C15 Structure Research Articles

Thermodynamic properties of Laves phases in the Mg–Al–Ca system at finite temperature from first-principles

First-principles calculations are employed to investigate the structural and thermodynamic properties of binary Laves phases (C14, C15 and C36 structures) in the Mg–Al–Ca system. The enthalpies of formation at 0 K are predicted. The vibrational contributions to Helmholtz free energy for the stable C14-Mg 2Ca and C15-Al 2Ca phases are determined using both first-principles phonon calculations and Debye–Grüneisen model. The predicted thermodynamic properties of the stable phases, including enthalpy, entropy, bulk modulus, heat capacity, and thermal expansion coefficient, agree well with available experimental data. For the other nonstable phases, the thermodynamic properties are estimated by Debye–Grüneisen models of Moruzzi et al. and of Wang et al. The entropies predicted from these two Debye models have a general agreement with about ±0.5 J/mol K differences for all the three structures.

Study of the structural, elastic and electronic properties of ordered Ca(Mg1−xLix)2 alloys from first-principles calculations

Theoretical investigations were performed to study the structural, elastic and electronic properties of ordered ternary Ca(Mg1−xLix)2 (x=0, 0.25, 0.75, 1) Laves phases with C14 structure from density functional theory. The optimized lattice constants of the Ca(Mg1−xLix)2 phase agreed well with the experimental data, and stabilities were lowered with increase in Li content. Elastic properties, including elastic constants, elastic moduli and elastic anisotropies, were studied in detail. The obtained results indicated that the ductilities of ternary Ca(Mg1−xLix)2 (x=0.25, 0.75) phases were better, while the anisotropies were more significant in comparison with binary Ca(Mg1−xLix)2 (x=0, 1) phase. The electronic structures were further investigated to uncover the underlying mechanism for structural stability and elastic properties.

Unexpected influence of Mn addition on the creep properties of a cast Mg–2Al–2Ca (mass%) alloy

The addition of 0.3% Mn to a Mg–2Al–2Ca (mass%) alloy improves the minimum creep rate by one order of magnitude compared with the Mn-free alloy. Network-shaped Mg2Ca (C14 structure) and (Mg,Al)2Ca (C36 structure) compounds coexist in the interdendritic regions, while plate-shaped Al2Ca (C15 structure) phases are dispersed in the matrix. Ordered Guinier–Preston (GP) zones form dynamically on the basal plane of the α-Mg matrix during creep deformation. The number density of the fine GP zones in the Mn-containing alloy was found to be higher than that in the Mn-free alloy.

Pressure-induced changes in the structural and magnetic properties of YFe2D4.2

The study of the structural and magnetic properties of YFe${}_{2}$D${}_{4.2}$ under high pressure has been performed by combining energy dispersive x-ray diffraction at room temperature up to 5.5 GPa, neutron diffraction studies at low temperature up to 2.5 GPa, and magnetization measurements up to 1 GPa. The monoclinic structure of YFe${}_{2}$D${}_{4.2}$ at ambient temperature and pressure is related to a distortion of the initial cubic C15 structure of YFe${}_{2}$ by the ordering of inserted D atoms. A structural transition from monoclinic to cubic structure is observed at 4 GPa. The high pressure cubic YFe${}_{2}$D${}_{4.2}$ has a 19% higher cell volume than that of YFe${}_{2}$. The application of an external pressure leads to the progressive decrease of the transition temperature ${T}_{M}$${}_{0}$ from ferro to antiferromagnetic order (${T}_{M}$${}_{0}$ $=$ 84 K at ambient pressure) and even to the suppression of the ferromagnetic ground state for pressures larger than 0.54 GPa. Moreover using the compressibility value determined by x-ray diffraction (\ensuremath{\kappa} $=$ 0.013 GPa${}^{\ensuremath{-}1}$), the decrease of volume at the critical pressure of 0.54 GPa (0.70%) is in very good agreement with the increase of volume observed at the transition from antiferromagnetic to ferromagnetic state at ambient pressure (0.65%), indicating the crucial role of volume effect. An antiferromagnetic structure was detected between ${T}_{M}$${}_{0}$ and ${T}_{N}$ and for pressures larger than 0.54 GPa in the whole temperature range below ${T}_{N}$. In addition, a large pressure effect on the spontaneous magnetization ${M}_{S}$ for pressures below 0.4 GPa, $d$ ln ${M}_{S}$/d P $=$ \ensuremath{-}7.3 \ifmmode\times\else\texttimes\fi{} 10${}^{\ensuremath{-}2}$ GPa${}^{\ensuremath{-}1}$ was discovered. This clearly proves the delocalized character of the iron 3$d$ band magnetism in YFe${}_{2}$D${}_{4.2}$ compound. The pressure evolution of the magnetic phase diagram of YFe${}_{2}$D${}_{4.2}$ has been determined.

