Miedema's Semi-empirical Model Research Articles

Phase transformation of AB5 to AB2 type phase on substitution of Mn with Zr in TiVCoNi (ZrxMn2-x) (x = 0, 0.3, 0.6, 1.0) high entropy alloys

In this present investigation, we discussed the synthesis, microstructure, and phase transformation from BCC (AB5) to C14 Laves (AB2) phase in TiVCoNi (ZrxMn2-x) (x = 0, 0.3, 0.6, 1.0) high entropy alloys on substituting Mn with Zr. These high entropy alloys were synthesized using a 35 kW radio frequency induction furnace under an argon atmosphere. At x = 0 (i.e. in quinary HEA), the single BCC phase was observed, whereas at x = 1 (i.e. in hexanery HEA), the single C14 Laves phase was found to be stable. The calculations of the thermodynamic parameters were done with the help of Miedema's semi-empirical model and other models available in the literature. TiVCoNi (ZrxMn2-x) high entropy alloys exhibited mixing enthalpy at x = 0, 0.3, 0.6, 1 as −15.6 kJ/mol, −18.1 kJ/mol, −22.8 kJ/mol, −25.3 kJ/mol respectively. The corresponding atomic size mismatch was found to be 10.03%, 11.85%, 10.18%, and 9.86%. It is established that on replacing Mn with Zr, the mixture of the BCC and Laves phase was observed, which was converted into a single C14 intermetallic Laves phase at equiatomic composition, i.e., x = 1. Further, the study of surface morphology and elemental composition of these as-cast high entropy alloys gives us the idea that hardness increases on substitution of Mn in BCC (at x=0) phased-based; TiVCoNi (ZrxMn2-x) (x = 0, 0.3, 0.6, 1.0) high entropy alloys due to the evolution of harder C14 Laves phase.

Monte Carlo simulations of surface segregation to discover new hydrogen separation membranes

Surface compositions play a predominant role in the efficiency and lifetime of membranes and catalysts. The surface composition can change during operation due to segregation, thus controlling and predicting the surface composition is essential. Computational modelling can aid in predicting alloy stability, along with designing surface alloys and near-surface alloys that can outperform existing materials. In this work, a computational model to predict surface segregation in ternary alloys is developed. The model, based on Miedema's semi-empirical model and Monte Carlo simulations, enables to predict long- and short-range ordering in the surface and subsurface layers. It is used to screen a vast range of alloy compositions to design a novel ternary Pd-based material for H2 separation membranes. The addition of specific amounts of Cu and Zr to Pd is expected to reduce poisoning and enhance the permeability as compared to pure Pd.

Geometrical Thermodynamic Investigation on Fe-Co-Ni(Mn-Si) <sub>x</sub> High Entropy Alloys And Correlation with Their Structural and Magnetic Properties

In the present study, different symmetrical and asymmetrical geometrical thermodynamic models such as Muggianu, Luck chou, Kohler, Colinet, Hillert, Toop, General solution model (GSM) were modelled by using the Redlich-Kister formalism for all the possible binary alloy system and then applied to FeCoNi(Mn-Si)x (x=0.0,0.1,0.25,0.5,0.75,1.0) HEAs at 1273 K (FCC phase). The results revealed that asymmetrical GSM model with a similarity coefficient ξ(ij)(k) of ~0.5 shows maximum negative excess Gibbs free energy (G1-2-E3-4-5) and associated activity coefficients (Υa) decreases with the elevation of excess energy as well as Mn-Si content. The Miedema semi-empirical model was also evaluated in order to confirm the G1-2-E3-4-5 and associated Υα greatly influenced by a high negative value of enthalpy of mixing (ΔΗmix) and melting temperature (Tm). These negative value of ΔΗmix and G1-2-3E-4-5 plays a significant role during the formation of the solid solution produced by non-equilibrium process i.e. mechanical alloying (MA). Therefore, an experimental approach has been carried out in the proposed alloy system on the basis of phase evolution, physical parameters such as lattice parameter (LP), crystallite size (Dcrystal), microstrain (es) and dislocation density (ρdis), microstructure and magnetic properties were performed at 300 K.

