A New Finding About Conditions for More Than One Kirkendall Marker Plane in Binary Single Phase Diffusion Couples

It is now well known that there are experimental results of bifurcate, trifurcate or more Kirkendall marker planes (K-plane) in a multiple phase diffusion couple (M-couple). In the case of Au-Zn binary alloy system, for example, even in a β’/β’ single phase diffusion couple (S-couple) there is a possibility of the bifurcate K-planes because the ratio R = D _Zn/D _Au of the intrinsic diffusion coefficients in the β’ phase is smaller than 1 in the Au rich side and larger than 1 in the Zn rich side. It has been reported that the positions of the K-planes in a diffusion zone can be found graphically as intersections between the plot of marker moving distance \(2t\upsilon_{\text{k}}^{\text{D}}\) versus X _k and the plot of a straight line \(2t\upsilon_{\text{k}}^{\text{EX}}\) versus X _k. Here, \(\upsilon_{\text{k}}^{\text{D}}\) is the marker velocity with respect to the volume fixed frame of reference (V-frame) defined by,

$$\upsilon_{\text{k}}^{\text{D}} = \upsilon_{\text{k}} - \upsilon_{\text{V}} = V_{\text{B}} \left( {D_{\text{B}}^{\text{V}} - D_{\text{A}}^{\text{V}} } \right)\left( {\frac{{\partial C_{\text{B}} }}{\partial X}} \right),$$

and \(\upsilon_{\text{k}}^{\text{Ex}}\) is that determined experimentally by the following equation,

$$\upsilon_{\text{k}}^{\text{Ex}} = \upsilon_{\text{k}} - \upsilon_{0} = \frac{{X_{k} - X_{0} }}{2t}.$$

In this work, we studied the alignments of multiple markers (M-Ms) after diffusion anneal embedded in a S-couple for widely different constant values of ratio of intrinsic diffusion coefficients, R = D _B /D _A, with respect to the mole fixed frame of reference (N-frame) by our numerical technique taking the change in molar volume into account. For this purpose, new two plots to know the K-plane(s) for the N-flame were derived. A possibility was indicated that Kirkendall markers can locate not only at the intersection(s) between these new two plots but also at an unexpected place where the intersection cannot be found.

     

Interdiffusion in <Emphasis Type="Italic">L</Emphasis>1<Subscript>2</Subscript>-Ni<Subscript>3</Subscript>Al Alloyed with Re

Ternary interdiffusion in L1₂-Ni₃Al with ternary alloying addition of Re was investigated at 1473 K using solid-to-solid diffusion couples. Interdiffusion flux of Ni, Al, and Re were directly calculated from experimental concentration profiles and integrated for the determination of average ternary interdiffusion coefficients. The magnitude of main interdiffusion coefficients and was determined to be much larger than that of the main interdiffusion coefficient A moderate tendency for Re to substitute for Al sites was reflected by its influence on interdiffusion of Al, quantified by large and positive coefficients. Similar trends were observed from ternary interdiffusion coefficients determined by Boltzmann-Matano analysis. Profiles of concentrations and interdiffusion fluxes were also examined to estimate binary interdiffusion coefficients in Ni₃Al, and tracer diffusion coefficients of Re (5.4 × 10⁻¹⁶ ± 2.3 × 10⁻¹⁶ m²/s) in Ni₃Al.     

Quasi-Ternary System Ag2Se-CdSe-Ga2Se3

Phase equilibria in the quasi-ternary system Ag₂Se-CdSe-Ga₂Se₃ were investigated by differential thermal and x-ray phase analysis methods. Phase diagrams of nine vertical sections were constructed. The boundaries of seven single-phase fields were determined which are solid solution ranges of system components and intermediate phases. We constructed the isothermal section at 820 K and the liquidus surface projection, and have determined the position in the system of six invariant processes with the participation of liquid: $ {\text{L}}_{{{\text{U}}_{1} }} + {\upzeta} {\leftrightarrows} {\upbeta} + {\upeta} $ L U 1 + ζ ? β + η (1145 K), $ {\text{L}}_{{{\text{U}}_{ 2} }} + \upzeta \leftrightarrows \upgamma + \upeta $ L U 2 + ζ ? γ + η (1138 K), $ \text{L}_{{U_{3} }} + \upeta \leftrightarrows \updelta + \upgamma $ L U 3 + η ? δ + γ (1113 K), $ {\text{L}}_{{{\text{E}}_{ 1} }} \leftrightarrows \upbeta + \updelta + \upeta $ L E 1 ? β + δ + η (1083 K), $ {\text{L}}_{{{\text{E}}_{ 2} }} \leftrightarrows \upalpha + \upbeta + \upvarepsilon $ L E 2 ? α + β + ε (969 K), $ {\text{L}}_{{{\text{E}}_{ 3} }} \leftrightarrows \upbeta + {\updelta} + \upvarepsilon $ L E 3 ? β + δ + ε (963 K). Two invariant processes in the sub-solidus part, $ \upbeta + \updelta \leftrightarrows \upeta + \uplambda $ β + δ ? η + λ and $ \upbeta + \updelta \leftrightarrows \upvarepsilon + \uplambda $ β + δ ? ε + λ at 968 and 938 K, respectively, were investigated as well.     

