The packing fraction of the oxygen sublattice: its impact on the heat of mixing.

The heat of mixing of some petrological relevant substitutions (i.e., Mg-Al, Si-Al, Mg-Ti, Mg-Ca, and Mg-Fe) was investigated systematically in silicates, titanates, tungstates, carbonates, oxides, hydroxides, and sulphates by density functional theory calculations (e.g., melilite, chlorite, biotite, brucite, cordierite, amphibole, talc, pseudobrookite, pyroxene, olivine, wadsleyite, ilmenite, MgWO4, ringwoodite (spinel), perovskite, pyrope-grossular, magnesite-calcite, MgO-CaO, anhydrous and different hydrated MgSO4). A specific substitution is characterised by different microscopic interaction energies in different minerals, e.g., the octahedral Mg-Al exchange on a single crystallographic site in pyroxene has a microscopic interaction energy that is more than twice compared to that in biotite. A comparative investigation of the heat of mixing using microscopic interaction energies on a single crystallographic site has the advantage that they are not influenced by cation ordering. They could be successfully correlated with the stiffnesses of the minerals, which in turn were scaled to the oxygen packing fraction, a parameter that is easily available for poorly investigated minerals. With this information, the interaction energies of a certain substitution can be transferred from minerals where they are well-known to mineral groups where they are less- or unknown. Using the cross-site terms and the microscopic interaction energies, the macroscopic interaction energies of the coupled substitution, e.g., Mg + Si = Al + Al, of biotite and pyroxene were calculated, which are, however, affected by cation ordering and different degrees of local charge balance, for which appropriate models are necessary. Supplementary Information: The online version contains supplementary material available at 10.1007/s00269-024-01277-6.

Vibrational entropy of disordering in omphacite.

The cations of an ordered omphacite from the Tauern window were gradually disordered in piston cylinder experiments at temperatures between 850 and 1150 °C. The samples were examined by X-ray powder diffraction and then investigated using low-temperature calorimetry and IR spectroscopy. The low-temperature heat capacity data were used to obtain the vibrational entropies, and the line broadening of the IR spectra served as a tool to investigate the disordering enthalpy. These data were then used to calculate the configurational entropy as a function of temperature. The vibrational entropy does not change during the cation ordering phase transition from space group C2/c to P2/n at 865 °C but increases with a further temperature increase due to the reduction of short-range order. Supplementary Information: The online version contains supplementary material available at 10.1007/s00269-023-01260-7.

The magnetic properties of MAl4(OH)12SO4·3H2O with M = Co2+, Ni2+, and Cu2+ determined by a combined experimental and computational approach.

The magnetic properties of the nickelalumite-type layered double hydroxides (LDH), MAl4(OH)12(SO4)·3H2O (MAl4-LDH) with M = Co2+ (S = 3/2), Ni2+ (S = 1), or Cu2+ (S = 1/2) were determined by a combined experimental and computational approach. They represent three new inorganic, low-dimensional magnetic systems with a defect-free, structurally ordered magnetic lattice. They exhibit no sign of magnetic ordering down to 2 K in contrast to conventional hydrotalcite LDH. Detailed insight into the complex interplay between the choice of magnetic ion (M2+) and magnetic properties was obtained by a combination of magnetic susceptibility, heat capacity, neutron scattering, solid-state NMR spectroscopy, and first-principles calculations. The NiAl4- and especially CoAl4-LDH have pronounced zero-field splitting (ZFS, easy-axis and easy-plane, respectively) and weak ferromagnetic nearest-neighbour interactions. Thus, they are rare examples of predominantly zero-dimensional spin systems in dense, inorganic matrices. In contrast, CuAl4-LDH (S = 1/2) consists of weakly ferromagnetic S = 1/2 spin chains. For all three MAl4-LDH, good agreement is found between the experimental magnetic parameters (J, D, g) and first-principles quantum chemical calculations, which also predict that the interchain couplings are extremely weak (< 0.1 cm-1). Thus, our approach will be valuable for evaluation and prediction of magnetic properties in other inorganic materials.

Investigations on the polymorphism of K4CaSi6O15 at elevated temperatures.

