Cubic to tetragonal transformation

Title: The transformation sequences in the cubic → tetragonal decomposition

Authors: Y. Ni, Y.M. Jin and A.G. Khachaturyan

Source: Acta Materialia, Volume 55, Issue 14, August 2007, Pages 4903-4914

Abstract:

The decomposition of a generic supersaturated binary cubic solid solution into a mixture of cubic and tetragonal phases is investigated by phase field microelasticity modeling and simulations. It is shown that the decomposition in such a system is not necessarily developed by conventional nucleation and growth of the tetragonal phase. There are three temperature and composition ranges where the sequences of transient structures formed are different. The transformation pathways are predicted and the corresponding thermodynamic parameters are identified. In particular, the simulations reveal unusual transformation sequences occurring in the process of isostructural decomposition followed by cubic → tetragonal MT confined within one of the decomposed cubic phases. Mechanisms for the formation of the stress-accommodating multi-domain aggregates of the tetragonal phase and the checkerboard-like structures comprised of parallel rods of cubic and tetragonal phases are discussed.

Effect of stress on pearlite formation

Title: The influence of lattice strain on pearlite formation in Fe–C

Authors: I. Steinbach and M. Apel

Source: Acta Materialia, Volume 55, Issue 14, August 2007, Pages 4817-4822

Abstract:

The effect of stress and strain on the transformation kinetics of pearlite is investigated by phase-field simulation. Strain is considered in terms of expansion/contraction during transformation and due to concentration gradients in austenite. It is demonstrated that due to the concentration dependence of the eigenstrain, an inhomogeneous stress distribution ahead of the transformation front enhances diffusion in the austenitic phase and reduces chemical supersaturation in both austenite and ferrite. The main result of the investigation is that transformation strain inhibits the cooperative growth mode of cementite and ferrite, as considered by the Zener–Hillert model, and provokes the salient growth of cementite needles ahead of the ferrite front, which we call “staggered growth”. The predicted growth velocities give the right order of magnitude compared to the experiment and close the gap between theoretical models based on diffusion only, and experimental observations.

Nanoparticle arrays as elastic membranes

Title: Elastic membranes of close-packed nanoparticle arrays

Author: Klara E. Mueggenburg, Xiao-Min Lin, Rodney H. Goldsmith and Heinrich M. Jaeger

Source: Nature Materials, Advanced Online Publication, July 22

Abstract: Nanoparticle superlattices are hybrid materials composed of close-packed inorganic particles separated by short organic spacers. Most work so far has concentrated on the unique electronic, optical and magnetic behaviour of these systems. Here, we demonstrate that they also possess remarkable mechanical properties. We focus on two-dimensional arrays of close-packed nanoparticles and show that they can be stretched across micrometre-size holes. The resulting free-standing monolayer membranes extend over hundreds of particle diameters without crosslinking of the ligands or further embedding in polymer. To characterize the membranes we measured elastic properties with force microscopy and determined the array structure using transmission electron microscopy. For dodecanethiol-ligated 6-nm-diameter gold nanocrystal monolayers, we find a Young’s modulus of the order of several GPa. This remarkable strength is coupled with high flexibility, enabling the membranes to bend easily while draping over edges. The arrays remain intact and able to withstand tensile stresses up to temperatures around 370 K. The purely elastic response of these ultrathin membranes, coupled with exceptional robustness and resilience at high temperatures should make them excellent candidates for a wide range of sensor applications.

Notes: Via Scienceblog

In Nature this week

1. Markus Kindermann comments on a paper that shows that electron waves from different sources do interfere, and tells us the profound consequences that follow such interference;
2. Guust Nolet pays his tributes to Anthony Dahlen, a theoretical geophysicist who passed away recently; and,
3. Gerard t’ Hooft explains why the standard model in physics is more than a model.

Happy reading!

Lattice mismatch strain induced pattern formation in nanocrystals

Title: Spontaneous Superlattice Formation in Nanorods Through Partial Cation Exchange

Authors: Richard D. Robinson, Bryce Sadtler, Denis O. Demchenko, Can K. Erdonmez, Lin-Wang Wang, and A. Paul Alivisatos

Source: Science 20 July 2007: Vol. 317. no. 5836, pp. 355 – 358

Abstract:

Lattice-mismatch strains are widely known to control nanoscale pattern formation in heteroepitaxy, but such effects have not been exploited in colloidal nanocrystal growth. We demonstrate a colloidal route to synthesizing CdS-Ag₂S nanorod superlattices through partial cation exchange. Strain induces the spontaneous formation of periodic structures. Ab initio calculations of the interfacial energy and modeling of strain energies show that these forces drive the self-organization of the superlattices. The nanorod superlattices exhibit high stability against ripening and phase mixing. These materials are tunable near-infrared emitters with potential applications as nanometer-scale optoelectronic devices.

C coding standards

Though not strictly for scientific computations, these might still be handy:

GNU coding standard
http://www.gnu.org/prep/standards/

Programming in C
http://www.lysator.liu.se/c/index.html

C coding standards:
http://www.jetcafe.org/~jim/c-style.html
http://www.psgd.org/paul/docs/cstyle/cstyle.htm
http://www.alma.nrao.edu/development/computing/docs/joint/0009/2001-02-28.pdf

Phase field study of elastic stress driven rafting

Our paper on rafting made it to the Articles in Press section of Acta–today.

Title: Phase field study of precipitate rafting under a uniaxial stress

Authors: M P Gururajan and T A Abinandanan

Source: Acta Materialia, Articles in Press, Corrected Proof

Abstract:

We examine rafting of two-phase microstructures under a uniaxial applied stress, a process in which a mismatch in elastic moduli (elastic inhomogeneity) plays a central role. For this purpose, we have used a phase field model of an elastically inhomogeneous alloy; elastic stress and strain fields are calculated using a method adapted from the homogenization literature. We have characterized the efficiency of the resulting iterative algorithm based on Fourier transforms. Our simulations of rafting in two-dimensional systems show that rafting (unidirectionally elongated microstructures) is promoted when the precipitate phase is softer than the matrix and when the applied stress has the same sign as the eigenstrain. They also show that migration (for both hard and soft precipitates) and coalescence (for soft precipitates) have significant contributions to rafting.

Grain boundaries and Nye dislocation density tensor

Title: Stress-free states of continuum dislocation fields: Rotations, grain boundaries, and the Nye dislocation density tensor

Authors: Surachate Limkumnerd and James P Sethna

Source: Phys. Rev. B 75, 224121 (2007) (9 pages)

Abstract:

We derive general relations between grain boundaries, rotational deformations, and stress-free states for the mesoscale continuum Nye dislocation density tensor. Dislocations generally are associated with long-range stress fields. We provide the general form for dislocation density fields whose stress fields vanish. We explain that a grain boundary (a dislocation wall satisfying Frank’s formula) has vanishing stress in the continuum limit. We show that the general stress-free state can be written explicitly as a (perhaps continuous) superposition of flat Frank walls. We show that the stress-free states are also naturally interpreted as configurations generated by a general spatially dependent rotational deformation. Finally, we propose a least-squares definition for the spatially dependent rotation field of a general (stressful) dislocation density field.