The U–Ti system: Strengths and weaknesses of the CALPHAD method

Input from Density Functional Theory (DFT) calculations is used to understand phase equilibria in a binary metallic alloy fuel system: U–Ti. The CALPHAD approach is employed to calculate a U–Ti phase diagram that is consistent not only with experimental data but also—more importantly—with thermodynamic data from DFT calculations: heat of formation of γ(bcc)-U–Ti alloys as a function of composition, and formation enthalpy of the δ-U 2Ti compound. Three DFT-based electronic structure methods are utilized: SR-KKR-ASA-CPA, SR-EMTO-CPA, and FPLMTO-SQS, and the use of derived ab initio data avoids the manifestation of unreasonable or inaccurate phase stabilities that result from an otherwise unconstrained Gibbs energy minimization within the CALPHAD approach. We also investigate phase formation of the δ-U 2Ti phase in the U–Ti system, that stabilizes in the same C32 structure as other binary metallic fuel alloys such as U–Zr and Np–Zr.

Microstructures and mechanical properties of Fe–Al–Ta alloys with strengthening Laves phase

The addition of Ta to Fe–Al alloys results in the formation of a stable Ta(Fe,Al)2 Laves phase with hexagonal C14 structure in the Fe–Al phase at temperatures of 800, 1000 and 1150 °C. It was found that the solubility of Ta in Fe–Al is generally low and the solubility of Ta varies with Al content. Respective isothermal sections of the Fe–Al–Ta system have been established. Particular attention has been given to precipitation in the Fe3Al phase with a small addition of Ta. At intermediate temperatures, 600–750 °C, an additional Heusler-type phase with L21-structure precipitates, which transforms at longer times and high temperatures to the stable C14 Laves phase. The yield stress in compression and the creep behaviour of the Fe–Al–Ta alloys with various microstructures were studied. Due to the presence of the L21-Heusler phase, the yield stress and the creep resistance at temperatures below 700 °C was increased considerably.

Effect of the Ca content on the microstructural evolution of Ca containing AZ31 cast alloys

Microstructural changes with varying amounts of Ca in cast AZ31-xCa (x: 0.7 wt.%, 2.0 wt.%, 5.0 wt.%) alloys were investigated. According to transmission electron microscopy (TEM) analyses, it was experimentally confirmed that the C36-(Mg,Al)2Ca phase with a di-hexagonal structure formed at interdendritic regions in as-cast AZ31 alloys with no more than 2 wt.% Ca. On the other hand, as the Ca content exceeded 2 wt.%, the lamellar structure consisting of the α-Mg phase and the Mg2Ca phase with a C14 structure formed at interdendritic regions instead of C36 phase. Plate-like Al2Ca precipitates with a C15 structure also formed on the basal plane inside the α-Mg grains.

