We demonstrate the importance of accounting for the complex magnetic ground state and finite temperature magnetic excitations in theoretical simulations of structural and elastic properties of transition metal alloys. Considering Fe_{72}Cr_{16}Ni_{12} face centered cubic (fcc) alloy, we compare results of first-principles calculations carried out for ferromagnetic and non-magnetic states, as well as for the state with disordered local moments. We show that the latter gives much more accurate description of the elastic properties for paramagnetic alloys. We carry out a determination of the magnetic ground state for fcc Fe-Mn alloys, considering collinear, as well as non-collinear states, and show the sensitively of structural and elastic properties in this system to the detailed alignment between magnetic moments. We therefore conclude that it is essential to develop accurate models of the magnetic state for the predictive description of properties of transition metal alloys.
We report on the results of a systematic ab initio study of the magnetic structure of Fe rich fcc FeNi binary alloys for Ni concentrations up to 50 at. %. Calculations are carried out within density-functional theory using two complementary techniques, one based on the exact muffin-tin orbital theory within the coherent potential approximation and another one based on the projector augmented-wave method. We observe that the evolution of the magnetic structure of the alloy with increasing Ni concentration is determined by a competition between a large number of magnetic states, collinear as well as noncollinear, all close in energy. We emphasize a series of transitions between these magnetic structures, in particular we have investigated a competition between disordered local moment configurations, spin spiral states, the double layer antiferromagnetic state, and the ferromagnetic phase, as well as the ferrimagnetic phase with a single spin flipped with respect to all others. We show that the latter should be particularly important for the understanding of the magnetic structure of the Invar alloys.
We review results of recent combined theoretical and experimental studies of Ti_{1−}_{x}Al_{x}N, an archetypical alloy system material for hard-coating applications. Theoretical simulations of lattice parameters, mixing enthalpies, and elastic properties are presented. Calculated phase diagrams at ambient pressure, as well as at pressure of 10 GPa, show a wide miscibility gap and broad region of compositions and temperatures where the spinodal decomposition takes place. The strong dependence of the elastic properties and sound wave anisotropy on the Al-content offers detailed understanding of the spinodal decomposition and age hardening in Ti_{1−}_{x}Al_{x}N alloy films and multilayers. TiAlN/TiN multilayers can further improve the hardness and thermal stability compared to TiAlN since they offer means to influence the kinetics of the favorable spinodal decomposition and suppress the detrimental transformation to w-AlN. Here, we show that a 100 degree improvement in terms of w-AlN suppression can be achieved, which is of importance when the coating is used as a protective coating on metal cutting inserts.
We study influence of the local chemical environment, the so-called local environment effects, on the electronic structure and properties of magnetic systems with reduced dimensionality and chemical disorder, and show that they play a crucial role in a vicinity of magnetic instability. As a model, we consider Fe–Ni Invar. We present results obtained from ab initio calculations of the electronic structure, magnetic moments, and exchange interactions in random fcc Fe–Ni alloy, for a single monolayer alloy film on a Cu (0 0 1) substrate as well as in the bulk. We analyze the difference between the film and the bulk magnetization, which is found to be most pronounced for dilute alloys. We also analyze a sensitivity of the individual magnetic moments and effective exchange parameters to the local chemical environment of the atoms.
This book is published in honor of the 2005 Hume-Rothery Award Recipient, Uichiro Mizutani. It emphasizes both theoretical and experimental aspects of electronic, structural, and thermodynamic properties of complex alloy phases. Leading experts provide an assessment of our current understanding of the structural properties of complex materials, including quasicrystalline and amorphous alloys. Special emphasis is placed on our understanding of why nature is able to stabilize complex atomic arrangements and on recent results related to structurally complex alloy phases. These topics, in the spirit of the work carried out by U. Mizutani, constitute the main theme of the book
The exact muffin-tin orbitals (EMTO) method belongs to the third and latest generation of first-principles methods of calculating the electronic structure of materials in the so-called approximation of muffin-tin (MT) orbitals within the framework of the density functional theory. A study has been performed of its applicability for modeling the thermodynamic and mechanical properties of the pure components of Ti and Zr based alloys. The total energies of Ti, Zr, Nb, V, Mo, and Al are calculated in three crystal structures - face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP). For all of these elements and crystal structures, we have calculated the theoretical values of the lattice constants, elastic constants, and equations of state. The stable crystal structures have been determined. In all cases, calculations by the EMTO method predict the correct structure of the ground state. For stable structures we compared the obtained results with experiment and with calculations using full potential methods. We have demonstrated the reliability of the EMTO method and conclude that its further application for effective modeling of the properties of disordered alloys based on Ti and Zr is possible.