Study of NiAl3-Ni2Al3 nanostructure intermediate: Kinetic parameters and thermodynamic modeling

In this study, a mixture of nickel and aluminum powder in a planetary ball mill was mixed to determine the mechanism of production of the mechanical milling process for different times. Gibbs free energy has been calculated for the formation of solid solution, intermetallic and amorphous phase using the Miedema's semi-empirical model and the effect of defects produced during milling such as grain boundaries and Dislocations were considered in the thermodynamics. The results showed that the intermetallic phase has been the most stable phase after mechanical processing. Kinetic parameter was determined for the formation of intermediate phase during the mechanical alloying. Activation energy was calculated using free-model and model-fitting methods such as Friedman, Flynn-Wall-Ozawa and Coats-Redfern. The milled powders have been heat treated at various temperature and In order to evaluate the phases and compare the theoretical and experimental results, analyzes SEM and XRD have been done. Lattice strain and crystallite size have been calculated using XRD patterns and Williamson-Hall equation.

Thermochemistry of some Zinc-Transition metal(TM) compounds and some Bismuth-TM compounds by high temperature direct synthesis calorimetry

Intermetallic compounds such as Heusler and half-Heusler alloys have a number of interesting properties and are being developed for numerous applications. Such alloy development requires thermodynamic data and our work is aimed at providing such data to the scientific community.The standard enthalpies of formation of some zinc, bismuth and transition metal(TM) compounds have been measured by high temperature direct synthesis calorimetry at 1273 ± 2 K. The following values for the TM-Zn compounds are reported in kJ/mole of atoms:ScZn (-41.4 ± 3.0); PdZn (-37.0 ± 3.0); Hf2Zn (-9.8 ± 2.3); PtZn (-24.8 ± 2.5).Bismuth yields approximately 15–20 binary transition metal compounds and 12–20 binary compounds with lanthanide elements. Some of these compounds have semiconductor properties and as such could be potentially useful for industrial endeavors, which is particularly noted for PdBi, RhBi, HfBi and ZrBi.The standard enthalpies of formation of some Bi-TM compounds have been measured by high temperature direct synthesis calorimetry at 1273 ± 2 K. The following values are reported in kJ/mole of atoms; Ti2Bi (-15.2 ± 3.2); Y5Bi3 (-81.7 ± 2.5); ZrBi (-47.3 ± 3.1); BiRh (-17.2 ± 2.8);PdBi (-30.2 ± 3.1); BiPt (-17.8 ± 2.9). All the measurements refer to 298 K.The results for both the TM-Zn and the TM-Bi compounds are compared with available thermodynamic data from the published literature and with predicted values from both Miedema's semi-empirical model and from ab initio calculations.

Characterization, thermodynamic analysis and magnetic investigation of new soft magnetic amorphous/nanocrystalline Co50Fe21Ti19Ta5B5 powders produced by mechanical alloying

In this work, the microstructure, thermal stability and magnetic properties of a new Co50Fe21Ti19Ta5B5 alloy prepared by mechanical alloying (MA) were investigated. Quantitative X-ray diffraction (XRD) analysis performed via Rietveld refinement demonstrated a high glass-forming ability (GFA) of this alloy through a fast amorphization with a glass fraction of about 98 wt% after 20 h milling. In addition, a large driving force for amorphization in Co50Fe21Ti19Ta5B5 alloy was indicated via a great difference between the Gibbs free energy changes for amorphization (−68 kJ/mol) and solid-solution formation (−6 kJ/mol), calculated based on the extended Miedema's semi-empirical model. Thermal analysis confirmed a higher crystallization temperature of new alloy compared to some of mechanically alloyed Co-based glassy powders, recently produced. The presence of few remained nanocrystals with an average size of 5 nm and little un-dissolved boron nanoparticles inside the amorphous matrix were confirmed by high-resolution transmission electron microscopy (HRTEM) measurements. The magnetic measurements revealed that the powders after an optimized milling time and annealing condition show a promising magnetic softness. The new powders exhibited a larger saturation magnetization (78 Am2/kg) and significantly a lower coercivity (0.2 kA/m) with respect to the most of the Co-based amorphous powders prepared by MA.

Mechanism of amorphous state formation, crystalline structure, and hyperfine interactions in DyMn6−xGe6Fex (≤x≤6) alloys

