Computer-aided thermodynamic study of solid Co---Pd alloys by Knudsen cell mass spectrometry, and calculation of the phase diagram

F.c.c. solid Co---Pd alloys have been investigated thermodynamically by means of computer-aided Knudsen cell mass spectrometry. Thermodynamic evaluation has been performed by applying the “digital intensity ratio” method. The thermodynamic excess properties can be described algebraically by means of thermodynamically adapted power series with two adjustable parameters, i.e. C₁^G (−20 810 + 9.608T) J mol⁻¹) and C₂^G (−30 720 + 6.78T) J mol⁻¹). At 1470 K, f.c.c. solid Co---Pd alloys are characterized by negative molar excess Gibbs energies G^E, exothermic molar heats of mixing (H^E) and small negative molar excess entropies S^E. At 1470 K, the minimum G^E value is −4600 J mol⁻¹ (61.9 at.% Pd), the minimum H^E value is −9400 J mol⁻¹ (59.5 at.% Pd) and the minimum S^E value is −3.3 J mol⁻¹ K⁻¹ (55.9 at.% Pd). The thermodynamic activities of Co show small positive deviations from the ideal case for the Co-rich alloys (x_Pd < 0.34), and negative deviations from Raoults' law for alloys with higher Pd contents. The Pd activities a_Pd show negative deviations from the ideal case for all compositions. The phase diagram has been computed by means of a generally applicable procedure for the calculation of the equilibrium compositions of coexisting phases. This was achieved using the results of this work, thermodynamic data from earlier mass spectrometric studies on the liquid phase, and literature data for the heat capacities and enthalpies of Co and Pd.     

Calorimetric measurements on some undercooled metals and alloys

Undercooling was achieved directly in the cell of a high temperature calorimeter (Setaram HTDSC) for Ni, Fe, Cu, Pd and several alloys, using cooling rates between 1 and 15 K min⁻¹. The samples were immersed in alumina powder inside a standard alumina crucible under flowing helium. Ag, Au and Al were not undercooled significantly. The reproducibility of the measurements was within 1.5%. The heat of solidification of Ni at an undercooling of ΔT = 220 K was −17.5 ± 0.2 kJ mol⁻¹, which is the same absolute value of the heat of fusion at the equilibrium melting point T_m. This implies that the specific heat of the undercooled liquid is very close to that of the crystalline solid in this temperature range. Fe appears to display a similar behavior at ΔT = 220 K. The difference between the heat of fusion at T_m and the heat of solidification at an average value of ΔT = 95 K is significant for a Pd_77.5Cu₆Si_16.5 glass-forming alloy. From these data, we calculated an average specific heat difference between the liquid and crystal phases of 7 ± 5 J mol⁻¹ K⁻¹. The enthalpy data for Pd₈₂Si₁₈ comply with those of the ternary Pd---Cu---Si.     

The limiting molar partial enthalpies of mixing of iron, cobalt, nickel, palladium and platinum in liquid gallium and indium

Gallium and indium have been used as solvents for the determination of the molar partial enthalpy of mixing Δ_mixh_m^o(TM, Ga or In) (denoting liquid transition metal (TM) in infinite liquid gallium or indium) of the pure liquid transition metals Fe, Co, Ni, Pd and Pt by direct reaction calorimetry between 1000 K and 1500 K with the exception of Δ_mixh_m^o(Fe, In) (because of the shape of its equilibrium phase diagram). All the limiting enthalpies listed below refer to the liquid state. With pure gallium as solvent, they correspond to the reaction

TM(liq) − nGa(liq) → TM₁Ga_n(liq)

at the experimental temperature T_e, with n 1.

1. (i) Δ_mixh_m^o in gallium is found for Fe, Co, Ni, Pd and Pt to be −2, −44, −82, −144 and −155 kJ mol⁻¹.

2. (ii) Δ_mixh_m^o in indium is found for Co, Ni, Pd and Pt to be +28, −25, −127 and −114 kJ mol⁻¹.

In both solvents, these limiting enthalpies vary with a similar trend. This observation makes it possible to predict the limiting molar partial enthalpy Δ_mixh_m^o(Fe, In) of mixing of iron in indium as +70 kJ mol⁻¹. The results have been compared with the data proposed by Miedema and co-workers.     