In the present study, single crystals and polycrystalline material of K4CaSi6O15 were prepared from solid-state reactions between stoichiometric mixtures of the corresponding oxides/carbonates. Heat capacity (C p) measurements above room temperature using a differential scanning calorimeter indicated that two thermal effects occurred at approximately T 1 = 462 K and T 2 = 667 K, indicating the presence of structural phase transitions. The standard third-law entropy of K4CaSi6O15 was determined from low-temperature C p's measured by relaxation calorimetry using a Physical Properties Measurement System and amounts to S°(298K) = 524.3 ± 3.7 J·mol-1·K-1. For the 1st transition, the enthalpy change ΔH tr1 = 1.48 kJ·mol and the entropy change ΔS tr1 = 3.25 J·mol-1·K-1, whereas ΔH tr2 = 3.33 kJ·mol-1 and ΔS tr2 = 5.23 J·mol-1·K-1 were determined for the 2nd transition. The compound was further characterized by in-situ single-crystal X-ray diffraction between ambient temperature and 1063 K. At 773 K, the high-temperature phase stable above T 2 has the following basic crystallographic data: monoclinic symmetry, space group P21/c, a = 6.9469(4) Å, b = 9.2340(5) Å, c = 12.2954(6) Å, ß = 93.639(3)°, V = 787.13(7) Å3, Z = 2. It belongs to the group of interrupted framework silicates and is based on tertiary (Q3-type) [SiO4]-tetrahedra. Together with the octahedrally coordinated Ca-cations, a three-dimensional mixed polyhedral network structure is formed, in which the remaining K-ions provide charge balance by occupying voids within the net. The intermediate temperature modification stable between T 1 and T 2 shows a (3+2)-dimensional incommensurately modulated structure that is characterized by the following q-vectors: q1 = (0.057, 0.172, 0.379), q2 = (-0.057, 0.172, -0.379). The crystal structures of the high- and the previously studied ambient temperature polymorph (space group Pc) are topologically equivalent and show a group-subgroup relationship. The index of the low- in the high-symmetry group is six and involves both, losses in translation as well as point group symmetry. The distortion is based on shifts of the different atom species and tilts of the 4- and 6-fold coordination polyhedra. Actually, for some of the oxygen atoms, the displacements exceed 0.5 Å. A more detailed analysis of the distortions relating to both structures has been performed using mode analysis, which revealed that the primary distortion mode transforms according to the Λ1 irreducible representation of P21/c. However, other modes with smaller distortion amplitudes are also involved.

The Specific Heat of Astro-materials: Review of Theoretical Concepts, Materials, and Techniques.

We provide detailed background, theoretical and practical, on the specific heat of minerals and mixtures thereof, 'astro-materials,' as well as background information on common minerals and other relevant solid substances found on the surfaces of solar system bodies. Furthermore, we demonstrate how to use specific heat and composition data for lunar samples and meteorites as well as a new database of endmember mineral heat capacities (the result of an extensive literature review) to construct reference models for the isobaric specific heat c P as a function of temperature for common solar system materials. Using a (generally linear) mixing model for the specific heat of minerals allows extrapolation of the available data to very low and very high temperatures, such that models cover the temperature range between 10 K and 1000 K at least (and pressures from zero up to several kbars). We describe a procedure to estimate c P (T) for virtually any solid solar system material with a known mineral composition, e.g., model specific heat as a function of temperature for a number of typical meteorite classes with known mineralogical compositions. We present, as examples, the c P (T) curves of a number of well-described laboratory regolith analogs, as well as for planetary ices and 'tholins' in the outer solar system. Part II will review and present the heat capacity database for minerals and compounds and part III is going to cover applications, standard reference compositions, c P (T) curves, and a comparison with new and literature experimental data. Supplementary Information: The online version contains supplementary material available at 10.1007/s10765-022-03046-5.

Excess heat capacity and entropy of mixing along the hydroxyapatite-chlorapatite and hydroxyapatite-fluorapatite binaries.

