Order into chaos : inaugural lecture delivered at Rhodes University

Inaugural lecture delivered at Rhodes UniversityRhodes University Libraries (Digitisation

Additive single atom values for thermodynamics II: Enthalpies, entropies and Gibbs energies for formation of ionic solids

In part I of this series we established optimised sum values, for each of the chemical elements, of formula volumes, of absolute entropies, and of constant pressure heat capacities, together with their temperature coefficients. These atom values, when summed for a chemical formula, provided zero-level estimates of the corresponding property of that chemical material. Atom sums have the particular advantage of being essentially complete because of the finite number of chemical elements and are of use in prediction and checking of values for chemical materials. However, this is at the expense of an inability to distinguish among isomers and phases with the same chemical formula nor do they allow for effects of atom interactions. In the present publication, we present optimised atom sums for formation entropies, formation enthalpies and their relation to formation Gibbs energies. In order to check the reliability of the results, comparison is made among methods of prediction using each of DFT calculations, a proprietary group contribution method, and the proposed single atom sum method. The single atom sum method is found to be most suitable as an initial estimate for large formation entropies and also for large values of formation enthalpies, which includes ionic hydrates. The energy contributions of the elements group into the Groups of the Periodic Table so that strict atom independence and thus additivity is not predominant while entropy terms are relatively constant (for the non-gaseous elements) implying that the atoms behave independently and thus additively in contributing to the entropy terms resulting from their vibrations within the ionic solids. This is possibly a unique demonstration resulting from this single atom sum collection. This now comprises a complete set for simple zero-order thermodynamic prediction and for checking, which should be complemented by whatever other resources are available to the researcher

Thermodynamic estimation: Ionic materials

Thermodynamics establishes equilibrium relations among thermodynamic parameters (“properties”) and delineates the effects of variation of the thermodynamic functions (typically temperature and pressure) on those parameters. However, classical thermodynamics does not provide values for the necessary thermodynamic properties, which must be established by extra-thermodynamic means such as experiment, theoretical calculation, or empirical estimation.While many values may be found in the numerous collected tables in the literature, these are necessarily incomplete because either the experimental measurements have not been made or the materials may be hypothetical. The current paper presents a number of simple and relible estimation methods for thermodynamic properties, principally for ionic materials. The results may also be used as a check for obvious errors in published values.The estimation methods described are typically based on addition of properties of individual ions, or sums of properties of neutral ion groups (such as “double” salts, in the Simple Salt Approximation), or based upon correlations such as with formula unit volumes (Volume-Based Thermodynamics)

The effective volumes of waters of crystallization & the thermodynamics of cementitious materials

Hydrates are significant components of cements and concrete. We examine the effective volumes of waters of crystallization for these materials, where the “effective volumes” are the difference per water molecule between the formula volume of the hydrate and of its parent anhydrate. These effective volumes cover a small range around 15 cm3 mol−1 (≅ 23 Å3 per water molecule), unlike the wider range for general inorganic materials. We also examine the thermodynamic properties of the cementitious phase, which follow the generally observed correlation of relating to their molar volumes. We establish “effective” additive oxide parameters for enthalpy and for molar volume, which are useful in confirming experimental values and in predicting as-yet undetermined values. Their Debye temperatures approximate to 600 K; this Debye temperature is well above ambient temperature and suggests that the vibrational modes of these cementitious phases are only partially excited and that the materials are hard. Ferrate-containing materials generally have a lower Debye temperature (∼273 K) implying that they may be softer than other cementitious materials. These observations may be useful in checking for errors in data and anomalies in behavior among related cementitious materials

The Equivalence of the Charge Interaction Sum and the Ionic Strength

The electrostatic interaction among a neutral and finite set of point charges is based on the sum of their pairwise charge products, , yet many analyses yield terms which simply contain a sum of the squares of the separate charges, corresponding to the ionic strength, 1/2 Σ 2 . This submission collects together a number of important instances of this result and explains their equivalence. In effect, the ionic strength-like terms provide conveniently calculated coulomb sums for systems with finite collections of charges