We discuss theoretical description of pressure-induced phase transitions by means of first-principles calculations in the framework of density functional theory. We illustrate applications of theoretical tools that allow one to take into account configurational and vibrational disorders, considering Ti-V alloys as a model system. The universality of the first-principles theory allows us to apply it in studies of different phenomena that occur in the Ti-V system upon compression. Besides the transitions between different crystal structures, we discuss isostructural transitions in bcc Ti-V alloys. Moreover, we present arguments for possible electronic transitions in this system, which may explain peculiar behaviour of elastic properties of V upon compression.
We review recent developments in the field of first-principles simulations of magnetic materials above the magnetic order disorder transition temperature, focusing mainly on 3d-transition metals, their alloys and compounds. We review theoretical tools, which allow for a description of a system with local moments, which survive, but become disordered in the paramagnetic state, focusing on their advantages and limitations. We discuss applications of these theories for calculations of thermodynamic and mechanical properties of paramagnetic materials. The presented examples include, among others, simulations of phase stability of Fe, Fe-Cr and Fe-Mn alloys, formation energies of vacancies, substitutional and interstitial impurities, as well as their interactions in Fe, calculations of equations of state and elastic moduli for 3d-transition metal alloys and compounds, like CrN and steels. The examples underline the need for a proper treatment of magnetic disorder in these systems. (C) 2015 Elsevier Ltd. All rights reserved.
We have performed a theoretical study of the effect of doping the half-Heusler alloy NiMnSb with the magnetic 3d metals Cr, Mn, Fe, Co, and Ni, with respect to both energetics and magnetic properties. Starting from the formation energies, we discuss the possibility of placing the dopant on different crystallographic positions in the alloy. We calculate total and local magnetic moments, effective exchange interactions, and density of states and also outline strategies to tune the magnetic properties of the alloy. Doping of NiMnSb with Cr as well as substituting some Ni with extra Mn have the largest impact on magnetic interactions in the system while preserving its half-metallic property. Therefore, we suggest the possibility that these dopants increase the thermal stability of half-metallicity in NiMnSb, with implications for its possible usage in spintronics applications.
The stability of rock salt structure cubic Cr1-xAlxN solid solutions at high Al content and high temperature has made it one of the most important materials systems for protective coating applications. We show that the strong electron correlations in a material with dynamic magnetic disorder is the underlying reason for the observed stability against isostructural decomposition. This is done by using the first-principles disordered local moments molecular dynamics technique, which allows us to simultaneously consider electronic, magnetic, and vibrational degrees of freedom.
The phenomenon of superhardening in TiN/SiNx nanocomposites and the prediction of extreme hardness in bulk gamma-Si3N4 have attracted a large interest to this material system. Attempts to explain the experimental findings by means of first-principles calculations have so far been limited to static calculations. The dynamical stability of suggested structures of the SiNx tissue phase critical for the understanding of the nanocomposites is thus unknown. Here, we present a theoretical study of the phonon-dispersion relations of B1 and B3 SiN. We show that both phases previously considered as metastable are dynamically unstable. Instead, two pseudo-B3 Si3N4 phases derived from a L1(2)- or D0(22)-type distribution of Si vacancies are dynamically stable and might explain recent experimental findings of epitaxial SiNx in TiN/SiNx multilayers.
We have used first-principles calculations to investigate the mixing enthalpies, lattice parameters and electronic density of states of the ternary nitride systems Ti1-xAlxN, Cr1-xAlxN, Sc1-xAlxN and Hf1-xAlxN in the cubic B1 structure where the transition metals and aluminium form a solid solution on the metal sublattice. We discuss the electronic origins of the possible isostructural decomposition in these materials relevant for hard coatings applications. We find that in the systems Ti1-xAlxN and Hf1-xAlxN the electronic structure effects strongly influences the phase stability as d-states are localised at the Fermi level in AlN-rich samples. This leads to a strongly asymmetric contribution to the mixing enthalpy, an effect not present in Cr1-xAlxN and Sc1-xAlxN. The lattice mismatch is large in Sc1-xAlxN and Hf1-xAlxN, giving a symmetric contribution to the mixing enthalpies in those systems.
