## Grain rotation, growth, nucleation, magnetic thin films, stress, …

### August 4, 2009

Some recent papers from scripta:

F Yang and W Yang

A kinetic model is developed to quantify the rate of grain rotations driven by either grain boundary energy or stress. The critical roles of triple junctions and grain shape are emphasized. The size effects for the rotation rate are analyzed. As the grain size decreases, the model predicts shifts in the dominating driving forces and dissipation mechanisms.

S S West et al

A 30% deformed aluminum sample was mapped non-destructively using Three-Dimensional X-ray Diffraction (3DXRD) before and after annealing to nucleation of recrystallization. Nuclei appeared in the bulk of the sample. Their positions and volumes were determined, and the crystallographic orientations were compared with the orientations of the deformed grains. It was found that nuclei with new orientations can form and their orientations have been related to the dislocation structure in the deformed grains.

J Ciulik and E M Taleff

Dynamic abnormal grain growth (DAGG) is a newly discovered phenomenon which can be used to produce large single crystals from polycrystalline material in the solid state at temperatures above approximately half the melting temperature. The unique aspect of DAGG, compared to previously understood abnormal grain growth phenomena, is the requirement of plastic straining for initiation and propagation of abnormal grain growth. Our findings demonstrate that DAGG can be used to produce large single crystals of molybdenum in the solid state.

J Torrens-Serra et al

The kinetic data obtained from the analysis of experimental measurements of nanocrystallization in Fe65Nb10B25 metallic glass are used to successfully estimate the molten alloy viscosity, Fe23B6 crystallization driving force and solid-liquid interface energy in the framework of the classical theory of nucleation and growth. We use a Vogel-Fulcher-Tamman law for the viscosity and linear temperature dependence for the crystallization driving force and interfacial energy. A negative temperature coefficient for the crystal-melt interfacial energy is obtained. Both the thermal stability and the glass forming ability of this alloy are discussed.

X N Xu et al

The miscibility gap (MG) of the Au–Pt binary system in the temperature range 600–1050 °C has been experimentally determined by the diffusion couple technique. The results show that the determined MG deviates from the currently accepted one, which shifts to the Au-rich side of the Au–Pt system. Based on the present experimental data, the Au–Pt system has been thermodynamically reassessed, with the result that the critical point of the miscibility gap is not, vert, similar1200 °C at 56 at.% Pt, in contrast to the currently accepted 1260 °C at 61 at.% Pt. The chemical and coherent spinodals of the Au–Pt system have been thus calculated.

C Garcio-Mateo et al

It is possible by means of high-resolution dilatometry, together with a model based on isotropic dilatation and atomic volumes, to estimate the dislocation density introduced in the microstructure as a consequence of the isothermal decomposition of austenite into bainitic ferrite. The relatively high dislocation density associated with this microstructure is attributed to the fact that the shape deformation accompanying this displacive transformation is accommodated by plastic relaxation.

This paper reports an investigation of the structure, magnetic phase transition and magneto-optical properties of FeRh0.95Pt0.05 thin film. A first-order magnetic phase transition occurs at a temperature around 180 °C, accompanied by a lattice expansion in the c-axis. The effect of substitution on the phase transition in ordered FeRh-based alloy systems is discussed. The nucleation and growth mechanism of the phase transition is quite similar to that of the crystallization of solids. In addition, the Kerr rotation spectrum was also studied.

## Questioning Gibbs, anisotropy in phase field models and solidification under magnetic fields

### March 1, 2009

A few papers of interest — to be published in Acta and Scripta:

A Perovic et al

Our observation of the spinodal modulations in gold-50 at% nickel (Au-50Ni) transformed at high temperatures (above 600K) contradicts non-stochastic Cahn theory with its $\approx$500 degree modulation suppression. These modulations are stochastic because simultaneous increase in amplitude and wavelength by diffusion cannot be synchronized. The present theory is framed as a 2nd order differential uphill/downhill diffusion process and has an increasing time-dependent wave number and amplitude favouring Hillert’s one dimensional (1D) prior formulation within the stochastic association of wavelength and amplitude.

