Pavel Holba

Heat inertia and temperature gradient in the treatment of DTA peaks

Historical development of methods and theoretical basis of differential thermal analysis (DTA) are outlined. DTA is a procedure in which the heat transfer toward the sample plays an important function and the associated process in the sample is manifested by deviation of temperature difference from its background. This difference ΔT is not directly proportional to the rate of the process (dα/dt) but includes also the effect of heat inertia proportional to the slope dΔT/dt as it was derived and incorporated into DTA equation by Vold (Anal Chem 21:683–688, 1949), Borchardt and Daniels (J Am Chem Soc 79:41–46, 1957), and suggested to be corrected in the authors’ previous papers (1976). However, the correction with respect to heat inertia has so far been omitted (particularly after the boom of non-isothermal kinetics started by paper of Kissinger (Anal Chem 29:1702–1706, 1957)). DTA experiments with rectangular pulses realized by micro-heater inside the sample show that the correction of DTA signal employing calculated heat inertia term of the DTA equation is reliable but not yet fully sufficient. It was a reason to derive a more complete DTA equation including a term expressing the changes in the temperature field inside the sample during process. Possibilities for improving of DTA (and DSC) data processing are discussed. Itemized 150 references with titles.

Kinetics with Regard to the Equilibrium of Processes Studied by Non-Isothermal Techniques

The non-isothermal degree of conversion and the equilibrium advancement for the process Aeq are denned by the relationship = ?.eq, where is the isothermal degree of conversion. The precise meaning of non-isothermal kinetics in relation to basic types of processes studied under dynamic conditions is discussed. For an invariant type of process the correct form of the kinetic equation is investigated. For the universal non-isothermal kinetic equation, a modified rate for the process is given by

Heat inertia and its role in thermal analysis

The history of the term inertia is mentioned, and the effect of the heat inertia phenomenon is found in equations derived by Newton and Tian as well as in works of Vold and Borchard and Daniels. The mathematical correction of heat inertia consequences can be portrayed using the both differential and/or integral forms. It has been confirmed by the effective rectification applied to DTA (and heat-flux DSC) responses reflecting well the need of heat inertia corrections as to attain the original shape of inserted rectangular heat pulse.

Imperfections of Kissinger evaluation method and crystallization kinetics

The famous Kissinger’s kinetic evaluation method (Anal. Chem. 1957) is examined with respect to: a) the relation between the DTA signal θ (t) and the reaction rate r(t) ≡ dα/dt; b) the requirements on reaction mechanism model f(α); and c) the relation of starting kinetic equation to the equilibrium behavior of sample under study. Distorting effect of heat inertia and difference between the temperature Tp of extreme DTA deviation and the temperature Tm at which the reaction rate is maximal are revealed. The kinetic equations respecting the influence of equilibrium temperature Teq, especially fusion temperature Tf, are tested as bases for a modified Kissinger-like evaluation of kinetics.

Heat capacity equations for nonstoichiometric solids

The equations for heat capacity measured under isodynamical conditions (fixed activity of a single component) are derived for partly open systems exchanging one component with the surroundings while keeping the contents of all other components constant. Compared to conventional isobaric (and isoplethal) heat capacity of a strictly stoichiometric phase, the isodynamical heat capacity of a nonstoichiometric phase is found to involve two additional terms—the saturation contribution due to incorporation (or release) of the free component and the contribution due to deviation from stoichiometry reflecting a different number of the involved phonon modes (due to different free component content) and in some cases a variation of free component incorporation mechanism.

Doubts on Kissinger´s method of kinetic evaluation based on several conceptual models showing the difference between the maximum of reaction rate and the extreme of a DTA peak

The famous Kissingers kinetic evaluation method (Anal. Chem. 1957) is examined with respect to the feasible impact of the individual quantities and assumptions involved, namely the model of reaction mechanism, f(a) (with the iso- and nonisothermal degrees of conversion, α and λ) the rate constant, k(T) (and associated activation energy, E), heating/cooling rate, b (supplementing additional thermodynamic term for the melt undercooling, ΔT) and above all, the association of the characteristic temperature, Tm, with the DTA peak apex. It is shown that the Kissinger/s equation, in contrary to the results of Vold (Anal. Chem. 1949), is omitting the term of heat inertia arising from the true balance of heat fluxes. The absence of this term skews the evaluated values of activation energies.

Ehrenfest equations for calorimetry and dilatometry

Ehrenfest classification of phase transitions discerns between two categories: first-order transitions obeying Clapeyron equation and second-order transitions that should obey Ehrenfest equations. Considering the equilibrium phase diagram of binary systems with lentiform two-phase field and with bell-shaped miscibility gap, the corresponding Ehrenfest equations applicable for calorimetry and dilatometry are derived.

Heat Transfer and Phase Transition in DTA Experiments

Early principles of thermometry (Sestak J, Mares JJ, From caloric to statmograph and polarography. J Therm Anal Calorm 88:3–9, 2007; Proks I, Evaluation of the knowledge of phase equilibria. In: Chvoj Z, Sestak J, Třiska A (eds) Kinetic phase diagrams: nonequilibrium phase transformations. Elsevier, Amsterdam, pp 1–60, 1991; Proks I, Celok je jednoduchsi ako jeho casti (Whole is simpler than its parts). Publishing house of Slovak Academy of Sciences, Bratislava (in Slovak), 2011) were already established by Galileo Galilei (1564–1642), whose idea was to make use of the volume changes of gases while observing the accompanying changes in thermal state of given bodies (air thermometer). The first liquid thermometer was likely constructed by J. Rey in 1631, and the description of the mercury thermometer is ascribed to Daniel G. Fahrenheit in 1724. The elaboration of the earliest ice calorimeter is credited to A.L. Lavoisier and Pierre S. Laplace around 1790 (Lavoisier LA, Laplace PS, Presentation of a new means for measuring heat as the first chapter of their book “Memoire sur la Chaleur”, Paris, 1783; Thenard L, Treatise of chemistry, 6th edn. Crochard, Paris, 1836), coining the term from the Latin “calor” and the Greek “meter.” Sourced on the work by B. Telesio (1509–1588) (Telesio B, De Rerum Natura Iuxta Propria Principia, 1565), Jan A. Comenius (1592–1670) (Comenius JA, Physicae synopsis, Leipzig, 1633; Disquisitiones de Caloris et Frigoris Natura, Amsterdam, 1659) made use of the term “caloric” when describing the importance of concepts of cold and warm (Sestak J, Mares JJ, From caloric to statmograph and polarography. J Therm Anal Calorm 88:3–9, 2007).

Reinstatement of thermal analysis tradition in Russia and related East European interactions

History of thermal science is shortly described accentuating the impact of Russian, Czech and other East European thermoanalysts, thematic books, journals, personalities as well as showing the gradual development of associated conferences. It is documented by some unfamiliar photographs of the historic range.

Material properties of nonstoichiometric solids

Following our recently reported theoretical description of heat capacity of nonstoichiometric solids published in this journal, we extended this approach based on redefining the heat capacity conventionally valid for isoplethal conditions (fixed content of all components) to isodynamical conditions (controlled activity of a component shared with surroundings) and formulated a similar ansatz for other material characteristics such as thermal expansion and isothermal compressibility. As for the heat capacity, two additional terms are identified: the saturation contribution due to incorporation (or release) of the free component and the contribution due to deviation from stoichiometry. Involving some newly defined quantities reflecting the variation of stoichiometry with temperature, pressure, and activity, the resulting equations provide a direct link to experiment.