Application Notes

The structure of the Fe₂O₃ (0001) surface as a function of oxygen partial pressure and temperature is computed using first-principles thermodynamics. The results reveal an active four-fold coordinated surface Fe atom which releases oxygen atoms at approximately 850 K at ambient oxygen partial pressure. This property is likely to be related to the catalytic activity of hematite for selective oxidation reactions such as the oxidation from ethylbenzene to styrene.

First-principles calculations reveal the atomistic structures of the active phases of CoMoS and NiMoS hydrodesulfurization catalysts. The reliable determination of the catalyst surface is critical, as it represents the starting point for subsequent adsorption and reaction path simulations. The predicted dominant structures are consistent with experimental STM, EXAFS and magnetic susceptibility measurements.

First-principles calculations reveal a three-fold increase in the Young’s modulus of graphite as it is lithiated (C→LiC₆). A linear expression is determined that describes the approximate stiffness of Li intercalated graphite as a function of loading which may lead to greatly improved continuum models of electrode deformation and failure.

First-principles calculations reveal the dominant acid sites on the amorphous silica-alumina (ASA) catalyst surface. Based on the strength of interaction with Lewis base probe molecules, the bridging and pseudo-bridging silanol (PBS) species are determined to be the most acidic and therefore catalytically active groups. Evident in the calculations is the interplay between the Lewis acid and the Brønsted acid sites on the ASA catalyst surface, giving rise to the enhanced acidity of the PBS species. This work provides mechanistic insight to inform efforts at rationally engineering enhanced ASA-based solid acids.

First-principles calculations using VASP reveal the lowest energy reaction pathway for the catalyzed skeletal isomerization of 2-pentene by the acidic zeolite H-ZSM. Three potential mechanisms were evaluated: an ethyl-shift pathway, a dimethylcyclopropane (DMCP) intermediate pathway and a pathway involving an edge-protonated DMCP species. The results indicate that the DMCP intermediate pathway is the kinetically preferred pathway with a classical barrier height of 98 kJ/mol. Evident in the calculations is the influence of the transient intermediate stability along the reaction path; with secondary carbenium ions leading to energetically favored mechanisms.

The compressibility, tensile strength, and mechanical resistance to shear of a solid are related to the corresponding moduli (bulk, Young’s, and shear modulus), which are derived from the coefficients of elasticity. First-principles calculations of these fundamental mechanical properties give values of the same quality as experimental data, but at a substantially smaller effort and cost. This is demonstrated here for cubic silicon carbide, β-SiC, corundum, α-Al₂O₃, and a tourmaline with a fairly complex crystal structure. First-principles calculations are a valuable source for these fundamental materials property data.

The crystal structure of a purely organic, hydrogen-bonded molecular crystal is very well described by density functional theory with a gradient-corrected Perdew-Becke-Ernzerhof potential. The computations were preformed with the VASP program using the projector augmented wave method with a plane wave basis set. The agreement between computed and experimental lattice parameters is better than 2% with a tendency of the calculations to overestimate the bond lengths. The calculations provide equilibrium positions for the hydrogen atoms, which are difficult to place based on x-ray diffraction data.

MEDEA GIBBS calculates equilibrium properties of fluids either pure or mixed, in a single phase or in multiple phases, using a force field based Gibbs ensemble technique.
The present application note focuses on the vapor pressure curve of methane, in other words we will deal with a one-component two-phase system.

In many metal-ceramic composites the interface between the metallic and ceramic phases determines the mechanical properties of the material. A prominent example is the WC-Co composite, where the combination of high WC hardness and Co ductility results in advantageous mechanical properties for applications in the tool manufacturing industry. The outstanding performance of WC-Co can be explained by the low interface energies (high stability) of the contacting surfaces of WC and Co.

The energy of adsorption and dissociation of molecules on surfaces plays a critical role in technological processes such as chemical vapor deposition, catalysis, and corrosion. The present case shows the calculation of the energy of the dissociative chemisorption of a silane molecule on a Si (001) surface.

This application shows the interaction of carbon monoxide with rutile.
An answer is given to the question whether CO binds with the carbon or the oxygen molecule to the surface.

The physics and chemistry of materials containing defects is of great interest in areas such as semiconductors, metal alloys and compounds, magnetic systems and optical materials.
Destabilizing or stabilizing crystalline bulk systems, surfaces and interfaces through additives is a common technique, for example recent research into complex hydrides aims to tune the kinetics of the adsorption/desorption changing the stoichiometry and composition of the base materials.

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.

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.

The molecular builder (Molecular Builder) is part of the MEDEA standard suite of building tools. This tutorial provides an overview of the Molecular Builder’s basic functionality.

In this application note, we show how to build the isomers ethyl alcohol and di-ethyl ether and calculate their respective heats of formation.

