New trends in physics teaching, v.4; The ... - unesdoc - Unesco

New Trends in Physics Teaching IV
1. 0 0 01
no vacancies
one vacancy
two vacancies four vacancies 2
melting point: breakdown of
long range order
Figure 7. Vacancies in a crystal due to thermal motion.
Figure 8 shows Fo, F1, F2 as functions of the temperature. The number of vacancies results from
the condition that the free energy be a minimum for each given temperature. This leads to no
vacancies up to a temperature To = ~/2.8 k, one vacancy for To < T < TI = e/2.1 k and more
vacancies at higher temperature.
The theoretical prediction of the number of vacancies as a function of temperature can be
checked experimentally by measuring the density of the crystal. This density decreases at higher
temperatures due to an increase in the number of vacancies. The vacancies contribute therefore
to the thermal expansion. The main contribution to this expansion is due, however, to the
increase of the lattice constant with temperature, a consequence of anharmonic lattice vibrations.
These effects - vacancies and change in lattice constant - can be measured separately by
determining the lattice constant as a function of temperature with the help of X-ray diffraction.
The difference between the observed change in the lattice constant and the observed thermal
expansion is the contribution of the vacancies shown in figure 9.
TO ERR IS THERMAL: MOLECULES ARE LOUSY COPISTS
In the introductory sections of this paper, we noted that the entropy of isolated thermal systems
always increases, corresponding to a decrease in information about the system. The statement of
the second law of thermodynamics seems to contradict the evolution of life, which has led to a
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