ANALYSIS OF THERMOELECTRIC POWER OF Li, Na & K LIQUID ALKALI METALS

Thermoelectric power of Li, Na & K liquid alkali metals have been studied using pseudo potential approach. The present study concludes that the recent value of the thermoelectric power departs only by 3% from its experimental value and does not require any arbitrary reduction of Vopw as (3 = 1. This method gives uniformly good agreement for these alkali metals.


INTRODUCTION
In the analysis of physical properties of metals Parameterized model potentials have been widely used by Heine and Weaire [Solid State Physics, Vol.-24, p. 3 (1970)]. For the calculations the parameters have generality been adjusted to some gross property of metals. Harrison's first principle method ["Pseudopotential in the theory of metals" (W. A. Benjamin, Inc. New York, 1966)] provides the crystal potential involving the energy value and eigen function of core electrons. In this scheme core electron eigen functions are generally assumed to be identical in the metal and in the free ion [Phys. Rev., 135, A-1363, (1965)].
This approach has been applied by Cutler et al [J. Phys. F 5, 1801 (1975)] to the study of phonon frequencies of alkali metals. Hafner  2 Computation of form-factor: The screened form factor is expressedas where Vq a b are the valence charge and core potentials, Vq c is the conduction-band-core exchange potential. Vq The constants A and B for the metals are A = 1.00714 and B = 6.2986 (for Lithium) and A = 1.00778 and B = 0.2855 (for sodium), e (q) is the Hartree -dielectric function given by A modification of equation (1) for Harrison's form factor has been done in respect of Vopw appearing in equation (4) and Vq° appearing in equation (1) Vopw has been replaced by where e is the electronic charge, kB in the Boltzmann constant, EF is the free electron Fermi energy and X is a dimensionless parameter and is known as the thermopower coefficient defined by where R(E) is the electrical resistivity, Bradley et al.
[Phil. Mag. 7, 865 (1962)] have expressed X as where k refers to the wave vector of the incident electron and is taken to be kF in the evaluation.

RESULTS AND DISCUSSION
The thermoelectric power of alkali metals (Li, Na, and K) at melting point has been calculated through the equation (5) It may be noted that Hafner used the value of α= 1 [Phys. Rev., 81, 3185, (1951)] which necessitated to reduce the V opw arbitrarily by a factor β = 5/8 in order to set excellent agreement with the experimental phonon ftequency. But the recent values of α = 0.78147 ["Quantum theory of molecules and atoms" (McGraw-Hill Pub. Co. Inc. New York, 1972) (P-27)] on the basis of the generalized statistical exchange approximation with β = 1 gives consistently good results for the thermoelectric power. This does not require any arbitrary reduction of Vopw as was done by Hafner. Table-4. also demonstrates the same effect for Na. Hafner has taken α = 2/3 of Kohn and Sham (Phys. Rev., 140, A-1133 (1965)) and here also he has to take β = 5/8 in order to get better agreement in the phonon frequency. The calculated thermoelectric power comes out to be -7.14 ΩV/K whereas the reported experimental values is-9.9 (Cusack, Rep. Progr, Physics, 26, 361(1963)) and -8.9 ΩV/K (Bradley, Phil. Mag., 7, 1337 (1962)). If one takes the recent value of α = 0.73115 (9) with β = 1, the thermoelectric power comes out to be -10.18 ΩV/K. In this case, however the thermoelectric power departs only by 3% from its experimental value and does not require any arbitrary reduction of V0Pw as = 1.

(In atomic units) and energy (In Ryd) For
Li and Na  Table 1 gives the constants for Li and Na, computed form factors of Li and Na with different values of α and β are given in Table 1. Table -3    The present study concludes that the recent value of slater's exchange does not require any arbitrary reduction of Vopw by a factor It has been observed that the thermoelectric powers of Potassium is in poor agreement.
It has been observed from Table 3 that in the case of Lithium for the values of = 1 and = 5/8 as used by Hafner the thermoelectric power calculation yields a negative a negative value whereas the experimental value is of positive sign. This makes the situation ambiguous and one cannot accept the combination. Further with the recent value of α equal to 0.78147 (9) and =1, we find that the situation improves considerably. The calculated vatue of the thermoelectric power comes out to be 15.57 μV/K in comparison with the experimental value of 21.5 μV/K (Cusack, Rep. Progr. Physics, 26, 361(1963)).
The cause behind this low value of thermoelectric power in magnitude in the case of K is the higher value of form-factor at q = 2KF. This increases the value of P in Bradley et al's formula (equation-8) and hence in turn reduces the value of thermoelectric power coefficient (X).