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. 2013 Sep;3(5):438-448.
doi: 10.1002/wcms.1125. Epub 2013 Jan 8.

Density functional theory in materials science

Jörg Neugebauer  1 , Tilmann Hickel  1
Affiliations
Free PMC article

Density functional theory in materials science

Jörg Neugebauer et al. Wiley Interdiscip Rev Comput Mol Sci. 2013 Sep.
Free PMC article

Abstract

Materials science is a highly interdisciplinary field. It is devoted to the understanding of the relationship between (a) fundamental physical and chemical properties governing processes at the atomistic scale with (b) typically macroscopic properties required of materials in engineering applications. For many materials, this relationship is not only determined by chemical composition, but strongly governed by microstructure. The latter is a consequence of carefully selected process conditions (e.g., mechanical forming and annealing in metallurgy or epitaxial growth in semiconductor technology). A key task of computational materials science is to unravel the often hidden composition-structure-property relationships using computational techniques. The present paper does not aim to give a complete review of all aspects of materials science. Rather, we will present the key concepts underlying the computation of selected material properties and discuss the major classes of materials to which they are applied. Specifically, our focus will be on methods used to describe single or polycrystalline bulk materials of semiconductor, metal or ceramic form.

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Figures

Figure 1
Figure 1
Total energy versus volume curve for two crystallographic (fcc, bcc) and three magnetic structures (non- (nm), ferro- (fm), antiferro- (afm, afmd) magnetic) of single crystalline iron. The calculations provide the equilibrium volume (minimum) of the individual phases as well as information on the crystallographic and magnetic preferences. The example shown here reveals that the T = 0 K thermodynamic ground state of bulk iron is the ferromagnetic bcc structure.
Figure 2
Figure 2
Relative errors between density functional theory computed and experimental bulk moduli (y-axis) and lattice constants (x-axis). Local density approximation and various generalized gradient approximations for the exchange correlation functional have been employed (PBE, PW91, AM05, PBEsol17). The figure is adapted from Refs 18 and 19.
Figure 3
Figure 3
Formation energy of various point defects in bulk GaN as function of the Fermi energy [Image: see text] . VN and VGa are N and Ga vacancies, NGa and GaN antisites (a N(Ga) atom on a Ga(N) site respectively), and Ni and Gai the corresponding interstitials. The numbers give the (energetically) most favorable charge state of the respective defect. The kinks in the formation energies give the position of the electronic charge transfer level. (Reproduced with permission from Ref 30. Copyright 2004, American Institue of Physics.)
Figure 4
Figure 4
Isobaric heat capacity of aluminum including the quasiharmonic, electronic, anharmonic, and vacancy contributions compared to experiment. The modification due to the last three contributions with respect to the quasiharmonic result is for the case of the generalized gradient approximations shown in the inset (note the different scale). The melting temperature Tm of Al (933 K) is indicated by a vertical dashed line. (Adapted with permission from Ref 59. Copyright 2011, IOP publishing. References for the experimental data can be found in Ref 57.)
Figure 5
Figure 5
Calculated heat capacity (lines) of cementite in comparison with available experimental data (open symbols). The calculated vibrational, electronic, and magnetic contributions to the heat capacity are shown in shaded gray (lower area), blue (middle), and red (upper area) correspondingly. (Adapted with permission from Ref 59. Copyright 2011, IOP publishing. References for the experimental data can be found in Ref 58.)
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