## Computational Materials Engineering:

*A tool whose time has come*

Isaac Newton (1643−1727) and Robert Hooke (1635–1703) were contemporaries, and their work forms the basis of modern engineering. Newton's calculus found fertile ground and grew into the core computational techniques that are the foundation of mechanical design. Finite element analysis, for example, is a numerical integration technique that permits analysis of systems that are too difficult to solve by other means. Hooke's law of elasticity laid the foundation for computing the internal distortions of physical objects subjected to external stresses and for predicting strain induced failures.

Since the time of Newton and Hooke, accurate property determination was limited to those materials readily available for characterization in the laboratory. All material properties arise from the interaction of electrons with atomic nuclei; consequently, the ability to compute engineering properties for a given material was not possible until the advent of quantum physics.

Atomic interactions are described by quantum physics. While writing the equations describing atomic interactions is easy, solving these equations is not. Systems composed of more than two or three atoms frequently involve more than 30 electrons. This type of problem requires the numerical integration techniques spawned by Newton’s work.

##### A Fistful of Atoms

Raytheon often uses novel materials in order to expand the performance envelope of its products, and is currently using computational materials engineering (CME) as an aid to characterize these novel materials. CME is simply the application of advanced computing techniques to the solution of quantum physics problems involving the mechanical, thermal, electrical and optical properties of engineering materials.

Recent advances in computing power have increased computer speed and reduced computing costs. Now computations are a viable alternative to experimentation for engineering problems.

As input, CME needs only the identity and geometric arrangement of a small group of atoms (less than 100) to predict the total energy of that arrangement. Figure 1 is an example of the required input. All other required parameters are known physical constants.

Comparing the energy of several different arrangements leads to amazing insight into material properties and material stability. Mechanical properties (modulus, strength); thermal properties (heat capacity, coefficient of thermal expansion); Optical properties (index of refraction, spectral absorption); and electrical properties (band gap) can all be computed by systematically distorting the input geometry.

Because the basic physics and fundamental constants are known and the geometry is defined, all the input parameters are known, making this truly an ab initio, or first principles, technique. The results do not depend on empirical relationships or assumed relationships between input parameters. Interpretation of results, however, does require a detailed understanding of statistical thermodynamics and quantum theory.

Just as finite element analysis (FEA) revolutionized mechanical engineering, the ability to compute a material’s mechanical properties (modulus and strength); optical properties (absorption, THz phonon spectra, dielectric constant, etc.); and electrical properties (band gap, ionization potential, etc.) will revolutionize materials engineering. Its ability to map out spatial energy fields is creating new opportunities to predict kinetic phenomena such as diffusion and structural relaxation, as well.

CME is maturing at a rapid rate. It will not replace laboratory testing, but can substantially reduce the cost of testing by focusing testing on critical parameters and providing insight to eliminate or suggest new materials suitable for a particular application. CME can also suggest alternate test methods, which may not have been previously considered.

##### A Fresh Perspective on Persistent Problems

The ability to tailor properties of a given material to optimize it for a specific application expresses the essence of engineering. This technique will quickly be adopted by the engineering community as a standard tool. This is especially attractive for the aerospace industry, where performance envelopes can be limited by materials problems that evade solution for decades. Getting an alternate perspective on these persistent problems is invaluable.

As an example of the power of CME, we apply it to the current industry problem of tin whiskers. If lead (Pb) is not added to tin (Sn) solder in sufficient quantities, solder lines will slowly grow tin whiskers of sufficient length to eventually cause shorting and component failure. Recent environmental restrictions on the use of lead require the formulation of new solders and whisker inhibitors.

Figure 1 shows a particular arrangement of atoms that represents a zinc atom (Zn) moving along a tin grain boundary. A fixed atom arrangement is input to the quantum computation engine, which uses iteration to find the lowest energy arrangement of electron density around the nuclei. The lowest energy state is determined by convergence. The result is an approximation of the energy of that configuration at absolute zero.

Repeating this same procedure for slight variations in geometry shows us the lowest energy configuration of atoms. Figure 2 shows the energy of the entire group of atoms as the zinc atom is moved along the grain boundary. The height of the curve is the activation energy for diffusion of zinc through a tin grain boundary.

Zinc is known to move quickly through tin grain boundaries and may promote the growth of tin whiskers. Lead is known to inhibit the growth of tin whiskers. The bulk tin that forms the whiskers is known to travel to the whisker root along grain boundaries. If we restrict the movement of tin through the grain boundary, then we should be able to slow or inhibit whisker growth. The diffusion activation energy is a measure of how difficult it is to move an atom from one location to another. A large activation energy implies slower transport.

Figure 2 clearly shows that the activation energy for transport of lead and zinc are different from each other. The activation energy for transport is greater for lead than for tin. The activation energy for zinc is substantially lower than that of either lead or tin.

We surveyed binary alloys comprised of tin. Each alloy combines tin with each element in the entire periodic table. Most elements have activation energies lower than of tin. A few have activation energies greater than tin and fewer still have activation energies greater than or equal to lead.

We can now use this knowledge to focus experiments on alloys with elements that we think will behave, like lead, as whisker inhibitors. This effort should reduce the time to find a suitable replacement for lead solders for electronics, which are the heart of many of Raytheon's products.

Unfortunately, the reliability of tin-lead in electronics is not limited to whisker inhibition by lead, but relies on the unique mechanical and thermal properties of the tin–lead alloy. Any viable solder replacement should have mechanical thermal properties very similar to tin–lead alloys. The computed properties of candidate alloys can be verified later by testing.

Raytheon is performing these calculations using the MedeA software package, written and distributed by Materials Design, Inc. Raytheon has been working with Materials Design since 2005, initially to understand the capabilities and limits of the tool. More recently we have been applying it to a diverse range of engineering problems. Raytheon and Materials Design are designing a virtual chemical vapor deposition (CVD) chamber, based on the MedeA software, to complement the zinc sulfide CVD system recently installed at Raytheon in Tucson.

##### A Few Atoms More

Dramatic growth in computing power, and insights enabled by quantum theory, now makes it possible to apply quantum mechanics to industrial materials problems. Quantum mechanics is as important to materials engineering as Newtonian statics and dynamics.

Characterizing the mechanical properties of materials is no longer restricted to the laboratory. We can now investigate new materials, and variations of existing materials, outside of the laboratory using computational methods. In addition, the computational analysis can be used to tailor materials to specific needs — engineering of materials is no longer science fiction.

Computational materials engineering has shown us what we can obtain from a *fist full of atoms, *can you imagine what we can achieve for *a few atoms more?*

D. Brooke Hatfield, Brian J. Zelinski