Activation Energy For Interdiffusion Research Articles

Effect of microwave heating on the interdiffusion in BaTiO3–SrTiO3 binary ceramic system

An investigation on the effect of microwave heating (2.45 GHz) on the interdiffusion process was carried out and compared with conventional heating for BaTiO3–SrTiO3 binary system in the temperature range of 1200–1400 °C. Interdiffusion coefficients were extracted using Boltzmann–Matano analysis for both heating methods. Consequently, microwave heating was determined to result in higher interdiffusion coefficients compared to conventional heating. Correspondingly, ∼27% decrease in the apparent activation energy of interdiffusion was found which was associated with faster diffusion under electromagnetic irradiation due to increased vacancy concentration and more open lattice structure in Ba-rich regions which could be exploited for unique experimentations and non-equilibrium/non-stoichiometric phase transformations to study their kinetics and formation mechanisms and grasp a better understanding on the dielectric properties of such perovskites.

Evaluation of diffusion behavior and mechanical characteristics in the ZrC-NbC pseudo-binary system

Accurate information on diffusion kinetics and mechanical characteristics for the ZrC-NbC pseudo-binary system is essential for developing high-performance ZrC-based alloys. At present work, we have employed the diffusion couple method to investigate systematically the diffusion kinetics of the ZrC-NbC pseudo-binary system in the temperature range of 1373–1673 K. The mechanical characteristics of the diffusion region have been studied by the nanoindentation technique. Evaluations have been conducted on the impurity diffusion and inter-diffusion coefficients of the ZrC-NbC pseudo-binary system. As Nb concentration increases, the inter-diffusion coefficients of the ZrC-NbC pseudo-binary system decline. The inter-diffusion activation energies of the ZrC-NbC pseudo-binary system increase as Nb concentration increases, with the largest value of 395.3 kJ/mol at 55 at. % Nb concentration. The impurity diffusion activation energies of C in ZrC, C in NbC, Nb in ZrC, and Zr in NbC are 242.4 kJ/mol, 167.9 kJ/mol, 388.3 kJ/mol, and 288.0 kJ/mol, respectively. The Vickers hardness and Young's modulus of Zr1-xNbxC have also been measured, with the highest values of 29.4 ± 2.7 GPa and 650.7 ± 12.9 GPa, respectively. With an increase of Nb concentration, Young's modulus of Zr1-xNbxC increases, while its Vickers hardness first increases and subsequently declines. The results of this study could be advantageous to develop ZrC-based alloys and improve their properties.

Interdiffusion in body-centred cubic β-(Ti, Al) solid solution phase

A study has been conducted to quantify the effect of Al on diffusion in the dilute β-(Ti, Al) solid solution phase by determining the interdiffusion and impurity diffusion coefficients using the diffusion couple technique. An increase in interdiffusion coefficients with an increase in Al content in β-(Ti, Al) is rationalized by a decreasing trend of activation energy for interdiffusion and an increase in driving force for diffusion. Higher activation energy of impurity diffusion coefficient of Al in β-Ti than that of self-diffusion coefficient of β-Ti may further suggest lower interaction tendency of vacancies with Al atoms in the β-(Ti, Al) phase.

Interdiffusion and impurity diffusion behavior in polycrystalline Mg-Y binary system

The diffusion behavior in binary Mg-Y system was investigated using polycrystalline Mg/Y diffusion couples at temperatures ranging from 573 to 823 K. For all diffusion couples, electron microprobe analysis was utilized for the measurement of concentration profiles. The interdiffusion coefficients in Mg solid solution and intermetallic phases were determined via the Boltzmann-Matano and Heumann-Matano method, respectively. In addition, the Hall method was employed to extrapolate the impurity diffusion coefficients of Y in pure polycrystalline Mg and Mg in pure polycrystalline Y. The results showed that the interdiffusion coefficient in Mg solid solution increased with an increase of Y concentration, and the corresponding pre-exponential factor and activation energy both increased nearly linearly. The pre-exponential factor and activation energy for Y impurity diffusion in Mg were determined to be 2.36×10−8 (±9.0×10−9) m2/s and 85.61 (±2.0) kJ/mol, while those for Mg impurity diffusion in Y were determined to be 3.47×10−7 (±7.6×10−7) m2/s and 95.90 (±6.7) kJ/mol. Simultaneously, the pre-exponential factor and activation energy for interdiffusion in intermetallic phase Mg24Y5 were determined to be 9.96×10−9 (±2.9×10−9) m2/s and 68.98 (±2.0) kJ/mol；while those for Mg2Y were determined to be 1.18×10−9 (±9.0×10−10) m2/s and 64.54 (±3.2) kJ/mol. Additionally, the vacancy diffusion was dominant mechanism above 723 K, while the grain boundary diffusion mechanism dominated below 723 K in polycrystalline Mg-Y binary system.

