High-temperature diffusion of hydrogen in zirconium, niobium, and tantalum

The diffusion coefficients of hydrogen in refractory metals D _H ^M are of interest for the theory of liquid metals at the temperatures close to their melting points and in the liquid state. These coefficients are useful for the purification and manufacture of membranes designed for hydrogen purification. The D _H ^M data for Zr, Nb, and Ta are systematized. Molecular dynamics simulation is applied to calculate D _H ^M diffusion coefficients for these molten metals. An analysis of Arrhenius equations for D _H ^M and their extrapolation to the premelting range with allowance for the Gorsky effect is used to estimate D _H ^M in the temperature range where an experiment is difficult to perform.     

Interaction coefficients in Fe-C-Ti-i (i = Si,Cr, AI,Ni) systems

Ever since Schroeder and Chipman_[10] initiated the application of the silver bath iso-activity method to the study of activity interaction coefficients of components in iron alloys, the method was only applied to some ternary systems in which only one component dissolves in both liquid iron and liquid silver. The authors of the present work proposed a method which enables the silver bath iso-activity method to be utilized to study the activity interaction coefficients of two components simultaneously dissolvable in both liquid iron and liquid silver by establishing an iso-i-j-activity state for several Fe-C-i-j quarternary samples through a common silver bath. This new “quarternary silver bath iso-activity method” was applied to quarternary Fe-C-Ti-i (i = Si,Cr, Al,Ni) melts at 1600 °C and estimated the activity interaction coefficients as follows: ε _Ti ^¡ = 7.96, ρ _Ti ^¡ = ?6.88, ρ _si ^Ti = 0.51, ρ _Ti ^Ti,si = ?2.27, ρ _Ti ^Ti,si = ?5.66 ε _Ti ^? = 3.46, ρ _Ti ^? = 10.43, ρ _Ti ^Cr,Ti = 17.40 ε _Ti ^Al = 0.93, ρ _Ti ^? = 10.22, ρ _Ti ^Al,Ti = 25.11 ε _Ti ^Ni = 2.49, ρ _Ti ^Ni = 9.33, ρ _Ti ^Ni,Ti = 16.37     

Self-diffusion in substitutional solid solutions with Fcc lattice

With the use of the results from the previous paper¹ and from the papers of the other authors it has been ascertained that in some solid solutions with fcc lattice the self-diffusion frequency factorD _oAB ^A and activation enthalpy ΔH _AB ^A of the element A in the alloy A-B are given by the equations , whereK ₀,K ₁ are constants,T _m andT _m A are melting points of the alloy or of element A respectively,X _B is the atomic percent of element B,D _{o A} ^A and ΔH _A ^A are diffusion characteristics of the pure element A. For the frequency factor of regular or nearly regular solid solutions with fcc lattice that present a mutual solubility and for which the diffusion data for the whole concentration interval are available, the following relation has been found For the activation enthalpy of these solutions the equation $$\Delta H_{AB}^A = {{T_m } \over {100}}\left[ {{{\Delta H_A^A } \over {T_{mA} }}X_A + {{\Delta H_B^A } \over {T_{mB} }}X_B } \right]$$ is satisfied, whereD _oB ^A and ΔH _B ^A are the characteristics of heterodiffusion of element A in element B andT _m B is the melting point of element B.     

Hydration effects in quaternary amine extraction systems

The extraction of Al⁺⁺⁺, Cd⁺⁺, Co⁺⁺, Cu⁺, Cu⁺⁺, Fe⁺⁺, Fe⁺⁺⁺, In⁺⁺⁺, Ni⁺⁺, and Zn⁺⁺ with quaternary amine was studied using chloride and sulfate as ligands. On the basis of loading experiments and slope analyses, the species extracted were: CdCl ₄ ⁼ , CoCl ₄ ⁼ , CuCl ₂ ^? , CuCl ₄ ⁼ , FeCl ₄ ^? , and ZnCl ₄ ⁼ . Water content of the organic phase was analyzed as a function of loading by Karl Fischer titration. These experiments indicate that unhydrated complex ions are extracted by amine.     

