Contains reports on three research projects.United States Navy, Office of Naval Research (Contract Nonr-1841(51)

Dennis, Jane H.

Manley, O. P.

Tavernier, J.

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III. THERMOELECTRIC PROCESSES AND MATERIALS'Prof. R. B. Adler Prof. P. AigrainHtR. E. Nelson L. GodefroyfJane H. Dennis J. TavernierlO. P. ManleyA. ANISOTROPIC THERMOELECTRIC EFFECTS1. THEORYIt was shown in Quarterly Progress Report No. 53, page 34, that the analysis of anondegenerate semiconductor would yield an anisotropic thermoelectric power, providedthat the relaxation times T11 (E) and T1 (E) differ as functions of energy by more than amultiplicative constant.According to the deformation-potential theory of lattice scattering, as generalizedto anisotropic media by Herring and Vogt (1), the relaxation time that results fromlattice scattering alone will be different in different directions but the difference involvesonly a multiplicative constant. That is, T 11 = c 1f (E) and T = cf (E) when the c's areconstants. With this scattering mechanism operating alone, the thermoelectric powerremains isotropic.Suppose, however, that there are two scattering mechanisms operating simultane-ously. Let the additional scattering be isotropic, T.i(E) = f'(E). Then, if the relaxationtimes add as reciprocals,1 1 1I - -+ Tresultant IT iwe have1 1 1 fi(E) + clf (c)T i + -r,1  c1if (E) f (E) c11 f (E) fi(c)1 1 1 fi(E)+ f (E)r1  cIf (E) f i() cf (E) fi (E)from which the energy dependence is no longer factorable.In order for the preceding analysis to be valid, the material must be nondegenerate,This work was supported in part by the U.S. Navy (Office of Naval Research) underContract Nonr-1841(51). Reproduction in whole or in part is permitted for any purposeof the United States Government.tPart-time visiting professor in the Department of Electrical Engineering, M. I. T.tLaboratoire Central des Industries Electriques, Fontenay-aux-Roses, France.(III. THERMOELECTRIC PROCESSES AND MATERIALS)and the doping must be high enough for impurity scattering to be comparable with latticescattering. Ordinarily, this much doping would make the material degenerate. We wantto obtain many impurities, but few free carriers. One way to obtain such a condition isby compensation. A bismuth-telluride crystal grown from a bismuth-rich melt withiodine doping, or a tellurium-rich melt with lead doping, would therefore be likely toexhibit an anisotropic thermoelectric power. This conclusion is being pursued.Jane H. DennisReferences1. C. Herring and E. Vogt, Transport and deformation-potential theory for many-valley semiconductors with anisotropic scattering, Phys. Rev. 101, 944-961 (1956).2. EXPERIMENTWe have succeeded in pulling good single crystals of bismuth telluride, with dimen-sions 12 cm X 1 cm X 2 mm, from a stoichiometric melt. Crystals made in this waywere carefully potted in de Khotinsky cement and cut at a very slow rate on a high-speedsaw. Etching revealed cracks extending 1/4 inch from the edge of the cut. Cuttingwith a hot wire was tried, but such a large wire was required to carry the necessaryheating power that the precision of the cut was not very high. Further attempts to solvethe cutting problem are being made.Jane H. Dennis, O. P. ManleyB. TRANSPORT OF CONTACT MATERIALS IN BISMUTH TELLURIDE1. EXPERIMENTConstruction of a furnace for reacting bismuth and tellurium in an inert atmospherehas been completed, and it is in use in conjunction with the crystal puller. The furnaceconsists of a hermetically sealed vycor tube into which a crucible containing up to 100 gof bismuth and tellurium can be inserted. The inert atmosphere is maintained insidethe furnace by a continuous flow of helium at the rate of approximately 4 ft3/hr.2. THEORYTwo papers dealing with the theory of diffusion have been submitted for publication.A paper co-authored with S. A. Rice, entitled "Comments on 'Dynamical Theory ofDiffusion in Crystals'," was submitted to the Physical Review. This paper correctsthe errors in Rice's original publication (1); it also includes a calculation that greatly(III. THERMOELECTRIC PROCESSES AND MATERIALS)simplifies the ultimate appearance of the pair correlation functions introduced by Rice.A second paper, entitled "A Method of Evaluating Diffusion Coefficients in Crystals,"was submitted to the Journal of the Physics and Chemistry of Solids. This paper recon-siders Rice's model for diffusion with the aid of an extension of Kac's theorem (2). Theanalysis yields an activation energy which, as predicted by Zener (3), is simply relatedto the minimal local deformation energy. It is also found that, in contrast with Rice'streatment, the activation energy may, in the first approximation, be calculated directlyfrom the atomic force constants without resorting to normal-mode analysis.O. P. ManleyReferences1. S. A. Rice, Dynamical theory of diffusion in crystals, Phys. Rev. 112, 804(1958).2. M. Kac, On the distribution of values of trigonometric sums with linearlyindependent frequencies, Am. J. Math. 65, 609 (1943).3. C. Zener, Imperfections in Nearly Perfect Crystals (John Wiley and Sons, Inc.,New York, 1952), p. 289.C. THERMAL CONDUCTIVITY STUDIES1. THEORYThe Tavernier theory of thermal conductivity (1) predicts a proportionality relationbetween thermal conductivity and powers of the parameters Tf, M, p, E, T. For agiven crystal structure, the proportionality constant in the theory has previously beenobtainable only from experimental data. Now the theoretical interpretation of the con-stant is being considered. Knowledge of the anharmonic terms in the crystal potentialenergy is necessary for the development of this theory. An expression for the constantis being sought in terms of macroscopic parameters, such as Gruneisen's constant,compressibility, and so forth, but results are not yet available.2. EXPERIMENTEquipment for the thermal-diffusivity method of measuring heat conductivity isnow available (see Fig. III-1). The first measurements were made at room tempera-ture in high vacuum on germanium and silicon samples. Values of 1 watt/oC cm and0. 6 watt/oC cm for silicon and germanium, respectively, have been observed, but theprecision of the measurements on these high-conductivity materials is very poor.This work is being performed at Laboratoire Central des Industries Electriques,Fontenay-aux-Roses, France.(III. THERMOELECTRIC PROCESSES AND MATERIALS)ROTATION PERIOD, 2 MINUTESSAMPLEI__________ -Fig. III-1. Thermal diffusivity method of measuring heat conductivity.The apparatus is now being used for thermal-conductivity measurements on mixedcrystals in the selenium-tellurium system. The crystals are prepared by melting thedesired quantities of the elements in vacuum-sealed tubes. The first samples purifiedby zone melting in sealed tubes are now available. Measurements of the resistivity pand thermoelectric power Q of these mixed crystals at room temperature have yieldedthe results given in Table III-1.Table III- 1.Composition p Q Type(atomic percentage) (ohm cm) (4v/o C)20o Se 0.8 500 p30% Se 5 600 p40% Se 50 800 pWith 0. 02 watt/°C cm for the thermal conductivity of tellurium, Tavernier's theoryshows that thermal conductivities of approximately 10- 3 watt/°C cm can be obtainedfor such mixed crystals.The reason for interest in solid solutions in the selenium-tellurium system forthermoelectric applications is apparent from these initial results.Other mixed crystals with low percentages of selenium (less then 20 per cent) arebeing prepared. J. TavernierReferences1. P. Aigrain, Thermal conductivity studies, Quarterly Progress Report No. 54,Research Laboratory of Electronics, M.I.T., July 15, 1959, p. 4 9.

Thermoelectric Processes and Materials

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Thermoelectric Processes and Materials

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