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I'm investigating a material, that under high temperature-pressure conditions undergoes a phase transition. In order to correctly calculate the temperature, or even estimate a reasonable value, I need to know the specific heat of the material post phase transition. Unfortunately these values haven't been determined for the materials I'm interested in, and I'm not in a position to easily determine them experimentally.

My question then is, do reasonably straightforward techniques exist for the estimation of specific heat of fairly arbitrary materials? I suspect I could look at molecular dynamics or atomistic techniques, but these feel as involved as doing the work experimentally.

Edit with some extra information

The phase change is solid-solid, and compression to the high PT state occurs sufficently quickly that isothermal conditions, or temperature control are not credible. I can't say which material I'm interested in exactly due to commerical confidence, but sucrose is a not unreasonable analogue.

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  • $\begingroup$ Difficult to answer on a completely general basis. Knowing which material and if the solid phase you are referring to is a crystalline or not could help. It is strange that in an experiment there is no direct control of temperature. $\endgroup$
    – GiorgioP
    Jan 30 '19 at 23:42
  • $\begingroup$ Both phases are solid, and are crystaline. The compression occurs sufficently rapidly that isothermal, or even temperture controlled, conditions are not possible unfortunately. $\endgroup$ Jan 31 '19 at 14:07
  • $\begingroup$ ok, now I understand the difficulty to get the temperature. Still a realistic estimate about its order of magnitude may help. A few hundreds K ? thousand ? $\endgroup$
    – GiorgioP
    Jan 31 '19 at 14:49
  • $\begingroup$ With no specific heat data post phase change its hard to pin down, but up the the phase change its an increase of a few hundred Kelvin over ambient conditions, so around 500 - 600 K. $\endgroup$ Jan 31 '19 at 14:58
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On the basis of the available information on the system, I would consider unsafe to use results from models in conditions where it is highly probable that strong anharmonicity and/or potentially unknown structural changes take place.

For a system not too different from sucrose, ab-initio simulations would be the method of choice to get reliable values for specific heat (which would not be a too difficult quantity to evaluate).

I agree that performing an ab-initio simulation requires some specific expertise, but here we are moving out of the scientific ground. Maybe it could not be too difficult to find a person with the right expertise interested in working on the problem.

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If your material is a pure substance and your final phase is a solid or gas, you could estimate the specific heat using the equipartition theorem as

$$ c_v = \frac{f}{2} \frac{R_\text{u}}{M} $$

where

  • $f$ is the number of internal degrees of freedom per particle, which is $6$ for a solid, $3$ for a monoatomic gas, and $5$ (at room temperature) or $7$ (at very high temperature) for a diatomic gas, but can also be evaluated for larger molecules,
  • $R_\text{u}$ is the universal gas constant, and
  • $M$ is the molar mass of the substance.
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  • $\begingroup$ It's a solid-solid phase transition. I'll add a note to the original question to that affect. $\endgroup$ Jan 31 '19 at 14:05
  • $\begingroup$ Equipartition provides the specific heat of a solid only under the assumption that the system behaves like an ideal harmonic solid. Reality is often not as much ideal. Defects and anharmonicity play an important role. $\endgroup$
    – GiorgioP
    Jan 31 '19 at 15:26
  • $\begingroup$ Fair point. I mention it because it is a very straightforward way of getting a rough estimate, which is what the question was seeking. $\endgroup$ Feb 1 '19 at 0:52

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