Metallic glass formation is observed in rapidly quenched quaternary DyMn6−xGe6Fex (0≤x≤6) alloys. The easy formation of amorphous states competes with the nucleation of ternary 1:6:6 rare earth-transition metal-metal compounds DyMn6Ge6 and DyFe6Ge6. The ribbon shaped samples were quenched and investigated by x-ray diffraction, differential scanning calorimetry, and F57e Mössbauer spectrometry. Melt-spun alloys from the series of DyMn6−xGe6Fex with x=0, 2≤x≤3, and x=6 do not display an amorphous state but a crystalline chemically disordered structure similar to that of TbCu7- or TbFe6Sn6-type (space group P6/mmm). Amorphous samples exhibit two crystallization steps but there is no clear evidence for a glass transition effect in the calorimetric data. The Kissinger analysis was performed to calculate the effective activation energy Ea, which is equal to 345±20 kJ/mol for amorphous DyMn5.5Ge6Fe0.5 alloy. Mössbauer spectra at 77 and 300 K consist of either magnetic sextets or quadrupolar doublets for high and low Fe content, respectively. The features reflect the dilution of Fe on crystallographic sites and the subsequent increase in topological and chemical disorder when the Mn content increases. The Miedema's semiempirical model was used to calculate the formation enthalpies of amorphous alloys (ΔHform). The calculated values are consistent with experimental results. The present model allows thus to explain the better glass forming ability for the compositions with high Mn content, where ΔHform is the most negative.

Glass forming ability of the binary Cu–Hf system studied by thermodynamic calculation and ion beam mixing

Based on Miedema's semi-empirical model, a Gibbs free energy diagram is constructed for the Cu–Hf system and shows that the amorphous phase is favored to be formed over 8–94 at.% Hf, which is much broader than the experimentally determined 30–70 at.% Hf. Three Cu–Hf multilayered films were therefore designed with the overall compositions of Cu 93Hf 7, Cu 81Hf 19 and Cu 23Hf 77, respectively, and then an ion beam mixing experiment was conducted using 200 keV xenon ions to see whether the metallic glass forming range of the Cu–Hf system could be extended beyond the previously reported range. Interestingly, ion beam mixing results show that a uniform amorphous phase can be obtained in the Cu 23Hf 77 sample and the amorphous phase is also observed to coexist with crystalline Cu in the Cu 81Hf 19 sample. These results suggest that the metallic glass forming range of the Cu–Hf system could, at least, be extended to 77 at.% Hf, which falls in the range predicted by the Gibbs free energy diagram.

Applications of an extended Miedema's model for ternary alloys

The extension of Miedema's semi-empirical model to ternary systems by means of an energy minimization scheme was implemented to demonstrate a number of physical phenomena associated with select ternary alloys. In order to gain a thermodynamic understanding of glass forming ability of Zr based alloys, a combination of extended Miedema's model and lattice strain energies has been invoked. The extended Miedema approach has also been used to study the phase selection during crystallization for amorphous Zr–Cu–Ni alloys. Also extended Miedema's model was used to illustrate its applicability to study the phase stability of Mo–Nb–Si alloys around M 3Si composition (M = Mo, Nb), by predicting the amount of Nb (30 at.%) required to destabilize the structure.

Origin on amorphization of Co–Mo magnetic thin films: Experiments and thermodynamic calculation

Amorphisation of Co–Mo magnetic thin films has been studied by using X-ray diffraction technique, and thermodynamic calculation based on Miedema's semi-empirical model has been used to clarify the nature of amorphisation in this binary alloy system. The transition composition from the hexagonal cubic packed structure to the amorphous (H/A) is about 19 at.%Mo when the Co–Mo thin films are deposited at room temperature (RT) under a working Ar pressure of 0.2 Pa and a deposition rate of about 0.7 Å/s, but increases up to about 23 at.%Mo when deposited at 300 °C. The calculated transition composition at RT based on the Miedema's model or the thermodynamically assessed parameters is 18.7 at.%Mo or 16.1 at.%Mo, respectively, well consistent with the experimental value of ~ 19.0 at.%Mo. Higher deposition rate and lower pressure shift the H/A transition composition to a higher Mo content.

Prediction of the crystallization temperature and crystallization driving force for Mg-Ni-Nd amorphous alloys

A method for predicting the crystallization temperature and crystallization driving force of ternary amorphous alloys was provided. This method is an extension of the smallest-vacancy model suggested by Buschow for evaluating crystallization temperatures. The crystallization enthalpy and crystallization driving force are evaluated by using Miedema's semi-empirical model and the crystallization temperature is predicted. Calculation of the crystallization temperatures and enthalpy for (Mg70.6Ni29.4)1-xNdx(x＝5,10,15) amorphous alloys are performed by using this method. The calculated results accord well with experimental data and the relative error is less than 8% and 7% for crystallization temperature and crystallization enthalpy, respectively. It is found that with the increasing of crystallization driving force the retention rates of discharge capacity of Mg-Ni-Nd amorphous alloys decreases. For the (Mg70.6Ni29.4)1-xNdx(x＝1—20) amorphous alloys, the lowest crystallization driving force appears when the Nd content reaches 6.3%. That means (Mg70.6Ni29.4)93.7Nd6.3 amorphous alloy could have better retention rate of discharge capacity.

