Heat Transfer Handbook part 133. The Heat Transfer Handbook provides succinct hard data, formulas, and specifications for the critical aspects of heat transfer, offering a reliable, hands-on resource for solving day-to-day issues across a variety of applications. | 1318 MICROSCALE HEAT TRANSFER 0 1 0 Wavevector k Figure Plot of the frequency of a plane wave propagating in the crystal as a function of wavevector. Note that the relationship is linear until k 1 a. where M is the mass of an individual atom. By taking the time dependence of the solution to be of the form exp -i t the frequency of the solution as a function of the wavevector can be determined as given by eq. . Figure shows the results of this equation plotted over all the values that produce independent results. Values of k larger than n a correspond to plane waves with wavelengths less than the interatomic spacing. Because the atoms are located at dcscrete points tolutions to the equations above yielding wavelengths less than the interatomic spacing are not unique solutions and tl se oolutions can be equally well represented yy long-wavelength solutions. ÄK k V M 1 sin - ka 2 The results shown in Fig. apply for a Bravais lattice in one dimension which can be representedby a linear chain of identical atoms connectedby springs with the same spring constant K. A Bravais lattice with a two-point basis can be represented in one dimension by either a linear chain of alternating masses M1 and M2 separated by a constant spring constant K or by a linear chain of constant masses M with the spring constant of every other spring alternating between K1 and K2. The theoretical results are similar in both cases but only the case of a linear chain with atoms connected by two diHc iont spriggs K1 and K2 where the springs alternate between the atoms is discussed. The results are shown in Fig. . The displacement of each atom from each equilibrium point is given by either u na for atoms with the K1 spring on their right and v na for atoms with the K1 spring on their left. The reason for selecting this case is its similarity to the diamond structure. Recall that the diamond structure is a FCC Bravais lattice with a two-point basis all the atoms are .
