LiFePO 4 powders were synthesized under various conditions and the performance of the cathodes was evaluated using coin cells, The samples were characterized by X-ray diffraction, scanning electron microscope observations, Brunauer, Emmett, and Teller surface area measurements, particle-size distribution measurements, and Mossbauer spectroscopy. Ab initio calculation was used to confirm the experimental redox potentials and Mossbauer parameters. The choice of a moderate sintering temperature (500°C 95% of the 170 mAh/g theoretical capacity at room temperature. There are two main obstacles to achieving optimum charge/discharge performance of LiFePO 4 : (i) undesirable particle growth at T > 600°C and (ii) the presence of a noncrystalline residual Fe 3+ phase at T < 500°C.

https://iopscience.iop.org/article/10.1149/1.1348257/pdf

Optimized LiFePO4 for Lithium Battery Cathodes

Calculations of ground-state and excited-state properties of materials have been one of the major goals of condensed matter physics. Ground-state properties of solids have been extensively investigated for several decades within the standard density functional theory. Excited-state properties, on the other hand, were relatively unexplored in ab initio calculations until a decade ago. The most suitable approach up to now for studying excited-state properties of extended systems is the Green function method. To calculate the Green function one requires the self-energy operator which is non-local and energy dependent. In this article we describe the GW approximation which has turned out to be a fruitful approximation to the self-energy. The Green function theory, numerical methods for carrying out the self-energy calculations, simplified schemes, and applications to various systems are described. Self-consistency issue and new developments beyond the GW approximation are also discussed as well as the success and shortcomings of the GW approximation.

https://iopscience.iop.org/article/10.1088/0034-4885/61/3/002/pdf

The GW method

The WIEN2k program is based on the augmented plane wave plus local orbitals (APW+lo) method to solve the Kohn-Sham equations of density functional theory. The APW+lo method, which considers all electrons (core and valence) self-consistently in a full-potential treatment, is implemented very efficiently in WIEN2k, since various types of parallelization are available and many optimized numerical libraries can be used. Many properties can be calculated, ranging from the basic ones, such as the electronic band structure or the optimized atomic structure, to more specialized ones such as the nuclear magnetic resonance shielding tensor or the electric polarization. After a brief presentation of the APW+lo method, we review the usage, capabilities, and features of WIEN2k (version 19) in detail. The various options, properties, and available approximations for the exchange-correlation functional, as well as the external libraries or programs that can be used with WIEN2k, are mentioned. References to relevant applications and some examples are also given.

/pdf/wien2k-an-apw-lo-program-for-calculating-the-properties-of-3o6g3g0hz7.pdf

WIEN2k: An APW+lo program for calculating the properties of solids

Solid state calculations using WIEN2k

The density functional theory (DFT) foundations date from the 1920s with the work of Thomas and Fermi, but it was after the work of Hohenberg, Kohn, and Sham in the 1960s, and particularly with the appearance of the B3LYP functional in the early 1990s, that the widespread application of DFT has become a reality. DFT is less computationally demanding than other computational methods with a similar accuracy, being able to include electron correlation in the calculations at a fraction of time of post-Hartree-Fock methodologies. In this review we provide a brief outline of the density functional theory and of the historic development of the field, focusing later on the several types of density functionals currently available, and finishing with a detailed analysis of the performance of DFT across a wide range of chemical properties and system types, reviewed from the most recent benchmarking studies, which encompass several well-established density functionals together with the most recent efforts in the field. Globally, an overall picture of the level of performance of the plethora of currently available density functionals for each chemical property is drawn, with particular attention being dedicated to the relative performance of the popular B3LYP density functional.

General performance of density functionals.

Recently, Engel and Vosko have proposed an alternative form of a generalized gradient approximation (GGA) [Phys. Rev. B 47, 13 164 (1993)] within density-functional theory. This version of the GGA (EV93) was obtained by optimizing the exchange-correlation potential ${\mathit{V}}_{\mathrm{xc}}$ instead of the corresponding energy ${\mathit{E}}_{\mathrm{xc}}$. We have applied this functional to various solids and found that equilibrium lattice constants generally are far too large in comparison to experiment, so that the total-energy aspect is unsatisfactory. However, EV93 describes FeO and CoO as antiferromagnetic insulators, while the local-spin-density approximation or the Perdew-Wang version of the GGA yields a metallic ground state. EV93 favors magnetism, e.g., the spin susceptibility of V is increased, but Pd remains nonmagnetic in agreement with experiment.