Microstructure, kinetics and thermodynamics of HEA Al0.5CoCrFeNi at T ≥ 800 °C

Al0.5CoCrFeNi contains a mixture of the ductile fcc (A1) phase and the hard ordered bcc (B2) phase. In this paper, the microstructure, composition, precipitation kinetics, and thermodynamic calculation of the equilibrium state of the Al0.5CoCrFeNi alloy were studied. It was found that the morphology of the B2 phase (rich AlNi) is temperature-dependent; up to 1000 °C the dominant morphology is needle/plate-like whereas above this temperature, equiaxed morphology takes over until the needle morphology disappears completely at above 1200 °C. It was confirmed experimentally, and by thermodynamic calculation with good agreement between the two, that the phase compositions are temperature dependent. Nevertheless, there is still disagreement between the thermodynamic model and the experimental results for the A1 to B2 phase ratios and compositions at ~1200 °C and above.The inter-diffusion activation energy (Q = 187 ± 20 kJ/mol) for the B2 phase growth was found to be lower than the activation energy reported for the AlCoCrFeNi alloy. This result is attributed to the different lattice distortion parameters of the two alloys. It is further suggested that the morphology transformation of the B2 phase from needle-like to equiaxed with increase in temperature, occurs because of increased density of dislocations at the B2/A1 interface.

Interdiffusion study of the topologically closed packed μ phase and the phase boundary compositions in the Fe–Mo system

Fe/Mo bulk diffusion couples are annealed at 1050–1200 °C to study the growth and diffusion behaviour of μ phase in the Fe–Mo system. Parabolic growth constants and integrated interdiffusion coefficients are determined in the μ phase. The activation energies for the growth of μ phase and for the integrated interdiffusion coefficients are estimated as 228±22 and 733±10 kJ/mol, respectively. The relatively high activation energy for interdiffusion in μ phase, determined at high homologous temperature of 0.8–0.9, indicates that μ phase grows by lattice diffusion. Phase boundary compositions, measured by EPMA, indicates the homogeneity range of μ phase to be ~3 at.% higher towards the Fe–rich side (i.e., 36 at.% Mo) as compared to the reported composition of 39–44 at.% Mo in the phase diagram.

Revisiting the Diffusion of Niobium in an As-Cast Nickel-Based Superalloy During Annealing at Elevated Temperatures

While understanding the interdiffusion of Nb in the austenite matrix of Ni-based superalloys is important for studying the precipitation reactions (Laves phase, γ″-precipitates and δ-phase) and homogenization of the as-cast structure, there is no report on the activation energy (Q) and pre-exponential factor (D0). Moreover, for the Ni–Nb diffusion couple, the reported Q values of 202.6 and 257 kJ/mol are not consistent. In the present work, based on the concept of residual segregation index during homogenization treatment and elemental analyses from dendrite cores and interdendritic segregated regions, Q and D0 were respectively determined as ~ 236 kJ/mol and 0.0053 cm2/s for the Ni-based superalloys. Improved analysis of the Ni–Nb system resulted in Q and D0 values of ~ 234 kJ/mol and 0.1618 cm2/s, respectively. Therefore, it was concluded that the activation energy for interdiffusion of Nb in superalloys and Ni–Nb diffusion couple is the same. However, due to the presence of other alloying elements in the superalloys, D0 for Ni–Nb diffusion couple is ~ 30 times that of the superalloys.

X-ray reflectivity with a twist: Quantitative time-resolved X-ray reflectivity using monochromatic synchrotron radiation

We have developed an improved method of time-resolved x-ray reflectivity (XRR) using monochromatic synchrotron radiation. Our method utilizes a polycapillary x-ray optic to create a range of incident angles and an area detector to collect specular reflections. By rotating the sample normal out of the plane of the incident fan, we can separate the surface diffuse scatter from the reflectivity signal, greatly improving the quality of the XRR spectra compared to previous implementations. We demonstrate the time-resolved capabilities of this system, with the temporal resolution as low as 10 ms, by measuring XRR during the annealing of Al/Ni nano-scale multilayers, and use this information to extract the activation energy for interdiffusion in this system.