The^{ }effect of nitrogen substoichiometry on the isostructural phase stabilities of^{ }the cubic Ti_{1−x}Al_{x}N_{1−y} system has been investigated using first-principles calculations.^{ }The preferred isostructural decomposition pattern in these metastable solid solutions^{ }was predicted from the total energy calculations on a dense^{ }concentration grid. Close to the stoichiometric Ti_{1−x}Al_{x}N_{1} limit, N vacancies^{ }increase the tendency for phase separation as N sticks to^{ }Al while the vacancies prefers Ti neighbors. For nitrogen depleated^{ }conditions, N sticks to Ti forming TiN_{} (0<<1) while Al^{ }tends to form nitrogen-free fcc-Al or Al–Ti alloys.
We study the impact of lattice vibrations on magnetic and electronic properties of paramagnetic bcc and fcc iron at finite temperature, employing the disordered local moments molecular dynamics (DLM-MD) method. Vibrations strongly affect the distribution of local magnetic moments at finite temperature, which in turn correlates with the local atomic volumes. Without the explicit consideration of atomic vibrations, the mean local magnetic moment and mean field derived magnetic entropy of paramagnetic bcc Fe are larger compared to paramagnetic fcc Fe, which would indicate that the magnetic contribution stabilizes the bcc phase at high temperatures. In the present study we show that this assumption is not valid when the coupling between vibrations and magnetism is taken into account. At the gamma-delta transition temperature (1662 K), the lattice distortions cause very similar magnetic moments of both bcc and fcc structures and hence magnetic entropy contributions. This finding can be traced back to the electronic densities of states, which also become increasingly similar between bcc and fcc Fe with increasing temperature. Given the sensitive interplay of the different physical excitation mechanisms, our results illustrate the need for an explicit consideration of vibrational disorder and its impact on electronic and magnetic properties to understand paramagnetic Fe. Furthermore, they suggest that at the gamma-delta transition temperature electronic and magnetic contributions to the Gibbs free energy are extremely similar in bcc and fcc Fe.
Two different methods for the modeling of a magnetically disordered CrN stateusing a supercell approach are investigated. They are found to give equivalentresults of the total energy, being also similar to results obtained with an effectivemedium approach. Furthermore, CrN is shown to be better described using aLDA+U framework for the treatment of electron-electron correlations as comparedto GGA or LDA calculations. Modeling the cubic paramagnetic phase with ourmodels for magnetic disorder and considering the strong electron correlations, thetemperature and pressure induced phase transitions in CrN can be explained.
In this comment we show that the main conclusion in a previous article, claiminga drastic increase in compressibility of CrN at the cubic to orthorhombic phasetransition, is unsupported by first-principles calculations. We show that if thecubic CrN phase is considered as a disordered magnetic material, as supported bydifferent experimental data, rather then non-magnetic, the bulk modulus is almostunaffected by the transition.
In^{ }order to investigate the stability of the cubic phase of^{ }Cr_{1−x}Al_{x}N at high AlN content, first principles calculations of magnetic^{ }properties, lattice parameters, electronic structure, and mixing enthalpies of the^{ }system were performed. The mixing enthalpy was calculated on a^{ }fine concentration mesh to make possible the accurate determination of^{ }its second concentration derivative. The results are compared to calculations^{ }performed for the related compound Ti_{1−x}Al_{x}N and with experiments. The^{ }mixing enthalpy is discussed in the context of isostructural spinodal^{ }decomposition. It is shown that the magnetism is the key^{ }to understand the difference between the Cr- and Ti-containing systems.^{ }Cr_{1−x}Al_{x}N turns out to be more stable against spinodal decomposition^{ }than Ti_{1−x}Al_{x}N, especially for AlN-rich samples which are of interest^{ }in cutting tools applications.
The influence of pressure on the phase stabilities of Ti_{1−x}Al_{x}N solid solutions has been studied using first principles calculations. We find that the application of hydrostatic pressure enhances the tendency for isostructural decomposition, including spinodal decomposition. The effect originates in the gradual pressure stabilization of cubic AlN with respect to the wurtzite structure and an increased isostructural cubic mixing enthalpy with increased pressure. The influence is sufficiently strong in the composition-temperature interval corresponding to a shoulder of the spinodal line that it could impact the stability of the material at pressures achievable in the tool-work piece contact during cutting operations
We demonstrate the importance of thermal effects such as temperature-induced electronic, magnetic and vibrational excitations, as well as structural defects in the first-principles calculations of the magnetic critical temperature of complex alloys using half-Heusler Ni1-xCuxMnSb alloys as a case study. The thermal lattice expansion and one-electron excitations have been accounted for self-consistently in the Curie temperature calculations. In the Ni-rich region, electronic excitations, thermal expansion, and structural defects substantially decrease the calculated Curie temperature. At the same time, some defects are shown to increase T-C in Cu-rich samples.
