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The temperature dependence of EQ/E-comes from the factor C V T. The line in Fig. 1 represents the fit of (EQ/EJ) to the product of T and a Debye specific-heat function. This is a twoparameter fit; the Debye temperature is found from the fit to be 14.8°K and the low-temperature limit of (EQ/E^ to be Eo/E f = 1. 6 x 1CT 7 T 4 . At very low temperatures all of the thermally excited phonons interact with the electrons and C v is the total lattice specific heat of the crystal. Thus, the right-hand side of Eq. (3) involves no adjustable parameters in the low-temperature limit. Using values measured on our specimen for JLI, W, and t, and Bryant and Keesom's 5 value for C v , in Eq. (3) gives EQ/EJ = 1.1 xKT 7 T 4 , about two thirds of the measured value. value.The value of 0, the effective Debye temperature of the interacting phonons, is a measure of q m , the maximum wave vector of the interacting phonons, or of the number of phonon modes which interact with the electrons. The observed value, 9 = 14. 8 °K, corresponds to 8 x 10 18 modes per cm 3 , in other words, about one mode per electron. Although calculation of the number of phonons which drift with the electrons is difficult because of the anisotropy of the electronic energy bands, we would have expected that the electronic motion would impart the drift velocity to a large Null-deflection torque magnetometer studies 1 ' 2 have been carried out on annealed homogeneous Pb-Tl alloys (4. 3-12. 3 at.% Tl) in the form of thick films (1.4-4.2 /i) and foils (25-100 jx) over the interval 1.1 ^ T < 4.2°K, with the applied field H very nearly in the plane of the specimen. By this method, the measured field dependence of the torque r defines a characteristic field H T at which T/H departs from its initially linear dependence on H. The departure from linearity can be ascribed to flux penetration, in accord with our measurements on thick annealed pure Pb films which exhibit linear T/H behavior until number of phonons. In the case of a spherical Fermi surface, phonons with wave vector less than twice the Fermi wave vector can scatter electrons directly. The sphere of such directly interacting phonons in wave-number space contains 12 phonon states (including the three polarization branches) per electron. Since each of the electron valleys contain 1/4 of the electrons, the number of directly interacting phonons might be reduced to three per electron. However, because not all valleys interact with the same phonons, the number should be somewhat larger than three. The number might be reduced if the higher energy scattered phonons had short momentumloss relaxation times, so that they remained in equilibrium even though scattered by the electrons.

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takes place whenf(w) = (jOrr/sq, an equation that can be solved graphically to obtain the frequency wd where the acoustic and electromagnetic branches are degenerate. Ordinarily this transcendental equation possesses only one real root. However, there is a range of the magnetic field for which it can have up to three real roots. In this Letter we shall limit ourselves to the former situation. By treating the right-hand side of Eq. (5) as a perturbation, the solution for the eigenfrequencies at the crossover to first order in O 0 is For a metal such as sodium in a magnetic field of the order of 5xl0 4 G, the crossover frequency u) d is approximately equal to 3.6xl0 9 sec" 1 . The splitting at this point is about 12% of u^. The considerable admixture of acoustic and helicon modes in this region suggests the possibility of exciting transverse phonons in metals by means of electromagnetic radiation of the appropriate frequency. In Fig. 1 we give a graphical representation of the zeros of Eq. (5) in terms of the parameter w =qvQAV For tlie purpose of this calculation we have considered sodium at aThe Fermi surfaces of nonferromagnetic metals have been extensively investigated by de Haas-van Alphen (dHvA) and related techniques. Corresponding data on the magneto-oscillatory properties of ferromagnetic metals are much less complete, although preliminary dHvA effect results on Fe have been reported by Anderson and Gold, 1 and Shubnikov-de Haas oscillations have been detected in Co by Fawcett and Reed. 2 In this Letter we describe dHvA oscillations observed in nickel single crystals by means of a null deflection torsion balance in steady magnetic fields up to 40 kG. The dHvA oscillations were studied as a function of magnetic field orientation in the (001) and (11~0) crystallographic planes. The variation of the period of the oscillations in these planes suggests that at least one sheet of the Fermi surface of nickel is similar to that of the noble metals, in accord with a model of the Fermi surface proposed by magnetic field for which w at the crossover is Wfi = 2. Under this assumption £ 0 = 4.8 x 10 4 G i-and/(w^) = 0. 684. The foregoing results are, of course, only valid if CU 0 T » 1. Further details of this work will be the subject of a subsequent publication.The authors would like to thank J. Bok and D. N. Langenberg for communicating their results 6 prior to publication, M. Lampert for many helpful suggestions, and K. M. Brown for kindly assisting with the numerical calculations.Fawcett and Reed on the basis of magnetoresistivity studies.The torsion balance used for this study was modified so that the large steady torques exerted on the sample due to the ferromagnetic anisotropy of nickel could be nullified. Samples were cut from a single crystal nickel rod [p(300°K)/ p(4.2°K)*990] in the form of disks (0.20-in. diamx0.030 in. thick) and each was mounted with its axis of rotation vertical. In the first sample the [110] axis coincided with the disk axis, so that the magnetic field was located in the (1 TO) plane....

Low dimensional systems, nanowires (NWs), in particular, have exhibited excellent optical and electronic properties. Understanding the thermal properties in semiconductor NWs is very important for their applications in electronic devices. In the present study, the thermal conductivity of a freestanding silicon NW is estimated by employing Raman spectroscopy. The advantage of this technique is that the excitation source (laser) acts as both the heater and probe. The variations of the first-order Raman peak position of the freestanding silicon NW with respect to temperature and laser power are recorded. From the analysis of effective laser power absorbed by exposed silicon NW and a detailed Raman study along with the concept of longitudinal heat distribution in silicon NW, the thermal conductivity of the freestanding silicon NW of ∼112 nm diameter is estimated to be ∼53 W m−1 K− 1.