X-ray reflectivity measurement of interdiffusion inmetallic multilayers during rapid heating.

A technique for measuring interdiffusion in multilayer materials during rapid heating using X-ray reflectivity is described. In this technique the sample is bent to achieve a range of incident angles simultaneously, and the scattered intensity is recorded on a fast high-dynamic-range mixed-mode pixel array detector. Heating of the multilayer is achieved by electrical resistive heating of the silicon substrate, monitored by an infrared pyrometer. As an example, reflectivity data from Al/Ni heated at rates up to 200 K s-1 are presented. At short times the interdiffusion coefficient can be determined from the rate of decay of the reflectivity peaks, and it is shown that the activation energy for interdiffusion is consistent with a grain boundary diffusion mechanism. At longer times the simple analysis no longer applies because the evolution of the reflectivity pattern is complicated by other processes, such as nucleation and growth of intermetallic phases.

Effect of Small Amount of Manganese on the Interdiffusivities in Fe-Al Alloys

The ability to weld aluminum and steel sheets depends strongly on the formation of intermetallic phases; a process that is, in turn, controlled by the interdiffusion of iron and aluminum across the welded interface. Understanding the interdiffusion behavior, and how it is influenced by tertiary elements such as manganese, will allow for better prediction of the properties of the spot weld. Hence, interdiffusion coefficients and activation energies for interdiffusion were determined in the α solid solution and B2 intermetallic phases of Fe-Al alloys in the presence of 1.5-2 at.% manganese with pseudo-binary diffusion couples investigated at 900-1095 °C. The interdiffusion coefficients in α were found to increase in the presence of Mn at all temperatures compared with those reported in the binary Fe-Al alloys. The activation energies for interdiffusion in α are correspondingly lower than those in the binary Fe-Al alloys. The increase in the main interdiffusion coefficients in the presence of Mn indicates that diffusional interactions between Fe and Al are increased in the presence of Mn. The expected increase in diffusional interactions of Fe and Al are found to be consistent with the thermodynamic interactions between Fe and Al in the binary Fe-Al and ternary Fe-Al-Mn system as estimated from the literature. The presence of Mn is found to decrease the solubility of Al in the α solid solution, which, in turn, is expected to decrease the growth rate of the intermetallic at the interface between steel and aluminum.

A Study of Interdiffusion in the Fe-C/Ti System Under Equilibrium and Nonequilibrium Conditions

In the present study, diffusion behavior under equilibrium and nonequilibrium conditions in a Fe-C/Ti system is studied in the temperature range of 773 K to 1073 K (500 °C to 800 °C). A defect-free weld joint between mild steel (MS) (Fe-0.14 pct C) and Ti Grade 2 obtained by friction welding is diffusion annealed for various durations to study the interdiffusion behavior under equilibrium conditions, while an explosive clad joint is used to study interdiffusion under nonequilibrium conditions. From the elemental concentration profiles obtained across the MS-Ti interface using electron-probe microanalysis and imaging of the interface, the formation of distinct diffusion zones as a function of temperature and time is established. Concentration and temperature dependence of the interdiffusion coefficients (D(c)) and activation energies are determined. Under equilibrium conditions, the change in molar volume with concentration shows a close match with the ideal Vegard’s law, whereas a negative deviation is observed for nonequilibrium conditions. This deviation can be attributed to the formation of secondary phases, which, in turn, alters the D(c) values of diffusing species. Calculations showed that the D0 and activation energy for interdiffusion under equilibrium is on the order of 10−11 m2/s and 147 kJ/mol, whereas it is far lower in the nonequilibrium case (10−10 m2/s and 117 kJ/mol) in the compositional range of 40 to 50 wt pct Fe, which also manifests as accelerated growth kinetics of the different diffusion zones.