Structural, elastic, and thermal properties of Laves phase ZrV2 under pressure

The structural, electronic, elastic and some thermodynamic properties of the cubic C15 structure ZrV2 compound under pressure are investigated by first-principles calculations. Our results for the equilibrium unit cell volume, bulk modulus and band structure are consistent with the calculated and experimental results. Cubic ZrV2 is mechanically stable according to the elastic stability criteria and shows ductile with the G/B and Cauchy pressure analysis. Moreover the pressure and temperature dependence of the bulk modulus, specific heat, Debye temperature and thermal expansion coefficient are discussed, among them our calculated Debye temperature is in good agreement with experiments.

Microstructural Evolution in Multiphase NiAl-2.5Ta-7.5Cr Alloy during Annealing at Different Temperatures

Abstract The microstructure evolution of NiAl-2.5Ta-7.5Cr alloy during annealing at different temperatures was investigated. It is found that the microstructure of the as-cast alloy consists of coarse Laves phase Ta(CrNiAl)2 with C14 structure at grain boundaries and Cr-rich particles with sizes in the range of 400-500 nm in the NiAl matrix. The Ta and Cr concentrations in the NiAl are ∼0.6% and ∼2.5% (at%), respectively. When the alloy is annealed at the temperature above 1000 °C, fine rod-like Laves phases with C15 structure begin to precipitate dispersively in the NiAl. After annealing at 1200 °C for 2 h, the volume fraction of the particles increases, and in the mean time, the Ta concentration in NiAl matrix reduces to ∼0.2at%. As the annealing temperature further increases to 1400 °C, the Laves phase precipitates dissolve in the NiAl matrix completely. Therefore, the precipitation of Laves phase in NiAl during the annealing in the temperature range of 1000∼1300 °C may be attributed to the diffusing followed by the supersaturation of Ta in NiAl after the solidification.

Crystal Structure Analysis of the Mg<sub>2</sub>Si<sub>1-x</sub>Sn<sub>x</sub> System Having Potential Thermoelectric Properties at High Temperature

Laves phases of C15 type of the system Mg2Si1-xSnx with x = 0, 0.4, 0.6 and 1 were synthesized in polycrystalline state in tantalum ampoule heated by high frequency coupling. The as-cast materials were analysed first at room temperature by X-ray diffraction (XRD). Systematically, XRD patterns were recorded up to 700 °C and Differential Scanning Calorimetry analysis was performed up to 1200°C to control the chemical and structural phase transformations. From these experiments, a C15 to C36 structure transformation was pointed out around 600°C in Mg2Si1-xSnx.solid solutions.

Ab initio study of phase transformations in transition-metal disilicides

We suggest and investigate three possible displacive structural transformation paths between the ideal C11 b, C40 and C54 structures in MoSi 2, VSi 2 and TiSi 2. They involve shifts of the (110) atomic planes in the C11 b structure, (0001) planes in the C40 structure and (001) planes in the C54 structure. These planes are shifted in the directions experimentally observed as slip directions during plastic deformation. An analysis of ab initio calculated total energies in MoSi 2, VSi 2 and TiSi 2 along these transformation paths is presented. Since the transition-metal and Si atoms come close together during proposed transformations, and, consequently, the energy barriers between individual structures are high, the estimated transition temperatures are comparable with the melting temperatures of the disilicides studied. This confirms their high thermal stability and indicates that if a phase transformation between C11 b, C40 and C54 structures of the disilicides takes place, then its prevailing mechanism should be diffusional rather than martensitic like. During the transformations studied, atoms come as close together as, for example, in configurations of interstitials. Hence, the present ab initio results can also be employed in fitting adjustable parameters of semi-empirical interatomic potentials for the transition-metal disilicides, in particular of the repulsion at short separations of atoms.

Transformation Paths in Transition-Metal Disilicides

We suggest and investigate three possible displacive transformation paths between the ideal C11b, C40 and C54 structures in MoSi2, VSi2 and TiSi2 by calculating ab initio total energies along these paths. An estimate of transition temperatures based on the calculated energy barriers leads to values comparable with the melting temperatures of the disilicides studied. This confirms their high temperature stability and indicates that if a phase transformation between C11b, C40 and C54 structures of the disilicides takes place, then its prevailing mechanism should be diffusional rather than martensitic like. During the transformations studied, atoms come as close together as, for example, in configurations with interstitials. Hence, the present ab initio results can also help in fitting adjustable parameters of semi-empirical interatomic potentials for the transition-metal disilicides, in particular of the repulsion at short separations of atoms.