Thermodynamic properties of dilute solutions of oxygen in liquid Fe−Co and Fe−Ni systems

Ther modynamic properties of oxygen in liquid Fe?Co and Fe?Ni binary mixtures have been investigated by equilibration with appropriate mixtures of H₂ and H₂O. The results show that Henry's law is obeyed by dissolved oxygen at all the possible concentrations of oxygen in each binary mixture. The standard Gibbs energy of solution of oxygen ΔG _Q ^° has been presented as a function of temperature for various binary compositions. The variation of ΔG _Q ^° with composition at 1550°C for each system follows a theoretical correlation based on a new treatment of the first approximation to the regular solutions.     

Structure and Properties of Ferrites Based on CuFe2O4

We have studied the magnetic and structural properties of the solid solutions M _x ²⁺ Cu _1?x ²⁺ Fe ₂ ³⁺ O₄, where M = Mg, Ni, Co, Zn, Mn, Me _0.5x ⁺ Cu _1?x ²⁺ Fe _2+0.5x ³⁺ O₄, were Me = Li, Cu, and (Mn₃O₄)_x(CuFe₂O₄)_1?x. We have developed a new method for detecting a tetragonal phase and have used this method to determine the range of existence for solutions with a tetragonal structure. We explain the dependence of these ranges on the nature of M and Me.     

Ternary diffusion: The (2~D) matrix of an ideal solid solution

The elements (~D _ik ³ ) of the (²~D) matrix of an interdiffusing ideal ternary solid solution have been determined for Manning’s random alloy model, and the relationships among the elements and the tracer diffusion coefficients (D_i*’s) of the atom species have been examined. It is shown that for physically realistic choices of tracer diffusion coefficients a quasi-linear relationship exists between the ~D _ik ³ of the ith atom species and its atom fraction over the entire composition triangle. It is also, shown that a ~D _ii ³ diagonal element will never be negative for any physically realistic values of the D_i*’s. Finally, the implications of the equality ~D ₂₂ ³ = ~D ₂₂ ³ are demonstrated.     

Thermodynamics of titanium alloys: I. Development of a triple Knudsen cell and its use to study the activity of copper in the Ti−Cu system

A new experimental technique for the determination of thermodynamic activity of alloys has been developed utilizing a triple Knudsen cell with a pure enriched natural isotope as the standard reference state. The alloy for which activity is to be determined is placed in one of the two effusion chambers of the triple cell and the pure isotopic standard in the other. The molecular beams from each chamber effuse into a third upper chamber and through a collimating hole into the ion source of a Bendix time-of-flight mass spectrometer. Since the recorded intensities are proportional to the vapor pressures within the chambers, a simple calculation based upon their ratio gives a direct determination of the activity of the solute in the alloy. The accuracy of the triple cell technique for the experimental determination of activities was checked by the measurement of the copper activity in a Ni?Cu alloy containing 30.6 wt pct Cu. A value ofRT γ_Cu=1778±142 cal per g-atom at 1450°K was obtained, which is in excellent agreement with values in the literature. The activity of copper in the bcc β phase when then determined for four Ti?Cu alloys (X _Cu=0.033 to 0.085), using pure enriched Cu⁶⁵ as the standard reference state. The composition range investigated was limited to alloys belowX _Cu=0.10, the maximum solubility within the experimental temperature range between 1423° and 1573°K, the activity of copper in the bcc β phase can be expressed using pure liquid copper as the standard state by the following equation:RT Ina _Cu=RT InX _Cu+X _Ti ² (1.92±0.30) in kcal per g-atom. The activity of titanium is given byRT Ina _Ti=RT InX _Ti+X _Cu ² (1.92±0.30) in kcal per g-atom.     