Calorimetric study of maltitol: correlation between fragility and thermodynamic properties

The heat capacity of maltitol was measured with an adiabatic calorimeter. The crystalline form was measured from 100 to 425 K (T_m=420 K), the glass form from 249 K to T_g (around 311 K) and the liquid form from T_g to 400 K. The heat of melting is 55.068 kJ mol⁻¹. The calorimetric glass transition occurs at about T_g=311 K with a sudden jump of the heat capacity ΔC_p(T_g) of about 243.6 J mol⁻¹ K⁻¹. The excess entropy between the under-cooled liquid and the crystal was calculated from the heat capacity data and was used to estimate the Kauzmann temperature T_K, which was found to be 50 K below T_g. ΔC_p(T_g) and T_K values for maltitol were compared with those of other compounds such as sugars, polyols and hydrogen-bonded liquids. It was found that the glass former maltitol is a ‘fragile’ liquid from the thermodynamic point of view.     

Molar enthalpies of formation of BaCmO3 and BaCfO3

The enthalpies of solution of BaCmO₃ and BaCfO₃ in 1.00 mol dm⁻³ HClO₄ were measured at 298.15 ± 0.05 K and p° = 101.325 kPa as −(345.3±4.7) and −(347.2 ± 1.9) kJ mol⁻¹, respectively. The resulting standard molar enthalpies of formation, Δ_fH_m°(BaCmO₃, cr) = −(1517.8 ± 7.1) kJ mol⁻¹ and Δ_fH_m°(BaCfO₃, cr) = −(1477.9 ± 5.6) kJ mol⁻¹, together with other corresponding experimental values for several lanthanide, actinide and transition metal complex oxides with barium and strontium, are used to estimate the molar enthalpies of formation of a number of homologous actinide compounds. The present results also provide additional information on the standard molar enthalpy of formation of CfO₂ and on the Cf⁴⁺/Cf³⁺ standard potential.     

Calorimetric investigation on the Pb---Sm and Sn---Sm alloys

The integral enthalpy of formation of the Sm---Pb and Sm---Sn melts at 1203 K, h^f, was determined by direct reaction calorimetry (drop method) in the Pb and Sn rich sides with the help of a high-temperature Tian-Calvet calorimeter. The results can be fitted respectively with reference to the mole fraction of samarium, x, as follows:

h^f/kJ mol⁻¹=x(1−x)(−109.8−372.0.7x) with0> X_Sm >0.27

and

h^f/kJ mol⁻¹=x(1−x)(−277.0−105.4.x) with0> X_Sm >0.27

for the Sm---Pb and Sm---Sn melts respectively. They yield the following partial enthalpies of samarium at infinite dilution: −109.8 and −277.0 kJ mol⁻¹ respectively.

Such negative values suggest the existence of a strong short-range order in the liquid state. The stoichiometry and the thermal stability of these associations needs additional thermodynamic determinations concerning mainly the free enthalpy of formation. It will be determined by Knudsen-effusion combined with mass spetrometry in a further work.     

Lanthanide(III) halides: Thermodynamic properties and their correlation with crystal structure

Temperatures and enthalpies of phase transitions of 17 lanthanide(III) halides determined experimentally are reported. Correlations were made between temperature of fusion of lanthanide(III) halides, on the one hand, and enthalpy of fusion, on the other, versus atomic number of lanthanide. According to this classification, the lanthanide(III) halides split into groups, as also do the corresponding crystal structures. A correlation between the crystal structure of lanthanide(III) halides and their respective entropy of fusion (or entropy of fusion + entropy of solid–solid phase transition) was inferred from the aforementioned features. Fusion in those halides with hexagonal, UCl₃-type and orthorhombic, PuBr₃-type, structures entails an entropy of fusion change (or entropy of fusion + entropy of solid–solid phase transition change) by 50 ± 4 J mol⁻¹ K⁻¹. The homologous entropy change within the group of halides having the rhomboedric, FeCl₃-type, structure, is smaller and equals 40 ± 4 J mol⁻¹ K⁻¹. Halides with monoclinic, AlCl₃-type, crystal structure constitute a third group associated to an even smaller entropy change upon fusion, only 31 ± 4 J mol⁻¹ K⁻¹. The halides with lower entropies of fusion also have a lower S_1300 K − S_298 K indicating either a higher degree of order in the liquid or a higher entropy in the solid at room temperatures.     