Phase Equilibria in the System Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-CaO-CoO and Gibbs Energy of Formation of Ca<Subscript>3</Subscript>CoAl<Subscript>4</Subscript>O<Subscript>10</Subscript>

An isothermal section of the system Al₂O₃-CaO-CoO at 1500 K has been established by equilibrating 22 samples of different compositions at high temperature and phase identification by optical and scanning electron microscopy, X-ray diffraction, and energy dispersive spectroscopy after quenching to room temperature. Only one quaternary oxide, Ca₃CoAl₄O₁₀, was identified inside the ternary triangle. Based on the phase relations, a solid-state electrochemical cell was designed to measure the Gibbs energy of formation of Ca₃CoAl₄O₁₀ in the temperature range from 1150 to 1500 K. Calcia-stabilized zirconia was used as the solid electrolyte and a mixture of Co + CoO as the reference electrode. The cell can be represented as: From the emf of the cell, the standard Gibbs energy change for the Ca₃CoAl₄O₁₀ formation reaction, CoO + 3/5CaAl₂O₄ + 1/5Ca₁₂Al₁₄O₃₃ → Ca₃CoAl₄O₁₀, is obtained as a function of temperature: /J mol⁻¹ (±50) = −2673 + 0.289 (T/K). The standard Gibbs energy of formation of Ca₃CoAl₄O₁₀ from its component binary oxides, Al₂O₃, CaO, and CoO is derived as a function of temperature. The standard entropy and enthalpy of formation of Ca₃CoAl₄O₁₀ at 298.15 K are evaluated. Chemical potential diagrams for the system Al₂O₃-CaO-CoO at 1500 K are presented based on the results of this study and auxiliary information from the literature.     

Transformations of Carbides During Tempering of D3 Tool Steel

The studies were performed on D3 tool steel hardened after austenitizing at 1050 °C during 30 min and tempering at 200-700 °C. Based on the diffraction studies performed from the extraction replicas, using electron microscopy, it was found that after 120-min tempering in the consecutive temperatures, the following types of carbides occur: $$ 200\;^\circ {\text{C}} \to \upvarepsilon + \upchi + {\text{ Fe}}_{ 3} {\text{C}},\quad 3 50\;^\circ {\text{C}} \to \upvarepsilon + \upchi + {\text{ Fe}}_{ 3} {\text{C,}} $$ $$ 500\;^\circ {\text{C}} \to \upchi + {\text{ M}}_{ 3} {\text{C }} + {\text{ M}}_{ 7} {\text{C}}_{ 3} ,\quad 600\;^\circ {\text{C}} \to \upchi + {\text{ M}}_{ 3} {\text{C }} + {\text{ M}}_{ 7} {\text{C}}_{ 3} , $$ $$ 700\;^\circ {\text{C}} \to {\text{M}}_{ 3} {\text{C }} + {\text{ M}}_{ 7} {\text{C}}_{ 3} . $$ Apart from higher mentioned carbides, there are also big primary carbides and fine secondary M₇C₃ carbides occurring, which did not dissolve during austenitizing.     

Diffusion Research in BCC Ti-Al-Ni Ternary Alloys

Interdiffusion in BCC phase of Ti-Al-Ni ternary system was investigated at 1473 K (1200 °C) by employing the diffusion-couple technique. The raw composition profiles resulting from interdiffusion treatment and retrieved from EMPA were first analytically represented by error function expansion (ERFEX), and the ternary interdiffusion and impurity diffusion coefficients were then extracted by the Whittle-Green and generalized Hall methods, respectively. The obtained main interdiffusion coefficients \( \tilde{D}_{\text{AlAl}}^{\text{Ti}} \) and two cross coefficients, i.e. \( \tilde{D}_{\text{AlNi}}^{\text{Ti}} \) and \( \tilde{D}_{\text{NiAl}}^{\text{Ti}} \), were found to increase with increasing composition of diffusing species, whereas the values of \( \tilde{D}_{\text{NiNi}}^{\text{Ti}} \) show no noticeable compositional dependence. The impurity diffusivities \( \tilde{D}_{{{\text{Al}}\left( {\text{Ti - Ni}} \right)}}^{*} \) and \( \tilde{D}_{{{\text{Ni}}\left( {\text{Ti - Al}} \right)}}^{*} \) increase with decreasing the Ni and Al compositions, respectively. The results imply that Al diffusion in β Ti-Al-Ni alloys would occur via an ordinary vacancy diffusion mechanism, whereas Ni diffusion, at least one order magnitude faster than Al, very likely benefits from interstitial diffusion as Fe and Co anomaly diffuse in BCC Titanium alloys.     