We use a study of the cubic Ti1−xAlxN system to illustrate a practical way of combining the major methodologies within alloy theory, the Connolly-Williams cluster expansion and the generalized perturbation method, in order to solve difficult alloy problems. The configurational, concentration dependent, Hamiltonian is separated into a fixed-lattice and a local lattice relaxation part. The effective cluster interactions of the first part is obtained primarily with a GPM-based approach while the later is obtained using cluster expansion. In our case the impact on the isostructural phase diagram of considering short range clustering beyond the mean field approximation, obtained from the mixing enthalpy and entropy of the random alloy, is rather small, especially in the composition region x ≤ 0.66, within reach of thin film growth techniques.
Wedescribe an efficient first-principles method that can be used tocalculate mixing enthalpies of transition metal nitrides with B1 structureand substitutional disorder at the metal sublattice. The technique isbased on the density functional theory. The independent sublattice modelis suggested for the treatment of disorder-induced local lattice relaxationeffects. It supplements the description of the substitutional disorder withinthe coherent potential approximation. We demonstrate the excellent accuracy ofthe method by comparison with calculations performed by means ofthe projector augumented wave method on supercells constructed as specialquasirandom structures. At the same time, the efficiency of thetechnique allows for total energy calculations on a very finemesh of concentrations which enables a reliable calculation of thesecond concentration derivative of the alloy total energy. This isa first step towards first-principles predictions of concentrations and temperatureintervals where the alloy decomposition proceeds via the spinodal mechanism.We thus calculate electronic structure, lattice parameter, and mixing enthalpiesof the quasibinary alloy c-Ti_{1−x}Al_{x}N. The lattice parameter follows Vegard'slaw at low fractions of AlN but deviates increasingly withincreasing Al content. We show that the asymmetry of themixing enthalpy and its second concentration derivative is associated withsubstantial variations of the electronic structure with alloy composition. Thephase diagram is constructed within the mean-field approximation.
The first material to be predicted from first-principles calculations as half-metallic was NiMnSb, and the research on this material has been intense due to its possible applications in spintronics devices. The failure of many experiments to measure spin polarization to more than a fraction of the predicted 100% has partly been blamed on structural defects. In this work a complete first-principles treatise of point defects, including nonstoichiometric antisites, interstitial and vacancy defects, as well as stoichiometric atomic swap defects in NiMnSb, is presented. We find that the formation energies of the defects span a large scale from 0.2 to 14.4 eV. The defects with low formation energies preserve the half-metallic character of the material. We also find that some of the defects increase the magnetic moment and thus can explain the experimentally observed increase of magnetic moments in some samples of NiMnSb. Most interesting in this respect are Mn interstitials which increase the magnetic moment, have a low formation energy, and keep the half-metallic character of the material.
By means of ab initio molecular dynamics (AIMD) simulations we carry out a detailed stdly of the electronic and atomic structure of Mo upon the thermal stabilization of its dynamically unstable face-centered cubic (fcc) phase, Wc calculate how the atomic positions, radial distribution function, and the ei<xtronic density of states of fcc Mo evolve with temperature. The results are compared with those for dynamically stable body-centered cubic (bcc) phase of Mo, as well as with bcc Zr, which is dynamically unstable at T = OK, but (in contrast to fcc Mo) becomes thermodynamically stable at high temperature, In particular, wc emphasize the difference between the local positions of atoms in the simulation boxes at a particular step of AIMD simulation and the average positions, around which the atoms vibrate, and show that the former are solcly responsible for the electronic properties of the material. WE observe that while the average atomic positions in fcc Mo correspond perfectly to the ideal structure at high temperature, the electronic structure of the metal calculated from AIMD differs substantially from the canonical shape of the density of states for the ideal fcc crystaL From a comparison of our results obtained for fcc Mo arid bcc Zr, we advocate the use of the electronic structure calculations, complemented with studies of radial distribution functions, as a sensitive test of a degree of the temperature induced stabilization of phases, which are dynamically unstable at T = OK.
