## A couple of quick links

### July 12, 2011

## Solid-state transformation kinetics

### March 4, 2011

Kinetics of solid-state transformation subjected to anisotropic effect: Model and application

S J Song et al

Abstract

In the present work, a growing particle subjected to anisotropic effect, if not influenced by other particles, is assumed to be an isotropically growing particle with constant volume. Accordingly, how to describe the anisotropic growth just becomes how to solve the blocking effect arising from the anisotropic growth. Following the statistical description of Johnson–Mehl–Avrami–Kolmogorov kinetics, the blocking effect was investigated further. Consequently, a series of analytical models for solid-state transformation, where a particle undergoes 1-scale blocking, k-scale blocking and infinite-scale blocking, were developed. On this basis, it was analytically proved for the first time that the classical phenomenological equation accounting for the anisotropic effect (f=1-[1+(ξ-1)xe]-1/ξ-1) corresponds to an extreme case where a particle encounters infinite-scale blocking. From the model analysis, the anisotropic effect on the transformation depends on two factors: the non-blocking factor γ and the blocking scale k. From the model calculations, the Avrami exponent, subjected to the anisotropic effect, changes as a function of the transformed fraction, whereas the effective activation energy is not affected by the anisotropic effect. The present models were adopted to describe isothermal crystallization of amorphous Fe33Zr67 ribbons; good agreement with the published results was achieved.

Research highlights

► A statistical treatment accounting for blocking effect is proposed and analyzed. ► Phenomenological equation of anisotropic effect corresponds to an extreme case. ► Blocking effect depends on not only non-blocking factor but also blocking scale. ► Avrami exponent subjected to anisotropic effect changes with transformed fraction. ► Effective activation energy is not affected by anisotropic effect.

## Papers of interest from Acta and Scripta

### April 17, 2010

[1] A new ultrahigh-strength stainless steel strengthened by various coexisting nanoprecipitates

W Xu et al

A general computational alloy design approach based on thermodynamic and physical metallurgical principles and coupled with a genetic optimization scheme is presented. The model is applied to develop a new ultrahigh-strength maraging stainless steel. The alloy composition and heat treatment parameters are integrally optimized so as to achieve microstructures of fully lath martensite matrix strengthened by multiple precipitates of MC carbides, Cu particles and Ni3Ti intermetallics. The combined mechanical properties, corrosion resistance and identification of actual strengthening precipitates in the experimental prototype produced on the basic of the model predictions provide a strong justification for the alloy design approach.

[2] An investigation of the effect of structural order on magnetostriction and magnetic behavior of Fe–Ga alloy thin films

A Javed et al

This paper reports results from a comprehensive study of Fe–Ga films fabricated over a wide range of growth conditions. Polycrystalline Fe100−xGax films (14 less-than-or-equals, slant x less-than-or-equals, slant 32) were deposited (using three different combinations of growth parameters) on Si(1 0 0) using a co-sputtering and evaporation technique. The growth parameters (sputter power, Ga evaporation rate and chamber pressure) were used primarily to control the Fe:Ga ratio in the films. X-ray diffraction showed that all films had left angle bracket1 1 0right-pointing angle bracket crystallographic texture normal to the film plane. The lattice parameter increased with % Ga up to x = 22 and was independent of growth parameters. Conversion electron Mössbauer spectroscopy studies showed a predominance of the disordered A2 phase in all films. It appears that the use of vacuum deposition with appropriate parameters can effectively suppress the D03 ordered phase. Systematic studies of the effective magnetostriction constant as a function of composition support this conclusion. It was found that films of high effective saturation magnetostriction constant and low stress could be fabricated using low Ar pressure, irrespective of sputter power or evaporation rate, giving properties useful for application in microelectromechanical systems.

[3] Coarsening of a multimodal nickel-base superalloy

K Coakley et al

The coarsening of γ′-Ni3Al precipitates in the nickel superalloy Ni115 has been examined and compared to the results of a numerical model based on LSW coarsening theory. Ni115 has a γ′ fraction of around 60%, and at the coarsening temperatures of interest the γ′ distribution is bimodal, with two populations not, vert, similar5 nm and not, vert, similar90 nm in radius. It is found that during the initial transient (around 2000 h at 800 °C), the fine γ′ dissolve, leading to a rapid increase in the mean radius followed by a plateau. At long times, the expected steady-state unimodal t1/3 coarsening is observed. The model reproduces these features in form and approximately in magnitude, a first for LSW model-experiment comparisons in nickel superalloys.

