The Molecular Tactics of a CrystalKelvin, William Thomson, Baron
Science
The Molecular Tactics of a Crystal
Kelvin, William Thomson, Baron
Crystallography, Mathematical
§ 33. In the case of globes packed together in closest order (and
therefore also in the case of ellipsoids, if all similarly oriented),
our condition of coherent contact between each molecule and twelve
neighbours implies absolute rigidity of form and constancy of bulk.
Hence our convex solid must be neither ellipsoidal nor spherical
in order that there may be the changes of form and changes of bulk
which we have been considering as dependent on three independent
variables specifying the orientation of each solid relatively to rows
of the assemblage. An interesting dynamical problem is presented by
supposing any mutual forces, such as might be produced by springs, to
act between the solid molecules, and investigating configurations of
equilibrium on the supposition of frictionless contacts. The solution
of it of course is that the potential energy of the springs must be a
minimum or a minimax or a maximum for equilibrium, and a minimum for
stable equilibrium. The solution will be a configuration of minimum or
minimax, or maximum, volume, only in the case of pressure equal in all
directions.
§ 34. A purely geometrical question, of no importance in respect to
the molecular tactics of a crystal but of considerable interest in
pure mathematics, is forced on our attention by our having seen (§ 27)
that a homogeneous assemblage of solids of given shape, each touched
by twelve neighbours, has three freedoms which may be conveniently
taken as the three angles specifying the orientation of each molecule
relatively to rows of the assemblage as explained in § 30.
Public-domain text, read in full here on John Shaqi.
Reviews
Reviews
No reviews yet
Be the first to share your thoughts on this work.
Join the Discussion
Join the discussion
Sign in to leave a comment or review.
Sign InorCreate an account