependences of magnetization curves undergo remarkable spin glass behaviour at low temperatures, and transform from ferromagnetism to paramagnetism at high temperature in applied fields. Temperature dependence of magnetic susceptibility curve is in qualitative agreement with experimental result.     

Dynamic phase transitions and dynamic phase diagrams of the spin-2 Blume-Capel model under an oscillating magnetic field within the effective-field theory

The dynamic phase transitions are studied in the kinetic spin-2 Blume-Capel model under a time-dependent oscillating magnetic field using the effective-field theory with correlations. The effective-field dynamic equation for the average magnetization is derived by employing the Glauber transition rates and the phases in the system are obtained by solving this dynamic equation. The nature (first- or second-order) of the dynamic phase transition is characterized by investigating the thermal behavior of the dynamic magnetization and the dynamic phase transition temperatures are obtained. The dynamic phase diagrams are constructed in the reduced temperature and magnetic field amplitude plane and are of seven fundamental types. Phase diagrams contain the paramagnetic (P), ferromagnetic-2 (F₂) and three coexistence or mixed phase regions, namely the F₂+P, F₁+P and F₂+F₁+P, which strongly depend on the crystal-field interaction (D) parameter. The system also exhibits the dynamic tricritical behavior.     

Expanding the thermodynamical potential and analysis of the possible phase diagram of deconfinement in the FL model

Deconfinement phase transition is studied in the FL model at finite temperature and chemical potential. At MFT approximation, phase transition can only be first order in the whole μ-T phase plane. Using a Landau expansion, we further study the phase transition order and the possible phase diagram of deconfinement. We discuss the possibilities of second order phase transitions in the FL model. From our analysis, if the cubic term in the Landau expansion could be cancelled by the higher order fluctuations, second order phase transition may occur. By an ansatz of the Landau parameters, we obtain a possible phase diagram with both the first and second order phase transitions, including the tri-critical point which is similar to that of the chiral phase transition.     

Atomic coherent trapping and phase property of the field in the system of two-level atoms interacting with a single-mode field

In this paper,the condition of the atomic coherent trapping in the system of twotwo-level atoms interacting with a single-mode coherent field has been obtained.And proper-ties of the light field in this case has also been analysed by means of the phase theory intro-duced by Barnett and Pegg,     

纯物质晶界结构及运动的晶体相场法模拟

采用晶体相场模型,分别模拟了纯物质小角度晶界和大角度晶界结构及变形过程中的晶粒转动及晶界迁移.结果表明,小角度晶界迁移的主要机理是构成晶界的位错的滑移和攀移,而大角度晶界的迁移主要依靠晶界两侧原子的跳动及晶界位错等缺陷的运动. 关键词： The phase field crystal model was used to simulate the structure of the small angle and the large angle grain boundary (GB) the grain rotation and the GB migration during deformation. Simulated results show that the dislocation glide and climb are the ma     

Dynamic phase transitions and the effects of frequency of oscillating magnetic field on the dynamic phase diagrams in the bilayer honeycomb lattice with AB stacking geometry

We study some dynamic properties of the bilayer honeycomb lattice with AB stacking geometry in the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the mean-field dynamical equations. First, we obtain dynamic phases in the system and observe the paramagnetic (p), ferromagnetic (f), compensated (c) antiferromagnetic (af), surface ferromagnetic (sf) and mixed (m) phases. Besides, coexistence phase regions also exist in the system. Second, we investigate the thermal behavior of the dynamic order parameters. From these study, the natures (first- or second-order) of the transitions are characterized and the dynamic phase transition (DPT) points are presented. The DPTs are obtained and the dynamic phase diagrams (DPD) are constructed plane of the temperature versus the amplitude of the magnetic field. We investigate the effect of the frequency of the oscillating external magnetic field on the DPD.