Judging from the figures and from what she actually observed, Alice noticed
that when the radius of the sphere became larger than or about 2.8Å, most of
the time she was able to count four atoms of oxygen in that sphere. This was
exactly what she had observed in the ice phase. In contrast, in the liquid phase,
there were some deviations from that exact number. Infrequently, a fifth atom
would enter into the sphere and even more rarely, a sixth or more counts.
Wanting to put together a substantial report, Alice meticulously and systematically
examined the frequencies of the number of oxygen molecules in a sphere
of radius 3.5Å, taking many snapshots of the scene around her, counting the
number of oxygen atoms that were found inside that sphere — but excludingthe oxygen atom she was sitting on. Satisfied with her work, she then made a
histogram, a plot of the occurrence of various frequencies (Fig. 6.6).
Repeating the same measurements at different temperatures as she had done
previously, she noticed that the general appearance of the histogram did not
change much although it appeared that the whole histogram was veering gradually
to the right. As the temperature increased, the average occupancy of
the sphere of radius 3.5Å increased — the maximum coordination number
increased. The spread of the molecules over the various coordination numbers
also increased.Alice was convinced and felt confident that she had gathered enough ‘new’
data worth discussing with Professor Holmes. With these thoughts fresh in her
mind, she yelled the password and before she knew it, she was back with the
professor once again.
Beaming with pride, she showed the Professor all the tables and charts
she had painstakingly put together. Her report was a clear demonstration of
her thoroughness and attention to detail — something that did not escape the
Professor’s attention.
“You’ve done a very good job Alice,” said the professor, clearly impressed.
“This is an important start. What you have discovered is what scientists call the
distribution of coordination number. This is exactly what you have recorded in
your graph of the frequencies of occurrence of different numbers of ‘neighbors,’
which is also referred to as coordination numbers. As you may well remember,
the coordination number in ice was fixed.”