Comparative Analysis of Growth Rate Enhancement and Ge Redistribution during Silicon-Germanium Oxidation by Rapid Thermal Oxidation

The demand for higher speed and lower power consumption ICs has motivated research for higher mobility channel materials (1). Compressively strained SiGe is known to feature higher hole mobility than Si and is largely compatible with the Si CMOS manufacturing platform. Besides, the FDSOI transistor architecture allows power consumption reduction (2), thus making SiGe-On-Insulator (SGOI) channels promising. SGOI layers can be fabricated by the so-called condensation technique, which is based on concurrent Si selective thermal oxidation of SiGe and SiGe composition homogenization by Si and Ge interdiffusion (see Figure 1) (3). Therefore, a sound understanding of kinetics of oxidation and interdiffusion of SiGe is required to develop optimized SGOI structures. SiGe dry oxidation rate has been reported to be higher (4) than or equal (5)(6) to the one of Si. It therefore remains unclear. Few groups investigated Rapid Thermal Oxidation (RTO) (4) while most of them looked at furnace oxidation. Moreover, most studies only considered the initial Ge content to compare oxidation kinetics. Indeed, the Ge concentration below the SiGe-oxide interface is strongly varying with time because of two mechanisms: firstly, the Si-selective oxidation of SiGe tends to pile-up Ge below the oxidizing interface; and secondly, interdiffusion of SiGe favors homogenization of the layer (6). This paper focuses on the oxidation rate of SiGe in regards to the varying Ge concentration in the SiGe layer for various oxidation conditions. Thick (> 20 nm) SiGe layers with either 10% or 30% Ge concentrations were epitaxially grown on bulk Si wafers. Oxidation was performed by RTO in 1 atmosphere of pure O2, with different oxidation temperatures and durations. Oxide thickness and SiGe composition versus depth were measured by Spectroscopic Ellipsometry and X-Ray Reflectivity, and by Secondary Ion Mass Spectroscopy respectively. Figure 2 shows the Ge concentration profile below the oxide. A rapid creation of a pile-up layer is observed at all temperatures. Then, three regimes of evolution of the pile-up layer are distinguished: the Ge concentration at the oxidizing interface (a) increases, (b) is constant, and (c) decreases. The regime of evolution of the pile-up layer is determined by a competition between the oxidation speed and the interdiffusion speed. As schematically illustrated Figure 3, the interdiffusion speed overcomes the oxidation one at higher temperatures because the activation energy of interdiffusion in SiGe ([4,5] eV (7)) is well above the one of SiGe oxidation ([2,2.6] eV (4)). Phrased in a different way, the temperature dependence of interdiffusion is higher than the oxidation one. Figure 4 shows the oxide thickness versus the oxidation duration for dry RTO at 900°C, 1000°C and 1100°C. A higher oxidation rate is observed for SiGe compared to Si for all temperatures. Then, to highlight the effect of the Ge concentration at the oxidizing interface, we fitted the curves to extract oxidation rates for each oxidation conditions. We define the Growth Rate Enhancement (GRE) as the ratio of the oxidation rate of SiGe to the one of Si at a given oxide thickness and for identical oxidation conditions. It is indeed important to highlight that comparing oxidation rates at the same oxide thickness is mandatory: if we want to examine the effect of Ge on the oxidation rate, we have to take into consideration the fact that the oxidation rate also decreases with the oxide thickness. Such an approach allows us to freeze the system and to find more easily correlations. We report on Figure 5 four GRE values extracted from our data versus the Ge concentration at the oxidizing interface. We thus observe that the higher the Ge concentration at the oxidizing interface is, the higher the GRE tends to be. We thus showed that Ge redistribution by interdiffusion during SiGe oxidation can follow different regimes. We also evidenced that for dry RTO conditions, the higher the Ge concentration at the oxidizing interface is, the higher the GRE is. Understanding the interdependence of these two mechanisms is essential to get an accurate picture of the condensation process. Therefore, data for dry RTO will be completed and an in-depth discussion will be led. A similar study will also be conducted for a wet oxidation process called In-Situ Steam Generation (ISSG). (1) Pillarisetty, R., Nature 479.7373 (2011): 324-328. (2) Weber, O., et al., VLSIT IEEE, 2014. (3) Tezuka, T., et al., JJAP 40.4S (2001): 2866. (4) Spadafora, M., et al. MSSP 8.1 (2005): 219-224. (5) LeGoues, et al., APL 54.7 (1989): 644-646. (6) Long, E., et al., PSS (a) 209.10 (2012): 1934-1939. (7) Kube, R., et al., JAP 107.7 (2010): 073520. Figure 1