The heat capacity, C p, of synthetic hydroxyapatite [Ca5(PO4)3OH-OH-Ap], as well as of ten compositions along the OH-Ap-chlorapatite (Cl-Ap) join and 12 compositions along the OH-Ap-fluorapatite (F-Ap) join have been measured using relaxation calorimetry (heat capacity option of the Physical Properties Measurement System-PPMS) and differential scanning calorimetry (DSC) in the temperature range of 5-764 K. Apatites along the Cl-OH and F-OH joins were synthesized at 1100 °C and 300 MPa in an internally heated gas pressure vessel via an exchange process between synthetic fluorapatite or chlorapatite crystals (200-500 µm size) and a series of Ca(OH)2-H2O solutions with specific compositions and amounts relative to the starting apatite. The standard third-law entropy of OH-Ap, derived from the low-temperature heat capacity measurements, is S° = 386.3 ± 2.5 J mol-1 K-1, which is ~ 1% lower than that resulting from low-temperature adiabatic calorimetry data on OH-Ap from the 1950's. The heat capacity of OH-Ap above 298.15 K shows a hump-shaped anomaly centred around 442 K. Based on published structural and calorimetric work, this feature is interpreted to result from a monoclinic to hexagonal phase transition. Super ambient C p up to this transition can be represented by the polynomial: C p OH - Ap 298 K - 442 K J mol - 1 K - 1 = 1013.7 - 13735.5 T - 0.5 + 2.616718 10 7 T - 2 - 3.551381 10 9 T - 3 . . The DSC data above this transition were combined with heat capacities computed using density functional theory and can be given by the C p polynomial: C p OH - Ap > 442 K J mol - 1 K - 1 = 877.2 - 11393.7 T - 0.5 + 5.452030 10 7 T - 2 - 1.394125 10 10 T - 3 . Positive excess heat capacities of mixing, ∆C p ex, in the order of 1-2 J mol-1 K-1, occur in both solid solutions at around 70 K. They are significant at these conditions exceeding the 2σ-uncertainty of the data. This positive ∆C p ex is compensated by a negative ∆C p ex of the same order at around 250 K in both binaries. At higher temperatures (up to 1200 K), ∆C p ex is zero within error for all solid solution members. As a consequence, the calorimetric entropies, Scal, show no deviation from ideal mixing behaviour within a 2σ-uncertainty for both joins. Excess entropies of mixing, ∆Sex, are thus zero for the OH-Ap-F-Ap, as well as for the OH-Ap-Cl-Ap join. The C p-T behaviour of the OH-Ap endmember is discussed in relation to that of the F- and Cl-endmembers. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s00269-021-01167-1.

Excess enthalpy of mixing of mineral solid solutions derived from density-functional calculations.

Calculations using the density-functional theory (DFT) in combination with the single defect method were carried out to determine the heat of mixing behaviour of mineral solid solution phases. The accuracy of this method was tested on the halite-sylvite (NaCl-KCl) binary, pyrope-grossular garnets (Mg3Al2Si3O12-Ca3Al2Si3O12), MgO-CaO (halite structure) binary, and on Al/Si ordered alkali feldspars (NaAlSi3O8-KAlSi3O8); as members for coupled substitutions, the diopside-jadeite pyroxenes (CaMgSi2O6-NaAlSi2O6) and diopside-CaTs pyroxenes (CaMgSi2O6-CaAlAlSiO6) were chosen for testing and, as an application, the heat of mixing of the tremolite-glaucophane amphiboles (Ca2Mg5Si8O22(OH)2-Na2Mg3Al2Si8O22(OH)2) was computed. Six of these binaries were selected because of their experimentally well-known thermodynamic mixing behaviours. The comparison of the calculated heat of mixing data with calorimetric data showed good agreement for halite-sylvite, pyrope-grossular, and diopside-jadeite binaries and small differences for the Al/Si ordered alkali feldspar solid solution. In the case of the diopside-CaTs binary, the situation is more complex because CaTs is an endmember with disordered cation distributions. Good agreement with the experimental data could be, however, achieved assuming a reasonable disordered state. The calculated data for the Al/Si ordered alkali feldspars were applied to phase equilibrium calculations, i.e. calculating the Al/Si ordered alkali feldspar solvus. This solvus was then compared to the experimentally determined solvus finding good agreement. The solvus of the MgO-CaO binary was also constructed from DFT-based data and compared to the experimentally determined solvus, and the two were also in good agreement. Another application was the determination of the solvus in tremolite-glaucophane amphiboles (Ca2Mg5Si8O22(OH)2-Na2Mg3Al2Si8O22(OH)2). It was compared to solvi based on coexisting amphiboles found in eclogites and phase equilibrium experiments.