Thermodynamic modeling of Laves phases in the Ta–V system: Reassessment using first-principles results

The Ta–V system is an interesting system exhibiting the existence of Laves phases among elements of the same group in the periodic system, and with an unusual order of stability of Laves phase structures at 0 K. Whereas the hexagonal C14 Laves phase is stable at 0 K and at high temperatures, the C15 structure is the most stable Laves phase at intermediate temperatures. The ab initio calculations of the total energies of formation for both C14 and C15 Laves phases employed two- and three-sublattice models to revise the thermodynamic description of the system published recently. The remodeled Gibbs energies of Laves phases require less fitting parameters than those obtained in previous treatments and the corresponding phase diagrams provide an excellent agreement with the experimental data on the phase stability and phase boundaries found in the literature. The new fitting procedure proposed involves a temperature dependent heat capacity for the C15 structure and allows us to compare the optimized heat capacity differences between the Laves phase and Standard Element Reference structure with those determined experimentally and theoretically.

Initial growth of SrTiO3 on Sr/Si(001) studied by scanning tunneling microscope

SrTiO3 ultra-thin film was deposited on the Sr/Si(001) surface using pulsed laser deposition (PLD) at room temperature and studied using scanning tunneling microscopy (STM). After annealing at 660 ℃ for about 60 minutes in ultrahigh vacuum (UHV), nanosize islands were formed on the Sr/Si(001) surface. High resolution STM images and dI/dV mapping of islands on Sr/Si(001) were obtained. The islands can be attributed to TiSi2 islands with C49 and C54 structures. The existence of Sr on Si is not sufficient to prevent the reaction between Si and Ti in preparation of ultra-thin SrTiO3 films.

Phase equilibria in the Al–Mo–Si system

The ternary Al–Mo–Si phase diagram was investigated by a combination of optical microscopy, powder X-ray diffraction (XRD), differential thermal analysis (DTA), electron probe microanalysis (EPMA) and scanning electron microscopy (SEM). Ternary phase equilibria were investigated within two isothermal sections at 600 °C for the Mo-poor part and 1400 °C for the Mo-rich part of the phase diagram. The solubility ranges of several phases including MoSi 2 (C11 b) as well as Mo(Si,Al) 2 with C40 and C54 structure were determined. The binary high temperature phase Al 4Mo was found to be stabilized at 600 °C by addition of Si. DTA was used to identify 9 invariant reactions and thus constructing a ternary reaction scheme (Scheil diagram) in the whole composition range. A liquidus surface projection was constructed on basis of the reaction scheme in combination with data for primary crystallization from as-cast samples determined by SEM measurements.

Thermodynamic study of the Np–Zr system

A thermodynamic model of the Np–Zr system is developed using the CALPHAD method, and a review of previous work performed on this system is presented here. In general, results obtained are in good agreement with those proposed from experimental observations. It is found that the nature of reactivity of Np with Zr, is different from that of U and Pu: an expected elevation of melting point of Np–Zr alloys was not seen and a miscibility gap existed between the high-temperature bcc phases of Np and Zr. Formation enthalpy of the bcc phase obtained from the model is compared with results from KKR–ASA–CPA calculations. Lattice stabilities of various phases in the system are compared to values obtained from first-principles LDA and GGA calculations. The δ-NpZr 2 phase is modeled as a non-stoichiometric phase with a C32 structure, similar to what has been determined for the δ-phase in the U–Zr system. This phase is analogous to ω-phase in pure Zr, which is stabilized at high pressures. Two different possibilities for stability of the δ and ω phases have been proposed in the present work. Finally, calculated changes in enthalpy versus temperature are plotted for two alloys to guide future experimental work in resolving important issues in this system.