Investigation of the diffusion behavior in Sn-xAg-yCu/Cu solid state diffusion couples

The interfacial reactions and growth behavior of the Cu3Sn and Cu6Sn5 phases in Sn-3.0%Ag-0.5%Cu/Cu and Sn-3.5%Ag-0.7%Cu/Cu diffusion couples were investigated at 130 °C, 150 °C, 170 °C and 200 °C and compared with those in binary Sn/Cu diffusion couples using identical experimental conditions. The Ag solubility in the Cu3Sn and Cu6Sn5 phases was found to be quite small. The parabolic growth constants of Cu3Sn and Cu6Sn5 in Sn-xAg-yCu/Cu diffusion couples were calculated. A transient stage for the growth of Cu3Sn was observed. A pseudo-binary method was proposed and performed to obtain the integrated interdiffusion coefficients and activation energies for diffusion of the intermetallics with limited solubility in one of the elements. The growth of Cu3Sn in Sn-xAg-yCu/Cu diffusion couples was found to be a little slower than that in binary Sn/Cu diffusion couples. The growth rate of the Cu6Sn5 phase in ternary Sn-xAg-yCu/Cu diffusion couples is quite close to that in Sn/Cu diffusion couples. The Cu addition in the Sn-based end-member is expected to favor the growth of Cu6Sn5 providing instantly available Cu atoms for the formation of Cu6Sn5. The Ag addition is suggested to slightly decrease the thermodynamic activity of Sn and further decrease the diffusion of Sn. These interpretations were confirmed by a study of the diffusion behavior in Sn-3.5%Ag/Cu and Sn-1.0%Cu/Cu diffusion couples. The calculated activation energy for interdiffusion in the Cu3Sn and Cu6Sn5 phases in Sn-xAg-yCu/Cu diffusion couples are quite close to those obtained for binary Cu/Sn couples. The obtained conclusions are informative for the Ag-Cu-Sn solder design.

Interdiffusion and Reaction between Pure Magnesium and Aluminum Alloy 6061

Using solid-to-solid couples investigation, this study characterized the reaction products evolved and quantified the diffusion kinetics when pure Mg bonded to AA6061 is subjected to thermal treatment at 300°C for 720 hours, 350°C for 360 hours, and 400°C for 240 hours. Characterization techniques include optical microscopy, scanning electron microscopy with X-ray energy dispersive spectroscopy, and transmission electron microscopy. Parabolic growth constants were determined for γ-Mg17Al12, β-Mg2Al3, and the elusive ε-phase. Similarly, the average effective interdiffusion coefficients of major constituents were calculated for Mg (ss), γ-Mg17Al12, β-Mg2Al3, and AA6061. The activation energies and pre-exponential factors for both parabolic growth constant and average effective interdiffusion coefficients were computed using the Arrhenius relationship. The activation energy for growth of γ-Mg17Al12 was significantly higher than that for β-Mg2Al3 while the activation energy for interdiffusion of γ-Mg17Al12 was only slightly higher than that for β-Mg2Al3. Comparisons are made between the results of this study and those of diffusion studies between pure Mg and pure Al [1] to examine the influence of alloying additions in AA6061.

Interdiffusion in binary Ni-Re alloys

Processes of interdiffusion have been studied in the Ni-Re system. The method of electron-microprobe analysis was used to measure the interdiffusion coefficients D in Ni4.4Re/Ni, Ni7Re/Ni Ni9Re/Ni, and Ni9Re/Ni4.4Re (wt %) diffusion pairs in the temperature range of 1050–1350°C. The averaged values of the preexponential factor and the activation energy for interdiffusion were found to be D0 = 1.16 × 10−4 m2/s and Q = 317 kJ/mol, respectively. The value D0 ∼ 10−4 m2/s is typical of substitutional alloying elements in fcc metals; the value of Q is determined to be close to that for W and is significantly higher than those that correspond to other alloying elements in nickel superalloys. No clearly pronounced concentration dependence of the coefficients of interdiffusion has been revealed at a rhenium concentration of 4.4–9 wt %.

