# Degeneracies in Optical Modes in relation to Heat Capacity in a Solid

1. Nov 2, 2014

### war485

Technically I'm supposed to have a total of 8 optical modes but only 4 of them were seen in a solid (by spectroscopy). So I suspect there's some degeneracies and symmetries involved, but I don't know which ones.
I have two sets of assigned degeneracies:

frequency; degeneracy set 1; degeneracy set 2
f#1 ; 2 ; 5
f#2 ; 2 ; 1
f#3 ; 2 ; 1
f#4 ; 2 ; 1

This is what I'm attempting below:
I'm doing some quick calculations assuming Einstein's model of a solid for heat capacity at several temperatures.
What I want is to find the individual contributions of each optical mode to the heat capacity.
For each frequency per degeneracy set, I'm taking: (calculated heat capacity)*(4 observed modes)*(corresponding degeneracy assignment for given frequency) / (8 total optical modes).
For example, for f#1: (heat capacity)*(4*2/8) + (heat capacity)*(4*5/8).
Is that the correct way to incorporate/weigh/factor/scale degeneracy into heat capacity per optic mode?

2. Nov 7, 2014