Thermodynamic Analysis of Nb-Cr Powders of Mechanical Alloying

In this study, Nb-Cr binary mixtures were prepared by mechanical alloying. And mechanical alloying process of mixed Nb-Cr(1:2) powders was studied, and the phases of milling powders analyzed by XRD and SEM. It has been found that the powders form solid solution first, then amorphous phase appeared gradually and crystallization of amorphous takes place with the different milling time. A thermodynamic model of MA of Nb-Cr system was developed based on Miedema Semi-experimental theory to explain the phase transformations of Nb-Cr system during milling. Using Miedema semi-empirical model the free energies of the ordered Laves-phase NbCr2 intermetallics, solid solution and amorphous alloy were calculated. From XRD and SEM analysis of Nb/2Cr powders prepared by mechanical alloying in a planetary ball milling, it was found that the calculated results were in accordance with the experiments.

On the formation of LaFe5Hn

We explore the formation of a LaFe 5 H n hydride by means of density functional theory. Enthalpies of formation Δ H with respect to the elemental metals and H 2 are calculated for various hydrogen configurations in four prototype crystal structures. We find Δ H < 0 in many cases, suggesting the existence of LaFe 5 H n , as does Miedema's semi-empirical model. Δ H is a minimum for the LaFe 5 H 7 stoichiometry with hydrogen occupying the 4e, 8g, and 16m sites in the orthorhombic Cccm structure. Phonon dispersion relations and elastic constants computed for that structure exhibit no anomalies, demonstrating vibrational stability. Similar results for LaFe 5 indicate the possible formation of that compound under pressure.

Computer-Aided Development of Multicomponent Metallic Glasses

ABSTRACTAsynthesized calculation model for developing metallic glasses has been created by taking into account criteria for the achievement of high glass-forming ability (GFA) and viscosity. The model deals with amorphous-forming composition region (AFCR), crystallization temperature (Tx) and three GFA factors: critical cooling rate (Rc), reduced glass-transition temperature (Tg/Tm) and supercooled liquid region (ΔTx=Tx-Tg) where Tg and Tm are glass transition and melting temperature, respectively. The principle of the model is based on thermodynamic functions for multicomponent systems, i.e., mismatch entropy and mixing enthalpy which express the criteria in terms of the number of elements, atomic size differences and the heat of mixing. By combining these thermodynamic quantities with the Miedema's semi-empirical model, AFCR was calculated, and was compared with the experimental results. The GFA factors were also analyzed from viscosity. The Rc was derived from transformation diagram of metallic glasses for crystallization while ΔTx was calculated by solving a differential equation expressing the change in free volume with temperature. As a result of these analyses, Rc-Tg/Tm and R-ΔTx diagrams were found to fit with the experimental results qualitatively. Furthermore, crystallization temperature (Tx) was also calculated for multicomponent metallic glasses by the modification of the Miedema's binary model for the calculation of Tx. The reduced crystallization temperature (Tx/Tl), where Tl is liquidus temperature, was calculated for evaluating GFA of metallic glasses instead of Tg/Tm. Some of the calculation methods used in the present study have theadvantage giving results as a function of composition; thus, there exists possibility to lead to the prediction of glassy alloys compositions. In this sense, the present calculation methods are completely different to the current method for the development of new metallic glasses relying on the empirical criteria which suggest only appropriate systems and/or elements of the alloysfor the achievement of high GFA. In near future, this kind of calculation technique can be used for the prediction of optimal compositions of the metallic glasses with high GFA.

The standard enthalpies of formation of the compounds of early transition metals with late transition metals and with noble metals as determined by Kleppa and co-workers at the University of Chicago — A review

Since the early 1980s, experimental studies of the standard enthalpies of formation of the binary intermetallic compounds of early transition metals with late transition metals and with noble metals have been a major long-term research project in this laboratory. Tabulated in this review are 290 enthalpy of formation values for 273 such compounds, all determined in this laboratory during the last two decades. The calorimetric methods used in these investigations have included solution calorimetry, solute–solvent drop calorimetry, and direct synthesis calorimetry. Among these methods, the direct synthesis approach has been the most frequently used technique. In this review, our results will be compared with values published by other laboratories and with values predicted by the Miedema semi-empirical model. However, the emphasis will be placed on the systematic variation from group to group in the periodic table. A few examples will be presented to show the correlation between the enthalpy of formation and the pertinent atomic number in the binary alloy families.