Solid-State Diffusion Reaction and Formation of Intermetallic Phases in the Fe-Al System

The solid-state diffusion reaction between Fe and Al was studied using bulk diffusion couples in the temperature range 450°C to 600°C for annealing durations up to 240 h. The Al-rich intermetallic phase Fe2Al5 formed in the diffusion zone at all annealing temperatures. However, for diffusion couples annealed at and above 600°C, additional intermetallic phases Fe3Al, FeAl, and FeAl2 appeared in the diffusion zone. The existence of these phases at and below 640°C and the composition range of their existence were investigated, and these results provided better insight into the existing Fe-Al phase diagram. It was observed that Fe2Al5 is the dominant phase in the diffusion zone, and the formation of this phase was rationalized based on the modified effective heat of formation model. Both kinetic and diffusion parameters were evaluated for Fe2Al5, and the activation energy for interdiffusion of this phase was found to be 146.8 kJ/mol; these results were compared with previously published work.

Growth of MnSi1.7 Layers on MnSi Substrate by Molten Salt Method

MnSi1.7 layers have been successfully grown using a molten salt method. It was found that homogeneous MnSi1.7 layers with columnar domain structure can be grown on MnSi substrates. The dependence of the thickness and domain structure of the layers on the growth conditions was investigated. It was found that the deposited atoms, namely Si, were the dominant diffusion species, and the formation of Kirkendall voids was avoided for the silicidation reaction based on interdiffusion. The layer thickness could be controlled by the growth temperature and time, and was diffusion controlled. The interdiffusion coefficient was approximately 5 × 10−10 cm2/s for growth temperature of 900°C. The activation energy of interdiffusion was deduced to be approximately 1.1 eV for growth of the MnSi1.7 layers. This growth technique provides a simple and controllable method to grow large-area, high-quality MnSi1.7 layers.

Atomic interdiffusion in Ni–Cu system under high magnetic field

The effect of high magnetic field on the atomic interdiffusion in Ni–Cu system was studied using the Cu/Ni/Cu diffusion couples. During the atomic interdiffusion in Ni–Cu system, it was found that the interdiffusion coefficients increased with the increase of molar fraction of Ni atoms in the interdiffusion zones when the couples were annealed with or without the magnetic field. It was noted that all corresponding interdiffusion coefficients under the magnetic field are smaller than those without the magnetic field. The results demonstrate that the magnetic field retards the atomic interdiffusion in Ni–Cu system. This retardation is achieved through reducing the frequency factors but not changing the interdiffusion activation energies.

Effect of millimeter-wave irradiation on cation interdiffusion in the calcium titanate/strontium titanate ceramic couple

Interdiffusion between the perovskite CaTiO3 and SrTiO3 diffusion couple was investigated in an annealing method using 24-GHz MMW irradiation as the heating source. Interdiffusion was enhanced by MMW irradiation, and the apparent activation energy for interdiffusion decreased 54%, compared with conventional furnace heating. The intrinsic diffusions for both Ca2+ and Sr2+ were also enhanced, although their relative degrees of enhancement differed, partly as a result of differences in MMW absorptivity between the two ceramics. The observed isothermal diffusion enhancement could be ascribed to a nonthermal effect, apart from the differential degree of enhancement between the transport species.

Interdiffusion and Phase Growth Kinetics in Magnesium-Aluminum Binary System

Binary interdiffusion data as functions of composition in the Mg-Al system are essential in modeling kinetics of phase transformations in multicomponent Mg and Al alloys. Interdiffusion and phase growth kinetics were studied in the binary Mg-Al system using multiphase diffusion couples assembled between pure Mg and pure Al at 380, 400 and 420 °C. Two phases, Al3Mg2 (β) and Mg17Al12 (γ) were formed between Al and Mg at the three temperatures studied. Both β and γ phases were observed to follow parabolic growth with time, which suggests that the growth of the two phases is controlled by bulk diffusion mechanisms. The activation energies for the growth of β and γ phases in the temperature range of 380-420 °C were found to be 37.3 ± 4.1 and 187.7 ± 1.9 kJ/mol, respectively. The interdiffusion coefficients were evaluated as functions of compositions in various phases at the three temperatures studied, which were further utilized for evaluating the activation energies and frequency factors for interdiffusion in each phase. The activation energy for interdiffusion in FCC-Al is found to increase with increasing Mg-content whereas the activation energies for interdiffusion in HCP-Mg and γ phases do not vary significantly with composition.