Simulation in Materials Science

In his early survey of computer experiments in materials science , Beeler (1970), in the book chapter already cited, divides such experiments into four categories. One is the Monte Carlo approach. The second is the dynamic approach (today usually named molecular dynamics), in which a finite system of N particles (usually atoms) is treated by setting up 3A equations of motion which are coupled through an assumed two-body potential, and the set of 3A differential equations is then solved numerically on a computer to give the space trajectories and velocities of all particles as function of successive time steps. The third is what Beeler called the variational approach, used to establish equilibrium configurations of atoms in (for instance) a crystal dislocation and also to establish what happens to the atoms when the defect moves each atom is moved in turn, one at a time, in a self-consistent iterative process, until the total energy of the system is minimised. The fourth category of computer experiment is what Beeler called a pattern development 

Beeler defined the broad scope of computer experiments as follows Any conceptual model whose definition can be represented as a unique branching sequence of arithmetical and logical decision steps can be analysed in a computer experiment... The utility of the computer... springs mainly from its computational speed. But that utility goes further as Beeler says, conventional analytical treatments of many-body aspects of materials problems run into awkward mathematical problems computer experiments bypass these problems. 

One type of computer simulation which Beeler did not include (it was only just beginning when he wrote in 1970) was finite-element simulation of fabrication and other production processes, such as for instance rolling of metals. This involves exclusively continuum aspects particles , or atoms, do not play a part. 

In what follows, some of these approaches will be further discussed. A very detailed and exhaustive survey of the various basic techniques and the problems that have been treated with them will be found in the first comprehensive text on computational materials science , by Raabe (1998). Another book which covers the principal techniques in great mathematical detail and is effectively focused on materials, especially polymers, is by Frenkel and Smit (1996). 

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Cillan M J 1991. Calculating the Properties of Materials from Scratch, In Meyer M and V Pontikis (Editors). Computer Simulation, NATO ASI Series E 205 (Computer Simulations in Materials Science) pp. 257-281. 

Gale J D, C R A Catlow and W C Mackrodt 1992. Periodic Ab Initio Determination of Interatomic Potentials for Alumina. Modelling and Simulation in Materials Science and Engineering 1 73-81. 

As we have repeatedly seen in this chapter, proponents of computer simulation in materials science had a good deal of scepticism to overcome, from physicists in particular, in the early days. A striking example of sustained scepticism overcome, at length, by a resolute champion is to be found in the history of CALPHAD, an acronym denoting CALculation of PHAse Diagrams. The decisive champion was an American metallurgist, Larry Kaufman. 

Galli, G., Parrinello, M., Ab initio molecular dynamics principles and practical implementation. In Computer Simulation in Material Science, Meyer, M., Pontikis, V., Eds. Kluwer Dordecht, 1991, p. 283... 

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Madeleine Meyer and Vassilis Pontikis, Computer Simulation in Materials Science Interatomic Potentials, Simulation Techniques and Applications. Proceedings of the NATO Advanced Study Institute on Computer Simulation in Materials Science Interatomic Potentials, Simulation Techniques and Applications, in Aussols, France, 25 March—5 April 1991, in NATO ASI Series, Ser. E Applied Sciences, Vol. 205, Kluwer, Dordrecht, 1991. 

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G. Galli, and M. Parinello, 1991, in Computer Simulations in Material Science, NATO ASI Series E edited by M. Meyer and V. Pontikis Kluver Academic, Dordrecht, Applied Science Vol. 205, p. 283. 

Galli, G., and Parrinello, M., In Computer Simulations in Materials Science, Kluwer, Dordrecht, 1991. 

E. Kostenko and A. Melker, Proc. SPIE-Int. Soc. Opt. Eng., 3345 (New Approaches to High-Tech Materials Nondestructive Testing and Computer Simulations in Materials Science and Engineering), 187-192 (1998). 

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Vakhrouchev, A.V Simulation of nano-elements interactions and self-assembling . Modeling and Simulation in Materials Science and Engineering. 2006,14, 975-991... 

Y. Y. Zhao. Analysis of flow development in centrifugal atomization Part I. Film thickness of a fuUy spreading melt. Modelling and Simulation in Materials Science and Engineering, 12(5) 959, September 2004. 

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