The determination of the enthalpy of formation and the enthalpy increment of Cd0.5Te0.5 by Calvet calorimetry

The enthalpy of formation of Cd_0.5Te_0.5(s) has been determined using a Calvet calorimeter at 785 K by direct reaction calorimetry. The heat changes were measured for the additions of Cd(s) or Te(s) from 298 K to a reaction crucible containing the other liquid metal at 785 K. Measurements were also carried out to determine the enthalpy changes due to the direct reaction of the Te(l) and Cd(l) at 785 K. The enthalpies of formation of Cd_0.5Te_0.5 calculated from the two sets of experiments were in agreement. The H_T°---H₂₉₈° values of the Cd_0.5Te_0.5 compound have also been determined in the temperature range 406–826 K by the drop method. Using ΔH_fm° at 785 K and H_T---H₂₉₈° values of Cd_0.5Te_0.5, ΔH_fm° at 298 K was determined to be −(50.349±0.510) kJ mol⁻¹.     

Isotope effects on hydrogen absorption by Pd–4at.%Pt alloy

Isotope effects on hydrogen absorption were investigated for a Pd–4at.%Pt alloy by using a high vacuum microbalance. The absorption kinetics were well explained by a model assuming comparative contributions of the dissociative adsorption and associative desorption on the surface, and the diffusion into the bulk. The activation energies for adsorption were determined to be 29.1 and 32.8 kJ mol⁻¹(H₂, D₂) for protium and deuterium, respectively. The activation energies for desorption were 48.1 kJ mol⁻¹(H₂) and 49.0 kJ mol⁻¹(D₂). Accordingly, the heat of absorption was evaluated to be −19.0 kJ mol⁻¹(H₂) for protium and −16.2 kJ mol⁻¹(D₂) for deuterium. The activation energies for diffusion were determined to be 28.7 kJ mol⁻¹(H, D) for both protium and deuterium, but the frequency factor for deuterium was about 1.5 times greater than that for protium.     

Thermodynamic investigation of the Lu---Pb system

The Lu---Pb alloys were studied by different techniques. The molar heat capacities of the solid compounds Lu₅Pb₃ and Lu₆Pb₅ were determined in the range 525–823 K using differential scanning calorimetry. The enthalpy of formation of LuPb₂ was obtained by both emf and calorimetric methods. Potentiometric measurements were performed in the range 610–730 K and a value of −35 ± 2 kJ (mol at.)⁻¹ was obtained for the enthalpy of formation of LuPb₂ in the solid state at 298 K. By using a direct isoperibolic aneroid differential calorimeter the value Δ_formH = −34 ± 2 kJ (mol at.)⁻¹ was determined. The data obtained in this study are compared with those of other similar rare earth-lead compounds and discussed briefly.     

Characterization of crystallization kinetics of a Ni- (Cr, Fe, Si, B, C, P) based amorphous brazing alloy by non-isothermal differential scanning calorimetry

The thermal stability and crystallization kinetics of a Ni- (Cr, Si, Fe, B, C, P) based amorphous brazing foil have been investigated by non-isothermal differential scanning calorimetry. The glass transition temperature T_g, is found to be 720 ± 2 K. The amorphous alloy showed three distinct, yet considerably overlapping crystallization transformations with peak crystallization temperatures centered around 739, 778 and 853 ± 2 K, respectively. The solidus and liquidus temperatures are estimated to be 1250 and 1300 ± 2 K, respectively. The apparent activation energies for the three crystallization reactions have been determined using model free isoconversional methods. The typical values for the three crystallization reactions are: 334, 433 and 468 kJ mol⁻¹, respectively. The X-ray diffraction of the crystallized foil revealed the presence of following compounds Ni₃B (Ni₄B₃), CrB, B₂Fe₁₅Si₃, CrSi₂, and Ni_4.5Si₂B.     

