PKD Research Group

Phase Diagram

Phase diagram investigations using density functional theory (DFT) enable quantitative prediction of phase stability across composition, temperature, and pressure space from first principles. DFT provides static 0 K energies, which are then corrected using the quasi-harmonic approximation (QHA) to incorporate vibrational contributions and thermal expansion. Within QHA, phonon spectra are computed at several volumes, allowing the vibrational free energy and hence Gibbs free energy surface to be mapped. By computing total energies and deriving formation enthalpies of all relevant compounds and competing structures, we construct convex hulls that identify thermodynamically stable and metastable phases. These calculations guide experiments under extreme conditions, such as high-pressure polymorphs or multicomponent alloys where empirical data are scarce. Coupling DFT energetics with thermodynamic modeling or machine-learning potentials further allows finite-temperature phase boundaries and complex multicomponent diagrams to be mapped efficiently and systematically.

Mechanical Properties

Investigations of mechanical behaviour using density functional theory (DFT) provide atomistic insight into how materials respond to external loads. By applying small strains to fully relaxed structures and computing the resulting stress tensors, one can extract the full elastic constants tensor, and from it bulk, shear, and Young’s moduli as well as Poisson’s ratio. These quantities indicate stiffness, incompressibility, and elastic anisotropy, and feed into criteria such as Pugh’s ratio and Cauchy pressure to assess intrinsic ductility versus brittleness. Beyond linear elasticity, non-linear stress–strain calculations quantify ideal tensile and shear strengths and reveal elastic or phonon instabilities that precede fracture or phase transformations, enabling truly predictive mechanical materials design.

Electronic Properties

Electronic properties within density functional theory are investigated by solving the Kohn–Sham equations to obtain the ground-state electron density and eigenvalues for a given atomic structure. From these, we generally compute band structures and densities of states, which reveal band gaps, band dispersion, and effective masses governing charge transport. Projected and partial densities of states further identify orbital character and hybridization that control bonding and localization of carriers. Charge-density and electron-localization-function maps visualize covalent, ionic, and metallic bonding, while Bader or similar analyses quantify charge transfer and oxidation states. Work functions, dielectric response, and related quantities follow from total-energy differences and linear-response formalisms, yielding insights into screening, polarization, and surface electronic behavior. Collectively, these outcomes link atomic-scale structure to conductivity, optical activity, and chemical reactivity, guiding rational design of functional materials and interfaces.

Vibrational Properties

Vibrational properties are investigated through density functional theory (DFT) primarily via the direct (frozen phonon) method (also known as Finite displacement method) or density-functional perturbation theory (DFPT). In the direct approach, small atomic displacements generate force constants from the dynamical matrix's eigenvalues, yielding phonon dispersion curves, frequencies, and densities of states across the Brillouin zone. DFPT computes analytic second derivatives of the energy with respect to atomic positions and wavevectors, efficiently handling supercells and long-range interactions without explicit displacements. Outcomes of both methods include mode-specific assignments via partial densities of states, revealing lattice dynamics, bonding strength, and anharmonicity. Phonon spectra identify dynamical instabilities (imaginary modes) signaling structural transitions or novel ground states. Thermodynamic quantities like free energies, heat capacities, and thermal expansion emerge from quasi-harmonic integration of phonon data, enabling phase diagram construction and finite-temperature stability assessments essential for materials design.

Magnetic Properties

Density functional theory (DFT) investigates magnetic properties through spin-polarized calculations, solving Kohn-Sham equations for separate spin-up and spin-down electron densities. Spin-dependent exchange-correlation functionals (e.g., PBE, LDA+U) capture electron interactions, yielding self-consistent magnetization densities, atomic magnetic moments, and total spin polarization at the ground state. Key techniques include collinear/non-collinear magnetism setups and constrained magnetism to map energy landscapes versus spin configurations. Outcomes explain ferromagnetic, antiferromagnetic, or ferrimagnetic ordering; quantify exchange integrals J_ij for Curie temperatures; and reveal magneto-crystalline anisotropy driving easy axes in permanent magnets. Outcomes explain paleomagnetism: stable remanent magnetization in single-domain magnetite grains records ancient geomagnetic field directions and intensities, preserved over billions of years in rocks. These investigations lead to link rock magnetism to Earth's geodynamo, a core-generated field from convective molten iron motion, sustaining habitability by shielding the atmosphere from solar wind since Hadean times (4.2 Ga). Such insights validate dynamo models and constrain core evolution.

Optical Properties

DFT investigations of optical properties employ time-dependent density functional theory (TDDFT) or linear-response methods like the Bethe-Salpeter equation (BSE) on top of ground-state calculations. These compute the dielectric function (ϵ1 arises from vertical electronic transitions between Kohn-Sham states, and ϵ2 via Kramers-Kronig relations). Outcomes yield absorption coefficients α(ω), refractive indices n(ω), reflectivity, and loss functions across photon energies, revealing band-edge absorption, excitonic effects, and interband transitions. Significance lies in high-throughput screening of band gaps, solar-spectrum matching for photovoltaics, and tailoring transparency windows for LEDs or coatings, accelerating discovery of next-generation optoelectronic materials without exhaustive synthesis.

Adsorption Properties

Adsorption energy in DFT is found by subtracting the energies of the isolated surface and adsorbate from the combined system's energy. It shows how strongly a molecule binds to a surface. This is important in materials science for catalysis and surface design, and in earth sciences for studying mineral interactions and environmental processes.

Page updated

Google Sites

Report abuse