Dipole of edge misfit dislocations and critical radius conditions for buried strained cylindrical inhomogeneity

Q H Fang, Y W Liu and P H Wen

A theoretical model is proposed for elastic stress relaxation of a buried strained cylindrical inhomogeneity, which assumes the edge misfit dislocation dipole formation in the soft matrix at some distance from the interface. The critical radius of the inhomogeneity for the formation of the edge misfit dislocation dipole is given and the influence of various parameters on the critical radius is evaluated. The result indicates that the critical radius decreases with increasing misfit strain and core radius of the misfit dislocation. It is also found that, compared to the edge misfit dislocation dipole formation in the interface, the critical radius of the inhomogeneity decreases when the location of an edge misfit dislocation dipole formation is in the soft matrix at some distance from the interface.

## Synchrotron tomography and AlN-GaN growth on silicon

### June 27, 2009

Sub-μm synchrotron tomography of multiphase metals using Kirkpatrick-Baez optics

G Requena et al

High resolution 3D imaging of heterogeneous metals is performed by high energy magnified synchrotron tomography using Kirkpatrick-Baez focusing optics achieving voxel sizes of (50-60 nm)3. Absorption and phase contrast are exploited applying holotomographic reconstructions. Microstructural features as small as not, vert, similar 180 nm are detected in ternary eutectic Al-Mg2Si-Si, SiC particle reinforced AlCu4, near β Ti-10V-2Fe-3Al, and in TiB reinforced α+β Ti-6Al-4V. The phase retrieval procedure yields enough contrast to segment the individual phases and analyze their shapes and 3D architecture.

Sequential growths of AlN and GaN layers on as-polished 6H–SiC(0001) substrates

Z J Reitmeier et al

Microstructures of surfaces and defects generated during initial and subsequent growths via metalorganic vapor-phase epitaxy of AlN(0001) films on 6H–SiC(0001) substrates and GaN(0001) films on AlN/SiC(0001) substrates have been investigated using atomic force microscopy and cross-sectional and plan-view transmission electron microscopy. Scratches present on the SiC surfaces did not appear to bias the nucleation of AlN. The lateral growth rate of AlN was greater than the vertical growth rate, leading to almost planar layers at 15 and 100 nm thicknesses. Partially coalesced islands were observed after nominally not, vert, similar15 nm of growth. Increasing the thickness to 100 nm resulted in complete island coalescence, formation of undulating films from the polishing scratches in the SiC substrate, a surface microstructure containing steps, terraces and small pits, and a reduced dislocation density relative to the 15 nm layers. The AlN/SiC interfaces contained steps and complex dislocation networks. GaN islands nucleated and grew on the AlN films. Complete coalescence of these islands occurred at thicknesses less than 100 nm. Dislocation density in the GaN films was reduced by increasing the thickness of either the AlN and or the GaN. Arguments are developed to account for these observations.

Elastic energy of a straight dislocation and contribution from core tractions

E Clouet

We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent with the work of the Peach-Koehler forces. This contribution needs also to be considered when extracting from atomic simulations core energies. The core energies thus obtained are real intrinsic dislocation properties: they do not depend on the presence and position of other defects. This is illustrated by calculating core energies of edge dislocation in bcc iron, where we show that dislocations gliding in lcub110rcub planes are more stable than those gliding in lcub112rcub planes.

## 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.

## Imaging twins and dislocations in SEM

### June 19, 2009

I Gutierrez-Urrutia, S Zaefferer, and D Raabe

Dislocation cells and mechanical twins have been imaged by electron channeling contrast imaging (ECCI) in a scanning electron microscope under controlled diffraction conditions in a deformed Fe-22Mn-0.6C twinning induced plasticity steel using a novel set-up. The approach uses electron backscattered diffraction (EBSD) for orientation-optimized ECCI with enhanced dislocation and interface contrast. The observations provide new insights into the strain hardening mechanisms of TWIP steels.