Study on phase formation and sintering kinetics of BaTi0.6Zr0.4O3 powder synthesized through modified chemical route

BaTi_0.6Zr_0.4O₃ powder was prepared from barium oxalate hydrate, zirconium oxy-hydroxide and titanium dioxide precursors. Barium oxalate hydrate and zirconium oxy-hydroxide were precipitated from nitrate solution onto the surface of suspended TiO₂. Phase formation behaviour of the materials was extensively studied using XRD. BaTiO₃ (BT) and BaZrO₃ (BZ) start forming separately in the system upon calcinations in the temperature range 600–700 °C. BT–BZ solid solution then forms by diffusion of BT into BZ from 1050 °C onwards. The precursor completely transforms into BaTi_0.6Zr_0.4O₃ (BTZ) at 1200 °C for 2 h calcination. The activation energy (AE) of BT (134 kJ mol⁻¹) formation was found to be less than that of BZ (167.5 kJ mol⁻¹) formation. BTZ formation requires 503.6 kJ mol⁻¹ of energy. The sintering kinetics of the powder was studied using thermal analyzer. The mean activation energy for sintering was found to be 550 kJ mol⁻¹.     

High-field magnetization process in Mn1.9Cr0.1Sb

The compound Mn_1.9Cr_0.1Sb shows a first-order transition from the ferrimagnetic (FI) to the antiferromagnetic (AF) state at T₁ = 265 K with decreasing temperature. High magnetic fields (up to 60 T) produce AF-FI transitions below T_t. The temperature dependence of the critical field is nonlinear and shows T² character at low temperatures (T < 150 K), in contrast to the exchange inversion model of Kittel. This behavior is connected with the itinerant magnetism of 3d-electrons of Mn atoms resulting in a large electronic contribution to the change in free energy at the field-induced first-order AF-FI transition. The field-induced phase transition from the AF to the FI state is accompanied by an increase in the electronic specific heat coefficient γ by 13 mJ K⁻² mol⁻¹ as estimated from the magnetization measurements using thermodynamic relation.     

Vaporization behavior and thermodynamic stability of V2P(s)

The vaporization behavior and thermodynamic stability of V₂P(s) were investigated by mass loss effusion and effusion mass spectrometry, the latter by an ion current ratio method. Enthalpies of formation with white phosphorus as the reference state and enthalpies of atomization were calculated. Results from the two types of experiments are in good agreement. Mean values of V₂P(s): Δ_fH°_298.15 = −209.0±5 kJ mol⁻¹, Δ_atH°_298.15 = 1556.4 kJ mol⁻¹. Recalculated values for V₃P(s): Δ_fH°_298.15 = −233.13±5 kJ mol⁻¹, Δ_atH°_298.15 = 2096.0 kJ mol⁻¹.     

Enthalpies of formation of solid Sm---Al alloys

A direct isoperibolic differential calorimeter was used to measure the formation heats of the Sm---Al intermetallic compounds. X-ray powder diffraction, optical and scanning electron microscopy and electron probe microanalysis were used to check the composition of the samples. The following values of Δ_fH⁰ for the different compounds were obtained in the solid state at 300 K: Sm₂Al, = −38.0 ± 2 kJ (mol atoms)⁻¹; SmAl, −49.0 ± 2 kJ (mol atoms)⁻¹; SmAl₂, −55.0 ± 2 kJ (mol atoms)⁻¹; SmAl₃, −48.0 ± 2 kJ (mol atoms)⁻¹. The results are discussed and compared with earlier experimental data.     

Sublimation enthalpy of tellurium tetrabromide by the torsion effusion method

The total vapour pressure of TeBr₄(s) was measured in the temperature range 423–485 K by the torsion effusion method. The total pressure as a function of temperature can be represented by the following equation: log(p/kPa)=(11.17 ± 0.20) − (6104 ± 100)(K/T)

The equilibrium involved in the vaporation process is described by: (x + y)TeBr₄(s) → xTeBr₄(g) + yTeBr₂(g) + yBr₂(g) where x = 0.06 and Y = 0.47.

The reaction enthalpy ΔH⁰(298) = 119 ± 4 kJ mol⁻¹ was obtained from the second and third law treatment of the data.     