Influence of Interdiffusion in Sn Solution on Growth of Cu<Subscript>3</Subscript>Sn and Cu<Subscript>6</Subscript>Sn<Subscript>5</Subscript> Formed in Semi-infinite and Finite Cu-Sn Diffusion Couples

Reactive diffusion in the Cu-Sn binary system has been studied by using pure Cu/electrically plated Sn with 0.1-0.2 mm thicknesses diffusion couples (EP-couples) at 473 K. The interdiffusion coefficients, \(\tilde{D}\), of the Cu₃Sn and Cu₆Sn₅ diffusion phase layers were determined at the center of these layers by supposing linear concentration (\(C_{\text{i}}\))-distance (X) curves in these layers and by neglecting the interdiffusion in the Sn terminal solution (IDS) as the previous researchers have neglected it. By using \(\tilde{D}\) thus determined, the phase boundary concentrations for the layers obtained in this work and these parameters for the Cu terminal solution chosen appropriately, \(C_{\text{i}}\)-X curves were determined numerically for various values of interdiffusion coefficient, \(\tilde{D}_{\text{in Sn}}\), and the solubility limit of Cu mole fractions, \(N_{\text{Cu}}^{\text{in Sn}}\), in the Sn terminal solution by our method reported previously taking the molar volume change effect into account. The \(C_{\text{i}}\)-X curves obtained experimentally could be reproduced numerically well by neglecting IDS. This result, on the other hand, suggests a large influence of IDS in the semi-infinite diffusion couples (S-couples) or the diffusion couples used by the previous researchers. The quantitative evaluation of the influence in S-couples revealed that it makes the widths of the diffusion layers thinner than those in the present EP-couples in which the influence on the widths is negligibly small. The evaluation of the influence in the diffusion couples used by the previous researchers indicates larger values of \(N_{\text{Cu}}^{\text{in Sn}}\) than those reported as the value of the equilibrium phase diagram.     

Comparative Oxidation Kinetics of a NiPtTi High Temperature Shape Memory Alloy

A high temperature shape memory alloy, Ni–30Pt–50Ti (at.%), with an M _s near 600 °C, was isothermally oxidized in air for 100 h over the temperature range of 500–900 °C. Nearly parabolic kinetics were observed in log–log and parabolic plots, with no indication of initial fast transient oxidation. On average the rates were about a factor of 4 lower than values measured here for a binary Ni–49Ti commercial SMA. The overall behavior could be best described by the Arrhenius relationships: $${\text{Ni}}{\text{Pt}}{\text{Ti}}{:}\,k_{\text{p}} = 1.54 \times 10^{12} \exp \left[(- 250\,{\text{kJ}}/{\text{mol}}) {RT} \right]{\text{mg}}^{2}/{\text{cm}}^{4} {\text{h}} $$ $${\text{Ni}}{\text{Ti}}{:}\,k_{\text{p}} = 6.39 \times 10^{12} \exp \left[(- 249\,{\text{kJ}}/{\text{mol}}) {RT} \right]{\text{mg}}^{2}/{\text{cm}}^{4} {\text{h}} $$ The activation energy was consistent with literature values for TiO₂ scale growth measured for elemental Ti and some NiTi alloys, at ~210–260 kJ/mol. However, a number of other studies produced activation energies in the range of 135–150 kJ/mol. This divergence may be related to various complex scale layers and depletion zones, however, no specific correlation can be identified at present.     

