In materials science, many phenomena depend on the shapes of interfaces and surfaces. Many properties depend on interface shape, stability, and associated potentials. Calculating the shape of an interface is not usually a very easy exercise. When it is necessary to find the shape of an interface, a materials scientist can sometimes obtain serviceable information by judiciously reducing the dimensionality of the problem, or make some other simplifying approximation. However, sometimes such approximations are not warranted.
In some cases, the pertinent interface shapes are those A which minimize a total energy which depends, in part, on the interfaces. Finding the functional form of the minimizing interface is typically posed as a problem in the calculus of variations. The forces due to the interface, the interface potential and stability are can also be cast in the calculus of variations. Solutions have been worked out for simple geometries[1]; however, general problems are typically intractable except to numerical methods.
In some cases, numerical algorithms are written to solve a particular class of such interface problems and this can be an effective yet time-consuming endeavor.
A general program to solve minimal interface problems
(and many others where a function is desired which minimizes other quantities)
exists: Ken Brakke's Surface Evolver[2]
is public domain
software[4] which is flexible and useful in materials
where such problems often arise.
Below, examples will be shown where: 1) the surface shape is the object of interest, 2) the surface stability is the quantity of interest, and 3) the potentials are the quantity of interest.
Each of these Evolver calculations are pertinent to the field of materials science and each is a valid subject for study. However, the purpose is to demonstrate the utility of Evolver -hopefully with enough detail that they can be extended by similarity to other materials science problems. A library or working evolver codes is also available in the public domain. [5].
Since Evolver gives a representation of a surface as its result, those surface representation may be utilized as input for other stand-alone software. For instance, the surface may be extended into a volume mesh on which finite element techniques for determination of stress concentrations could be applied to solder joint geometries. In such cases, solder volumes and wetting conditions are either variable or not completely known, systematic variation of such parameters could give a materials scientist methods for determining the robustness of a process; or, via a combination of bootstrap[6] methods and finite element methods, means to determine reliability and lifetime predictions.