Thermodynamic investigation of the solid and liquid Au---Sb alloys

The heat content of solid and liquid AuSb₂ compound was measured from 298 K to T (375–963 K) on heating (drop method) with the help of a Tian-Calvet calorimeter. The heat capacity of the liquid compound as well as its enthalpy of fusion were deduced. The enthalpy of the liquid decreases strongly when temperature increases between the melting point and 831 K.

The enthalpy of formation of the Au---Sb melts was also determined by direct reaction calorimetry at 916 K with respect to concentration. The enthalpy of mixing is weakly negative in the whole range of concentration (_min^f = −3·47 kJ/mol at x_Au = 0·775) in agreement with the results of Béja at 923 K. disagree with the much more negative earlier data of Kameda et al. and of Hino et al. by emf and vapor pressure measurements.

Finally, the liquid/Au(cr) phase boundary determined at 916 K from the break in the h^f (x_Au) curve agrees well with the phase diagram calculated by Okamoto and Massalski but not with their experimental results.     

Electrical properties of silver vanadate electrochemical cells

The silver iodide based ternary system xAgI-yAg₂O-zV₂O₅ (x = 10, 20, 30, …, 90; y/z = 2) was prepared by rapid quenching of the melt at liquid nitrogen temperature. X-ray diffraction confirmed the glassy or polycrystalline nature of the powdered phases. The 70AgI-20Ag₂O-10V₂O₅ phase has the highest room temperature (300 K) electrical conductivity of 0.011 S m⁻¹ at 1 kHz. Scanning electron microscopy showed that the surface of the 70AgI-20Ag₂O-10V₂O₅ as-quenched phase contains separate agglomerates. IR spectroscopy revealed bands at approximately 960, 920, 890, 850, 820 and 700 wavenumbers, indicating the possible existence of [VO₄]³⁻ clusters. Solid electrochemical cells fabricated from the phase with the highest electrical conductivity showed that the transference number is almost unity and that the phase is an ionic conductor. The internal resistance of this battery is approximately 460 ω. When discharged at a load current of 30 μA, the current density is 0.04 mA cm⁻², the discharge capacity is 3.78 C, the power density is 0.012 W kg⁻¹ and the energy density is 1.512 J g⁻¹ for a circular cell of mass 1.55 g and a surface area of 1.3 cm².     

Activity coefficients and partial molar volumes of boron in platinum-rhodium alloys

Activity coefficients of B in the phase of Pt and of three Pt---Rh alloys with 3, 6, and 10 wt.% Rh were obtained by equilibration of B₂O₃ with H₂-H₂O mixtures between 750 and 1000 °C and subsequent determination of the B mole fraction x_B 0.06 by the mass gain of the samples or by photometric analysis. Additions of Rh to Pt have rather large but opposing effects on the partial molar enthalpies and entropies of B, resulting in partial molar excess Gibbs energies within the modest range between −40 and −55 kJ mol⁻¹. The change in the lattice contraction from −13.5 to −3.2 pm/x_B in the phase of Pt and of Pt-10Rh can be fully described in terms of a substitutional solution model with strictly constant partial molar volumes of 9.09 cm³ mol⁻¹ and 8.28 cm³ mol⁻¹ for Pt and Rh respectively and a partial molar volume for B that increases linearly from 8.2 to 8.9 cm³ mol⁻¹ between pure Pt and Pt-10Rh.     

On the vapourization thermodynamics of cobalt trifluoride

The sublimation of CoF₃(s) was studied. The temperature dependence of the total vapour pressures as measured by the torsion method in the temperature range 700–830 K fit on the equation:

log(p/kPa)=(11.60±0.20)−10630±400)/(T/K)

Both the sublimation reactions:

Cof₃(s)= Cof₃(g) (1)

2Cof₃(s)=2Cof₂(s)+F₂(g) (2)

occur during the vapourization of CoF₃(s) where the molar fraction of the reaction (1) was found equal to 0.60±0.05, practically constant in the covered experimental temperature range. The standard enthalpies Δ_subH°(298)=216±4 and 204±3 kJ mol⁻¹ for reactions (1) and (2) respectively were derived from second- and third-law treatment of the data. New values for the enthalpy of formation of CoF₃(s) and CoF₃(g) equal to −773±5 and −557±10 kJ mol⁻¹, respectively, were derived.