We have ca1culated the equation of state and elastic properties of face-centered cubic Fe and Fe-rich FeMg alloy at ultrahigh pressures from first principles using the Exact Muffin-Tin Orbitals method. The results show that adding Mg into Fe influences strongly the equation of state, and cause a large degree of softening of the elastic constants, even at concentrations as small as 1-2 at. %. Moreover, the e1astic anisotropy increases, and the effect is higher at higher pressures.
The single-crystal and polycrystalline elastic constants and the elastic anisotropy in face-centered cubic and hexagonal close-packed FeNi alloys have been investigated at ultrahigh pressures by means of first-principles calculations using the exact muffin-tin orbitals method and the coherent-potential approximation. Comparisons with earlier calculations for pure Fe and experimental results are presented and discussed. We show that Ni alloying into Fe increases slightly the density and has very little effect on bulk moduli. Moreover, the relative decrease in c(44) elastic constant is much stronger in the hcp phase than in the fcc one. It is found that the elastic anisotropy is higher for face-centered cubic than for the hexagonal close-packed structure of FeNi, even though the face-centered cubic phase has a higher degree of symmetry. The anisotropy in face-centered cubic structure decreases with increasing nickel concentration while a very weak increase is observed for the hexagonal close-packed structure.
The energy differences between the ground state body-centered structure and closed-packed face-centered structure for transition metals in the middle of the series show unusually large disagreements when they are obtained by the thermochemical approach based on the analysis of experimental data or by first-principles electronic structure calculations. Considering a typical example, the lattice stability of Mo, we present a solution to this long-standing problem. We carry out ab initio molecular dynamics simulations for the two phases at high temperature and show that the configurational energy difference approaches the value derived by means of the thermochemical approach. The main contribution to the effect comes from the modification of the canonical band structure due to anharmonic thermal motion at high temperature.
Understanding of mechanical properties of materials and a possibility to predicting them from ab initio calculations have fundamental importance for solid state theory. In this work we establish a significant correlation between the product of the macroscopic parameters of localized plastic flow auto-waves in deforming alloys, their length and propagation rate and the product of the microscopic (lattice) parameters of these materials, the spacing between close-packed planes of the lattice and the rate of transverse elastic waves. Thus, these products can be regard as invariants of plastic and elastic deformation processes, respectively. Moreover, the established regularity suggests that the elastic and the plastic processes simultaneously involved in the deformation are closely related. Our work also demonstrates that ab initio simulations can be used for the prediction of parameters of localized plastic flow auto-waves in deforming alloys.
Computer simulations in the framework of the Density Functional Theory have become an established tool for computer simulations of materials properties. In most cases, however, information is obtained at ambient conditions, preventing design of materials for applications at extreme conditions. In this work we employ ab initio calculations to investigate the influence of stresses on structure and stability of Ti-Mo and Zr-Nb alloys, an important class of construction materials. Calculations reproduce known phase stability trends in these systems, and we resolve the controversy regarding the stability of body-centered cubic solid solution in Mo-rich Ti-Mo alloys against the isostructural decomposition. Calculated results are explained in terms of the electronic structure effects, as well as in terms of physically transparent thermodynamic arguments that relate phase stability to deviations of concentration dependence of atomic volume from the linear behavior.
The interaction potentials of the palladium and hydrogen sublattices at different hydrogen concentrations have been obtained in terms of the density functional theory and ab initio pseudopotentials. It has been shown that the anharmonicity of this interaction depends on the hydrogen concentration. The phonon spectrum of palladium hydride PdH has been calculated in the harmonic approximation and taking into account the anharmonic effects. The temperature-dependent effective potential technique accounting for the anharmonic effects of lattice vibrations has been described.
Ab initio total energy calculations based on the exact muffin-tin orbitals method, combined with the coherent potential approximation, have been used to study the thermodynamical and elastic properties of substitutional refractory Ru1-xNixAl alloys. We have found that the elastic constants C- and C-11 exhibit pronounced peculiarities near the concentration of about 40 at. % Ni, which we ascribe to electronic topological transitions. Our suggestion is supported by the Fermi surface calculations in the whole concentration range. Results of our calculations show that one can design Ru-Ni-Al alloys substituting Ru by Ni (up to 40 at. %) with almost invariable elastic constants and reduced density.