Applications of Engel and Vosko's generalized gradient approximation in solids.

We determine the nuclear quadrupole moment $Q$ of the most important M\"ossbauer nucleus ${}^{57}\mathrm{Fe}$ by comparing experimental quadrupole splittings with calculated electric field gradients (EFG) for a large number of different Fe compounds. These ab initio calculations are based on the linearized-augmented plane-wave band structure method. From the slope of the linear correlation between theoretical EFGs and experimental quadrupole splittings a new value of $Q{(}^{57}\mathrm{Fe})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.16\phantom{\rule{0ex}{0ex}}\mathrm{b}$ is deduced, twice as large as previously suggested. Our results should also stimulate nuclear physicists to revise nuclear structure shell model calculations of $Q$.

Determination of the nuclear quadrupole moment of 57Fe.

The local-spin-density approximation yields a metallic ground state for the antiferromagnetic insulators CoO, FeO, ${\mathrm{FeF}}_{2}$, and ${\mathrm{CoF}}_{2}$ By using the generalized gradient approximation (GGA) we find the difluorides to be insulators, while in CoO the GGA splits the bands near ${\mathit{E}}_{\mathit{F}}$ and opens a direct gap, but a small indirect band overlap remains For FeO a significant improvement is found but not quite enough to make it an insulator The magnetic moments and gaps increase The GGA improves angular (and also in-out) correlations and thus affects the energy bands, a feature in addition to the total-energy improvement

Generalized-gradient-approximation description of band splittings in transition-metal oxides and fluorides.

A theoretical approach for the calculation of hyperfine parameters in solids from first principles is presented. These calculations are based on the full potential linearized-augmented-plane-wave (LAPW) band structure method, which is currently one of the most accurate schemes to determine the electronic structure in ordered solids. Exchange and correlation is treated within density functional theory using the generalized gradient approximation. Once the electron density is calculated self-consistently with high accuracy, quantities like electric field gradients (EFG), isomer shifts or hyperfine fields can easily be obtained from this density without further approximations. Using this approach we have studied various systems including metals, insulators, ionic compounds or the highT
c superconductors. In general we find good agreement between theory and experiment, which proves that our method is very accurate. Having these results in mind we are confident that this method is accurate enough to determine the value of the nuclear quadrupole momentQ, provided experimental measurements of the quadrupole coupling constant are available. This procedure is demonstrated forQ of77Se and100Rh, two nuclei recently used in PAC measurements. An extensive study of EFGs at Fe sites in various Fe-compounds has been performed leading to a very reliable quadrupole moment ofQ(57Fe)=0.16 b, a value twice as large as that deduced from recent HF calculations but back to older estimates.

Calculation of electric hyperfine interaction parameters in solids

We present an ab initio study of the electronic and magnetic structure of the antiferromagnetic state of ${\mathrm{MnF}}_{2}$ and ${\mathrm{NiF}}_{2}$. From the band structures of these two compounds we derive densities of states (DOS), electron densities, spin densities, electric-field gradients, and total energies. We use a simple molecular-orbital scheme to interpret the results. The internal coordinate u is determined by total-energy minimization for ${\mathrm{MnF}}_{2}$ and agrees well with experiment as well as with the calculated electric-field gradients or the electron densities. Recent spin-dependent x-ray-absorption spectra are interpreted in terms of partial DOS of the unoccupied Mn 4p states.

Philipp Dufek

Papers

Applications of Engel and Vosko's generalized gradient approximation in solids.

Determination of the nuclear quadrupole moment of 57Fe.

Generalized-gradient-approximation description of band splittings in transition-metal oxides and fluorides.

Calculation of electric hyperfine interaction parameters in solids

Electronic and magnetic structure of MnF2 and NiF2.