Phase field theory of heterogeneous crystal nucleation

The phase field approach is used to model heterogeneous crystal nucleation in an undercooled pure liquid in contact with a foreign wall. We discuss various choices for the boundary condition at the wall and determine the properties of critical nuclei, including their free energy of formation and the contact angle as a function of undercooling. For particular choices of boundary conditions, we may realize either an analog of the classical spherical cap model or decidedly nonclassical behavior, where the contact angle decreases from its value taken at the melting point towards complete wetting at a critical undercooling, an analogue of the surface spinodal of liquid-wall interfaces.     

Irradiation-induced heterogeneous nucleation in uranium dioxide

Using classical molecular dynamics simulations, we have studied the first stages of defect cluster formation resulting from 10 keV displacement cascades in uranium dioxide. Nanometre size cavities and dislocation loops are shown to appear as a result of the irradiation process. A specifically designed TEM experiment involving He implanted thin foils have also been carried out to support this modelling work. These results, in conjunction with several other observations taken from the literature of ion implanted or neutron irradiated uranium dioxide, suggest a radiation damage controlled heterogeneous mechanism for insoluble fission product segregation in UO₂.     

噪声对均质形核过程影响的晶体相场法研究

采用晶体相场模型,模拟了有色噪声诱发的均质形核过程. 结果表明,噪声强度在一定范围内对系统平衡热力学参量、形核势垒、临界晶核尺寸影响甚微; 而对形核孕育时间影响较大,形核孕育时间随噪声强度的增大呈指数减小趋势. 进一步分析表明,噪声对形核孕育时间的影响主要是由于噪声的引入改变了原子动力学系数.     

Magnetic properties for heterogeneous weakly ferromagnetic alloys

Using the Landau theory of phase transitions, Arrott plots, the high field and the paramagnetic susceptibility and the magnetization of heterogeneous weakly ferromagnetic alloys are calculated analytically for a simple model for the heterogeneity.     

k-space propagation models for acoustically heterogeneous media: application to biomedical photoacoustics

Biomedical applications of photoacoustics, in particular photoacoustic tomography, require efficient models of photoacoustic propagation that can incorporate realistic properties of soft tissue, such as acoustic inhomogeneities both for purposes of simulation and for use in model-based image reconstruction methods. k-space methods are well suited to modeling high-frequency acoustics applications as they require fewer mesh points per wavelength than conventional finite element and finite difference models, and larger time steps can be taken without a loss of stability or accuracy. They are also straightforward to encode numerically, making them appealing as a general tool. The rationale behind k-space methods and the k-space approach to the numerical modeling of photoacoustic waves in fluids are covered in this paper. Three existing k-space models are applied to photoacoustics and demonstrated with examples: an exact model for homogeneous media, a second-order model that can take into account heterogeneous media, and a first-order model that can incorporate absorbing boundary conditions.     

Athermal heterogeneous nucleation of freezing: numerical modelling for polygonal and polyhedral substrates

In a number of cases of practical interest, nucleation of freezing occurs at small supercooling, on potent nucleant substrates. Nucleation is then deterministic, consisting of the onset of free growth at a supercooling related only to substrate size and shape. Existing analytical treatments have evaluated the critical supercooling only for substrates in the form of a plane circle or a sphere. We develop a numerical treatment for a substrate of arbitrary shape. Coefficients are derived to permit straightforward evaluation of the critical supercooling for shapes typical of actual nucleant particles.     

Formal determination of the nucleation probabilities in binary alloys: A hyperfinite approach and thermodynamic justification of the lattice models

We obtained an equation of the Burgers type modeling the glass transition process in binary alloys with inhomogeneous inclusions. The proposed equation is thermodynamically justified; conditions are indicated under which this equation converts into the classical Cahn–Hillard equation.     

Dimple‐assisted dewetting: heterogeneous nucleation in undercooled wetting films

Undercooled wetting films near a first‐order wetting transition exhibit an unusually long lifetime: the thermal nucleation barrier for formation of a critical hole in a film of thickness F diverges according to Γ ∼ exp (ℰ_c/k_BT) where the excess free energy ℰ_c ∼ F^ζ with ζ ≥ 2. Localized perturbations of the liquid‐vapor interface (‘dimples’) are shown to be a useful tool in reducing Γ in a controlled way: they act as heterogeneous nucleation centers for thermal critical nuclei. For ⁴He wetting films on weak‐binding alkali substrates (Cs, Rb) dimples can be generated either by vortices in a superfluid film or by surface electrons. The theory of the heterogeneous nucleation process initiated by the presence of surface dimples (‘dimple‐assisted dewetting’) is developed, accompanied by quantitative predictions for experiment.     