Extension of Miedema's semiempirical model to estimates of the formation enthalpies of point defects in intermetallic compounds with the B2 structure

Point-defect formation in B2 intermetallic compounds is discussed. It is shown that in fact the problem is complicated. Miedema's semiempirical model is extended for estimating the enthalpies involved. From those estimates the type of disorder for a compound at higher temperature and by ballistic action (ball milling) is assessed. Results of the calculations are compared with known experimental results.

Direct synthesis calorimetry of some binary alloys in the systems SiAs, GeAs and SnAs

Abstract The standard enthalpies of formation of SiAs, SiAs 2 , GeAs, GeAs 2 and SnAs have been determined by direct synthesis drop calorimetry in fused silica capsules at 1123 K (for SiAs), 1058 K (for GeAs) and 987 K (for SnAs). The following values of ΔH f o (298) (kJ mol atoms −1 ) are reported: SiAs, −5.4 ± 1.2; SiAs 2 , −3.7 ± 2.3; GeAs, −5.5 ± 2.6; GeAs 2 , −5.8 ± 3.2; SnAs, −9.5 ± 3.2. Using our measured values for the heats of reaction of the processes a As(s) + b Me(s) = c As x Me 1− x ( l ) at 1058 K for Ge and 987 K for Sn, we have calculated the liquid-liquid enthalpies of mixing for some alloys in these two systems. Adopting the sub-regular solution model, we have calculated the following approximate expressions for the enthalpies of mixing (kJ mol −1 ): ΔH 1−1 M (Ge-As, 1058 K) = (−9.86 – 2.77 x As ) x As x Ge ΔH 1−1 M ( Sn - As , 987 K ) = (−16.87 + 8.90 x As ) x As x Sn The calorimetric values for the solid and liquid alloys are compared with predicted values from Miedema's semi-empirical model. It is found that all of the predicted values are more than one order of magnitude more exothermic than our experimental results.

Standard enthalpies of formation of some borides of Ce, Pr, Nd and Gd by high-temperature reaction calorimetry

The standard enthalpies of formation of five lanthanide borides have been determined calorimetrically at 1473 ± 2 K. The following values of ΔH f 0 are reported: PrB 6, − 51.3 ± 5.7 kJ/g · atom (this value was determined by solute-solvent drop calorimetry); CeB 4, − 53.5 ± 1.5 kJ/g · atom; PrB 4, − 53.1 ± 1.6 kJ/g · atom; NdB 4, − 53.3 ± 1.5 kJ/g · atom; Gd 2B 5, − 43.1 ± 1.4 kJ/g · atom (these four values were all obtained by direct synthesis calorimetry from the elements). The results are compared with earlier experimental data and with values predicted from Miedema's semi-empirical model. Finally, a systematic comparison is presented between the considered boride data and values for compounds of the rare-earth metals with Al, Ga, In and Tl taken from the published literature.

Standard enthalpies of formation of AlB 12 and Al 4C 3 by high temperature direct synthesis calorimetry

The standard enthalpies of formation of α-AlB 12 and of Al 4C 3 have been determined by high temperature direct synthesis calorimetry at 1473 ± 2 K. The experiments were carried out in two different calorimeters of similar but not identical constructions. The following average values of ΔH f 0 are reported: for α-AlB 12, −11.4 ± 0.6 kJ (mol of atoms) −1; for Al 4C 3, −18.3 ± 1.0 kJ (mol of atoms) −1. The results are compared with earlier experimental values reported in the literature and with values predicted from Miedema's semi-empirical model.

Standard enthalpies of formation of some lutetium alloys by high-temperature direct synthesis calorimetry

The standard enthalpies of formation for some lutetium alloys in the binary systems Lu-X (where X=C, Si, Ge, Sn, B, Al) have been determined by direct synthesis calorimetry at 1473±2 K. The following values of ΔH0f in kJ g.atom−1 are reported: LuC2 −26.7±1.8; LuSi −78.3±2.1; Lu5Ge3 −73.8±1.5; Lu5Sn3 −73.6±1.4; LuB2 −29.8±0.9; LuAl2 −52.6±3.0; GdSi = −75.6±2.3. The results are compared with some earlier experimental data derived from e.m.f. or mass spectrometric measurements, with predicted values from Miedema's semi-empirical model and with reported calorimetric data for the corresponding compounds of some early lanthanide elements.