Recent content by Useful nucleus

Is self-nomination common for career awards in science and engineering? I was under the impression that nomination for awards is only by others but apparently self-nomination is an option too. Any PF member has an experience in this to share?

Upon reaching equilibrium, quantum mechanical calculations show that in rutile-TiO2 the dominant form is small electron polarons. In anatase-TiO2, the dominant form is free-like electrons (or large polarons). See for example: https://pubs.rsc.org/en/content/articlelanding/2014/cp/c4cp03981e

Thank you!

Please suggest a citation for anyone who wish to use these expressions (e.g. for homework problems...).

You are right the band diagram before doping is different that the band diagram after doping. Together both elements will form new valence and conduction bands.

If I understand this thread correctly, you seek a method to predict the levels of a dopant in a host. This is exactly what computational materials scientists/physicists do. The gold standard in this field is using density functional theory simulations to predict the energy levels of a dopan in...

For a random alloy, the lattice parameter reported is an average over all unit cells. Each unit cell can have a slightly different lattice parameter than other unit cells. Thus, we have an average lattice constant but a distrubition of bond lengths. The band diagram is a different story. If...

Alloys can be ordered or random. IF the alloy is ordered , then their will be a set of well defined bond lengths (Si-Si, Ge-Ge, and Si-Ge). IF the alloy is random, then we will have a "spectrum" of bond lengths.

I believe you will be missing all entropic contribution. Your suggestions can account for the energy but not for the free energy.

I do not believe there is a general rule of thumb. Especially in complex compund semiconductors (like oxides and nitrides). However in 2003, it was shown that hydrogen has a universal energy level provided that the band gap of the semiconductor is aligned according to unified scale (for example...

The usual normalization is that g(r) ---> 1 for large r. For comparison with smaller peaks, you can truncate the y-axis.

If there is no value for the constant a that ensures the equality of the two mixed derivative, then it looks to me that there is inconsistency in the experimental data. Note that a = 0, leads to the equation of state of the ideal gas as you can check by integration of dV(T,P).

You cannot integrate this way, in the presence of V(T,P) in the right hand side. You need to have T,P only in the right hand side. To check the validity of the expressions you should invoke the symmetry of the mixed second derivatives. Again when you calculate the second derivative make sure...

Thank you. I'm a bit confused about how your calculation of F leads to the expressions you wrote for V. But the first relevant equation you wrote is very useful because you can replace ∂V/∂P by -VκT and replace ∂V/∂T by Vα. Now the question in the problem sheet asks about something first...

I'm a bit curious about the source of this problem. Could you share the source, please?