Phase-field crystal study of grain-boundary premelting
Jesper Mellenthin, Alain Karma, Mathis Plapp
备注：
24 pages, 13 figures, some figure files with reduced resolution because of submission size limitations. In the 2nd version, some parts (and figures) have been modified, especially in Sec. V (discussion)
We study the phenomenon of grain-boundary premelting for temperatures below the melting point in the phase-field crystal model of a pure material with hexagonal ordering in two dimensions. We investigate the structures of symmetric tilt boundaries as a function of misorientation for two different inclinations and compute in the grand canonical ensemble the disjoining potential V(w) that governs the fundamental interaction between crystal-melt interfaces as a function of the premelted layer width w. The results reveal qualitatively different behaviors for high-angle grain boundaries that are uniformly wetted, with w diverging logarithmically as the melting point is approached from below, and low-angle boundaries that are punctuated by liquid pools surrounding dislocations, separated by solid bridges. This qualitative difference between high and low angle boundaries is reflected in the w-dependence of the disjoining potential that is purely repulsive (V'(w)<0 for all w) above a critical misorientation, but switches from repulsive at small w to attractive at large w for low angles. In the latter case, V(w) has a minimum that corresponds to a premelted boundary of finite width at the melting point. Furthermore, we find that the standard wetting condition (the grain boundary energy is equal to twice the solid-liquid free energy) gives a much too low estimate of the critical misorientation when a low-temperature value of the grain boundary energy is used. In contrast, a reasonable estimate is obtained if the grain boundary energy is extrapolated to the melting point, taking into account both the elastic softening of the material at high temperature and local melting around dislocations.
We employ molecular-dynamics (MD) simulations to study grain boundary (GB) premelting in ices confined in two-dimensional hydrophobic nano-channels. Premelting transition is observed in a symmetric tilt GB in monolayer ices an involves the formation of a premelting band of liquid phase water with a width that grows logarithmically as the melting temperature is approached from below, consistent with the existing theory of GB premelting. Based on current MD observations, one may expect GB premelting exists over a wide range of low dimensional phases of confined ice and shows important consequenc…
Phase field modelling of grain boundary premelting using obstacle potentials
本文研究了Steinbach和Pezzolla [I]的多序参量相场模型. Steinbach，F. Pezzolla，A generalized field method for physiological transformations using interface fields，Physica D 134（1999）385-393]关于其描述晶界预熔化的能力。对于单个序参量情况，固-熔界面总是吸引的，这允许在本体熔点以上具有（不稳定的）平衡固-熔-固共存。描述界面相互作用的温度依赖的熔体层厚度和分离势受热耦合函数的选择和定义液相量的措施的影响。由于严格有限的界面厚度，相互作用范围也是有限的。对于一个多序参量模型，我们发现要么是纯粹的吸引力，要么是纯粹的排斥力。预熔过渡，然后直接链接到晶界和固-熔界面能的比率。
Grain Boundaries (GB) whose energy is larger than twice the energy of the solid/liquid interface exhibit the premelting phenomenon, for which an atomically thin liquid layer develops at temperatures slightly below the bulk melting temperature. Premelting can have a severe impact on the structural integrity of a polycrystalline material and on the mechanical high temperature properties, also in the context of crack formation during the very last stages of solidification. The triple junction between a dry GB and the two solid/liquid interfaces of a liquid layer propagating along the GB cannot be…
We investigate the ability of a multi-order parameter phase field model with obstacle potentials to describe grain boundary premelting in equilibrium situations. In agreement with an energetic picture we find that the transition between dry and wet grain boundaries at the bulk melting point is given by the threshold $2σ_{sl}=σ_{gb}$, with $σ_{sl}$ being the solid-melt interfacial energy and $σ_{gb}$ the energy of a dry grain boundary. The predictions for premelting are confirmed by simulations using the phase field package OpenPhase. For the prediction of the kinetics of melting along grain bo…
While it is known that alloy components can segregate to grain boundaries (GBs), and that the atomic mobility in GBs greatly exceeds the atomic mobility in the lattice, little is known about the effect of GB segregation on GB diffusion. Atomistic computer simulations offer a means of gaining insights into the segregation-diffusion relationship by computing the GB diffusion coefficients of the alloy components as a function of their segregated amounts. In such simulations, thermodynamically equilibrium GB segregation is prepared by a semi-grand canonical Monte Carlo method, followed by calculat…
With gradual temperature increase in premelting regions of solid phase of methanol and high pressure phase of ethanol, and using novel procedure of separation of electrode polarization effects, we are able to register the contribution of relaxation process to low-frequency dielectric constant. This contribution is about half the liquid's dielectric constant near temperature of solidification , and is almost an order of magnitude higher than reported earlier for ambient pressure phase of methanol. As opposed to dielectric constant of water at ambient pressure, which does not change much during …
We find that laser-induced local melting attracts and deforms grain boundaries in 2D colloidal crystals. When a melted region in contact with the edge of a crystal grain recrystallizes, it deforms the grain boundary --- this attraction is driven by the multiplicity of deformed grain boundary configurations. Furthermore, the attraction provides a method to fabricate artificial colloidal crystal grains of arbitrary shape, enabling new experimental studies of grain boundary dynamics and ultimately hinting at a novel approach for fabricating materials with designer microstructures.
