Thermodynamics of titanium alloys: II. Titanium and aluminum activities in the Bcc β phase of the Ti-Al system

Thermodynamic activities have been measured at 1780°K in the bcc β phase of the Ti-Al system, using three vapor pressure techniques. The first technique utilized a conventional Knudsen cell configuration. The sample was placed in the cell and the ratio of the aluminum signal to the titanium signal was determined as a function of composition. The data were analyzed with the aid of a solid solution model and yielded the pairwise interaction parameter, Ω. The second technique also used a conventional Knudsen cell. Aluminum activity as a function of composition was determined by weight loss. The effects of composition changes or surface depletion during the experiment were accounted for by performing the experiment in a time-of-flight mass spectrometer (TOFMS) and monitoring the attenuation of the aluminum signal. The third technique utilized the “triple Knudsen cell”, consisting of two cells within a third cell. One inner cell contained the alloy of interest and the second isotopically-enriched pure titanium. Both effused into the outer cell which fed into the TOFMS. The instantaneous ratios of Ti⁴⁸ to Ti⁴⁶ measured by the mass spectrometer were then converted directly into activity values for the titanium. The results of this research indicate that at 1780°K when 0<X _Al <0.40, the partial molar free energies for titanium (relative to pure bcc titanium) and for aluminum (relative to liquid aluminum) can be expressed as follows:RT Ina _Ti=RT InX _Ti+X _Al ² (?12.4±0.8) in kcal per g-atomRT Ina _Al=RT InX _Al+X _Ti ² (?12.4±0.8)+(1.6±0.7) in kcal per g-atom     

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-Cr alloys using the mass spectrometer

The Knudsen effusion method was combined with a mass spectrometer sensing technique in order to determine thermodynamic interaction parameters of solid solution bcc alloys of V-Ti-Cr. A regular solution model was used to relate the vaporization data to ion current ratios obtained from the mass spectrometer. The temperature range of the vaporization experiments was 1400° to 1700°C, with alloy compositions ranging from 10 to 66 at. pct of each of the three components in the ternary system. Modified interaction parameters were calculated by assuming only binary interactions (which is a good approximation at low third component concentrations). The results are: Ω _TiV = 1.8 ± 0.2 kcal/g-atom; 0 <N _Cr < 0.2 ({iT} _AV = 1800 K) Ω _TiCr = 1.9 ± 0.4 kcal/g-atom; 0.1 <N _V < 0.4 ({iT} _AV = 1750 K) Ω _VCr = 3.1 ± 0.7 kcal/g-atom; 0.1 <N _Ti < 0.4 ({iT} _AV = 1850 K) A temperature dependent form was an appropriate refinement of the results for the Ti-Cr system from 1500 to 1840 K. That expression is $$\Omega {\text{ = 28 (1 - }}\frac{T}{{1840 K}}{\text{ kcal/g - atom}}$$ Overall, experimental results show important, but not complete, agreement with estimates from phase diagrams and theoretically calculated values.     

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.     

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     

The diffusion of hydrogen in liquid Ni,Cu, Ag,and Sn

The rates of absorption of hydrogen in stagnant liquid Ni, Cu, Ag, and Sn have been measured using 1) an unsteady-state gas-liquid metal diffusion cell technique similar to that used by El-Tayeb and Parlee for iron and 2) a steady-state diffusion cell technique recently developed in this laboratory. The rates of absorption are considered to be controlled by diffusion in the liquid. On this basis the chemical diffusion coefficients of hydrogen (D _H) in liquid Ni, Cu, and Ag, calculated from the rate data, can be described by:D _H ^Ni =7.47×10^?3 exp(?8550±1114/RT) cm²/secD _H ^Cu =10.91×10^?3 exp(?2148±349/RT) cm²/secD _H ^Ag =4.54×10^?2 exp(?1359±207/RT) cm²/sec In the above equations, the uncertainty in the activation energy (Q _H) corresponds to the 90 pct confidence level. No reliable Arrhenius equation could be obtained forD _H ^Sn , but theD _H values in tin are greater than for the other three metals. The following interesting and possibly significant correlations are observed betweenD _H,Q _H, and the hydrogen solubility (S _H):D _H ^Ni <D _H ^Fe <D _H ^Cu <D _H ^Ag <D _H ^Sn , andQ _H ^Ni >Q _H ^Fe >Q _H ^Cu >Q _H ^Ag , andS _H ^Ni >S _H ^Fe >S _H ^Cu >S _H ^Ag >S _H ^Sn .     