Thermodynamic consistencies and anomalies among end-member lanthanoid garnets

Lanthanoid (or lanthanide) garnets are ionic solids of technological importance in their use in electronic materials. They are also of interest in respect of their systematic relationships and as geochemical tracers. As a consequence, there is considerable published thermodynamic information for these garnets. Based principally on the computational results of Moretti and Ottonello (1998) [8], we here examine the thermodynamic information for consistencies and anomalies among the ferri-, alumino-, and gallo-garnets using relations between thermodynamic properties that we have established over recent years. The principal properties of interest are formula volume, heat capacity, entropy, and formation enthalpy (from which the Gibbs free energy may be obtained), and isothermal compressibility. We also establish additive single-ion values for trivalent lanthanide cations which may be applied in estimating properties for related materials. Since the results of the work of Moretti and Ottonello are based upon consistent computational analyses, we should expect generally smooth relations. These are, indeed, found for various of the properties (except for the europium garnets), with some uncertainty in the absolute entropies, and anomalies in the formation enthalpies of europium and ytterbium/lutetium garnets. The results of some more recent experimental work are included in our analyses. Values for the (unknown) promethium garnets are estimated by averaging the properties of the neighbouring neodymium and samarium garnets

Thermal stability of ionic solids: A melting points survey

While predictive correlations of the melting points of organic solids are well-established and reliable, the melting points of ionic solids are less understood. We provide a comprehensive survey of the related literature for ionic solids which shows that the primary factors to consider are the ambient temperature values of the formation enthalpies and the distances among the ions as enshrined in their crystal structures. These conclusions from standard thermodynamic analyses are supported by an independent current machine-learning program. This result contrasts with the common belief that lattice energies are a leading factor in melting. This basic idea is confounded by the irrelevant (but generally overwhelming) inclusion of the formation energy of gaseous ions in the evaluation of lattice energies through thermochemical cycles. The melting points of simple metal halides are correlated with their formation enthalpies per halide ion and distances among ions as determined by their crystal structures rather than their lattice energies. As the formula units of ionic solids increase in chemical and structural complexity the relations also become more complex

Volume-based thermoelasticity: Thermal expansion coefficients and the Gruneisen ratio

In an extension of our current studies of volume-based thermodynamics and thermoelasticity (VBT), we here consider the parameters at ambient temperature of the dimensionless Gruneisen ratio (or Gruneisen parameter), γth, which is a standard descriptor of the thermophysical properties of solids: γth=αKTVm/Cv=αVm/ βCv. It has earlier been established that the isothermal volume compressibility, β (which is the reciprocal of the bulk modulus, KT), and the ambient-temperature heat capacity, Cp, are strongly linearly correlated with the molar volume, Vm, among groups of materials with similar structures. Here, we examine possible correlations between the volumetric thermal expansion coefficient, α (the remaining Gruneisen parameter), and molar volume. Using the high-temperature limiting value, α°, as a surrogate for α, we find that α is essentially uncorrelated with volume among a range of materials. As a consequence of the lack of correlation through volume of α with the other Gruneisen parameters, we conclude that the dimensionless Gruneisen ratio at ambient temperatures itself is thereby poorly constant across materials and cannot be reliably used for predictive purposes. It is noted that, for thermodynamic reasons, the values of γth generally range from about 0.5 to 3, clustering around 2

Drinking-Straw Microbalance and Seesaw: Stability and Instability

The mechanics of a beam balance are little appreciated and seldom understood. We here consider the conditions that result in a stable balance, with center of gravity below the fulcrum (pivot point), while an unstable balance results when the center of gravity is above the fulcrum. The highly sensitive drinking-straw microbalance, which uses a plastic drinking straw as a rigid beam, is briefly described with some slight convenient modifications. Different placements of the center of gravity are considered analytically to explain the equilibrium neutrality, stability, and instability of such beam balances as the microbalance, the playground “seesaw” or “teeter-totter,” the “dipping bird,” and other toys and magic tricks

Predictive thermodynamics for condensed phases

Thermodynamic information is central to assessment of the stability and reactivity of materials. However, because of both the demanding nature of experimental thermodynamics and the virtually unlimited number of conceivable compounds, experimental data is often unavailable or, for hypothetical materials, necessarily impossible to obtain. We describe simple procedures for thermodynamic prediction for condensed phases, both ionic and organic covalent, principally via formula unit volumes ( or density); our volume-based approach (VBT) provides a new thermodynamic tool for such assessment. These methods, being independent of detailed knowledge of crystal structures, are applicable to liquids and amorphous materials as well as to crystalline solids. Examples of their use are provided