It is shown that the force constants of a solid cannot be deduced from the lattice frequencies alone. The fact that a set of force constants agrees with the frequencies exactly is no guarantee that the force constants are even approximately correct. Detailed eigenvector measurements would resolve the uncertainty. A solid has many more force constants than frequencies. The usual procedure gets round this by retaining only the largest force constants and then using at least as many frequencies as the number of retained force constants to calculate the latter. This procedure is incorrect, because neglecting the small force constants limits the accuracy to which the frequency data can be used to calculate the retained constants. In fact, the number of data that can be extracted from the frequency measurements is
always less
than the number of force constants one wants to calculate. Therefore, even if all the lattice frequencies were known exactly they could still be satisfied with a very wide range of very different sets of force constants. A large proportion of these sets cannot be rejected on the basis of physical criteria alone. Using the methods of continuous transformation theory, for diamond all the ways are constructed in which the force constant matrix can be changed continuously without altering the agreement with the frequencies. A numerical example is included.
Ab-initio density-functional lattice-dynamics studies of ice
