Thermo-electricity at low temperatures III. The absolute scale of thermo-electric power: a critical discussion of the present scale at low temperatures and preliminary measurements towards its redetermination

In order to compare exactly the present theory of thermo-electric power in metals with the behaviour of the simple alkali metals, particularly sodium, at low temperatures, it is necessary to know the absolute thermo-electric, power of one single conductor. There has been only one such determination of an absolute scale of thermo-electric power, and this was derived 23 years ago as the outcome of measurements which had been made primarily for other purposes. As measurements of the thermo-electric force of the alkali metals at low temperatures have recently become available, it is appropriate now to review critically the experimental basis of that scale. In view of new experimental evidence on the behaviour of the thermo-electric power of superconductors just above the transition point which has appeared in the last few years, it appears that a redetermination of the scale is necessary, at least at low temperatures. In this paper the present absolute scale of thermo-electric force is critically discussed particularly in relation to preliminary measurements towards its redetermination.

In earlier work, the absolute thermo-electric force, E of the alkalis was measured from about 60°K down to about 4°K. The absolute thermo-electric power ( S=dE/dT ) could then be derived with fair accuracy down to perhaps 8°K. The thermo-electric power of all the alkali metals has now been measured directly between 2 and 20°K, and the Thomson heats derived therefrom. The results are compared with the theory both of the ‘normal’ thermo-electric power and the Gurevich or ‘phonon-drag’ effect. It is clear from the work that experiments below 1 °K in this field will be of much interest and a programme has been started in this temperature range.


In the previous part (VII) the absolute thermo-electric power ( S ) of all the alkali metals was measured directly between 2 and 20°K. Measurements have now been made of the absolute thermo-electric force, E , of all the alkali metals below 2°K and down to about 0.1°K by means of adiabatic demagnetization techniques. The absolute thermo-electric power, S , is derived with fair accuracy from these results ( S = d E /d T ). The results are compared with theoretical developments, particularly those of Bailyn and Ziman.


In order to compare the fundamental theory of thermo-electricity at low temperatures with the behaviour of the ‘simple’ alkali metals (in particular of sodium and potassium) it is essential to have an accurate knowledge of the absolute thermo-electric power of one pure metallic conductor against which the measurements can be made. We have accordingly determined the absolute thermo-electric power of zone-purified lead up to 18°K by direct measurements against the superconductor Nb 3 Sn. The new measurements, because of the high superconducting transition temperature of Nb 3 Sn, leave only the very small region between 18 and 20°K in which the Thomson heat of lead must be interpolated to join the values obtained by Borelius and co-workers in earlier work, in order to extend the new scale of absolute thermo-electric power of lead up to room temperature. The variation of the Thomson heat of lead as a function of temperature below 20°K appears to be of some intrinsic interest.


The theory of the transport phenomena in metals is re-examined, the departure from equilibrium of both the electron and the lattice distribution functions being simultaneously taken into account in a consistent fashion. Simple expressions are derived for the conduction magnitudes which are exact at sufficiently high and sufficiently low temperatures and which are assumed to be approximately valid for all temperatures. The behaviour of the terms which arise from the non-equilibrium of the lattice depends upon the relative importance of the various causes responsible for scattering the lattice vibrations. In the case of the electrical conductivity these terms are estimated to be small in general, but they may have a bearing on some of the observed resistance anomalies at very low temperatures. Further, while the present theory gives nothing new in the case of the thermal conductivity, which is given by the sum of the usual electronic and lattice conductivities, the behaviour of the thermo-electric power is found to be profoundly modified, the non-equilibrium of the lattice leading in general to a considerably increased value which may show a complex temperature variation. The theory can account for the observed thermo-electric power of sodium at low temperatures and it suggests reasons for the complex character of the thermo-electric behaviour of metals in general, although in the present form the theory is not sufficiently general to account for all the observed anomalies even in the monovalent metals.


Makinson’s extension of Wilson’s treatment of the second-order effects in metals is used to derive an expression for the contribution of the lattice current to the thermo-electric power of metals at those temperatures where electron-phonon scattering predominates. It is found that in this temperature region one may expect the thermo-electric effect to show a sign opposite to the one which follows from the simple electron theory of metals. This is because the term due to the departure from equilibrium of the lattice distribution is larger than the usual term and is of opposite sign. If the temperature is greatly decreased or increased, the usual term predominates. The effect discussed may have a bearing on the behaviour of the thermo-electric power of the alkali metals, although it cannot explain this behaviour completely.


1964 ◽  
Vol 135 (4A) ◽  
pp. A890-A898 ◽  
Author(s):  
Ivars Henins ◽  
J. A. Bearden

A new method, employing a superconducting galvanometer and requiring a temperature difference of only 0·01° K between the ends of the specimen, has been used to measure the absolute thermo-electric powers of tin and silver at liquid-helium temperatures. It has been shown that the thermo-electric power of tin vanishes abruptly at the superconducting transition temperature; this observation disagrees with the conclusions of Casimir & Rademakers, who report a curious behaviour above the transition temperature which they hold to ‘foreshadow’ the onset of superconductivity. The thermo-electric behaviour of metals in the normal (non-superconducting) state shows striking disagreement with the predictions of the free-electron theory. Thus, the thermo-electric power does not vary linearly with the absolute temperature, and for silver has a positive, instead of a negative, sign. The thermo-electric power is profoundly influenced by the presence of strains in the specimen, and by very small amounts of impurity, the temperature dependence becoming more nearly linear for impure or highly strained specimens. A marked anisotropy has been found in the thermo-electric behaviour of single crystals of tin.


1964 ◽  
Vol 42 (1) ◽  
pp. 53-69 ◽  
Author(s):  
A. F. Dunn

In the past decade or two, the measurement of capacitance has become of much greater importance in many fields of scientific and technological investigation as well as forming the basis of many production applications. The capabilities of the capacitance measuring techniques available are of great importance, and the measurement and maintenance of an absolute scale of capacitance has become of prime importance. In the National Research Council of Canada, the absolute unit of capacitance is now known with an accuracy better than ±0.0005%, with the capability of scaling the unit of capacitance over six decades of capacitance both above and below 1 pf (1 × 10−12 f) without introducing an additional indeterminacy any greater than ±0.0005% or ±0.3 af (af = attofarad = 10−18 f).


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