## Effective properties of composites

### June 17, 2009

Composites with superspherical inhomogeneities

R Hashemi et al

In contrast to the traditional study of composites containing ellipsoidal inclusions, we highlight some calculated results for the effective moduli when the inclusion shape can be described by the superspherical equation, , such that when *p* = 2 it reduces to a sphere and when *p* → ∞ it becomes a perfect cube. We consider the cases of both aligned and randomly oriented superspherical inclusions with isotropic, cubic, and transversely isotropic properties, and show how the shape parameter, *p*, affects the overall moduli of the composites during the spherical to cuboidal transition.

Phil. Mag. lett., **89**, 7, 439-451, 2009.

[1] Transformation kinetics for nucleus clusters

E Villa and P R Rios

A rigorous mathematical approach based on stochastic geometry concepts is presented to extend previous Johnson–Mehl, Avrami, Kolmogorov treatment of transformation kinetics to situations in which nuclei are not homogeneously located in space but are located in clusters. An exact analytical solution is presented here for the first time assuming that nucleation sites follow a Matérn cluster process. The influence of Matérn cluster process parameters on subsequent growth kinetics and the microstructural path are illustrated by means of numerical examples. Moreover, using the superposition principle, exact analytical solutions are also obtained when nucleation takes place by a combination of a Matérn cluster process and an inhomogeneous Poisson point process. The new solutions presented here significantly increase the number of exactly solvable cases available to formal kinetics.

[2] Anisotropic sintering stress for sintering of particles arranged in orthotropic symmetry

F Wakai and Y Shinoda

Many sintering bodies shrink in an anisotropic manner when the particle packing is not isotropic. The thermodynamic driving force for the anisotropic shrinkage, i.e. the sintering stress tensor, is determined numerically for an open pore structure with orthotropic symmetry in three dimensions. The sintering stress tensor is calculated rigorously by the energy method, the force balance method and the volume averaging method. The deviatoric component of sintering stress is approximately proportional to the logarithm of the aspect ratio of the orthorhombic volume element, and acts so as to deform the elongated particles to be more isotropic in most cases.

[3] Phase field study of precipitate growth: Effect of misfit strain and interface curvature (Note: self-promotion!)

R Mukherjee et al

We have used phase field simulations to study the effect of misfit and interfacial curvature on diffusion-controlled growth of an isolated precipitate in a supersaturated matrix. Treating our simulations as computer experiments, we compare our simulation results with those based on the Zener–Frank and Laraia–Johnson–Voorhees theories for the growth of non-misfitting and misfitting precipitates, respectively. The agreement between simulations and the Zener–Frank theory is very good in one-dimensional systems. In two-dimensional systems with interfacial curvature (with and without misfit), we find good agreement between theory and simulations, but only at large supersaturations, where we find that the Gibbs–Thomson effect is less completely realized. At small supersaturations, the convergence of instantaneous growth coefficient in simulations towards its theoretical value could not be tracked to completion, because the diffusional field reached the system boundary. Also at small supersaturations, the elevation in precipitate composition matches well with the theoretically predicted Gibbs–Thomson effect in both misfitting and non-misfitting systems.

[4] Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy

D L Olmsted et al

The energies of a set of 388 distinct grain boundaries have been calculated based on embedded-atom method interatomic potentials for Ni and Al. The boundaries considered are a complete catalog of the coincident site lattice boundaries constructible in a computational cell of a prescribed size. Correlations of the boundary energy with other boundary properties (disorientation angle, *Σ* value, excess boundary volume and proximity of boundary normals to 1 1 1) are examined. None of the usual geometric properties associated with grain boundary energy are useful predictors for this data set. The data set is incorporated as supplementary material to facilitate the search for more complex correlations. The energies of corresponding boundaries in Ni and Al are found to differ by approximately a scaling factor related to the Voigt average shear modulus or C_{44}. Crystallographically close boundaries have similar energies; hence a table of grain boundary energies could be used for interpolation.