R S Qin and H K D H Bhadeshia

An expression is proposed for the anisotropy of interfacial energy of cubic metals, based on the symmetry of the crystal structure. The associated coefficients can be determined experimentally or assessed using computational methods. Calculations demonstrate an average relative error of <3% in comparison with the embedded-atom data for face-centred cubic metals. For body-centred-cubic metals, the errors are around 7% due to discrepancies at the {3 3 2} and {4 3 3} planes. The coefficients for the {1 0 0}, {1 1 0}, {1 1 1} and {2 1 0} planes are well behaved and can be used to simulate the consequences of interfacial anisotropy. The results have been applied in three-dimensional phase-field modelling of the evolution of crystal shapes, and the outcomes have been compared favourably with equilibrium shapes expected from Wulff’s theorem.

X Li et al

Thermoelectric magnetic convection (TEMC) at the scale of both the sample (L = 3 mm) and the cell/dendrite (L = 100 μm) was numerically and experimentally examined during the directional solidification of Al–Cu alloy under an axial magnetic field (Bless-than-or-equals, slant1T). Numerical results show that TEMC on the sample scale increases to a maximum when B is of the order of 0.1 T, and then decreases as B increases further. However, at the cellular/dendritic scale, TEMC continues to increase with increasing magnetic field intensity up to a field of 1 T. Experimental results show that application of the magnetic field caused changes in the macroscopic interface shape and the cellular/dendritic morphology (i.e. formation of a protruding interface, decrease in the cellular spacing, and a cellular–dendritic transition). Changes in the macroscopic interface shape and the cellular/dendritic morphology under the magnetic field are in good agreement with the computed velocities of TEMC at the scales of the macroscopic interface and cell/dendrite, respectively. This means that changes in the interface shape and the cellular morphology under a lower magnetic field should be attributed respectively to TEMC on the sample scale and the cell/dendrite scale. Further, by investigating the effect of TEMC on the cellular morphology, it has been proved experimentally that the convection will reduce the cellular spacing and cause a cellular–dendritic transition.

## Translation of a paper of J D van der Waals

### October 14, 2007

The translation of a Dutch paper (PhD thesis?) of van der Waals into English by J S Rowlinson is available here (Unfortunately, I have no access to the soft copy version):

Van der Waals justifies the choice of minimization of the (Helmholtz) free energy as the criterion of equilibrium in a liquid-gas system (Sections 1–4). If density is a function of height h then the local free energy density differs from that of a homogeneous fluid by a term proportional to (d 2 /dh 2); the extra term arises from the energy not from the entropy (Section 5). He uses this result to show how varies with h (Section 6), how this variation leads to a stable minimum free energy (Section 7), and to calculate the capillary energy or surface tension (Section 9). Near the critical point varies as ( k )3/2, where k is the critical temperature (Section 11). The paper closes with short discussions of the thickness of the surface layer (Section 12), of the difficulty of assuming that varies discontinuously with height (Section 14), and of the possible effect of derivatives of higher order than (d 2 /dh 2) on the free energy and surface tension (Section 15).

Generally, the origin of the concept (and name) of spinodal decomposition is credited to van der Waals. I do not know if this document discusses that aspect of van der Waals’ work — I have to go to the library tomorrow.

## Phase separation in complex perovskitic oxides

### August 1, 2007

Title: Nano-chessboard superlattices formed by spontaneous phase separation in oxides

Authors: Beth S. Guiton and Peter K. Davies

Abstract:

The use of bottom-up fabrication of nanostructures for nanotechnology inherently requires two-dimensional control of the nanostructures at a particular surface. This could in theory be achieved crystallographically with a structure whose three-dimensional unit cell has two or more—tuneable—dimensions on the nanometre scale. Here, we present what is to our knowledge the first example of a truly periodic two-dimensional nanometre-scale phase separation in any inorganic material, and demonstrate our ability to tune the unit-cell dimensions. As such, it represents great potential for the use of standard ceramic processing methods for nanotechnology. The phase separation occurs spontaneously in the homologous series of the perovskite-based Li-ion conductor, $(Nd_{2/3-x}Li_{3x})TiO_3$, to give two phases whose dimensions both extend into the nanometre scale. This unique feature could lead to its application as a template for the assembly of nanostructures or molecular monolayers.