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N.A.W. Holzwarth / Physics Procedia 57 (2014) 29 – 37 31 (Phillips and Kleinman (1959)) with the development of first-principles pseudopotentials (Hamann et al. (1979); Kerker (1980) ). A significant boost to the field was contributed by Car and Parrinello (Car and Parrinello (1985)) who showed that within the Born-Oppenheimer approximation, the self-consistent electronic structure algorithm could be efficiently coupled to the adjustment of the nuclear coordinates for structural and molecular dynamics studies. In addition to the adjustment of the nuclear coordinates, techniques were developed to allow for variable simulation cells in order to simulate the effects of pressure, stress, or phase transitions. (Andersen (1980); Parrinello and Rahman (1981); Wentzcovitch (1991)) Response function methods and density-functional perturbation theory methods were developed by Gonze, (Gonze (1997); Gonze and Lee (1997) ) allowing for the exploration of materials properties in the vicinity of equilibrium including the dynamical matrix and phonon modes. The efficiency and accuracy of the pseudopotential approach was significantly improved with the introduction of so-called ultra-soft pseudopotentials (USPP) by Vanderbilt (Vanderbilt (1990) ) and the projector augmented plane wave (PAW) method by Blo ̈chl. (Blo ̈chl (1994)) An invaluable contribution to the success of computational studies of materials, particularly those discussed in this contribution, has been the development of several open source software projects such as ABINIT (Gonze et al. (2009)) and QUANTUM ESPRESSO. (Giannozzi et al. (2009)) These codes make use of many of the state-of-the-art formalism developments including those listed above. These projects promote scientific productivity by reducing the duplication of coding efforts and by allow developers and users to share in the implementation and debugging of a common code system. The pseudopotential data files were generated using the ATOMPAW package (Holzwarth et al. (2001)) and the USPP package (Vanderbilt (1990)) Also important is the development of visualization tools. In the present work, OpenDx (OpenDX (1999)), XCrySDen (Kokalj (1999, 2003)), and VESTA (Momma and Izumi (2011)) were used. For solid electrolytes which are electronically insulating and which operate in their ground electronic states, the calculation of the electronic energy E(ρ,{Ra}) using density functional theory (Eq. (2)) works quite well. By using constrained optimization of the energy E(ρ, {Ra}) over the nuclear coordinates {Ra}, it is possible to study structural parameters of stable and meta-stable structures. A reasonable estimate of the heat of formation ΔH of each compound material can be computed from the ground state energies at zero temperature and these are useful in quantifying the expected stability of the materials in various structures and compositions. It is always important to question the reliability of computer simulations for describing real materials. Typically, it has been reported Du and Holzwarth (2007) that results obtained using the LDA exchange-correlation functional (Perdew and Wang (1992)) tend to underestimate the lattice parameters by 2% while results obtained using the GGA exchange-correlation functional (Perdew et al. (1996)) tend to overestimate the lattice parameters by 1%. On the other hand, for most materials, the fractional coordinates computed for the non-trivial site positions are nearly identical (within 0.1%) for LDA and GGA calculations in comparison with experiment. Similar findings have been reported in the literature for a wide variety of computational studies of insulating, non-transition metal materials. One quantitative indication of the accuracy of the calculations is the comparison of computed and measured normal modes of vibrations. Fortunately, there have been several reports of experimental measurements of Raman and infrared absorption spectra of crystalline Li3PO4 (Tarte (1967); Harbach and Fischer (1974); Riedener et al. (2000); Smith et al. (2002); Mavrin et al. (2003); Popovic ́ et al. (2003)); therefore our simulations of the zone center phonon modes serve as a validity check the calculations. Figure 1 shows two similar but distinct crystal structures of Li3PO4 for which the normal modes have been studied. Figure 2 shows the spectra of Raman active modes calculated using the LDA and GGA exchange-correlation functions and USPP (Vanderbilt (1990)) and PAW (Holzwarth et al. (2001)) pseudopotential datasets compared with various experimental measurements for the γ and β structures. There is variation among the various experimental mea- surements for γ-Li3PO4, some of which can be attributed to temperature and some attributed to resolution. In terms of comparing experiment to the calculations, it is striking that for frequencies ν > 600 cm−1, the results calculated using the LDA functional are in good agreement with experiment, while the agreement deteriorates at lower frequencies. These high frequency modes are mainly due to internal vibrations of the PO4 tetrahedra. The lack of agreement for the lower frequency modes is likely to be due to numerical error which is also reflected in the differences between the two LDA calculations using USPP and PAW datasets. The good agreement between the simulations and experiment for the higher frequency vibrational modes of these materials motivated the choice of the LDA functional for most of our simulation studies on the Li phosphates and thiophosphates (Du and Holzwarth (2007, 2008a,b); Holzwarth et al.PDF Image | First Principles Modeling of Electrolyte Materials in All-Solid-State Batteries
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