## Atomic structure determination at nanoscale

### April 28, 2007

Here is a review from the recent issue of Science by Simon J L Billinge and Igor Levin on the available experimental and theoretical methods for the determination of atomic structure at the nanoscale. Here is the abstract:

Emerging complex functional materials often have atomic order limited to the nanoscale. Examples include nanoparticles, species encapsulated in mesoporous hosts, and bulk crystals with intrinsic nanoscale order. The powerful methods that we have for solving the atomic structure of bulk crystals fail for such materials. Currently, no broadly applicable, quantitative, and robust methods exist to replace crystallography at the nanoscale. We provide an overview of various classes of nanostructured materials and review the methods that are currently used to study their structure. We suggest that successful solutions to these nanostructure problems will involve interactions among researchers from materials science, physics, chemistry, computer science, and applied mathematics, working within a “complex modeling” paradigm that combines theory and experiment in a self-consistent computational framework.

Take a look!

## In Nature this week

### April 27, 2007

1. Of course the big story, as I blogged elsewhere, is the higher dimensional generalizations of the Neumann-Mullins rule of grain growth by MacPherson and Srolovitz:

Cellular structures or tessellations are ubiquitous in nature. Metals and ceramics commonly consist of space-filling arrays of single-crystal grains separated by a network of grain boundaries, and foams (froths) are networks of gas-filled bubbles separated by liquid walls. Cellular structures also occur in biological tissue, and in magnetic, ferroelectric and complex fluid contexts. In many situations, the cell/grain/bubble walls move under the influence of their surface tension (capillarity), with a velocity proportional to their mean curvature. As a result, the cells evolve and the structure coarsens. Over 50 years ago, von Neumann derived an exact formula for the growth rate of a cell in a two-dimensional cellular structure (using the relation between wall velocity and mean curvature, the fact that three domain walls meet at 120° and basic topology). This forms the basis of modern grain growth theory. Here we present an exact and much-sought extension of this result into three (and higher) dimensions. The present results may lead to the development of predictive models for capillarity-driven microstructure evolution in a wide range of industrial and commercial processing scenarios—such as the heat treatment of metals, or even controlling the ‘head’ on a pint of beer.

2. Henry Gee reviews The Discovery of the Hobbit: The scientific breakthrough that changed the faceof human history; and, John Hawks is not happy about the review (though he seems to have liked the book)–his review of the review is a must read, at least for sections like these:

…Gee spends several paragraphs expositing on his own role in the publication of the Homo floresiensis announcement. We learn some interesting little facts, like how the authors wanted to name the species “Sundanthropus floresianus” until a reviewer pointed out that future students would confuse the name with a flowery butt.I kid you not. Nature has a layer of reviewers to take tushie references out of taxonomy. Somehow they can’t tell a left femur from a right, but they’re on the watch for sphincter-species!

3. How does one weigh molecules, single cell virus, and bacteria whose weight are of the order of a few hundreds of femtograms (and, which are in a solution)? Liesbeth Venema describes a method that has been developed recently and reported in the same issue of Nature.
4. Martin Campbell-Kelly pays his tributes to John Backus, the inventor of FORTRAN in an obituary piece.

## Atomistic and phase field grain boundary simulations

### April 23, 2007

Title: Relating atomistic grain boundary simulation results to the phase-field model

Authors: Catherine M Bishop, and W Craig Carter

Abstract: A coarse-graining method for mapping discrete data to a continuous structural order parameter is presented. This method is intended to provide a useful and consistent method of utilizing structural data from molecular simulations in continuum models, such as the phase field model. The method is based on a local averaging of the variation of a Voronoi tessellation of the atomic positions from the Voronoi tessellation of a perfect crystal (the Wigner–Seitz cell). The coarse-graining method is invariant to coordinate frame rotation. The method is illustrated with a simple two-dimensional example and then applied to a three-dimensional relaxation simulation using the silicon EDIP potential of a Σ5 grain boundary. Calculated results indicate that a continuous structural parameter is obtained that has grain boundary characteristics similar to phase-field models of grain boundaries. Comparisons to other coarse-graining measures of structure are discussed as well as applications to experimental data sets.

## Sparse matrix algorithms for phase field models of grain growth

### April 23, 2007

Phase field models are used, among other things, for a study of grain growth [1,2]. In one type of phase field models used to study grain growth, each grain orientation is represented by an order parameter $\eta_{i}$, where the index $i$ runs from 1 to $N$, where $N$ is the total number of orientations present in the system [3,4]. Though this method is simple to implement and has been used extensively, it is computationally intensive. So, recently there had been at least two attempts to come up with an efficient numerical implementation:

1. Efficient numerical algorithm for multiphase field simulations. Srikanth Vedantam and B S V Patnaik, Phys Rev E 73, 016703, 2006.

Phase-field models have emerged as a successful class of models in a wide variety of applications in computational materials science. Multiphase field theories, as a subclass of phase-field theories, have been especially useful for studying nucleation and growth in polycrystalline materials. In theory, an infinite number of phase-field variables are required to represent grain orientations in a rotationally invariant free energy. However, limitations on available computational time and memory have restricted the number of phase-field variables used in the simulations. We present an approach by which the time and memory requirements are drastically reduced relative to standard algorithms. The proposed algorithm allows us the use of an unlimited number of phase-field variables to perform simulations without the associated burden on computational time or memory. We present the algorithm in the context of coalescence free grain growth.

