I am calculating thermal properties in a crystal, i have managed to calculate thermal conductivity, electrical conductivity and seebeck coefficients at varying chemical potentials, how Do i calculate This at a Specific chemical potential? How Do i obtain thermal expansion? Especially, thermal expansion with varied temps.
Hallo James,
First, I would like to state that I am not an Expert in thermal conductivity in its essence. However, we do simulate space- and time-discrete propagation of Heat using predefined or self-adapted mathematical models depending on the body hosting propagation. To compute the thermal properties at a particular point of the body and at a particular time, usually there is no straight formula(it would be even surprising). Instead we use an algorithm starting from a known configuration to iterate over time and space until we reach the desired coordinates.
1. We discretize the volume or surface in regular or irregular cells
2. We establish a recurrent model of thermal propagation returning thermal properties at a point and time based on properties of neighborhood in the past, present and maybe in the future
3. We initialize the thermal distribution over the body
4. We start the simulation and run until the desired coordinate(space-time) is reached. The simulation can last 1s, 2 min , 2 weak, one year, one century... depending on the complexity of the simulator and the size of the body.
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