## Reactive diffusion

### March 31, 2009

Reactive diffusion in nanostructures of spherical symmetry

G Schmitz et al

To investigate reactive diffusion in nanosized spherical geometries, a clear model experiment has been designed. Thin film {Al/Cu/Al} and {Cu/Al/Cu} triple layers were deposited on tips of 25 nm apex radius and investigated by atom probe tomography (APT). At the interfaces within both samples, the growth of the reaction product proceeds parabolically from the very beginning but with remarkably different rates. Growth appears to be always faster if Cu is stacked to the outer side of Al. The complex quantitative analysis of reaction-induced stress, surface tensions and partial mobilities suggests that the different growth rates represent the Darken and the Nernst–Planck limits of interdiffusion. Since the curvature radius of the model samples ranges down to a few tens of nanometers, it is anticipated that an analogous effect may play a role in the oxidation of nanospheres or in chemical reactions of core–shell structures.

[1] Austenite–ferrite transformation kinetics under uniaxial compressive stress in Fe–2.96 at.% Ni alloy

Y C Liu et al

The effect of an applied constant uniaxial compressive stress on the kinetics of the austenite (γ) → ferrite (α) massive transformation in the substitutional Fe–2.96 at.% Ni alloy upon isochronal cooling has been studied by differential dilatometry. All imposed stress levels are below the yield stress of austenite and ferrite in the temperature range of the transformation. An increase in compressive stress results in a small but significant increase of the onset temperature of the γ → α transformation and a decrease of the overall transformation time. A phase transformation model, involving site saturation, interface-controlled growth and incorporation of an appropriate impingement correction, has been employed to extract the interface-migration velocity of the γ/α interface. The interface-migration velocity for the γ → α transformation is approximately constant at fixed uniaxial compressive stress and increases with increasing applied uniaxial compressive stress. Furthermore, the value obtained for the energy corresponding with the elastic and plastic deformation associated with the accommodation of the γ/α volume misfit depends on the transformed fraction and decreases significantly as the applied uniaxial compressive stress increases. An understanding of the observed effects is obtained, recognizing the constraints imposed on the phase transformation due to the applied stress.

M Greenwood et al

A new phase-field model of microstructural evolution is presented that includes the effects of elastic strain energy. The model’s thin interface behavior is investigated by mapping it onto a recent model developed by Echebarria et al. [Echebarria B, Folch R, Karma A, Plapp M. Phys Rev E 2004;70:061604]. Exploiting this thin interface analysis, the growth of solid-state dendrites are simulated with diffuse interfaces and the phase-field and mechanical equilibrium equations are solved in real space on an adaptive mesh. A morphological competition between surface energy anisotropy and elastic anisotropy is examined. Two dimensional simulations are reported that show that solid-state dendritic structures undergo a transition from a surface-dominated [Meiron DI. Phys Rev A 1986;33:2704] growth direction to an elastically driven [Steinbach I, Apel M. Phys D – Nonlinear Phenomena 2006;217:153] growth direction due to changes in the elastic anisotropy, the surface anisotropy and the supersaturation. Using the curvature and strain corrections to the equilibrium interfacial composition and linear stability theory for isotropic precipitates as calculated by Mullins and Sekerka, the dominant growth morphology is predicted.

O M Ivasishin et al

A three-dimensional Monte-Carlo (Potts) model was modified to incorporate the effect of grain-boundary inclination on boundary mobility. For this purpose, a straightforward geometric construction was developed to determine the local orientation of the grain-boundary plane. The combined effects of grain-boundary plane and misorientation on the effective grain-boundary mobility were incorporated into the Monte-Carlo code using the definition of the tilt–twist component. The modified code was validated by simulating grain growth in microstructures comprising equiaxed or elongated grains as well as the static recrystallization of a microstructure of deformed (elongated) grains.