2. Sparse data structure and algorithm for the phase field method. J Gruber, N Ma, Y Wang, A D Rollett, and G S Rohrer, Modelling and Simulation in Materials Science and Engineering, 14, 1189, 2006.

The concepts of sparse data structures and related algorithms for phase field simulations are discussed. Simulations of polycrystalline grain growth with a conventional phase field method and with sparse data structures are compared. It is shown that memory usage and simulation time scale with the number of nodes but are independent of the number of order parameters when a sparse data structure is used.

The source code for a C++ implementation of the method described in the paper of Gruber et al is available for download here (for non-profit scientific research purposes).

The idea behind these implementations is rather simple. Consider an arbitrary mesh point in a simulation cell. The mesh point either lies in the bulk of a given grain, or it lies in the interface. If it lies in the bulk, all the order parameters except the one corresponding to the grain orientation are zero, and there is nothing much to be done about the calculation at that point. On the other hand, if it lies in the interface, the total number of order parameters which have non-zero values are still a very small number as compared to the total number of orientations present in the entire system. Hence, if there is a database such that for any point (and its neighbours) we have the information of non-zero order parameters, then the calculation can be made more efficient.

Take a look and have fun!

References:

[1] Phase field methods for microstructure evolution. Long-Qing Chen, Annu. Rev. Mater. Res., 32, 113, 2002.

[2] Modeling grain boundaries using a phase-field technique. J A Warren, R Kobayashi, and W Craig Carter, J Cryst Growth, 211, 1, 18, 2000.

[3] A novel computer simulation technique for modeling grain growth. Long-Qing Chen, Scripta Metallurgica et Materialia, 32, 1, 115, 1995.

[4] A phase field concept for multiphase systems. I Steinbach, F Pezzolla, B Nestler, M Seeszelberg, R Prieler, G J Schmitz, and J L L Rezende, Physica D, 94, 3, 135, 1996.

## Creep resistant austenitic stainless steels

### April 21, 2007

Title: Creep-resistant Al2O3-forming austenitic stainless steels

Authors: Y Yamamoto, M P Brady, Z P Lu, P J Maziasz, C T Liu, B A Pint, K L More, H M Meyer, and E A Payzant

Abstract: A family of inexpensive, Al2O3-forming, high–creep strength austenitic stainless steels has been developed. The alloys are based on Fe-20Ni-14Cr-2.5Al weight percent, with strengthening achieved through nanodispersions of NbC. These alloys offer the potential to substantially increase the operating temperatures of structural components and can be used under the aggressive oxidizing conditions encountered in energy-conversion systems. Protective Al2O3 scale formation was achieved with smaller amounts of aluminum in austenitic alloys than previously used, provided that the titanium and vanadium alloying additions frequently used for strengthening were eliminated. The smaller amounts of aluminum permitted stabilization of the austenitic matrix structure and made it possible to obtain excellent creep resistance. Creep-rupture lifetime exceeding 2000 hours at 750°C and 100 megapascals in air, and resistance to oxidation in air with 10% water vapor at 650° and 800°C, were demonstrated.

## Model interfaces in nanocomposites

### April 18, 2007

In a News and Views piece, Linda Schadler puts the recent work of Rittigstein et al on interfaces in model polymer nanocomposites in perspective:

Three important conclusions arise from this work. First, the size of the interfacial region (which is half the interparticle spacing or film thickness) can be as large as 250 nm, and depends on the degree of interaction between the polymer and the particle. Although this functionality remains to be quantified, this is one of the first times this behaviour has been proved and quantitatively measured in a controlled nanocomposite system. Second, they show a quantitative correlation between thin-film thickness and an ‘effective interparticle spacing’ at which changes in Tg begin to occur. Third, they find that the ageing rate — the rate at which the amorphous polymer approaches its equilibrium state — decreases dramatically in both the ‘real’ and ‘model’ nanocomposites, which implies that nanocomposite properties will be more stable than pure polymers over time.

Take a look!

## All-electrically controlled magnetic memory devices

### April 18, 2007

In a News and Views piece in the latest Nature Materials, Russell P Cowburn writes about spintroics. Here is the abstract:

The magnetization direction in the centre of a submicrometre magnetic disk can now be switched by an electrical current. This discovery demonstrates the potential of realizing all-electrically controlled magnetic memory devices.

The article begins with a discussion of magnetoresistance (change in electrical resistance due to a change in the magnetic state of the material), and its complementary effect, spin transfer (change in the magnetization of the material due to the passage of current–the spin of the electrons, while moving through regions of magnetization gradients, change and in turn also exert a torque on the magnetization of the material).  And, then it proceeds to discuss vortex cores and the recent discovery that they can be manipulated by electric fields. Finally, the article ends with a discussion as to why technologists are excited about spin transfer. A lucidly written article worth your while.

PS: The wiki page on spintronics is also a nice place to look for resources–it links to this 2002 Scientific American article for example.