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.     

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.     

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.     

The Equilibrium Between Titanium Ions and Titanium Metal in NaCl-KCl Equimolar Molten Salt

The equilibrium between metallic titanium and titanium ions, 3Ti²⁺ ? 2Ti³⁺ + Ti, in NaCl-KCl equimolar molten salt was reevaluated. At a fixed temperature and an initial concentration of titanium chloride, the equilibrium was achieved by adding an excess amount of sponge titanium in assistant with bubbling of argon into the molten salt. The significance of this work is that the accurate concentrations of titanium ions have been obtained based on a reliable approach for taking samples. Furthermore, the equilibrium constant   $ {\text{K}}_{\text{C}} = (x_{{{\text{Ti}}^{{ 3 { + }}} }}^{\text{eql}} )^{3} /(x_{{{\text{Ti}}^{{ 2 { + }}} }}^{\text{eql}} )^{2} $ K C = ( x Ti 3 + eql ) 3 / ( x Ti 2 + eql ) 2 was calculated through the best-fitting method under the consideration of the TiOCl dissolution. Indeed, the final results have disclosed that the stable value of K_C could be achieved based on all modifications.     

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.     

The crystal structures of Hf3N2 and Hf4N3

The crystal structures of ε-Hf₃N₂ and ζ-Hf₄N₃ were determined from X-ray powder photographs. The structure of both phases is trigonal, space group D ₅ ^3d -R?3m, with unit cells ofa _R = 7.972Å, α= 23 deg 12 min (hexagonal axes:a = 3.206Å,c = 23.26Å) for ε-H₃H₂, and a_R= 10.54Å, α = 17 deg 32 min (hexagonal axes:a = 3.214Å,c = 31.12Å) for ζ-Hf₄N₃. The nine close packed metal layers in ε-Hf₃N₂ are stacked according to (hhc)₃, or ABABCBCAC. The structure of ζ-Hf₄sN₃, isomorphous with ζ-V₄C₃,¹ consists of twelve close-packed metal layers in a stacking sequence (hhcc)₃. The nitrogen atoms occupy octahedral interstices in the metal lattice. The experimentally observed compositions, Hf₃N₁.₆₉ and Hf₄N₂.₅₆, shows both phases to be substantially deficient in nitrogen. ε-Hf₃N₂ is unstable above 2000°C, and ζ-Hf₄N₃ above 2300°C.     

A mass-spectrometric study of the thermodynamics of the Fe−Cu and Fe−Cu−C(sat) systems at 1600°C

The Knudsen cell-mass spectrometer combination has been used to study the Fe?Cu and Fe?Cu?C_(sat) alloys at 1600°C. Activity coefficients in the Fe?Cu system are closely represented by the equations $$\begin{gathered} \ln \gamma _{Fe} = 1.86N_{Cu}^2 + 0.03, (0< N_{Fe}< 0.7) \hfill \\ \ln \gamma _{Cu} = 2.25N_{Fe}^2 - 0.19, (0.7< N_{Fe}< 1.0) \hfill \\ \end{gathered} $$ with an uncertainty in the quadratic terms of about 5 pct. For the iron-rich carbon-saturated alloys, the activity coefficient of copper is given by the equation $$\ln \gamma _{Cu} = 2.45(N'_{Fe} )^2 + 0.3N'_{Fe} + 0.03, (0< N'$$ to within an uncertainty of about 10 pct. N _Fe ^′ represents the fraction N_Fe/(N_Fe+N_Cu), etc. The activity coefficient of iron in this region is found to be essentially constant at 0.69±0.05.     

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).     