Thermodynamics of the double sulfates Na2M2+(SO4)2·nH2O (M = Mg, Mn, Co, Ni, Cu, Zn, n = 2 or 4) of the blödite-kröhnkite family.

The double sulfates with the general formula Na2M2+(SO4)2·nH2O (M = Mg, Mn, Co, Ni, Cu, Zn, n = 2 or 4) are being considered as materials for electrodes in sodium-based batteries or as precursors for such materials. These sulfates belong structurally to the blödite (n = 4) and kröhnkite (n = 2) family and the M cations considered in this work were Mg, Mn, Co, Ni, Cu, Zn. Using a combination of calorimetric methods, we have measured enthalpies of formation and entropies of these phases, calculated their Gibbs free energies (Δf G°) of formation and evaluated their stability with respect to Na2SO4, simple sulfates MSO4·xH2O, and liquid water, if appropriate. The Δf G° values (all data in kJ mol-1) are: Na2Ni(SO4)2·4H2O: -3032.4 ± 1.9, Na2Mg(SO4)2·4H2O: -3432.3 ± 1.7, Na2Co(SO4)2·4H2O: -3034.4 ± 1.9, Na2Zn(SO4)2·4H2O: -3132.6 ± 1.9, Na2Mn(SO4)2·2H2O: -2727.3 ± 1.8. The data allow the stability of these phases to be assessed with respect to Na2SO4, MSO4·mH2O and H2O(l). Na2Ni(SO4)2·4H2O is stable with respect to Na2SO4, NiSO4 and H2O(l) by a significant amount of ≈50 kJ mol-1 whereas Na2Mn(SO4)2·2H2O is stable with respect to Na2SO4, MnSO4 and H2O(l) only by ≈25 kJ mol-1. The values for the other blödite-kröhnkite phases lie in between. When considering the stability with respect to higher hydrates, the stability margin decreases; for example, Na2Ni(SO4)2·4H2O is still stable with respect to Na2SO4, NiSO4·4H2O and H2O(l), but only by ≈20 kJ mol-1. Among the phases studied and chemical reactions considered, the Na-Ni phase is the most stable one, and the Na-Mn, Na-Co, and Na-Cu phases show lower stability.

A new activity model for Mg-Al biotites determined through an integrated approach.

