Thermodynamic data for the condensed phases of 78 elements as currently used by SGTE (Scientific Group Thermodata Europe) are tabulated. SGTE is a consortium of seven organisations in Western Europe engaged in the compilation of a comprehensive, self consistent and authoritative thermochemical database for inorganic and metallurgical systems. The data are being published here in the hope that they will become widely adopted within the international community as a sound basis for the critical assessment of thermodynamic data, thereby, perhaps, limiting unnecessary duplication of effort. The data for each phase of each element considered aie presented as expressions showing, as a function of temperature, the variation of (a) G-HSER, the Gibbs energy relative to the enthalpy of the “Standard Element Reference” ie the reference phase for the element at 298.15 K and (b) the difference in Gibbs energy between each phase and this reference phase (ie lattice stability). The variation of the heat capacity of the various phases and the Gibbs energy difference between phases are also shown graphically. For certain elements the thermodynamic data have been assessed as a function of pressure as well as temperature. Where appropriate a temperature— pressure phase diagram is also shown.

Throughout this paper the thermodynamic data are expressed in terms of J mol−1. The temperatures of transition between phases have been assessed to be consistent with the 1990 International Temperature Scale (ITS90).

SGTE data for pure elements

A description is given of Thermo-Calc, a databank for thermochemistry and metallurgy developed at the division of Physical Metallurgy of the Royal Institute of Technology (KTH) in Stockholm. Using the facilities of Thermo-Calc one can tabulate thermodynamic data, calculate the heat change of chemical reactions and their driving force, evaluate equilibria for chemical systems and phase transformations and calculate various types of multicomponent phase diagrams by an automatic mapping procedure. The databank is quite general and can be applied to all systems where data assessed by a model implemented in the databank are available. The assessment procedure necessary to develop and extend the the databank is discussed. A brief description of the modules of Thermo-Calc is given and two examples are included which demonstrate how flexibly the calculations can be made. These examples will also show that the system is quite easy to use and that there are extensive on-line help facilities.

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The Thermo-Calc databank system☆

This paper reviews the crystal chemistry, synthesis, densification, microstructure, mechanical properties, and oxidation behavior of zirconium diboride (ZrB2) and hafnium diboride (HfB2) ceramics. The refractory diborides exhibit partial or complete solid solution with other transition metal diborides, which allows compositional tailoring of properties such as thermal expansion coefficient and hardness. Carbothermal reduction is the typical synthesis route, but reactive processes, solution methods, and pre-ceramic polymers can also be used. Typically, diborides are densified by hot pressing, but recently solid state and liquid phase sintering routes have been developed. Fine-grained ZrB2 and HfB2 have strengths of a few hundred MPa, which can increase to over 1 GPa with the addition of SiC. Pure diborides exhibit parabolic oxidation kinetics at temperatures below 1100°C, but B2O3 volatility leads to rapid, linear oxidation kinetics above that temperature. The addition of silica scale formers such as SiC or MoSi2 improves the oxidation behavior above 1100°C. Based on their unique combination of properties, ZrB2 and HfB2 ceramics are candidates for use in the extreme environments associated with hypersonic flight, atmospheric re-entry, and rocket propulsion.

Refractory Diborides of Zirconium and Hafnium

Vibrational thermodynamics of materials

Resistivity saturation is observed in many metallic systems with large resistivities---when the resistivity has reached a critical value, its further increase with temperature is substantially reduced. This typically happens when the apparent mean free path is comparable to the interatomic separations---the Ioffe-Regel condition. Recently, several exceptions to this rule have been found. This colloquium first reviews experimental results and early theories of resistivity saturation. It then describes more recent theoretical work, addressing cases both where the Ioffe-Regel condition is satisfied and where it is violated. In particular, the authors show how the (semiclassical) Ioffe-Regel condition can be derived quantum mechanically under certain assumptions about the system and why these assumptions are violated for high-${T}_{c}$ cuprates and alkali-doped fullerides.