Effect of inclusions on heterogeneous crack nucleation in nanocomposites

A two-dimensional theoretical model is proposed for the heterogeneous nucleation of a grain-boundary nanocrack in a nanocomposite consisting of a nanocrystalline matrix and nanoinclusions whose elastic moduli are identical to those of the matrix. The inclusions have the form of rods with a rectangular cross section and undergo dilatation eigenstrain induced by the differences in the lattice parameters and thermal expansion coefficients of the matrix and inclusions. In terms of the model, a mode-I–II nanocrack nucleates at the negative disclination of a biaxial dipole consisting of wedge grain-boundary (or junction) disclinations; then, the nanocrack opens along a grain boundary and reaches an inclusion boundary. Depending on the relative positions and orientations of the initial segment of the nanocrack and the inclusion, the nanocrack can either penetrate into the inclusion or bypass it along the matrix-inclusion interface. The nanocrack nucleation probability increases near an inclusion with negative (compressive) dilatation eigenstrain. A decrease in the inclusion size decreases (increases) the probability of a crack opening along the interface if the dilatation eigenstrain is negative (positive).     

Discussion notes: Phase field models and moving contact line in the long perspective

Basic concepts are recalled regarding phase field models and moving contact line.     

相场法研究Fe-Cu-Mn-Al合金富Cu相析出机制

基于Ginzburg-Landau理论采用连续相场法模拟了Fe-15%Cu-3%Mn-x Al(质量分数x=1%, 3%, 5%)合金在873 K等温时效时纳米富Cu析出相沉淀机制及Al含量对富Cu相析出的阻碍效应.通过计算成分场变量和结构序参数,研究了富Cu析出相的形貌、颗粒密度、平均颗粒半径、生长和粗化动力学.研究结果表明:在时效早期阶段,纳米富Cu相通过失稳分解机制析出,由于原子扩散速率存在差异,从而形成以富Cu相为核心的核壳结构.随着时效时间延长,富Cu相析出物结构由体心立方转变为面心立方.其中Al和Mn原子在富Cu核外偏析形成Al/Mn簇,可以将其视为阻碍富Cu析出相形成的缓冲层;在沉淀过程中,随着Al含量的增大, Al/Mn金属间相促进了缓冲层的生长,阻碍富Cu析出相的生长和粗化.     

Electronic contribution to electric field gradient in dilute alloys

A simple relation for calculating the electronic contribution to the electric field gradient in dilute alloys of transition metals is reported and is compared with the conduction electron charge shift model. The dependence of the field gradient on thes andd electrons and the difference in radii between the host and the probe atoms is considered for calculating the field gradient. It is found that thed electrons are the major contributors to the field gradient.     

Induction time as a measure for heterogeneous spherulite nucleation: Quantitative evaluation of early-stage growth kinetics

A theory is proposed indicating that the induction time characterizes the nucleation process in polymer crystallization. A microscopic method has been developed to monitor early stages of the spherulite growth. Using the method, based on photometric measurement of the depolarized light intensity during isothermal crystallization from the melt, nonzero nucleation induction time values were found for polypropylene (PP). From comparison of the theory with the experimental results obtained from polypropylene crystallization, it follows that the formation of PP crystal nuclei on admixtures is affected both by the formation of the first crystalline layer and by the size of the critical nucleus.     

Ising model for the alloys according to the effective field theory

FeAl alloys in their disordered structural phase have been investigated through an Ising model where besides exchange interactions between nearest-neighbors Fe atoms, a superexchange interaction mediated by Al atoms is also taken into account. The model has been approximately treated according to the effective field theory. Although the phase diagram, as a function of Al concentration, is similar to the one previously obtained from Bogoliubov variational approach for the free energy, a different behavior for the superexchange interaction is achieved, which can also be physically accepted for this system.     

Random cluster models for icosahedral phase alloys

We present results on computer generated random cluster models for icosahedral phase alloys. By the application of physically motivated constraints on the local atomic cluster configurations, the model achieves long range translational order comparable to, or greater than, that found in simple icosahedral alloys such asi-AlMnSi andi-AlLiCu. The parallel and perpendicular space structures are explored in some detail including a comparison with experimental powder diffraction patterns and an examination of the phason fluctuations. The latter are shown to decrease markedly with increased constraint on the local environment, but the remaining phason strain would seem finally not to vanish with increasing model size. Our model is compared with other cluster models for quasicrystalline materials and is shown to possess a density and connectivity very close to those of Elser's (best) model and those predicted by Henley for a canonical tiling. The relation of this model to recently discovered icosahedral phase alloys with resolution limited diffraction peak widths, which are essentially free of phason strain, is also discussed.     

Ginzburg-Landau-type multiphase field model for competing fcc and bcc nucleation

We address crystal nucleation and fcc-bcc phase selection in alloys using a multiphase field model that relies on Ginzburg-Landau free energies of the liquid-fcc, liquid-bcc, and fcc-bcc subsystems, and determine the properties of the nuclei as a function of composition, temperature, and structure. With a realistic choice for the free energy of the fcc-bcc interface, the model predicts well the fcc-bcc phase-selection boundary in the Fe-Ni system.