MedeA® Application Notes for Steel & Metal Alloys

MEDEA's MT-Elastic Properties automates the calculation of elastic properties from first-principles.
For a given input system, MT applies symmetry-relevant strains and computes the resulting stress tensor for each deformed structure. The elastic properties are derived by a multi-dimensional least-square fit of the strain-stress data.

 MEDEA MT in Depth: Forsterite Mg₂SiO₄

The stress-strain behavior of a Cu nanowire is simulated with the MedeA environment using a quasi-classical embedded atom potential and the LAMMPS molecular dynamics code. The monocrystalline wire has a diameter of 3.3 nm and is stretched in the [100] direction. The simulations show an initial elastic region with a linear increase in stress, which reaches a maximum just before the onset of slip in (111) planes. Upon further strain the model reveals the formation of more slip planes and necking until the break point is reached.

Stress-Strain Behavior of a Cu Nanowire Simulated with MedeA-LAMMPS

Ab Initio calculations (VASP) correctly predict the monoclinic phase to be the most stable at low temperatures, followed by the tetragonal, and the high-temperature cubic phases. The structural information and heat of formation obtained provide a sound starting point for calculations of thermodynamic properties.

The temperature-induced phase transition from monoclinic to tetragonal ZrO₂ is predicted from first principles calculations using a quasi-harmonic approach for the vibrational enthalpy and entropy. The computed transition temperature is within 15% of the experimental value. Relative trends due to vacancies, alloying elements, and mechanical stress can be expected to have a higher accuracy. The present results show the importance of thermal expansion, which is here also obtained from first principles.

Temperature-Dependent Phase Transitions of ZrO₂

Accurate measurements of diffusion coefficients of atoms in solids are difficult and deviations between different experiments can be several orders of magnitude. For the benchmark case of hydrogen diffusion in nickel first-principles calculations give a remarkable agreement with available experimental data especially near room temperature. Thus, computations of diffusion coefficients can be comparable in reliability with measured data. Simulations are possible for situations such as high strain, or slow processes where measurements are difficult or impractical.

Diffusion of Hydrogen in Nickel

This application shows the calculation of the elastic constants of TiB₂, a hexagonal structure.

Elastic Constants of TiB₂

The surface energy of a material is defined as the energy required to create a surface (h k l) from the bulk material. Surface energies are usually given in units of J/m2.

Surface Energy of Molybdenum

Iodine is a fission product of uranium. It can attack the inner side of zircaloy cladding in nuclear power reactors leading to cracking and fracture. Computations show that iodine molecules adsorb and dissociate on a zirconium surface without an energy barrier. The binding energy of iodine on this surface is large (nearly 300 kJ/mol per iodine atom), but the barriers for surface diffusion is only 6.8 kJ/mol. This gives rise to rapid surface diffusion allowing iodine atoms to reach the crack tips faster than the propagation of cracks.

Adsorption and Dissociation of Iodine Molecules on a Zr Surface

The correct lattice parameters of a crystalline structure are of fundamental importance for any reliable computational predictions of materials properties. This case study shows the calculation of the lattice parameters of titanium carbide, TiC.

Structure of bulk Titanium Carbide (TiC)

The insertion of interstitial impurities in a host lattice causes local deformations of the lattice. The
purpose of this case study is the comparison of such deformations caused by boron and fluorine
impurities in a silver lattice.

Deformation of Silver Lattice by Interstitial Boron and Fluorine Impurities

Ferromagnetism has its quantum mechanic origin in the difference of spin-up and spin-down
electron densities. It is driven by a balance between a gain in exchange energy due to larger spin-
polarization and a loss in Coulomb repulsion and kinetic energy of the electron system.

The purpose of this study is the computation of the cleavage energy of a material, i.e. the energy
required to split a material into two parts. This could be a bulk material, a grain boundary, or an
interface. To this end, one needs to compute the total energy of the bulk solid and the material
with a free surface.

Cleavage Energy of TiN

In Chromium and Chromium alloys antiferromagnetic ordering and spin-density-waves (SDW) states are at the origin of many physical properties like thermal expansion, elastic constants, and electrical resistivity among others.
This document summarizes structural and elastic properties of Chromium, computed from
first principles.

Chromium: Structure and Elastic Properties