Determination of thermodynamic interaction parameters in solid V-Ti alloys using the mass spectrometer

The Knudsen effusion method was combined with a mass spectrometer sensing technique in order to measure thermodynamic quantities of solid solution alloys of V-Ti binary system. The technique makes use of the regular solution model in order to treat the vaporization data in terms of ion current ratios obtained from the mass spectrometer. Within the experimental temperature range of 1500° to 1725°C and the composition range of 0.10 <N _Ti<0.90, the activity of titanium in the bcc (β) phase relative to pure titanium for the binary alloy is:RT lna _Ti=RT lnN _Ti+N _V ² (1.82±0.13) kcal per g-atom while the activity of vanadium is:RT lna _V=RT lnN _V+N _Ti ² (1.82±0.13) kcal per g-atom. The experimental result on the pairwise interaction parameter agrees well with the theoretically calculated value.     

Influence of carbon concentration and reaction temperature upon bainite morphology in Fe-C-2 Pct Mn alloys

Isothermal transformation of austenite to bainite was studied by optical, replication, and thin foil transmission electron microscopy (TEM) in both hypo- and hypereutectoid Fe-C-2 wt pct Mn alloys (and a single 3 pct Mn alloy) containing from 0.1 to 1.37 wt pct C in order to characterize and explain the transitions which occur in bainite morphology as a function of carbon content and reaction temperature. A “morphology map” was constructed showing the temperaturecarbon composition(T-x) regions in which four different bainite morphologies predominate: upper bainite, lower bainite, nodular bainite, and inverse bainite. Calculations of the volume free energy changes associated with the nucleation of ferrite, ?G _v ^α , and cementite, ?G _v ^c , and the parabolic rate constant for growth of ferrite, α_α, and cementite, α_c, were performed in order to explain the observed morphological transitions. In hypoeutectoid alloys, where |?G _v ^α | ? |ΔG _v ^c | and α_α ? α _c , the Widmanstätten ferrite-dominated morphologies of upper and lower bainite predominate. The upper-to-lower bainite transition appears to be associated with the emergence of edge-to-face sympathetic nucleation at high values of |ΔG _v ^α |. In hypereutectoid alloys, the ratios ΔG _v ^α /ΔG _v ^c and α_α/α_c are considerably smaller; hence, cementite can compete much more readily with ferrite during both nucleation and growth, resulting in the formation of nodular bainite. With decreasing temperature in the hypereutectoid regime,ΔG _v ^α /ΔG _v ^c , and especially α_ga/α_c, increase, resulting in the replacement of nodular bainite by lower bainite at temperatures below about 250 °C to 275°C.     

A thermodynamic study of the molten Pb-Sn-Ag system

Activity and partial free energy of mixing of tin in the molten Pb-Sn-Ag system were determined at 1073 K along three pseudobinary lines of fixedX _Ag/X _Pb ratios by the electromotive force method. The cell employed was Sn(l), SnO₂(s)/Calcia stabilized zirconia/Sn(alloy), SnO₂(s). Excess integral free energy of mixing (F _ter ^E ) and the activities of lead and silver were calculated by the Darken’s method. The values when extrapolated toX _Sn=0 agreed reasonably well with the literature data on the Pb-Ag binary. Error analysis revealed that the inconsistencies in the reported data arose as a result of the uncertainties inherently present in the integration and differentiation steps. A crosscheck onF _ter ^E corroborated the above observation.F _ter ^E were also calculated from the data on the bounding binaries by the method of Olson and Toop. Except in the silver-rich corner the predicted values were within 50 calories of those obtained from the experimental data.     

On the thermodynamics of oxygen in molten copper,Cu-Sn,and Cu-Ag alloys

Measurements of oxygen activity in molten copper, Cu-Sn, and Cu-Ag alloys at 1135°C have been made utilizing the solid-state electrolyte technique. The activity coefficient of oxygen in molten copper at low oxygen levels (<0.1 pet) was found to be 0.12. The interaction parameters of silver and tin on oxygen were found to be ε _O ^Ag = 4.52 and ε _O ^Sn =-10.5. Comparison of experimental data with solution models revealed that the behavior of oxygen in Cu-O-Ag alloys is in accordance with predictions of Alcock and Richardson’s quasichemical model when a coordination number between 1 and 4 is assumed, depending on the silver and oxygen content. Furthermore, agreement with Belton’s quasichemical model based on the assumption of Ag-O dipoles serves to strengthen the evidence for the existence of Ag-O species in solution. The behavior of oxygen in the Cu-O-Sn system also shows better agreement with the quasichemical model than with the random model, with low coordination numbers favored in dilute tin solutions, increasing to larger values in Cu-60 Sn solutions.     

