Ab initio calculations can be applied to almost any solid once the limitations in cell sizes and number of atoms are taken into account. Among the materials of nuclear interest that have been studied one can cite the following: metals, particularly iron, tungsten, zirconium, and plutonium; alloys, especially iron alloys (FeCr, FeC to tackle steel, etc.); models of fuel materials, UO2, U-PuO2, and uranium carbides; structural carbides (SiC, TiC, B4C, etc.); waste mate­rials (zircon, pyrochlores, apatites, etc.).

In this section, we rapidly expose the types of studies that can be done with ab initio calculations. The last two sections on metallic alloys and insulat­ing materials will allow us to go into detail for some specific cases.

1.08.3.1 Perfect Crystal

1.08.3.1.1 Bulk properties

Dealing with perfect crystals, ab initio calculations provide information about the crystallographic and electronic structure of the perfect material. The properties of usual materials, such as standard metals, band insulators, or semi-conductors, are basically well reproduced, though some problems remain, es­pecially for nonconductors (see Section 1.08.5.1 on SiC). However, difficulties arise when one wishes to tackle the properties of highly correlated materials such as uranium oxide (Section 1.08.5.2). For in­stance, no ab initio code, whatever the complexity and refinements, is able to correctly predict the fact that plutonium is nonmagnetic. In such situations, the nature of the chemical bonding is still poorly under­stood, so the correct physical ingredients are proba­bly not present in today’s codes. These especially difficult cases should not mask the very impressive precision of the results obtained for the crystal struc­ture, cohesive energy, atomic vibrations, and so on of less difficult materials.

1.08.3.1.2 Input for thermodynamic models

The information on bulk materials can be gathered in thermodynamical models. Most ab initio calculations are performed at zero temperature. Even with this restriction, they can be used for thermodynamical studies. First, ab initio calculations enable one to consider phases that are not accessible to experi­ments. It is thus possible to compare the relative stability of various (real or fictitious) structures for a given composition and pressure.

Considering alloys, it is possible to calculate the cohesive energy of various crystallographic arrange­ments. Solid solutions can also be modeled by so-called special quasi-random structures (SQS). Beyond a simple comparison of the energies of the various struc­tures, when a common underlying crystalline network exists for all the considered phases, the information about the cohesive energies can be used to parameter­ize rigid lattice inter-atomic interaction models (i. e., pair, triplet, etc., interactions) that can be used to per­form computational thermodynamics (see Chapter

1. 17, Computational Thermodynamics: Application to Nuclear Materials). These interactions can then be used in mean field or Monte-Carlo simulations to predict phase stabilities at nonzero temperature.2

As examples of this kind of studies one can cite the determination of solubility limits (e. g., Zr and Sc in aluminum22) and the exploration of details of the phase diagrams (e. g., the inversion of stability in the iron-rich side of the Fe-Cr diagram2 ).

Directly considering nonzero temperature in ab initio simulation is also possible, though more difficult. First, one can calculate for a given composi­tion and structure the electronic and vibrational entropy (through the phonon spectrum), which leads to the variation in heat capacity with temperature. Nontrivial thermodynamic integrations can then be used to calculate the relative stability of various struc­tures at nonzero temperature. Second, one can perform ab initio molecular dynamics simulations to model finite temperature properties (e. g., thermal expansion).