Pressure dependencies of copper oxidation for low- and high-temperature parabolic laws

Studies of the oxidation kinetics of copper have been conducted in the thin-film range at temperatures of 383–398 K and in the oxygen pressure range of 0.278–21.27 kPa; whereas in the thick-film regime at 1123 K, studies have been conducted in the oxygen pressure range of 2.53–21.27 kPa. Furthermore, the effect of continuously impressed direct current with oxygen pressure variation in Wagner's parabolic range has been studied also in order to have a better understanding of the effective charge on the migrating species. In the low-temperature range, the rate constant, k_P ∝ \(P_{O_2 }^{1/4} \) , suggesting that the migration of neutral vacancies in the growing film predominates. At high temperature, 1123 K, in the Wagnerian regime, the observed approximate pressure dependencies of the parabolic rate constants are the following: $$\begin{gathered} {\text{k}}_{\text{p}} (normal oxidation) \propto \sim {\text{P}}_{{\text{O}}_{\text{2}} }^{{\text{1/7}}} \hfill \\ {\text{k}}_{\text{p}} (sample cathodic) \propto \sim {\text{P}}_{{\text{O}}_{\text{2}} }^{{\text{1/5}}} \hfill \\ \end{gathered} $$ and $${\text{k}}_{\text{p}} (sample anodic) \propto \sim {\text{P}}_{{\text{O}}_{\text{2}} }^{{\text{1/10}}} $$ .     

Interdiffusion Coefficients in FCC Co-Rich Co-Ti-V Alloys at 1273, 1373 and 1473 K

Based on 18 bulk diffusion couples, the composition-dependent interdiffusion coefficients in the FCC Co-rich Co-Ti-V alloys at 1273, 1373 and 1473 K were obtained from the intersection points of the diffusion couples by means of EPMA technique applied to Whittle and Green method. The reliability of the experimental interdiffusivities is validated via thermodynamic constraints. Taking Co as the solvent element, the present results show that when the temperature is from 1273 to 1473 K, the ternary interdiffusion coefficients increases from 10^?16 to 10^?14 m²/s and the diffusion of Ti is generally faster than V. The ternary main interdiffusion coefficients of \(\tilde{D}_{\text{TiTi}}^{\text{Co}}\) and \(\tilde{D}_{\text{VV}}^{\text{Co}}\) at different compositions of Ti and V at 1473 K were compared with the values obtained for boundary binary Co-Ti and Co-V systems in the literature. A composition-dependent decreasing-increasing tendency was found for \(\tilde{D}_{\text{VV}}^{\text{Co}}\).     

Gibbs Energy of Formation of MnO: Measurement and Assessment

Based on the measurements of Alcock and Zador, Grundy et al. estimated an uncertainty of the order of ±5 kJ mol⁻¹ for the standard Gibbs energy of formation of MnO in a recent assessment. Since the evaluation of thermodynamic data for the higher oxides Mn₃O₄, Mn₂O₃, and MnO₂ depends on values for MnO, a redetermination of its Gibbs energy of formation was undertaken in the temperature range from 875 to 1300 K using a solid-state electrochemical cell incorporating yttria-doped thoria (YDT) as the solid electrolyte and Fe + Fe_1 − δO as the reference electrode. The cell can be presented as

Phase Identification of Cu-In Alloys with 45 and 41.25 at.% In Compositions

In this work, the thermal stability of Cu-In alloys with 45.0 and 41.2 at.% In nominal compositions was investigated by differential scanning calorimetry (DSC), scanning electron microscopy, wavelength dispersive spectroscopy, and in-situ synchrotron x-ray powder diffraction (S-PXRD) over a temperature range from 25 up to 400 °C. The studied samples are mainly composed of a Cu₁₁In₉ phase together with minor amounts of the B phase (based on the NiAs-Ni₂In type structure) and, in one of the samples, with a minor amount of pure In. No evidence of the Cu₁₀In₇ (41.2 at.% In) phase was detected, not even in the sample with 41.2 at.% In nominal overall composition. The combined use of the S-PXRD and DSC techniques allowed us to identify two phase transitions involving the Cu₁₁In₉ phase, one of them corresponding to the $ \upeta^{\prime} \rightleftharpoons {\text{B}} + {\text{Cu}}_{11} {\text{In}}_{9} $ reaction at T = 290 °C and the other to the peritectic $ \upeta^{\prime} + {\text{L}} \rightleftharpoons {\text{Cu}}_{11} {\text{In}}_{9} $ reaction at T = 311 °C.     