A nitrogen-rich compound, ReN(8)xN(2), was synthesized by a direct reaction between rhenium and nitrogen at high pressure and high temperature in a laser-heated diamond anvil cell. Single-crystal X-ray diffraction revealed that the crystal structure, which is based on the ReN8 framework, has rectangular-shaped channels that accommodate nitrogen molecules. Thus, despite a very high synthesis pressure, exceeding 100GPa, ReN(8)xN(2) is an inclusion compound. The amount of trapped nitrogen (x) depends on the synthesis conditions. The polydiazenediyl chains [-N=N-] that constitute the framework have not been previously observed in any compound. Abinitio calculations on ReN(8)xN(2) provide strong support for the experimental results and conclusions.
The phase stability of Ti_{2}AlC upon oxygen incorporation has been studied by means of first-principles calculations. Recent experimental observations of this so-called MAX phase (M = early transition metal, A = A-group element, and X = C or N) show that the characteristic nanolaminated structure is retained upon oxygen incorporation, with strong indications of O substituting for C. Therefore, a solid solution of C and O on the carbon sublattice has been simulated by the so-called special quasirandom structure method. Through a developed systematic approach, the enthalpy of formation of Ti_{2}Al(C_{1−}_{x},O_{x}) has been compared to all experimentally known competing phases, and has been found favorable for all C to O ratios at the composition of the MAX phase. A negative isostructural formation enthalpy has also been predicted for Ti_{2}Al(C_{1−}_{x},O_{x}). Altogether, the results indicate that a large amount of oxygen, at least up to x=0.75, might be present in the Ti_{2}AlC MAX-phase structure without decomposition of the material into its competing phases. Furthermore, an effect of an increased oxygen content is a corresponding increase in the bulk modulus and a change in electronic properties. These results are of importance for further understanding and identification of possible composition range of the MAX-phase oxycarbide, and hence for the prospect of tuning the material properties by a varying incorporation of oxygen.
The M(n+1)AX(n) (MAX) phases are nanolaminated compounds with a unique combination of metallic and ceramic properties, not yet including magnetism. We carry out a systematic theoretical study of potential magnetic MAX phases and predict the existence of stable magnetic (Cr(1-x)Mn(x))(2)AlC alloys. We show that in this system ferromagnetically ordered Mn layers are exchange coupled via nearly nonmagnetic Cr layers, forming an inherent structure of atomic-thin magnetic multilayers, and that the degree of disorder between Cr and Mn in the alloy can be used to tune the sign and magnitude of the coupling.
Inherently layered magnetic materials, such as magnetic M(n+1)AX(n) (MAX) phases, offer an intriguing perspective for use in spintronics applications and as ideal model systems for fundamental studies of complex magnetic phenomena. The MAX phase composition M(n+1)AX(n) consists of M(n+1)AX(n) blocks separated by atomically thin A-layers where M is a transition metal, A an A-group element, X refers to carbon and/or nitrogen, and n is typically 1, 2, or 3. Here, we show that the recently discovered magnetic Mn2GaC MAX phase displays structural changes linked to the magnetic anisotropy, and a rich magnetic phase diagram which can be manipulated through temperature and magnetic field. Using first-principles calculations and Monte Carlo simulations, an essentially one-dimensional (1D) interlayer plethora of two-dimensioanl (2D) Mn-C-Mn trilayers with robust intralayer ferromagnetic spin coupling was revealed. The complex transitions between them were observed to induce magnetically driven anisotropic structural changes. The magnetic behavior as well as structural changes dependent on the temperature and applied magnetic field are explained by the large number of low energy, i.e., close to degenerate, collinear and noncollinear spin configurations that become accessible to the system with a change in volume. These results indicate that the magnetic state can be directly controlled by an applied pressure or through the introduction of stress and show promise for the use of Mn2GaC MAX phases in future magnetoelectric and magnetocaloric applications.
The lattice parameters of InxAl1-xN in the whole compositional range are studied using first-principle calculations. Deviations from Vegards rule are obtained via the bowing parameters, delta(a)=0.0412 +/- 0.0039 A and delta(c)=-0.060 +/- 0.010 A, which largely differ from previously reported values. Implications of the observed deviations from Vegards rule on the In content extracted from x-ray diffraction are discussed. We also combine these results with x-ray diffraction and Raman scattering studies on InxAl1-xN nanocolumns with 0.627 <= x <= 1 and determine the E-2 phonon frequencies versus In composition in the scarcely studied In-rich compositional range.