. The Bell System technical journal . onstant volume and in it no allowance ismade for the energy due to thermal expansion. The experimentalpoints are derived from measurements of specific heat at constantpressure which have been transformed by using a thermodynamicalrelationship so as to give specific heat at constant volume. For these curves 6d was chosen so as to obtain the best fit. It is,however, possible to calculate do from theory by using the elasticconstants of the material to evaluate Ct and Cl and then substitutingin Eq. (8). For sodium the elastic constants have been calculatedenti
. The Bell System technical journal . onstant volume and in it no allowance ismade for the energy due to thermal expansion. The experimentalpoints are derived from measurements of specific heat at constantpressure which have been transformed by using a thermodynamicalrelationship so as to give specific heat at constant volume. For these curves 6d was chosen so as to obtain the best fit. It is,however, possible to calculate do from theory by using the elasticconstants of the material to evaluate Ct and Cl and then substitutingin Eq. (8). For sodium the elastic constants have been calculatedentirely from theory by the methods described in the section on Taken from E. Schroedinger, Handbuch der Physik, Vol. X, p. 307 (1926). THE QUANTUM PHYSICS OF SOLIDS 697 ^\§- + J + lo 1 - 1 ■■ I 1 SEPARATE PLOT FOR HIGHER TEMPERATURES FOR; o Tl X J ^ Na o Hg + cd • KBr \ •\ \. 1 -*^ ^ >^ ■^-.^J 1 ^•^-^ » a >. ^-* n o o ~^ -^ ^^^ isl OD <3 O^HlCK, --^ -<» ^^ • + ^^ ^i;, ^ Q- 0X 0 ■«»te.,^_^ ^ a SoU. SPECIFIC HEAT AT CONSTANT VOLUME, Cy, IN CALORIES PER GRAM ATOM PER DEGREE CENTIGRADE 698 BELL SYSTEM TECHNICAL JOURNAL Electrons in Crystals and extensions of them* to be discussed in thethird paper of the series. Using the theoretical values one obtainsa value of 143° K for 6d, whereas the value that fits experiment bestis 172° K. Recently calculations have been made from a model of the crystalas an assemblage of atoms rather than as a continuum as postulatedin deriving Eq. (7)—that is, a model like the coupled oscillators, ratherthan like the stretched membrane, is used. These calculations, prin-cipally by Blackman, have explained some discrepancies between theDebye theory and experiment. The Specific Heat of the Electrons We must now see why the electrons contribute only slightly to thespecific heat. Let us consider a case like that of sodium where we havea partially filled band. At the absolute zero of temperature, the elec-trons will fill all th
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