A new activity model for Mg-Al biotites was formulated through an integrated approach combining various experimental results (calorimetry, line-broadening in infrared (IR) spectra, analysis of existing phase-equilibrium data) with density functional theory (DFT) calculations. The resulting model has a sound physical-experimental basis. It considers the three end-members phlogopite (Phl, KMg3[(OH)2AlSi3O10]), ordered eastonite (Eas, KMg2Al[(OH)2Al2Si2O10]), and disordered eastonite (dEas) and, thus, includes Mg-Al order-disorder. The DFT-derived disordering enthalpy, ΔH dis, associated with the disordering of Mg and Al on the M sites of Eas amounts to 34.5 ± 3 kJ/mol. Various biotite compositions along the Phl-Eas join were synthesised hydrothermally at 700 °C and 4 kbar. The most Al-rich biotite synthesized had the composition X Eas = 0.77. The samples were characterised by X-ray diffraction (XRD), microprobe analysis and IR spectroscopy. The samples were studied further using relaxation calorimetry to measure their heat capacities (C p) at temperatures from 2 to 300 K and by differential scanning calorimetry between 282 and 760 K. The calorimetric (vibrational) entropy of Phl at 298.15 K, determined from the low-T C p measurements on a pure synthetic sample, is S cal = 319.4 ± 2.2 J/(mol K). The standard entropy, S o, for Phl is 330.9 ± 2.2 J/(mol K), which is obtained by adding a configurational entropy term, S cfg, of 11.53 J/(mol K) due to tetrahedral Al-Si disorder. This value is ~1% larger than those in different data bases, which rely on older calorimetrical data measured on a natural near-Phl mica. Re-analysing phase-equilibrium data on Phl + quartz (Qz) stability with this new S o, gives a standard enthalpy of formation of Phl, Δ H f o , Phl = - 6209.83 ± 1.10 kJ/mol, which is 7-8 kJ/mol less negative than published values. The superambient C p of Phl is given by the polynomial [J/(mol K)] as follows: C p = 667.37 ± 7 - 3914.50 ± 258 · T - 0.5 - 1.52396 ± 0.15 × 10 7 · T - 2 + 2.17269 ± 0.25 × 10 9 · T - 3 . Calorimetric entropies at 298.15 K vary linearly with composition along the Phl-Eas join, indicating ideal vibrational entropies of mixing in this binary. The linear extrapolation of these results to Eas composition gives S o = 294.5 ± 3.0 J/(mol K) for this end-member. This value is in excellent agreement with its DFT-derived S o, but ~ 8% smaller than values as appearing in thermodynamic data bases. The DFT-computed superambient C p of Eas is given by the polynomial [in J/(mol K)] as follows: C p = 656.91 ± 14 - 3622.01 ± 503 · T - 0.5 - 1.70983 ± 0.33 × 10 7 · T - 2 + 2.31802 ± 0.59 × 10 9 · T - 3 . A maximum excess enthalpy of mixing, ΔH ex , of ~6 kJ/mol was derived for the Phl-Eas binary using line-broadening from IR spectra (wavenumber region 400-600 cm-1), which is in accordance with ΔH ex determined from published solution-calorimetry data. The mixing behaviour can be described by a symmetric interaction parameter W Phl , Eas H = 25.4 kJ/mol. Applying this value to published phase-equilibrium data that were undertaken to experimentally determine the Al-saturation level of biotite in the assemblage (Mg-Al)-biotite-sillimanite-sanidine-Qz, gives a Δ H f , Eas o = - 6358.5 ± 1.4 kJ/mol in good agreement with the independently DFT-derived value of Δ H f , Eas o DFT = - 6360.5 kJ/mol. Application examples demonstrate the effect of the new activity model and thermodynamic standard state data, among others, on the stability of Mg-Al biotite + Qz.

Furfuryl Alcohol and Lactic Acid Blends: Homo- or Co-Polymerization?

Furfuryl alcohol (FA) and lactic acid (LA) are two of the most interesting biomolecules, easily obtainable from sugars and hence extremely attractive for green chemistry solutions. These substances undergo homopolymerization and they have been rarely considered for copolymerization. Typically, FA homopolymerizes exothermically in an acid environment producing inhomogeneous porous materials, but recent studies have shown that this reaction can be controlled and therefore we have implemented this process to trigger the copolymerization with LA. The mechanical tests have shown that the blend containing small amount of FA were rigid and the fracture showed patterns more similar to the one of neat polyfurfuryl alcohol (PFA). This LA-rich blend exhibited higher chloroform and water resistances, while thermal analyses (TG and DSC) also indicated a higher furanic character than expected. These observations suggested an intimate interconnection between precursors which was highlighted by the presence of a small band in the ester region of the solid state 13C-NMR, even if the FT-IR did not evidence any new signal. These studies show that these bioplastics are basically constituted of PLA and PFA homopolymers with some small portion of covalent bonds between the two moieties.

The accuracy of standard enthalpies and entropies for phases of petrological interest derived from density-functional calculations.