We use ultrasensitive electron backscatter diffraction (EBSD) to map the local crystal orientations, grains, and grain boundaries in CH3NH3PbI3 (MAPI) perovskite thin films. Although the true grain structure is broadly consistent with the morphology visible in scanning electron microscopy (SEM), the inverse pole figure maps taken with EBSD reveal grain structure and internal misorientation that is otherwise hidden. Local crystal misorientation is consistent with the presence of local strain which varies from one grain to the next. We acquire co-aligned confocal optical photoluminescence (PL) m…
We address a three-dimensional, coarse-grained description of dislocation networks at grain boundaries between rotated crystals. The so-called amplitude expansion of the phase-field crystal model is exploited with the aid of finite element method calculations. This approach allows for the description of microscopic features, such as dislocations, while simultaneously being able to describe length scales that are orders of magnitude larger than the lattice spacing. Moreover, it allows for the direct description of extended defects by means of a scalar order parameter. The versatility of this fr…
Nanocrystalline metals contain a large fraction of high-energy grain boundaries, which may be considered as glassy phases. Consequently, with decreasing grain size, a crossover in the deformation behaviour of nanocrystals to that of metallic glasses has been proposed. Here, we study this crossover using molecular dynamics simulations on bulk glasses, glass-crystal nanocomposites, and nanocrystals of Cu64Zr36 with varying crystalline volume fractions induced by long-time thermal annealing. We find that the grain boundary phase behaves like a metallic glass under constraint from the abutting cry…
We present a detailed comparison of multiple statistical grain metrics for previously reported experimental thin film samples of aluminum with 2D simulations obtained from the Phase-Field-Crystal (PFC) model and a Mullins grain boundary motion model. For all these results, ``universality'' is observed with respect to the dynamics and initial conditions. This comparison reveals that PFC reproduces geometric metrics such as area and perimeter, but does not capture grain shape and topology as accurately. Similarly, the Mullins model captures the number of sides distribution quite well but not oth…
According to classical grain growth laws, grain growth is driven by the minimization of surface energy and will continue until a single grain prevails. These laws do not take into account the lattice anisotropy and the details of the microscopic rearrangement of mass between grains. Here we consider coarsening of body-centered cubic polycrystalline materials in three dimensions using the phase field crystal model. We observe as function of the quenching depth, a cross over between a state where grain rotation halts and the growth stagnates and a state where grains coarsen rapidly by coalescenc…
Focused ion beam preparation of atom probe specimens containing a single crystallographically well-defined grain boundary
利用双束聚焦离子束（FIB）/扫描电子显微镜（SEM）系统的聚焦离子束（FIB）制备了含有单一晶界的针状原子探针试样。所提出的试样制备方法允许通过场离子显微镜（SEM）和断层原子探针（TAP）对其晶体取向进行表征的晶界的前所未有的研究。这种标本的分析，特别是允许在这个特定的晶界溶质过剩原子的测定，因此调查的偏析行为。本文详细讨论了40 at.ppm-Bi掺杂Cu双晶的S19 a {331}晶界的关键制备步骤<110>。透射电子显微镜（TEM）的图像和TAP分析的原子探针提示明确地证明了存在的选择性制备的晶界的顶点区域的一些标本。
We present results of a coherent x-ray diffractive imaging experiment performed on a single colloidal crystal grain. The full three-dimensional (3D) reciprocal space map measured by an azimuthal rotational scan contained several orders of Bragg reflections together with the coherent interference signal between them. Applying the iterative phase retrieval approach, the 3D structure of the crystal grain was reconstructed and positions of individual colloidal particles were resolved. As a result, an exact stacking sequence of hexagonal close-packed layers including planar and linear defects were …