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Colloquium : Saturation of electrical resistivity

Cohesive properties and vibrational entropy of 3d-transition metal carbides

The lattice stability is defined as the Gibbs energy of an element in a certain structure relative to its value in another structure. It is often assumed to vary linearly with temperature, an assumption which is either limited to a narrow range of temperature or implies that C p of the two phases are the same. A better method would be to use the information available for C p and derive a more realistic extrapolation. However, it is demonstrated that even the best assessment available today may give absurd results for the stability of a liquid phase relative to a solid. SGTE has recommended another method which makes use of the experimental difference in C p at the melting point. It is a simple method and guarantees that the results will be reasonable. The method should not be considered as ideal but it provides a workable framework until reliable physical models are available to represent thermodynamic data for phases outside their range of stability.

A new method of describing lattice stabilities

We let compounds between a 3{ital d} transition metal ({ital M}) and a nonmetal {ital X} ({ital X}=C,N,O,S) be characterized by three parameters: the average number of valence electrons per atom ({ital n}{sub {ital e}}), the average volume per atom ({Omega}), and the logarithmically averaged atomic mass ({ital M}{sub eff}). Three quantities with the dimension of energy are then considered: the cohesive energy {ital E}{sub coh} of the compound, its enthalpy of formation {Delta} {sup 0}{ital H}, and {ital E}{sub {ital S}}{equivalent to}{ital M}{sub eff}({ital k}{sub {ital B}}{Theta}{sub {ital S}}/{bar h}){sup 2}{Omega}{sup 2/3}. {Theta}{sub {ital S}} is a Debye temperature, properly defined to give the vibrational entropy at high temperatures. Remarkably accurate empirical relations are found between {ital n}{sub {ital e}} on one hand and {ital E}{sub coh}, {Delta} {sup 0}H, and {ital E}{sub {ital S}}. For compounds {ital MX} of the NaCl crystal structure one can understand the correlation from the electron band structure of ({ital p}-{ital d})-bonded systems. We then extend the correlation to carbides and nitrides of more complex structure, for which not much is known about the electron states. The relation between {ital E}{sub {ital S}} and {ital n}{sub {ital e}} is of particular importance, sincemore » it allows an estimate of cohesive properties and the vibrational entropy in systems where there is no, or uncertain, experimental information. The correlations are applied to e.g., a study of the phase stability of the NaCl structure for large {ital n}{sub {ital e}} and to the estimation of the standard entropies {sup 0}S and enthalpies of formation {Delta} {sup 0}H of various nitrides, carbides, and oxides. We also demonstrate how our method can be coupled with the so-called CALPHAD ( calculation of phase diagrams'') work.« less

Cohesive properties and vibrational entropy of 3d transition-metal compounds: MX (NaCl) compounds (X=C, N, O, S), complex carbides, and nitrides

The FeMo phase diagram and the thermodynamic properties of FeMo alloys have been evaluated from experimental information using thermodynamic models for the individual phases. The bcc phase was described with a model taking the strong magnetic effect into account. Three of the intermetallic phases were described with a three-sublattice model, allowing the width of the one-phase fields to be accounted for. The agreement between experimental data and calculated values is satisfactory.

An assessment of the FeMo system

The transition metal diborides MeB2 were chosen as an example to illustrate an approach introduced by us, by which existing thermodynamic information can be systematized and new information generated. We consider trends in the melting temperature, the enthalpy of formation and lattice vibration properties as the metal Me varies along the 3d, 4d and 5d transition metal series. The trends show a consistent picture which can be explained from the electronic density of states by a rigid-band like argument. This fact gives us confidence to apply the regularities and obtain new information by interpolation and extrapolation procedures. In particular, we estimate the standard entropy S⊖ at 298.15 K for stable AlB2 structure compounds where there are no previous measurements and for some metastable compounds (Me ≡ Sc, V, Cr, Mn, Y, Mo, Tc, WandRe). The results are compared with estimates based on various empirical methods. In the Me-B systems, the MeB2 phase may be stable at all temperatures, or be a high-temperature phase or a metastable phase. We explain the observed trend. Through the use of thermodynamic phase diagram calculations (the so-called CALPHAD method), we study the thermodynamic properties of the metastable AlB2 structure phase FeB2.

Armando Fernández Guillermet

Papers

Cohesive properties and vibrational entropy of 3d-transition metal carbides

A new method of describing lattice stabilities

Cohesive properties and vibrational entropy of 3d transition-metal compounds: MX (NaCl) compounds (X=C, N, O, S), complex carbides, and nitrides

An assessment of the FeMo system

Bonding properties and vibrational entropy of transition metal MeB2 (AlB2) diborides