Abstract
The application of a long wavelength limit to Debye theory is examined for small particles at low temperatures. The questions of choice and validity of cut-off are examined, as well as sources of error in the general theory of small particles. An approximate expression is given for the specific heat and Mössbauer recoil-free fraction, with curves showing magnitudes of this effect for various functional relations. Several other possible applications are mentioned.
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My special thanks are extended to Mr. C. C.Dickson, who first suggested this problem to me. I would also like to thank Dr. W. J.Caspers for his helpful criticism, as well as for stimulating discussion of this problem. And Drs. J. R.Luyten deserves thanks for handling the computer work for me.
This work is part of the research program of the “Stichting voor Fundamenteel Onderzoek der Materie” (Foundation for Fundamental Research on Matter) and was made possible by financial support from the “Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek” (Netherlands Organisation for Pure Scientific Research).
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Thiel, R.C. Effect of particle size on excitation of vibrational modes at low temperatures. Z. Physik 200, 227–238 (1967). https://doi.org/10.1007/BF01340527
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DOI: https://doi.org/10.1007/BF01340527