Contains reports on five research projects

Gyorgy, E. M.

Harvey, George G.

Kingston, R. H.

Kip, A. F.

Meckler, A.

Reiner, D.

Sondheimer, E. H.

Tisza, Laszlo

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III. SOLID STATE PHYSICSProf. G. G. Harvey E. M. GyorgyProf. A. F. Kip R. J. HarrisonProf. L. Tisza R. H. KingstonDr. E. H. Sondheimer A. MecklerD. ReinerA. THE THEORY OF SUPERCONDUCTIVITYThe quantum mechanical theory of superconductivity reported earlierwas based essentially on the use of many electron wave functions which cor-respond to covalent bond structures extending over the whole crystal. Thesupercurrent arises through quantum resonance between different bond struc-tures equivalent under the translation group of the crystal.The question arises whether such covalent bonds can be made plausiblefor actual superconductors on the basis of other properties of these crystals.This question could be answered in the affirmative.Superconductors appear in two neatly separated groups in the periodictable provided the A and B elements are listed side by side rather than beloweach other. The so-called soft superconductors (Al, Zn, Ga, Cd, In, Sn, Hg,Tl, Pb) turn out to be identical with a class of metals delimited by Hume-Rothery (1) on the basis of their irregular structure. The irregularitieshave been attributed by him to a slight tendency toward covalent bonding.A somewhat similar tendency of the hard superconductors (Ti, V, Zr,Cb, La, Hf, Ta, Re, Th) can be understood on the basis of a hypothesis ofPauling (2) according to which the d-shell of the transition elements splitsup into two bands, the lower one of which contributes through covalent bond-ing to the cohesive energy of the crystals. L. TiszaReferences(1) W. Hume-Rothery, uThe Structure of Metals and Alloys", p. 21, London(1936).(2) L. Pauling, Phys. Rev. 54, 899 (1938).B. SOFT X-RAY VACUUM SPECTROGRAPHThe vacuum systems for the spectrograph proper and for the x-ray chamberhave been completed and are now operating satisfactorily. A vacuum of1 x 10-6 mm of mercury can be maintained in the large spectrograph chamber,and somewhat better than this in the x-ray tube which is isolated from the-22-(III. SOLID STATE PHYSICS)chamber by the slit system.The grating and entrance slit have been lined up optically, Somefurther adjustment may be necessary in order to obtain best focusing, sincethis has not yet been tested. The travel system for the electron multipliercarriage has been lined up, and the leads and trolleys for carrying thevoltages to the multiplier installed. Parts for the multiplier itself,which will serve as the detector, are nearly ready for assembly.A preliminary electron gun for the x-ray tube has been constructed andtested. It will probably be satisfactory for trial, but we hope to obtainhigher current with a new gun. The present gun is set up for direct bombard-ment of the target, without deflecting plates for the electron stream, andso does not prevent tungsten from striking the target. It should, however,be satisfactory for use in checking the alignment of the grating and detectorsystem. G. G. Harvey, E. M. Gyorgy, R. H. Kingston, A. MecklerC, PARAMAGNETIC RESONANCE EXPERIMENTSEquipment for studying resonance absorption of paramagnetic salts atmicrowave frequencies is being modified to allow experiments at liquid heliumtemperatures. The immediate purpose of this is to allow the study of certainrare earth salts. Conventional susceptibility measurements on these saltsleave considerable uncertainty as to the details of the crystalline forcesacting on the paramagnetic ions. The microwave method will separate theeffects of each ion in the unit cell and will therefore add considerably tothe detailed knowledge of the crystalline forces. Low temperatures arenecessary in order to increase spin-lattice relaxation times, which at roomtemperature broaden the occurring resonances to such an extent that theycannot be detected. We are in the process of procuring single crystals ofPr2 (S04) * 8H20 and Nd2 (S04) 3 * 8H20 for these experiments.A. F. Kip, D. ReinerD. THE INFLUENCE OF A MAGNETIC FIELD ON THE CONDUCTIVITYOF THIN METALLIC FILMS (1)The numerical integrations necessary for the detailed evaluation ofthe theory are being carried out by the Joint Computing Group.E. H. SondheimerReference(1) Preliminary report in "Nature", November 1949.-23-(III. SOLID STATE PHYSICS)E. THE THEORY OF THE TRANSPORT PHENOMENA IN METALSThe theory of the transport phenomena in metals depends upon the solu-tion of a complicated integral equation for the velocity distribution func-tion of the conduction electrons (1). Exact solutions of this equationhave been obtained by A. H. Wilson for the two limiting cases of temperatureslow and high compared with the Debye temperature, and approximate interpola-tion formulas have been set up to join the exact solutions (2). These inter-polation formulas are known to give incorrect results at intermediate tem-peratures (3), and the problem of determining the temperature variation ofthe electric and thermal conductivities of a metal in the region close tothe Debye temperature presents considerable difficulties.It seems impossible to obtain an exact solution in closed form, butrecently a new line of advance has been opened up by M. Kohler who has shownthat the integral equation can be transformed into an equivalent variationalproblem (4). A solution may now be obtained by expanding the distributionfunction as a power series and using the variation principle to determinethe coefficients. It can be shown that, for a completely degenerate elec-tron gas, the calculations can be carried out explicitly to any order ofapproximation, the conductivities being finally obtained as the ratio oftwo infinite determinants. (A corresponding expression has been obtainedfor the thermoelectric power.) The interpolation formulas find a naturalplace in this scheme, being obtained as the zero approximation on retainingonly the lowest terms in the determinants which give a non-zero result.The higher approximations are of complicated algebraic form but are welladapted to numerical work; the first few correction terms are now beingevaluated numerically with the aid of the Joint Computing Group.The interpolation formulas were originally obtained by assuming thegeneral validity of Matthiessen's rule concerning the additivity of theresidual and ideal resistances of an impure metal. We find that the rulebreaks down in the important temperature region where the residual andideal resistances are of the same order of magnitude; and the numericalresults will enable us to discuss the nature and the extent of the devia-tions from Matthiessen's rule. The numerical results will also be of inter-est in connection with the thermal conductivity K. Wilson's interpolationformula predicts that K should pass through a minimum at intermediatetemperatures (5), but no such minimum has ever been observed. The exactsolution is known to lead to increased values of K and may, in fact, possessno minimum.E. H. Sondheimer(III. SOLID STATE PHYSICS)References(1) A. H. Wilson, "The Theory of Metals", p. 215, Cambridge (1936).(2) A. H. Wilson, Proc. Camb, Phil. Soc. 33, 371 (1937).(3) G. P. Dube, Proc. Camb. Phil. Soc. 34, 559 (1938).(4) M. Kohler, Z. Physik 124, 772 (1948); 125, 679 (1949).(5) R. E. B. Makinson, Proc. Camb. Phil. Soc. 34, 474 (1938).-25-

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