The internal energies and entropies of 21 well-known minerals were calculated using the density functional theory (DFT), viz. kyanite, sillimanite, andalusite, albite, microcline, forsterite, fayalite, diopside, jadeite, hedenbergite, pyrope, grossular, talc, pyrophyllite, phlogopite, annite, muscovite, brucite, portlandite, tremolite, and CaTiO3-perovskite. These thermodynamic quantities were then transformed into standard enthalpies of formation from the elements and standard entropies enabling a direct comparison with tabulated values. The deviations from reference enthalpy and entropy values are in the order of several kJ/mol and several J/mol/K, respectively, from which the former is more relevant. In the case of phase transitions, the DFT-computed thermodynamic data of involved phases turned out to be accurate and using them in phase diagram calculations yields reasonable results. This is shown for the Al2SiO5 polymorphs. The DFT-based phase boundaries are comparable to those derived from internally consistent thermodynamic data sets. They even suggest an improvement, because they agree with petrological observations concerning the coexistence of kyanite + quartz + corundum in high-grade metamorphic rocks, which are not reproduced correctly using internally consistent data sets. The DFT-derived thermodynamic data are also accurate enough for computing the P-T positions of reactions that are characterized by relatively large reaction enthalpies (> 100 kJ/mol), i.e., dehydration reactions. For reactions with small reaction enthalpies (a few kJ/mol), the DFT errors are too large. They, however, are still far better than enthalpy and entropy values obtained from estimation methods.

First-principles investigation of the lattice vibrations in the alkali feldspar solid solution.

The heat capacities of Al, Si ordered alkali feldspars of different Na, K compositions were calculated using the density functional theory. The effect of the Na, K distribution, if random, ordered or clustered, on the resulting heat capacity was investigated on different cells with Ab50Or50 composition. For all compositions and distributions studied, the excess heat capacity of mixing is positive at low temperatures with a maximum at ~60 K. This produces an increasing excess vibrational entropy that reaches a constant value above ~200 K. The amount of the excess heat capacity of Ab50Or50, however, depends on the Na, K distribution. Best agreement with measured excess heat capacities is achieved, if the distribution of Na and K is either ordered or clustered. The positive excess heat capacities can be attributed to a strong softening of the acoustic and the lowest optical modes related to a strong increase of Na-O bond lengths in samples with intermediate compositions. The softening of the lowest optical mode is, however, not reflected by thoroughly measured literature IR data. Comparing calculated and measured IR spectra suggests that the resolution of the measured spectra was insufficient for detecting the lowest IR-active modes.

The vibrational and configurational entropy of disordering in Cu3Au.

The thermodynamics of disordering in Cu3Au have been investigated by measuring the heat capacity of samples with different degrees of long- and short-range order between T = 5 and 720 K using relaxation and differential scanning calorimetry. The heat capacities of L12-ordered and fcc-disordered samples show similar behaviour at low temperatures (<300 K). They deviate positively from the linear combination of the end-member heat capacities between ∼30 and 160 K. However, small differences between the two samples exist, as the disordered sample has a larger heat capacity producing a vibrational entropy of disordering of ∼0.05 R. At temperatures higher than 300 K, the heat capacity of the ordered sample shows a prominent lambda-type anomaly at 675 K due to the diffusive L12-fcc phase transition. When starting these measurements with disordered samples, ordering effects are observed between 400 and 620 K, and the disordering reaction is observed at 660 K. Evaluation of the data gives an enthalpy and entropy of disordering at 683 K of 2.0 kJ mol-1 and 0.39 R, respectively. However, these values increase with increasing temperature, thereby reducing the short-range order. Because the vibrational and configurational disordering effects become active at different temperature regimes, i.e., the vibrational effects at low temperatures (T â‰ª 300 K) and the sum of both effects at higher temperatures (T > 300 K), they have been successfully separated.

The vibrational and configurational entropy of α-brass.

The heat capacities of two samples of a fcc Cu-Zn alloy with the composition CuZn15 and CuZn34 were measured from T = 5 K to 573 K using relaxation and differential scanning calorimetry. Below ∼90 K, they are characterised by negative excess heat capacities deviating from ideal mixing by up to -0.20 and -0.44 J · mol-1 · K-1 for CuZn15 and CuZn34, respectively. The excess heat capacities produce excess vibrational entropies, which are less negative compared to the excess entropy available from the literature. Since the literature entropy data contain both, the configurational and the vibrational part of the entropy, the difference is attributed to the excess configurational entropy. The thermodynamics of different short-range ordered samples was also investigated. The extent of the short-range order had no influence on the heat capacity below T = 300 K. Above T = 300 K, where the ordering changed during the measurement, the heat capacity depended strongly on the thermal history of the samples. From these data, the heat and entropy of ordering was calculated. The results on the vibrational entropy of this study were also used to test a relationship for estimating the excess vibrational entropy of mixing.