A key process in the semiconductor manufacturing is the reactive adsorption of molecules such as
silane (SiH₄) and dichlorosilane (SiCl₂H₂) on the surfaces of silicon wafers. This case study
demonstrates the calculation of the geometry of a silane molecule on a reconstructed Si(001)
surface.

First-principles computations correctly describe the ferroelectric distortions and the macroscopic polarization of BaTiO₃ in agreement with experiment. Computations of the vibrational properties (phonons) reveal that a cubic perovskite structure of BaTiO₃ becomes stable under compression of the lattice. This demonstrates the usefulness of first-principles calculations in the design and optimization of ferroelectric materials.

In addition to the lattice parameters, the rutile structure has an additional degree of freedom, namely the position of the oxygen atom. This case study shows the simultaneous calculation of all these structural degrees of freedom.

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

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/m^2.

The work function of the metal gate in a CMOS stack depends on the composition and structure of the interfaces. This is demonstrated here for the case of a Si-HfO₂-W stack by introducing a Hf vacancy at the Si/HfO₂ interface. At a concentration of 1.2 vacancies per nm² the work functions is increased by 500 meV.

First-principles calculations reveal that the magnetic moments of atoms on an Fe(001) surface are 30% larger than in the bulk. This enhancement decays within about three layers towards the bulk, which demonstrates the highly localized character of enhanced surface magnetism in transition metals such as iron.

Hydrides containing alkaline-earth metals are prototypes for hydrogen storage materials. For this purpose the heat of formation and the mechanical properties are of fundamental interest. First- principles electronic structure methods provide systematic values for these materials properties. The agreement with experimental data for the heat of formation is good. Presently, no experimental data for the elastic coefficients of these metal hydrides are available thus leaving the computed data as the sole source.

Increasingly stringent environmental regulations require a lowering of sulfur in Diesel fuels. This is accomplished by a catalytic process transforming sulfur-containing molecules into H₂S, which is removed from the liquid phase. Larger sulfur-organic molecules are more difficult to attack and new catalytic materials are needed. The present screening study demonstrates how the combination of experimental activity data, crystallographic information from structural databases and first- principles computation of binding energies are used to identify potential new candidates.

Elemental germanium is a semiconductor with a measured indirect band gap of 0.66 eV. Using a hybrid functional as implemented in VASP 5.2, the computed value is 0.66 eV while standard density functional approaches incorrectly predict Ge to have no band gap. Other features of the band structure such as the direct gap at Γ are also well reproduced by the current level of theory, namely 0.8 eV (measured) and 0.73 eV (computed), thus demonstrating the reliability of this level of approach in predicting energy band structures. This sets the stage for using computations to modify the band structure for example by uniaxial strain to meet specific design criteria.

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.

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.

Interfaces are present in most materials and have a large impact on mechanical properties such as stiffness and yield strength. Given that the properties of an interface can radically change by the presence of even minute amounts of impurities, it is of great interest to predict the effect of segregated atoms at interfaces.

As systematic experimental information on the impact of specific defect types on the grain boundary strength is hard to obtain, computational modelling is of great help.

The introduction of vacancies in a crystalline solid causes a local rearrangement of atoms around
the defect. The purpose of this case study is the prediction of such changes in α-quartz.

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.

The performance of catalytic materials depends on complex phenomena linked to chemical
composition, preparation, activation procedures, and surface conditions under operational
conditions. This complexity requires a comprehensive arsenal of R&D approaches including
theoretical and computational methods. While many fundamental research efforts are
currently directed at a detailed understanding of surface reaction mechanisms, PREDIBOND™
focuses on bond strength and local chemical environment as central descriptors of chemical
reactivity.

This application note deals with positioning molecules on surfaces. As an example we will investigate the adsorption of ethyl alcohol (ethanol) on a Cu (111) surface. In doing so we will consider two possible configurations for the adsorbed molecule:
1. adsorbed ethanol
2. dehydrogenated ethanol, i.e. an ethoxygen.
Running structure relaxations using VASP produces a first estimate of the relative stability of these two systems.

Calculation of elastic properties is straightforward with MedeA's Mechanical and Thermal Properties module.

This case study covers the practical use of MEDEA to calculate thermochemical functions for solids, molecules and atoms. We will use VASP and PHONON for this, but the current document focuses on the thermochemistry and not the details of the calculations.

Despite the enormous progress in experimental surface science, notably with spectroscopic
methods exploiting synchrotron radiation and scanning tunneling microscopy, computations
remain one of the most useful sources for accurate data on surface structures. In fact, quite often
it is the combination of experimental and computed results, which gives the most reliable data of
surface structures. As an example, let us apply MEDEA to the Si(001) surface. This surface is the
typical substrate in the manufacturing of semiconducting devices.

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.

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.

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.

The convergence of the total electronic energy as computed with VASP is determined by two key
computational parameters, namely the number of basis functions (plane wave cutoff) and the
number of k-points (k-spacing). In addition the integration of the states near the Fermi level is
influenced by a smearing parameter.