[5] Thermodynamics of grain boundary premelting in alloys. I. Phase-field modeling

Y Mishin et al

The rich nature of the premelting transition of grain boundaries in solid solutions is analyzed. Part I of this paper uses a multi-phase field model, whereas Part II employs atomistic Monte Carlo simulations. To enable comparison, Cu-rich Cu–Ag solid solutions are chosen for study. In the phase-field model, a system composed of two grains and a liquid phase is treated with three phase field parameters and with a realistic bulk thermodynamic description of Cu–Ag alloys obtained with the CALPHAD approach. Several different computation methods are employed, both rigorous and approximate, to examine the premelting behavior and relate it to the so-called “disjoining potential” between the solid–liquid interfaces in the grain boundary region. Depending on the grain boundary energy, temperature and grain composition chosen, several different classes of premelting transitions have been detected. As the grain concentration approaches the solidus line, one class shows a premelted layer whose thickness diverges continuously to infinity (complete wetting). Another class shows a discontinuity of the premelted layer thickness, exhibiting a first-order thin-to-thick transition prior to continuous thickening to infinity at the solidus line. In other cases, a metastable grain boundary state can exist above the solidus line, indicating the possibility of superheating/supersatuation of the grains together with the grain boundary. The possibility of such transitions has been predicted previously for generic thermodynamics by many authors. The results of the current investigation are compared with the atomistic calculations for the Cu–Ag system in Part II of this work.

Here are some interesting things that I learnt from the participants of Micro-09.

- Dr. Chandan Srivatsava, a Centenary post-doc at the Department of Materials Engineering, IISc spoke about compositional characterization of nanoparticles using TEM. Apparently, one of the problems that one encoutners while doing the experiments is the drift in TEM. While discussing several ways of minimizing it, he explained how if you set the equipment as if you are going to take the readings the next moment, and then leave the room for a cup of coffee and come back after 20-30 minutes, the drift problem is minimized. So, I guess, while mathematicians are busy converting coffee into theorems, the microscopists are busy concerting coffee into compositions — which, by the way, reminds me why the closure of coffee board at IISc is such a regrettable decision 😦
- Most materials are most brittle in Mode I. (Vikram)
- The image formation mechanisms in microscopes are three: optical, scanning and projection. The image formation mechanism in TEM is optical.TEM images are not only diffration but also aberration limited. And, the equivalent of SANS and SAXS exists for electrons also — fluctuation microscopy is the SAES. (G K Dey, Head, Division of Materials Science, BARC)
- Indian electrical power production has increased by a factor of 100 since independnece. Of the power generated, 40% if lost, of which 60% of the losses are technical. (I Samajdar)
- Using EBSD, you can obtain whatever grain size you want to!Severe plastic deformation (SPD) are those deformation in which there are large amount of high angle grain boundaries (where, high angle grain boundaries are defined as those with a misorientation exceeding 15 degrees); quantitatively, in SPD, there is a higih angle boundary from any point in the microstructure in any direction within 1 microns, and the ratio of high angle grain boundary to total grin boundaries is more than 70%.
Further, SPD materials are lean in dislocations since they are absorbed in low angle grain boundaries. This results in better ductility and more uniform corrosion.

High cycle fatigue, which is related to elastic strain, improves because of improved fracture strength in SPD materials, while low cycle fatigue which is related to plastic strain degrades.Al, Cu, and Ag belong to three different stacking fault energy regimes and hence are important for texture studies. (Satyam)

- The talks of Aloke Paul and his student Kiran as well as those of Santonu Ghosh and Prasad were very interesting too, and some of them raised some very interesting, unresolved issues which made the workshop very exciting.

I had fun time interacting with the participants as well as chatting with old friends. On the whole, it was a wonderful experience. I hope Abi keeps up the tradition and run one Micro conference once in a year — and invites me! 🙂

**PS**: The slides of my presentation titled Modelling elastic stress induced morphological instabilities is available for download in my googlepages homepage (in PDF format).