Calorimetric study of the entropy relation in the NaCl-KCl system.

The heat capacity of one Na-rich and two K-rich samples of the NaCl-KCl (halite-sylvite) crystalline solution was investigated between 5 and 300 K. It deviated positively from ideal behaviour with a maximum at 40 K. The thereby produced excess entropy at 298.15 K was described by a symmetric Margules mixing model yielding [Formula: see text] = 8.73 J/mol/K. Using enthalpy of mixing data from the literature and our data on the entropy, the solvus was calculated for a pressure of 105 Pa and compared with the directly determined solvus. The difference between them can be attributed to the effect of Na-K short range ordering (clustering).

Experimentally determined standard thermodynamic properties of synthetic MgSO(4)·4H(2)O (Starkeyite) and MgSO(4)·3H(2)O: a revised internally consistent thermodynamic data set for magnesium sulfate hydrates.

The enthalpies of formation of synthetic MgSO(4)·4H(2)O (starkeyite) and MgSO(4)·3H(2)O were obtained by solution calorimetry at T=298.15 K. The resulting enthalpies of formation from the elements are [Formula: see text] (starkeyite)=-2498.7±1.1 kJ·mol(-1) and [Formula: see text] (MgSO(4)·3H(2)O)=-2210.3±1.3 kJ·mol(-1). The standard entropy of starkeyite was derived from low-temperature heat capacity measurements acquired with a physical property measurement system (PPMS) in the temperature range 5 K

A relationship to estimate the excess entropy of mixing: Application in silicate solid solutions and binary alloys.

The paper presents new calorimetric data on the excess heat capacity and vibrational entropy of mixing of Pt-Rh and Ag-Pd alloys. The results of the latter alloy are compared to those obtained by calculations using the density functional theory. The extent of the excess vibrational entropy of mixing of these binaries and of some already investigated binary mixtures is related to the differences of the end-member volumes and the end-member bulk moduli. These quantities are used to roughly represent the changes of the bond length and stiffness in the substituted and substituent polyhedra due to compositional changes, which are assumed to be the important factors for the non-ideal vibrational behaviour in solid solutions.

A sample-saving method for heat capacity measurements on powders using relaxation calorimetry.

An experimental method is described for determining the low-temperature heat capacity (C(p)) of mg-sized powder samples using the Quantum Design "Physical Properties Measurement System" (PPMS). The powder is contained in an Al pan as an ∼1 mm thick compressed layer. The sample is not mixed with Apiezon N grease, as compared to other methods. Thus, it is not contaminated and can be used for further study. This is necessary for samples that are only available in tiny amounts. To demonstrate the method various samples, all insulating in nature, were studied including benzoic acid, sapphire and different silicate minerals. The measurements show that the method has an accuracy in C(p) to better than 1% at T above 30-50 K and ±3-5% up to ±10% below. The experimental procedure is based on three independent PPMS and three independent differential scanning calorimetry (DSC) measurements. The DSC C(p) data are used to slightly adjust the PPMS C(p) data by a factor CpDSC/CpPPMSat298K. This is done because heat capacities measured with a DSC device are more accurate around ambient T (⩽0.6%) than PPMS values and is possible because the deviation of PPMS heat capacities from reference values is nearly constant between about 50 K and 300 K. The resulting standard entropies agree with published reference values within 0.21% for the silicates, by 0.34% for corundum, and by 0.9% for powdered benzoic acid. The method thus allows entropy determinations on powders with an accuracy of better than 1%. The advantage of our method compared to other experimental techniques is that the sample powder is not contaminated with grease and that heat capacity values show less scatter at high temperatures.