The microstructure evolution due to thermomechanical treatment of metals can largely be described by viscoplastic deformation, nucleation and grain growth. These processes take place over different length and time scales which present significant challenges when formulating simulation models. In particular, no overall unified field framework exists to model concurrent viscoplastic deformation and recrystallization and grain growth in metal polycrystals. In this work a thermodynamically consistent diffuse interface framework incorporating crystal viscoplasticity and grain boundary migration is …
Plasticity in body-centred cubic (BCC) metals, including dislocation interactions at grain boundaries, is much less understood than in face-centred cubic (FCC) metals. At low temperatures additional resistance to dislocation motion due to the Peierls barrier becomes important, which increases the complexity of plasticity. Iron-silicon steel is an interesting, model BCC material since the evolution of the dislocation structure in specifically-oriented grains and at particular grain boundaries have far-reaching effects not only on the deformation behaviour but also on the magnetic properties, wh…
Using computer simulations we explore how grain boundaries can be removed from three-dimensional colloidal crystals by doping with a small fraction of active colloids. We show that for sufficient self-propulsion, the system is driven into a crystal-fluid coexistence. In this phase separated regime, the active dopants become mobile and spontaneously gather at the grain boundaries. The resulting surface melting and recrystallization of domains result in the motion of the grain boundaries over time and lead to the formation of a large single crystal. However, when the self-propulsion is too low t…
All-solid-state lithium batteries promise significant improvements in energy density and safety over traditional liquid electrolyte batteries. The Al-doped AlxLi7-3xLa3Zr2O12 (LLZO) solid-state electrolyte shows excellent potential given its high ionic conductivity and good thermal, chemical, and electrochemical stability. Nevertheless, further improvements on LLZOs electrochemical and mechanical properties call for an incisive understanding of its local microstructure. Here, we employ Bragg Coherent Diffractive Imaging to investigate the atomic displacements inside single grains of LLZO with …
Digital image correlation (DIC) and crystal plasticity simulation were utilised to study cold dwell behaviour in a coarse grain Ti-6Al alloy at 3 different temperatures up to 230 C. Strains extracted from large volume grains were measured during creep by DIC and were used to calibrate the crystal plasticity model. The values of critical resolved shear stresses (CRSS) of the two main slip systems (basal and prismatic) were determined as a function of temperature. Stress along paths across the boundaries of two grain pairs, (1) a `rogue' grain pair and (2) a `non-rogue' grain pair, were determin…
We derive a phase field crystal model that couples the diffusive evolution of a microscopic structure with the fast dynamics of a macroscopic velocity field, explicitly accounting for the relaxation of elastic excitations. This model captures better than previous formulations the dynamics of complex interfaces and dislocations in single crystals as well as grain boundary migration in poly-crystals where the long-range elastic field is properly relaxed. The proposed model features a diffusivity that depends non-linearly on the local phase. It induces more localized interfaces between a disorder…
Hexagonal boron nitride (h-BN) has attracted significant attention due to its superior properties as well as its potential as an ideal dielectric layer for graphene-based devices. The h-BN films obtained via chemical vapor deposition in earlier reports are always polycrystalline with small grains due to high nucleation density on substrates. Here we report the successful synthesis of large single-crystal h-BN grains on rational designed Cu-Ni alloy foils. It is found that the nucleation density can be greatly reduced to 60 per mm2 by optimizing Ni ratio in substrates. The strategy enables the …