Activity coefficient of titanium in iron-based melts under nitride formation/dissolution conditions

The initial parameters for calculating the activity coefficients of titanium in complex iron-based melts are determined. For this purpose, multiple regression analysis of 311 experimental results obtained by independent researchers is used. As a result, the initial parameters for calculating the activity coefficients of titanium (γ _Ti,1873 ^∞ = 0.059, its temperature dependence logγ _Ti ^∞ = ?14900/T + 6.73) and the temperature dependences of interaction parameters e _Ti ^j and r _Ti ^j are refined. The found value of γ _Ti,1873 ^∞ agrees with the results of a number of earlier investigations and is significantly higher than the values recommended in the most widely used handbooks. The application of the found parameters for calculating the nitrogen concentrations in equilibrium with TiN in the melts decreases the mean deviation of the calculated data from the experimental results to a level of at most ±13%, which is much better than in the case of using the data from the most widely used handbooks.     

The thermodynamics of stress-induced martensites in Cu Al Ni alloys

Stress-induced martensitic transformations have been studied in Β₁ Cu Al Ni single crystals in which two martensite crystal structures can form, Β _i ^′ and γ′. By straining specimens at one temperature and releasing the strain at either the same temperature or a different temperature, stresses corresponding to the transitions Β₁ ? Β _i ^′ ,Β ₁ ? γ′,Β _i ^′ ? γ′ could all be measured. This enabled a quantitative stress-temperature diagram to be drawn, giving the stability ranges of the Β₁,Β _i ^′ and γ′ phases. The slope of the stress-temperature lines separating the different phases enabled the value of the entropy changes for the transformations to be calculated. This was very small for theΒ _i ^′ → γ′ transformation (0.08 J/mole K) and much larger for the Β₁ →Β _i ^′ and Β₁ → γ′ transformations (-1.21 and -1.4 J/mole K, respectively). The hysteresis between the forward and reverse transformations enabled evaluation of the critical free energy for transformation. This was small for the Β₁ → Β _i ^′ transformation (-2.9 J/mole), and large for the Β₁ → γ′ and Β _i ^′ → γ′ transformations (-28 and -29 J/mole respectively).     

Self-diffusion of copper in Cu−Al solid solutions

Self-diffusion coefficients of copper in Cu?Al solid solutions in the concentration interval 0 to 19 at. pct Al and in the temperature range 800° to 1040°C have been determined by the residual activity method using the isotope Cu⁶⁴. The values of the self-diffusion coefficients in the concentration interval 0 to 14.5 at. pct Al satisfy the Arrhenius relation and their temperature dependence can be expressed by the following equations $$\eqalign{ & D_{Cu}^{Cu} = \left( {0.43_{ - 0.11}^{ + 0.15} } \right) exp \left( { - {{48,500 \pm 700} \over {RT}}} \right) cm^2 /\sec \cr & D_{Cu - 2.80 at. pct Al}^{Cu} = \left( {0.46_{ - 0.16}^{ + 0.23} } \right) exp \left( { - {{48,000 \pm 900} \over {RT}}} \right) cm^2 /\sec \cr & D_{Cu - 5.50 at. pct Al}^{Cu} = \left( {0.30_{ - 0.07}^{ + 0.09} } \right) exp \left( { - {{47,000 \pm 600} \over {RT}}} \right) cm^2 /\sec \cr & D_{Cu - 8.83 at. pct Al}^{Cu} = \left( {0.46_{ - 0.09}^{ + 0.11} } \right) exp \left( { - {{47,100 \pm 500} \over {RT}}} \right) cm^2 /\sec \cr & D_{Cu - 11.7 at. pct Al}^{Cu} = \left( {0.61_{ - 0.13}^{ + 0.17} } \right) exp \left( { - {{47,200 \pm 600} \over {RT}}} \right) cm^2 /\sec \cr & D_{Cu - 14.5 at. pct Al}^{Cu} = \left( {4.2_{ - 1.5}^{ + 2.2} } \right) exp \left( { - {{51,110 \pm 1000} \over {RT}}} \right) cm^2 /\sec \cr} $$ An analysis of the results leads to the conclusion that, in the concentration interval 0 to 11.7 at. pct Al, the frequency factor and activation enthalpy concentration dependences can be described by the following equations whereD _0Cu ^Cu and ΔH _Cu ^Cu are diffusion characteristics for self-diffusion in pure copper,X _Al is the atomic percent of aluminum, andK andB are experimental constants.     

