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.     

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.     

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.     

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.     

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.     

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.     

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.     

Standard enthalpies of formation of some carbides, silicides and germanides of cerium and praseodymium

The standard enthalpies of formation of some congruent-melting compounds in the binary systems Re---X, where Re Ce, Pr or La and X C, Si or Ge have been determined by direct-synthesis calorimetry at 1473 ± 2 K. The following values of ΔH_f^o are reported: CeC₂, −25.4 ± 1.4 kJ (mol atom)⁻¹; CeSi₂, −60.5 ± 2.0 kJ (mol atom)⁻¹; CeSi, −71.1 ± 3.3 kJ (mol atom)⁻¹; Ce₅Ge₃, −73.4 ± 2.3 kJ (mol atom)⁻¹; CeGe_1.6, −75.6 ± 1.9 kJ (mol atom)⁻¹; PrC₂, −29.4 ± 1.6 kJ (mol atom)⁻¹; PrSi₂, −61.5 ± 1.7 kJ (mol atom)⁻¹; PrSi, −78.1 ± 1.9 kJ (mol atom)⁻¹; Pr₅Ge₃, −70.4 ± 2.3 kJ (mol atom)⁻¹; PrGe_1.6, −81.7 ± 1.7 kJ (mol atom)⁻¹; LaSi₂, −56.8 ± 2.5 kJ (mol atom)⁻¹. The results are compared with earlier experimental data, with predicted values from Miedema's semiempirical model, and with available data obtained for Sn and Pb compounds by Borzone et al., by Palenzona and by Palenzona and Cirafici.     

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.     

Enthalpy increment measurements of PbI2: evidence for a reversible polytypic transition

The enthalpy increment of solid and liquid PbI₂ have been measured by drop calorimetry from 528 to 763 K and the X-ray diffraction pattern has been recorded from 300 to 633 K. The calorimetric data show evidence for a reversible transition at 580 K, the enthalpy difference between the two phases being small, 339 J mol⁻¹. The X-ray diffraction results show a transition of the 2H to the 4H polytype at 440 K, for which the reverse reaction is not observed. The melting point of PbI₂ has been found at (679 ± 1) K by DSC, the enthalpy of fusion was obtained as Δ_fusH° = 23471 J mol⁻¹ from the enthalpy increments of the solid and liquid phase.     

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.     

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.     

Thermochemistry of GaBO3 and phase equilibria in the Ga2O3–B2O3 system

Employing a Tian-Calvet-type calorimeter operating in the scanning mode at temperatures from 1120 to 1220 K, the enthalpy change, Δ_dH, associated with the decomposition of GaBO₃ (=1/2β-Ga₂O₃+1/2B₂O₃(liq.)) and the corresponding decomposition temperature, T_d, were determined: Δ_dH=30.34±0.6 kJ/mol, T_d=1190±5 K. Using the transposed-temperature-drop method the thermal enthalpy, H(T)−H(295 K), of GaBO₃ was measured as a function of temperature, T, in the region from 760 to 1610 K; the results obtained are

[H(T)−H(295 K)]/(J/mol)=104.8·(T/K)−31 300 (760 K<T<1190 K),

[H(T)−H(295 K)]/(J/mol)=138.8·(T/K)−41 480 (1190 K<T<1590 K).

On the basis of the experimental results, the enthalpy and entropy of formation, Δ_fH and Δ_fS, respectively, of GaBO₃ from the component oxides were derived:

Δ_fH=−30.34 kJ/mol,Δ_fS=−25.50 J/(K·mol) at 1190 K,

Δ_fH=−10.55 kJ/mol,Δ_fS=−5.48 J/(K·mol) at 298 K.

The enthalpy versus temperature curve shows, apart from a step associated with the decomposition of GaBO₃, a further step at 1593 K which is attributed to a monotectic equilibrium.     

An expression for the calculation of Gibbs free energy difference of multi-component bulk metallic glasses

We propose an expression, ΔG = ΔH_m[{(T − T_m)/(1 − )T_m}+{T/(1 − )T_m}ln(T_m/T)] (0 <  < 1), for the calculation of Gibbs free energy difference ΔG of multi-component metallic alloys. The results show that the theoretical ΔGs are in better agreement with the experimental values over entire under-cooling range than those given by the TS, KN1 and KN2 expressions. The glass-forming ability of the multi-component metallic alloys has been observed to increase with the increase in the difference of the glass transition temperature and isenthalpic temperature.     

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.     