Kinetics of Scheelite Conversion in Sulfuric Acid

Complete conversion of scheelite in H₂SO₄ solution plays a key role in exploration of cleaner technology for producing ammonium paratungstate. In this work, the factors influencing scheelite conversion were investigated experimentally to model its kinetics. The results indicated that the conversion rate increases with increasing temperature and reducing particle size, but is almost independent of stirring speed. Moreover, although the conversion rate increases with increasing initial H₂SO₄ concentration (≤ 1.25 mol/L), it decreases rapidly at 1.5 mol/L H₂SO₄ after 10 min due to formation of a H₂WO₄ layer. The experimental data agree quite well with the shrinking core model under chemical reaction control in ≤ 1.25 mol/L H₂SO₄ solution, and the kinetic equation was established as: \( 1- ( 1- \alpha )^{ 1 / 3} = 2 2 2 5 4 6. 6\cdot C_{{{\text{H}}_{ 2} {\text{SO}}_{ 4} }}^{ 1. 2 2 6} \cdot r_{ 0}^{ - 1} \cdot e^{{\frac{ - 3 9 2 6 0}{RT}}} \cdot t \) (t, min). This work could contribute to better understanding of scheelite conversion in H₂SO₄ solution and development of a new route for ammonium paratungstate production.     

On the Liquid/Solid Phase Equilibria in the Al-Rich Corner of the Al-Si-Ti Ternary System

The nature of liquid-solid phase equilibria in the Al-rich corner of the Al-Si-Ti system are determined by drawing three isothermal sections at 620, 680 and 727 °C. The solubility of Ti in Al-Si liquids is determined for four different compositions (0, 9, 13 and 18 at.%Si) at temperature below 800 °C. Combination of the two sets of experimental results leads to an attempt of liquidus projection. The primary crystallization surface of Al₃Ti is found to extend up to 9.5 at.%Si in the liquid phase at 620 °C and 11 at.%Si at 727 °C. The solubility of Ti is found to be not significantly dependent on the Si content of the liquid. From DSC measurements and deduction on microstructure, the last invariant reaction of the solidification path is found to be quasi-peritectic: ${\text{L}} + \uptau_{1} - {\text{Ti}}_{7} {\text{Al}}_{5} {\text{Si}}_{12} \Leftrightarrow {\text{Al}} + {\text{Si}} .$      

Crystal-Structure-Based Modeling Study of Temperature-Dependent Fracture Toughness for Brittle Coating Deposited on Ductile Substrate

The temperature-dependent fracture toughness of a brittle coating/ductile substrate system, WC-10Co4Cr deposited on 1018 low carbon steel, is evaluated at microscopic level using an indentation-based model in terms of the Arrhenius-type equation and rate-controlling theory. The formulation of the model utilizes the parameters of crystal structures of each phase in the coating material. The slip systems of hard hexagonal \( \updelta \)-WC phase and soft FCC \( \upalpha \)-Co phase are analyzed. The fracture toughness of the two-phase coating is obtained by integrating the fracture toughness of single \( \updelta \)-WC phase coating and that of single \( \upalpha \)-Co phase coating using either the basic mixture method or the unconstrained mixture method. The results suggest that the fracture toughness of WC-10Co4Cr coating/1018 low carbon steel substrate system may remain constant until the temperature reaches a critical value, about 200 K, and ranges from 2.16 to 10.82 \( {\text{MPa}}\;{\text{m}}^{1/2} \), with temperature increasing from room temperature (298 K) to 1000 K.     

Extended Hall–Petch Relationships for Yield,Cleavage and Intergranular Fracture Strengths of bcc Steel and Its Deformation and Fracture Behaviors

Extended Hall–Petch relationships for yield (\( \sigma_{y} \)), cleavage (\( \sigma_{\text{cl}} \)) and intergranular fracture (\( \sigma_{\text{ig}} ) \) strengths of pure iron have been established through the direct calculation of the proportional constant \( (k) \) and the estimation of the friction stress \( (\sigma_{0} ) \). The magnitude orders of \( k \) and \( \sigma_{0} \) are generally \( k_{y} < k_{\text{cl}} < k_{\text{ig}} \) and \( \sigma_{y0} < \sigma_{\text{cl0}} < \sigma_{\text{ig0}} \), respectively. Based on the Hall–Petch relationships, micro-yielding in a bcc steel occurs at the instance that the pile-up dislocations within a specific grain showing the Schmid factor of 0.5 propagate into the neighboring grain. The initial brittle crack is formed at the instance that the flow strength exceeds the brittle fracture strength. Once the brittle crack is formed, it grows catastrophically. Due to the smallest and \( k_{y} \) and \( \sigma_{\text{y0}} \), the cleavage and the intergranular fracture occur always after micro-yielding. The {100} cleavage fracture of the steel is due to the lowest theoretical {100} cleavage strength. Due to the thermal components included in cleavage and intergranular fracture strengths, they show also the temperature and strain rate dependence observed in yield strength. The increase in susceptibility to brittle fracture with decreasing temperature and increasing strain rate is due to the increase in dislocation density which causes the high work hardening rate.