Effect of the overheating of the gallium melt on its supercooling during solidification

The effect of overheating ΔT _L ⁺ of the gallium melt on its supercooling ΔT _L ^? during solidification is studied by cyclic thermographic analysis. The obtained data on ΔT _L ^? are used to calculate the thermodynamic and kinetic characteristics of gallium solidification.     

Determination of diffusion coefficient of oxygen in γ-iron from measurements of internal oxidation in Fe-Al alloys

The internal oxidation of iron alloys containing between 0.069 and 0.274 wt pct aluminum was investigated in the temperature range from 1223 to 1373 K for the purpose of determining the diffusion coefficients in γ-iron as well as in the internal oxidation layer. A parabolic rate law is obeyed in the internal oxidation of the present alloys. The rate constant for penetration of the oxidation front, the oxide formed, and the concentration of aluminum in the oxidation layer were determined. Pronounced enrichment of aluminum in the oxidation layer was observed, resulting from the counterdiffusion of aluminum. The oxygen concentration at the specimen surface was determined by combining the thermodynamic data on the dissociation of FeO and the solution of oxygen in y-iron. The diffusion coefficient of oxygen in the internal oxidation layer,D _o ¹⁰ , was evaluated on the basis of the rate equation for internal oxidation.D _o ¹⁰ increases at a given temperature as the volume fraction of oxide,f ¹⁰, in the oxidation layer increases. The diffusion coefficient of oxygen in γ-iron,D _o, was determined by extrapolation ofD _o ¹⁰ = 0.D _o may be expressed as $$D_o = \left( {1.30\begin{array}{*{20}c} { + 0.80} \\ { - 0.50} \\ \end{array} } \right) \times 10^{ - 4} \exp \left[ { - \frac{{166 \pm 5(kJ \cdot mol^{ - 1} )}}{{RT}}} \right]m^2 \cdot s^{ - 1} .$$ D _o is close to the diffusion coefficients of carbon and nitrogen in γ-iron.     

Activities in liquid Fe−Al−O and Fe−Ti−O alloys

The solubility and activity of oxygen in Fe?Al and Fe?Ti melts at 1600°C were measured. The activity was measured electrochemically using the following galvanic cells: Cr-Cr₂O₃(s) ? ThO₂(Y₂O₃) ? Fe-Al-O(l), Al₂O₃(s) Cr-Cr₂O₃(s) ? ThO₂(Y₂O₃) ? Fe-Ti-O(l, saturated with oxide) Cr-Cr₂O₃(s) ? ZrO₂(CaO) ? Fe-Ti-O(l, saturated with oxide) Aluminum and titanium decrease the solubility of oxygen in liquid iron to a minimum of 6 ppm at 0.09 wt pct Al and 40 ppm at 0.9 wt pct Ti, respectively. The value of the interaction coefficients ε ₀ ^(Al) and ε ₀ ^(Ti) are ?433 and ?222, respectively. the activity coefficient of aluminum at infinite dilution in liquid iron is 0.021, while that of titanium is 0.038. The value of the aluminum equilibrium constant, the solubility product at infinite dilution, is 5.6×10^?14 at 1600°C. The ThO₂(Y₂O₃) electrolyte exhibited insignificant electronic conductivity at 1600°C down to oxygen partial pressures of 10^?15 atm, which corresponds to about 0.3 ppm O in unalloyed iron.