Several isothermal experiments are generally needed to determine the parameters of the Avrami equation which describe most of the heterogeneous solid state reactions. Differential scanning calorimeters are suitable for such experiments. While most differential thermal analysis (DTA) apparatus cover a wider temperature range than DSC apparatus they cannot be used to perform isothermal determinations. However, Kissinger has already shown how activation energy and frequency factor can be calculated from DTA experiments for the case of homogeneous reactions following first order kinetics. We derive in this paper an extension of the Kissinger method and show its applicability to heterogeneous reactions described by an Avrami expression. The new method will allow the study of the kinetics of metallic reactions at the higher temperature range obtainable with DTA. The transformation kinetics of the metastable equiatomic tin-nickel alloy are given as an example. (1) n is a dimensionless exponent, k has the dimension of reaction rate and is given by an Arrhenius type of relationRT where v = frequency factor AE = activation energy R = gas constant T = Kelvin temperatureThe transformation can be completely described in time, temperature and transformed fraction co-ordinates if n, AE, and v are known. The easiest way to calculate these three parameters is to run isothermal experiments to determine the change of x with time. The data is generally reduced [2] by fitting the equation:1

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Electrodeposited hard gold with 0.6 at.% cobalt has a hardness about four times that of annealed bulk gold and this high hardness cannot be reproduced by standard metallurgical methods. By measuring the hardness for gold and gold alloys subjected to various quenching, annealing, and deformation processes, all common hardening mechanisms such as solution hardening, precipitation hardening, strain hardening, and ’’voids’’ hardening were eliminated as possible major hardening contributors with the exception of the grain size effect. Pure gold with grain sizes ranging from 200 Å to 3 μm were prepared using sputtering deposition by varying the substrate temperature during deposition from 55 to 310 °C. Larger grain sizes from 5 to 200 μm were prepared by annealing cold-drawn gold wire at 300–750 °C. The hardness versus grain diameter followed the Hall-Petch relation up to a grain size of 0.1 μm. Beyond that, the hardness increased less rapidly. At the grain size of electrodeposited hard gold of 250–300 Å, the sputtered pure gold gave the same hardness value also. Therefore, the grain size effect accounts for the observed high hardness of electrodeposited hard gold, with other mechanisms accounting for only small alterations.

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Using both differential scanning calorimetry (DSC) and differential thermal analysis (DTA), the kinetics of the transformation upon heating of the metastable tin-nickel alloy were studied. The solid-state reaction proceeds according to a classical Avrami equation. The parameters of the reaction equation were determined, and it is shown that the metastable alloy will not revert to the stable state, for all practical purpose, if kept at temperatures below 100~Variations of the kinetic parameters were observed which can explain most of the different stability evaluations reported by different authors.