SOME PROBLEMS OF CONDENSED MATTER

Abstract

The thesis has been divided 'into Five Chapters as given below: Chapter-I This chapter contains Introduction where the work done by other workers is briefly reviewed. The brief review is essential for the background of the problems to be taken up in the chapters to follow. 0 Chapter-I I This chapter deals with the basic assumption on the basis of which the work reported in the present thesis is carried out. The basic assumption taken is that the product of the isothermal bulk modulus, BT, and the thermal coeffi-cient of volume expansion, a , for a substance at a given temperature is pressure-independent parameter, i.e., BT(P, T) a(P, T) = BT(0, T) a(0, T) = C(T) The constancy of the product has been shown in some substances. The most important result of the basic assumption is that a new re.at ion for the isothermal Anderson-Grune isen parameter, FT, is obtained i.e. 6BT .1 a8T V aBT whereas Chang has given the relation as &T=E(a ) T It is shown that the present result suggests q=1 whereas Chang' s result suggests q=0 where q is defined as. Y(P,T) = Y(O, T) Thus,. .the present value of q=1 is really very close to reality. Further, sorry more applications of the basic assumption are discussed which support the basic assumption, Furthermore., a justification of the basic assumption has also been tried on the basis of thermodynamics. Chagte r- I This chapter deals with the pressure dependence of Gruneisen paraneter,Y. In this chapter, a simple theory for the pressure dependence of Grune isen parameter is developed on the basis of basic assumption of chapter II along with other thermodynamic relations. The final results show that Y varies linearly with pressure, i.e. Y(P,T) = Y(O,T) - rlP where q has been found as ("T) where B = T aP T , ~ aBs and B Hence, t is a temperature dependent but pressure independent par an ter. vi The important point is that n} may have positive or negative sign depending upon whether B1 > BS or BT < B The sign of i is very important as it will decide whether y decreases or increases . with pressure. The calculated results of Y(P, T) in the whole range of pressure and temperature have been shown in good agreement with the experimental results in all the systems studied like NaCl, CaF2, MgO, Na,K,Li etc. Further, it is also shown that the present theory is capable of giving the pressure dependent relations for q and. I (De bye temperature) . Cher— This chapter deals with the melting laws. Using (i) Linde_mann's relation and (ii) the results of chapter III, a relation for the melting temperature with pressure is developed. The relation so dev3loped identifies automatically the Simon constants in term of physical quantities whereas the theoretical methods used so far have been unsuccessful to identify them correctly. Thus, Simon relation has been shown to be based on the theoretical concepts rather being merely an empirical relation. Further, it is shown that the Kennedy's melting law as well as the law given by Reynolds, Faughnan and Barker (RFB) follow well from the present relation. vii Calculations of the melting temperatures with ,pressure have been done in many systems like sodium f.loride, Argon etc. A new melting law is also suggested during the course of the study. teo r V This chapter deals with the equation of state. First of all, a general approach of the problem is discussed and it is shown that the equation of state ,like (i) Tait (ii) Murnaghan (iii) Keane (iv) Grover, Getting and Kennedy (v) Line arlized Tait equation given by Couchman and Reynold and (vi) Birch can be easily obtained on the basis of the general approach. Further, a three parameter general equation of state is taken and the calculations done for pressure as a function of V/Vo are ,found in very good agreement with the experimental data. But, this general equation of state is also found to have its own drawbacks. In the second place, a new three parameter equation of state is developed based on a totally new point of view. This equation has been applied, successful in more than fifty solids and liquids. In each case, with no exception, the excellent agreement is obtained between the calculated and the experi- mental values of V/ 0 as a function of pressure.