Access Type

Open Access Dissertation

Date of Award

January 2020

Degree Type


Degree Name



Mechanical Engineering

First Advisor

Victor L. Berdichevsky

Second Advisor

Xin Wu


Materials with random microstructure are characterized by additional thermodynamic parameters, entropy and temperature of microstructure. It has been argued that there is one more law of thermodynamics: entropy of microstructure decays in isolated systems. This assertion has been checked experimentally for the process of grain growth which showed that entropy of grain structure decays indeed as expected. The equation of state for microstructure entropy has also been studied. In general, entropy of grain microstructure is expected to be a function of grain structure energy and the average grain size. Our experiments suggest that in fact, the equation of state degenerates and microstructure entropy becomes a function of either grain energy or grain volume. This follows from an unexpected by-product of the experiments, a seemingly universal relationship between grain volume and grain area, at least at the stage of self-similar grain growth. In addition, a statistical model containing two new characteristics of grain structure in pure metals and alloys is suggested. Non-equiaxed geometry of grains and grain structure are quantified by using new statistical characteristics. The equations for the probability distribution of grain sizes are derived in terms of these parameters. It describes the previously obtained experimental data reasonably well. Evolution of grain size distribution and the above mentioned parameters have been studied during grain growth.