[4] Growth morphologies in peritectic solidification of Fe–C: A phase-field study

A Choudhury et al

We use a thermodynamically consistent multi-phase, multi-component phase-field model, where the evolution equations for the different fields are derived from an entropy functional, for simulating peritectic growth structures in two and three dimensions. Different solidification morphologies are obtained in the computations and the characteristic properties of the growth forms are discussed. The phase-field method allows for a prediction of the surface energies in the three-phase system δ-ferrite, γ-austenite and liquid based on comparison between experimentally observed and simulated structures. Additionally an investigation of possible nucleation sites in evolving domains is presented and its dependence on the solid–solid surface energy is examined.

[5] Topological characteristics of plane sections of polycrystals

G S Rohrer and H M Miller

Homology metrics have been used to assess the connectivity of grain boundary networks in plane sections of polycrystals. The analysis is based on orientation maps, and four characteristic microstructure types were examined: SrTiO3 microstructures with normal and bimodal grain size distributions and two Ni microstructures with different concentrations of Σ3 grain boundaries. The inverse connectivity, defined as the ratio of the number of independent pieces of the network to the number of closed loops, is proposed as a metric for the extent to which certain types of grain boundaries are connected. The variation in inverse connectivity with disorientation threshold, below which boundaries are excluded from the network, produces distinct signatures for the different microstructures.

[6] Controlling Ag whisker growth by using very-thin metallic films

H Tohmyoh et al

The selective growth of Ag nano-whiskers on polycrystalline films has been realized by introducing an additional artificial layer onto the films. Ag nano-whiskers with diameters of about 200 nm and lengths of around 3 μm have been successfully generated from Ag films covered with a 1 nm-thick SiO2 layer. On the other hand, the formation of Ag whiskers/hillocks on the top surface of the film could be suppressed by using thick SiO2 layers or ductile Au layers.

## De-alloying and percolation, non-equilibrium melting, shear thinning, and discovery of local hidden symmetries

### July 15, 2009

Artymowicz et al

The parting limit or de-alloying threshold for electrolytic dissolution of the more reactive component from a homogeneous fcc binary alloy is usually between 50 and 60 at%. The system that has been most studied, dissolution of Ag from Ag-Au, shows a parting limit close to 55 at% Ag. Here, Kinetic Monte Carlo (KMC) simulations of ‘Ag-Au’ alloys and geometric percolation modeling are used to study the relationship between this parting limit and the high-density site percolation thresholds pc(m) for an fcc lattice, subject to the rule that atoms with coordination greater than nine are prevented from dissolution. The value of pc(9) is calculated from geometric considerations to be 59.97 ± 0.03%. In comparison, using KMC simulations with no surface diffusion and no dissolution allowed for ‘Ag’ atoms with more than nine total neighbors, the parting limit is found to be slightly lower (58.4 ± 0.1%). This slight discrepancy is explained by consideration of the local atomic configurations of ‘Ag’ atoms – a few of these configurations satisfy the percolation requirement but do not sustain de-alloying, while a larger number show the converse behavior. There is still, however, an underlying relationship between the parting limit and the percolation threshold, because being at pc(9) guarantees a percolation path in which successive ‘Ag’ atoms share at least one other ‘Ag’ neighbor. With realistic kinetics of surface diffusion for ‘Au’, the parting limit drops to 54.7 ± 0.3% because a few otherwise inaccessible dissolution paths are opened up by surface diffusion of ‘Au’.

[2] Non-equilibrium melting of colloidal crystals in confinement

E Villanova-vidal et al

A novel and flexible experiment is reported for investigation of the non-equilibrium melting behaviour of model crystals made from charged colloidal spheres. In a slit geometry, polycrystalline material formed in a low salt region is driven by hydrostatic pressure up an evolving gradient in salt concentration and melts at large salt concentration. Depending on particle and initial salt concentration, driving velocity and the local salt concentration, complex morphologic evolution is observed. Crystal-melt interface positions and the melting velocity are obtained quantitatively from time-resolved Bragg and polarisation microscopic measurements. A simple theoretical model predicts the interface to first advance, then for balanced drift and melting velocities to become stationary at a salt concentration larger than the equilibrium melting concentration. It also describes the relaxation of the interface to its equilibrium position in a stationary gradient after stopping the drive in different manners. The influence of the gradient strength on the resulting interface morphology and a shear-induced morphologic transition from polycrystalline to oriented single crystalline material before melting are discussed.

[3] Shear thinning in deeply supercooled melts

V Lubchenko

We compute, on a molecular basis, the viscosity of a deeply supercooled liquid at high shear rates. The viscosity is shown to decrease at growing shear rates, owing to an increase in the structural relaxation rate as caused by the shear. The onset of this non-Newtonian behavior is predicted to occur universally at a shear rate significantly lower than the typical structural relaxation rate, by approximately two orders of magnitude. This results from a large size—up to several hundred atoms—of the cooperative rearrangements responsible for mass transport in supercooled liquids and the smallness of individual molecular displacements during the cooperative rearrangements. We predict that the liquid will break down at shear rates such that the viscosity drops by approximately a factor of 30 below its Newtonian value. These phenomena are predicted to be independent of the liquid’s fragility. In contrast, the degree of nonexponentiality and violation of the Stokes–Einstein law, which are more prominent in fragile substances, will be suppressed by shear. The present results are in agreement with existing measurements of shear thinning in silicate melts.