Thermodynamic assessment of the Cr–Al–Nb system

Abstract A thermodynamic assessment of the Cr–Al–Nb system was performed using the CALPHAD technique on the basis of new experimental data on three isothermal sections at 1 150, 1300 and 1 450 °C as well as the available earlier literature data. The ternary phase diagram is dominated by an extended phase field of the Laves phase Nb(Cr, Al)2. Both the cubic C15 and the hexagonal C14 structure type of Laves phases occur as stable phase in the ternary system. A two-sublattice model was used for their thermodynamic description. The ternary solubilities of the (Nb) and (Cr) solid solutions and the binary phases NbAl3, Nb2Al and Nb3Al were taken into account in the ternary assessment. Several isothermal sections were calculated using the evaluated parameters. Good agreement between the calculations and the experimental data is achieved.

ChemInform Abstract: The Local Magnetic States in Spin-Ordered Amorphous and Crystalline Alloys

The review of experimental investigations of local magnetic states is given for three types of spin ordered materials: the cubic Laves phases with C15 structure, multicomponent heterophase alloys of Nd-R-Fe-M-B type and Heusler alloys. To obtain information on local magnetic states several kinds of experimental techniques were used: measurements of nuclear specific heat at T<1K. Mossbauer effect, nuclear spin-echo. The obtained results are treated in terms of several theoretical models and some essential parameters of itinerant and localized electron spectra are estimated and discussed.

The correlation of C14/C15 phase abundance and electrochemical properties in the AB 2 alloys

The C14/C15 phase abundance is an important parameter in the design of a suitable AB 2-based metal hydride electrode for use in nickel metal hydride batteries. In order to separate the contribution due to chemical composition from that of phase abundance, three multi-phase and multi-element AB 2 alloys with different C14/C15 phase abundances before and after annealing were studied by scanning electron microscope, transmission electron microscope, X-ray diffraction, pressure-concentration isotherm, half-cell, and full-cell measurements. After annealing at 800 °C for 14 h, the C14 phase abundances increased from 71 to 94% for the first alloy (Ti 12Zr 21.5V 10Ni 40.2Co 1.5Cr 8.5Mn 5.6Al 0.4Sn 0.3), remained unchanged at about 50% for the second alloy (Ti 12Zr 21.5V 10Ni 40.2Co 5.0Cr 5.5Mn 5.1Al 0.4Sn 0.3), and decreased from 32 to 7% for the third alloy (Ti 12Zr 21.5V 10Ni 40.2Co 8.0Cr 3.5Mn 4.1Al 0.4Sn 0.3). The effect of reduction in the amount of non-Laves Zr x Ni y secondary phases by annealing was established with the second alloy while the contribution of additional major phase (either C14 or C15) by annealing can be distilled by comparing various properties between samples before and after annealing. After the comparison, C15 structure was found to have a higher hydrogen storage capacity and higher reversibility in gas phase hydrogen storage, and better high-rate dischargeability, hydrogen bulk diffusion, specific power, and low temperature performance with a shortcoming of an inferior cycle life in electrochemistry. Results from gas phase hydrogen storage measurement also agree with those from electrochemical testing. Besides, the non-Laves Zr x Ni y secondary phases are found to play importance roles in the reversibility of hydrogen storage in the gas phase and battery performance in activation, rate capability, charge retention, and cycle life.

First principles prediction of the metastability of the Ge2Mn phase and its synthesis pathways

In this letter, we performed first principles calculations to investigate the stability of a [100]-compatible Ge2Mn compound. Based on a thermodynamical approach, we propose and assess the C16 structure (Al2Cu prototype) to be only slightly metastable as compared to the other Ge–Mn compounds. The reported structural and magnetic properties of this Ge2Mn compound make it a potentially interesting compound for spintronic applications, all the more since a simple way to stabilize it as a bulk film is proposed.