Adsorption behavior and mechanism of D113 resin for lanthanum

The sorption properties of macroporous weak acid resin (Dl13) for La3 ion were studied by chemical analysis and IR spectra. Experimental results indicate that the D113 resin has a good adsorption ability for La3 at pH = 6.0 in the HAc-NaAc medium. The statically saturated adsorption capacity is 273.3 mg/g. Separation coefficients of βLa3 / Ce3 , βLa3 / Gd3 , βLa3 / Er3 , and βLa3 /γ3 are 2.29, 3.64,4.27, and 0.627, respectively. The apparent activation energy of adsorption, Ea is 18.4 kJ/mol, the thermodynamics parameters △H, △S, and △G of Sorption are 4.53 kJ/mol, 61.8 J/(mol·K), -13.9 kJ/mol, respectively. The adsorption behavior of Dl13 for La3 obeys the Freundlich isotherm. La3 adsorbed on resin can be eluted by 2.0 mol/LHC1 quantitatively.     

Influence of Al- and Cu-doping on the thermodynamic properties of the LaNiIn–H system

The Pressure–Composition–Temperature (P–C–T) relations for the LaNiIn, LaNi_0.95Cu_0.05In and LaNiIn_0.98Al_0.02–H systems were measured by a volumetric Sieverts’ method at 398–423 K. All isotherms show plateau pressure regions indicating equilibria between two hydride phases. The replacements of Ni by Cu and In by Al affect the P–C–T diagrams, stability of the hydrides, homogeneity regions of the hydrides formed, slope of the isotherms and critical temperatures of the β–γ transition. In addition, the Cu-doping induces a significant hysteresis between the hydrogen absorption and desorption processes. The relative partial molar thermodynamic properties for the studied systems are: ΔH_H = −34.6 ± 2.1 kJ (mol_H)⁻¹, ΔS_H = −70.7 ± 3.6 J (K·mol_H)⁻¹ for LaNiIn–H; ΔH_H = −34.1 ± 0.5 kJ (mol_H)⁻¹, ΔS_H = −74.9 ± 1.0 J (K·mol_H)⁻¹ for LaNi_0.95Cu_0.05In–H; ΔH_H = −33.2 ± 0.8 kJ (mol_H)⁻¹, ΔS_H = −68.3 ± 1.2 J(K·mol_H)⁻¹ for LaNiIn_0.98Al_0.02–H.     

Gibbs free energy of formation of the ternary oxide Nd3RuO7

The Gibbs free energy of formation of Nd₃RuO₇(s) has been determined using solid-state electrochemical cell employing oxide ion conducting electrolyte. The electromotive force (e.m.f.) of the following solid-state electrochemical cell has been measured, in the temperature range from 929.3 to 1228.6 K.

Cell: (−)Pt/{Nd₃RuO₇(s) + Nd₂O₃(s) + Ru(s)}//CSZ//O₂(p(O₂) = 21.21 kPa)/Pt(+)

The Gibbs free energy of formation of Nd₃RuO₇(s) from elements in their standard state, calculated by the least squares regression analysis of the data obtained in the present study, can be given by:

{Δ_fG°(Nd₃RuO₇, s)/(kJ mol⁻¹) ± 1.6} = −3074.3 + 0.6097(T/K); (929.3 ≤ T/K ≤ 1228.6).

The uncertainty estimate for Δ_fG°(T) includes the standard deviation in e.m.f. and the uncertainty in the data taken from the literature. The intercept and the slope of the above equation correspond to the enthalpy of formation and entropy, respectively, at the average experimental temperature of T_av. = 1079 K.     

Evolution of magnetic hardness in the HfFe6Ge6-type RMn6Sn6−xGax and RMn6Sn6−xInx compounds (R=Tb, Dy; 0.2≤x≤1.4)

The HfFe₆Ge₆-type RMn₆Sn_6−xX_x′ solid solutions (R=Tb, Dy, X′=Ga, In; x≤1.4) have been studied by powder magnetization measurements. All the series are characterized by ferrimagnetic ordering and by a decrease in Curie temperatures with the substitution (ΔT_c/Δx≈−39 K for X′=Ga and ΔT_c/Δx≈−75 K for X′=In). The RMn₆Sn_6−xGa_x systems are characterized by a strong decrease in the spin reorientation temperature with substitution (ΔT_t/Δx≈−191 K and −78 K for R=Tb and Dy, respectively) while this transition almost does not change in systems containing indium. The coercive fields drastically decrease with the substitution in the TbMn₆Sn_6−xGa_x system while the substitution of In for Sn has a weaker effect. The coercive fields of the Dy compounds do not vary greatly with the substitution in both series. The behaviour of the TbMn₆Sn_6−xGa_x is compared with the evolutions observed in the TmMn₆Sn_6−xGa_x series. This comparison strongly suggests that the replacement of Sn by Ga changes the sign of the A₀² crystal field parameter.