[4] X-ray cross correlation analysis uncovers hidden local symmetries in disordered matter

P Wochner et al

We explore the different local symmetries in colloidal glasses beyond the standard pair correlation analysis. Using our newly developed X-ray cross correlation analysis (XCCA) concept together with brilliant coherent X-ray sources, we have been able to access and classify the otherwise hidden local order within disorder. The emerging local symmetries are coupled to distinct momentum transfer (Q) values, which do not coincide with the maxima of the amorphous structure factor. Four-, 6-, 10- and, most prevalently, 5-fold symmetries are observed. The observation of dynamical evolution of these symmetries forms a connection to dynamical heterogeneities in glasses, which is far beyond conventional diffraction analysis. The XCCA concept opens up a fascinating view into the world of disorder and will definitely allow, with the advent of free electron X-ray lasers, an accurate and systematic experimental characterization of the structure of the liquid and glass states.

## Leaping in full armour from the inspiration of Gibbs

### July 13, 2009

Here is the summary section of a pre-print in arXiv by Leo Kadanoff on phase transitions, which pays rich tributes to Gibbs and condensed matter theorists:

We have focused upon the nature of phase transitions and the mean field theory which describes them. The description of the phase transition “leaped in full

armor” from the inspiration of Gibbs, and his insight that a phase transition is an abrupt change which occurs only in a infinite system. Many years of investigation were given theoretical clothing in a mean eld theory set forward originally by van der Waals. This theory provided a generally satisfactory, but numerically inaccurate, description of the main events which occur in the phase diagrams of typical materials. It explains the various ordering of these materials, and some of the similarities and differences among the materials. It explains the universality of the phase diagrams, so that different materials can have rather similar phase diagrams. It fails to explain why the diagrams are inaccurate near the critical point, exactly the region in which the general formulation of Landau would have them be most accurate. But, Landau’s variational method would be the language for the advances to come.

## Solidification and precipitation in Mg alloys

### July 8, 2009

M Wang et al

A formulation of solid-liquid interfacial thermodynamic and kinetic anisotropic characteristics for hexagonal close-packed metals is proposed. The two- and three-dimensional dendritic growth of primary Mg in undercooled Mg-Al alloy melts are modeled using the phase-field method, with consideration of the integration of crystallographic lattice symmetry and experimental observations. The morphologies of three-dimensional dendrites are obtained and the calculated results have shown intricately hierarchical branched structures. The excess free energy of solution system is based on the Redlich-Kister model.

[2] Phase transformations in QE22 Mg alloy

G Barucca et al

The precipitation sequence in a QE22 Mg alloy is followed by differential scanning calorimetry, microhardness, electrical resistivity, positron annihilation spectroscopy and transmission electron microscopy (TEM) observations, after different thermal treatments. The decomposition of the supersaturated solid solution occurs via the formation of nanosized coherent structures (GP zones) followed by the co-precipitation of two metastable phases responsible for the peak ageing condition. The stable phase (Mg, Ag)12Nd appears at the highest annealing times, leading to over-ageing and hardness reduction. TEM observations provide information on the crystallographic structure of the forming phases, allowing some inconsistencies present in the literature to be clarified. Activation energies are derived from both calorimetric and resistometric measurements at different scanning rates.

## Thin film stresses and phase boundaries

### June 20, 2009

Z-X Zhu et al

A shift of the morphotropic phase boundary (MPB) and a superior piezoelectric response are observed in Nb-doped Pb(Zr* _{x}*Ti

_{1−}

*)O*

_{x}_{3}(PNZT) thin films epitaxially grown on Nb-doped SrTiO

_{3}(1 0 0) (Nb:STO) substrates. X-ray diffraction and Raman spectra characterizations confirm that a phase transition from a tetragonal structure to a rhombohedral structure occurs when the Zr/Ti ratio varies from 20/80 to 80/20. The phenomenological theory and experimental analyses suggest that the MPB of epitaxial PNZT thin films is shifted to the higher Zr/Ti ratio (around 70/30) from the conventional ratio (52/48) due to the misfit compressive stress induced by the substrate. A maximum local effective longitudinal piezoelectric coefficient (

*d*

_{33}) up to 307 pm V

^{−1}is observed at a Zr/Ti ratio of 70/30 in the current compositional range, again confirming the shifting of MPB in epitaxial PNZT thin films. These findings offer a new insight for the fabrication of epitaxial PZT thin films at MPB with a superior piezoelectric response.