How did Debye derive nu max and nu average?

[acherentia]

Homework Statement

In Atkins's physical chemistry textbook it is written that Debye considered atoms to oscillate from 0 up to a nu max. It is explained further in the text that the complication (i.e., not all atoms oscillating at same frequency as shown in Einstein's formula) is accounted for, by averaging over all the frequencies present.

An average is not a maximum however?! How did he measure the frequencies that were present so as to get the average?

Homework Equations

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The Attempt at a Solution

 

[NateD]

Debye's theory of specific heat did not necessarily involve measuring the frequencies present, but instead assumed that all oscillations of a particular atom occurred at the same frequency, known as the Debye frequency. This was determined by Einstein's formula. The complication of not all atoms oscillating at the same frequency was then accounted for by averaging over all the frequencies, which is known as the Debye-Waller factor. This factor takes into account the fact that some atoms oscillate faster than others and thus the average frequency is lower than the maximum frequency.