A microstructure-based model that accounts for the effect of grain size has been developed to study the effect of grain size on the fatigue life of Inconel 718 alloys. The fatigue behavior of two alloys with different grain size was determined by means of uniaxial cyclic deformation tests under fully-reversed deformation ($R_\varepsilon$ = -1) at 400$^\circ$C in the low cycle fatigue regime. The model was based in the determination of the fatigue indicator parameter (based on the local crystallographic strain energy dissipated per cycle) by means of computational homogenization of a representa…
Sensitivity of grain-averaged elastic strain and orientation predictions on the mesh density and boundary conditions in crystal plasticity finite element simulations
The University of Alabama（阿拉巴马大学）；Mines Saint-Etienne（圣艾蒂安国立高等矿业学校）；The Pennsylvania State University（宾夕法尼亚州立大学）
Crystal orientation mapping experiments typically measure orientations that are similar within grains and misorientations that are similar along grain boundaries. Such (mis)orientation data will cluster in (mis)orientation space and clusters are more pronounced if preferred orientations or special orientation relationships are present. Here, cluster analysis of (mis)orientation data is described and demonstrated using distance metrics incorporating crystal symmetry and the density-based clustering algorithm DBSCAN. Frequently measured (mis)orientations are identified as corresponding to grains…
Crystallization of metallic glass as a grain-boundary nucleated process: experimental and theoretical evidence for the grain structure of metallic glasses
Using first-principles calculations, we investigate the positional dependence of trace elements such as O and Cu on the crystal field parameter $A_2^0$, proportional to the anisotropy constant $K_u$ of Nd ions placed at the surface of Nd$_2$Fe$_{14}$B grains. The results suggest the possibility that the $A_2^0$ parameter of Nd ions at the (001) surface of Nd$_2$Fe$_{14}$B grains exhibits a negative value when the O or Cu atom is located near the surface, closer than its equilibrium position. At the (110) surface, however, O atoms located at the equilibrium position provide a negative $A_2^0$, …
High mobility and high on/off ratio field-effect transistors based on chemical vapor deposited single-crystal MoS2 grains
我们报告了场效应晶体管（FET）与单晶二硫化钼（MoS 2）的化学气相沉积（CVD）合成的通道。对于双层MoS 2 FET，迁移率为~17 cm ~ 2 V ~（-1）s ~（-1），开/关电流比为~108，这比基于CVD多晶MoS 2膜的FET高得多。通过避免由转移过程引入的晶界和污染的有害影响，直接沉积在SiO2上的CVD MoS 2原子层的质量与最佳剥离的MoS 2薄片相当。结果表明，CVD法是制备高质量MoS_2原子层的一种可行方法。
Laser surface remelting can be used to manipulate the microstructure of cast material. Here, we present a detailed analysis of the microstructure of Fe$_2$VAl following laser surface remelting. Within the melt pool, elongated grains grow nearly epitaxially from the heat-affected zone. These grains are separated by low-angle grain boundaries with 1°-5° misorientations. Segregation of vanadium, carbon, and nitrogen at grain boundaries and dislocations is observed using atom probe tomography. The local electrical resistivity was measured by an in-situ four-point-probe technique. A smaller increas…
Rapid solidification experiments on thin film aluminum samples reveal the presence of lattice orientation gradients within crystallizing grains. To study this phenomenon, a single-component phase-field crystal (PFC) model that captures the properties of solid, liquid, and vapor phases is proposed to model pure aluminium quantitatively. A coarse-grained amplitude representation of this model is used to simulate solidification in samples approaching micrometer scales. The simulations reproduce the experimentally observed orientation gradients within crystallizing grains when grown at experimenta…
It is thought that growing large, oriented grains of perovskite can lead to more efficient devices. We study MAPbI3 films fabricated via Flash Infrared Annealing (FIRA) consisting of highly oriented, large grains. Domains observed in the SEM are often misidentified with crystallographic grains, but SEM images don't provide diffraction information. We measure the grain size, crystal structure and grain orientation using Electron Back-Scattered Diffraction (EBSD) and we study how these affect the optoelectronic properties as characterized by local photoluminescence (PL) and time-resolved microwa…
