Note on Frequency Spectra of Simple Solids from Specific Heat Data
dc.contributor.author | Katz, Ernst | en_US |
dc.date.accessioned | 2010-05-06T21:26:00Z | |
dc.date.available | 2010-05-06T21:26:00Z | |
dc.date.issued | 1951-04 | en_US |
dc.identifier.citation | Katz, E. (1951). "Note on Frequency Spectra of Simple Solids from Specific Heat Data." The Journal of Chemical Physics 19(4): 488-493. <http://hdl.handle.net/2027.42/69971> | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/69971 | |
dc.description.abstract | If the specific heat C(T) of a solid is given as a function of temperature from T=0 to ∞ with infinite accuracy, the frequency spectrum f(ν) is uniquely determined. What information about f(ν) can be derived from specific heat data of experimental accuracy? The following conclusions give the answer.(1) Experimental specific heats determine accurately the low frequency part of the frequency spectrum but allow a latitude, wide enought to fit almost any theory, for its high frequency part.(2) In a Debye plot (effective Debye temperature θ versus T) peaks and dips in the region 0<T<θ/10 represent dips and peaks in the low frequency part of the frequency spectrum. The correspondence is so simple that it can be interpreted at a glance. The peaks and dips are superimposed on a simple Debye spectrum and presumably have a direct physical meaning, in terms of lattice irregularities. Only their centers and total weights are obtainable, so that they act effectively as single Einstein frequencies.(3) In the region θ/5<T<∞ all information obtainable about f(ν) consists of the first few even moments (three for specific heat errors of order one percent, five for 0.1 percent). These can be represented respectively by two or three weighted equivalent Einstein functions without direct physical meaning.(4) The region θ/10<T<θ/5 corresponds to the high frequency part of the frequency spectrum, but hardly any information can be derived here. | en_US |
dc.format.extent | 3102 bytes | |
dc.format.extent | 461576 bytes | |
dc.format.mimetype | text/plain | |
dc.format.mimetype | application/pdf | |
dc.publisher | The American Institute of Physics | en_US |
dc.rights | © The American Institute of Physics | en_US |
dc.title | Note on Frequency Spectra of Simple Solids from Specific Heat Data | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Physics Department, University of Michigan, Ann Arbor, Michigan | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/69971/2/JCPSA6-19-4-488-1.pdf | |
dc.identifier.doi | 10.1063/1.1748252 | en_US |
dc.identifier.source | The Journal of Chemical Physics | en_US |
dc.identifier.citedreference | M. Blackman, Rept. on Progress in Physics, Phys. Soc. London 8, 11 (1941). E. W. Montroll, J. Chem. Phys. 10, 218 (1942), and 11, 481 (1943). W. V. Houston, Revs. Modern Phys. 20, 161 (1948). R. B. Leighton, Revs. Modern Phys. 20, 165 (1948). | en_US |
dc.identifier.citedreference | S. H. Bauer, J. Chem. Phys. 6, 403 (1938), and 7, 1097 (1939). | en_US |
dc.identifier.citedreference | E. Blade and G. E. Kimball, J. Chem. Phys. 18, 626 (1950). | en_US |
dc.identifier.citedreference | H. Grayson‐Smith and J. P. Stanley, J. Chem. Phys. 18, 236 (1950). | en_US |
dc.identifier.citedreference | A combination of Debye and Einstein spectra was previously introduced by Nernst (see E. Schroedinger, Handbuch der Physik (1926), Vol. X, p. 314). His viewpoint, however, was entirely different. His Einstein components represented optical branches for polyatomic crystals and would not occur in monatomic lattices. In the present paper this form is chosen as a way of describing mathematically any empirical C(T)C(T) in a rapidly convergent series. | en_US |
dc.identifier.citedreference | The qualitative merit of this substitute spectrum was previously pointed out by E. W. Montroll, Quart. App. Math. 5, 223 (1947). | en_US |
dc.identifier.citedreference | This relation differs slightly from that given by Mott and Jones in Properties of Metals and Alloys (Oxford University Press, 1936), p. 8, whose factor is 16∕9 instead of 5∕3. | en_US |
dc.identifier.citedreference | See for instance F. Seitz, Modern Theory of Solids (McGraw‐Hill Book Company, Inc., New York, 1950), p. 104 or E. Schroedinger, reference 5. | en_US |
dc.identifier.citedreference | Mott and Jones, reference 7, p. 8, or M. Blackman, reference 1, p. 13. | en_US |
dc.identifier.citedreference | H. Cramer, Mathematical Methods in Statistics (Princeton University Press, Princeton, 1946), p. 255. | en_US |
dc.identifier.citedreference | H. B. G. Casimir, oral communication at the summer symposium lectures, Ann Arbor, 1948. It was suggested that Keesom’s measurements on KCl, which show a similar type of fine structure, were not accurate enough to warrant theorizing about this point. This suggestion was based on a discussion of this question between Casimir and Keesom. | en_US |
dc.owningcollname | Physics, Department of |
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