Solubility of hydrogen in liquid Fe−Co−Ni alloys

The solubility of hydrogen in the Fe−Co−Ni ternary has been determined by the Sieverts' method over the temperature range 1500° to 1700°C. The solubility of hydrogen at 1600°C and 1 atm hydrogen pressure is 0.00264 wt pct in iron, 0.00224 wt pct in cobalt, and 0.00448 wt pct in nickel. Hydrogen follows Sieverts' law for all alloy compositions. The solubility surface rises smoothly from the Fe−Co binary to the nickel corner of the ternary, and when expressed as the free energy of hydrogen solution the surface is planar. The enthalpy of hydrogen solution is 8.0 kcal per g-atom H in iron, 8.5 kcal per g-atom H in cobalt, and 5.2 kcal per g-atom H in nickel and is planar for the entire ternary. Interaction parameters with hydrogen for Al, Cu, and Mn were established: ɛ _H ^Al =2.0, ɛ _H ^Cu , and ɛ _H ^Mn and are constant for the entire Fe−Co−Ni ternary. This paper is based on a portion of a thesis submitted by R. G. BLOSSEY in partial fulfillment of the requirements for the degree of Doctor of Philosophy at The University of Michigan.     

Nitrogen solubility in liquid Fe-V and Fe-Cr-Ni-V alloys

Nitrogen solubility in liquid Fe, Fe-V, Fe-Cr-V, Fe-Ni-V and Fe-18 pct Cr-8 pet Ni-V alloys has been measured using the Sieverts’ method for vanadium contents up to 15 wt pct and over the temperature range from 1775 to 2040 K. Nitrogen solution obeyed Sieverts’ law for all alloys investigated. Nitride formation was observed in Fe-13 pet V, Fe-15 pet V and Fe-18 pet Cr-8 pet Ni-10 pet V alloys at lower temperatures. The nitrogen solubility increases with increasing vanadium content and for a given composition decreases with increasing temperature. In Fe-V alloys, the nitrogen solubility at 1 atm N₂ pressure is 0.72 wt pet at 1863 K and 15 pct V. The heat and entropy of solution of nitrogen in Fe-V alloys were determined as functions of vanadium content. The first and second order interaction parameters were determined as functions of temperature as: $$e_N^V = \frac{{ - 463.6}}{T} + 0.148 and e_N^{VV} = \frac{{17.72}}{T} - 0.0069$$ The effects of alloying elements on the activity coefficient of nitrogen were measured in Fe-5 pet and 10 pet Cr-V, Fe-5 pet and 10 pet Ni-V and Fe-18 pet Cr-8 pct Ni-V alloys. In Fe-18 pet Cr-8 pet Ni-10 pet V, the nitrogen solubility at 1 atm N₂ pressure is 0.97 wt pet at 1873 K. The second order cross interaction parameters, e _N ^Cr,V and e _N ^Ni,V , were determined at 1873 K as 0.00129 and ? 0.00038 respectively.     

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.     

Thermodynamics of the Fcc Fe−Ni−C and Ni−C alloys

The activity of carbon in the fcc solid solution of the Fe?Ni?C system has been measured at 800°, 1000°, and 1200°C by comparison with observed values in the Fe?C binary by equilibration with methane-hydrogen mixtures. Defining the lattice ratioz _C≡n _C/(n _Fe+n _Ni?n _C), the activity coefficient Ψ_C≡a _C/z _C has been determined as a function of temperature and composition. At infinite dilution log Ψ_C goes through a maximum at about 70 pct Ni in agreement with Smith. The partial molar free energy of carbon in the dilute solution referred to graphite is not a linear function of the base alloy composition, but has a large deviation with maximum at about 60 pct Ni. Similar maxima occur in both ΔH _C ^° and ΔS _C ^° . Linear equations are derived for the activity coefficient of carbon in three composition ranges of Fe?Ni?C alloys; a simplified equation applicable to nickel steels is included. The solubility of graphite in nickel has been determined. The marked deviation from linearity is ascribed to the existence of iron atoms in two electronic states, γ₁ and γ₂ which differ in energy and are antiferromagnetic and ferromagnetic, respectively.     

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.