[4] Effects of quenching speeds on microstructure and magnetic properties of novel SmCo6.9Hf0.1(CNTs)0.05 melt-spun ribbons

J-B Sun et al

By adding carbon nanotubes (CNTs) to SmCo6.9Hf0.1, novel SmCo6.9Hf0.1(CNTs)0.05 as-cast alloy has been prepared, which consists of Sm(Co,Hf)7 as the main phase, a small amount of SmCo5 and a particle-like grain boundary phase Hf(CNTs). SmCo6.9Hf0.1(CNTs)0.05 ribbons melt-spun at speeds of 10–50 m s−1 have a single TbCu7-type structure. Increasing the quenching speed can result in a decrease in ribbon thickness and grain boundary width. Meanwhile, the grain size tends to be smaller and the grain boundary phase tends to be more dispersed. A new Sm(Co,Hf)7(CNTs)x boundary phase may be formed in SmCo6.9Hf0.1(CNTs)0.05 ribbons. Increasing the quenching speed can also enhance coercivity, remanence and remanence ratio. The ribbons melt-spun at a speed of 50 m s−1 display the best magnetic properties: Hci = 18.781 kOe, Ms2T = 76.87 emu g−1, Mr = 66.79 emu g−1 and Mr/Ms2T = 0.87.

## Dihedral angles, martensitic transformation in thin films, and role of twin boundaries in domain evolution

### March 22, 2009

Did you know that Acta these days uploads supplementary material — like videos? I didn’t till I saw the paper on martensitic transformation in thin films by Buschbeck etal — wherein, a video of AFM surface topology as a function of temperature is also uploaded — which I think is a great move.

[1] Dihedral angles in Cu–1 wt.% Pb: Grain boundary energy and grain boundary triple line effects

D Empl et al

The dihedral angle shown by intergranular lead inclusions in Cu–1 wt.% Pb alloys is measured varying the purity of the metal and the temperature. Several measurement methods are used and compared, namely classical two-dimensional (2D) methods based on metallurgical cross-section analysis and a recently developed 3D stereoscopic method that yields the true three-dimensional angle value for individual inclusions straddling a flat grain boundary. We confirm and extend earlier measurements using the new method. We show that a discrepancy found between the literature data and the stereoscopic 3D dihedral angle measurements is not caused by impurity effects. Rather, the data indicate that the discrepancy has its origin in a difference in average dihedral angle values measured between inclusions straddling two grains and values found at inclusions located where three or more grains meet.

[2] In situ studies of the martensitic transformation in epitaxial Ni–Mn–Ga films

J Buschbeck et al

The martensitic transformation of epitaxial Ni–Mn–Ga films is investigated with respect to changes of structure, microstructure, magnetic and electronic properties. For this, temperature dependent atomic force microscopy (AFM), X-ray, magnetization and resistivity measurements are performed in situ, during martensitic transformation of a 500 nm thick film. The combination of these methods gives a comprehensive understanding of the martensitic transformation and allows to identify differences of constrained epitaxial films compared to bulk. Experiments show the formation of a twinned, orthorhombic martensite with high uniaxial magnetocrystalline anisotropy from the austenite around room temperature. High resolution AFM micrographs directly reveal how martensite variants grow and show the converging of variants nucleated at different nucleation sites. While most features are in agreement with a first-order transformation, the transformation proceeds continuously to lower temperatures, an effect which can be explained by the constraint from the substrate.

[3] Domain microstructure evolution in magnetic shape memory alloys: Phase-field model and simulation

Y M Jin

A phase-field micromagnetic microelastic model is employed to simulate domain microstructure evolution in magnetic shape memory alloys. The simulations reveal that coupled motions of martensite twin boundaries and magnetic domain walls depend not only on the external magnetic field but also on internal domain configurations. It is shown that a twin boundary can continue its motion under a decreasing magnetic field or even reverse motion direction without changing magnetic field. The domain microstructure-dependent driving forces for the coupled motions of martensite twin boundaries and magnetic domain walls are analyzed; these explain the complex domain processes and resultant peculiar magnetomechanical behavior of magnetic shape memory alloys.

## 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:

[1] A unique state of solid matter: Stochastic spinodal modulations in the Au-50Ni transition above 600K

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 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.