Photopyroelectric study of thermal properties and phase transitions in selected solids

This thesis presents in detail. the theoretical developments and calculations which are used for the simultaneous determination of thermal parameters, namely thermal diffusivity (a). thermal effusivity (e), thermal conductivity (K) and heat capacity (cr ) employing photopyroelectric technique. In our calculations. we have assumed that the pyroelectric detector is supported on a copper backing. so that there will be sufficient heat exchange between the heated pyroelectric detector and the backing so that the signal fluctuations are reduced to a minimum. Since the PPE signal depends on the properties of the detector that are also temperature dependent. a careful temperature calibration of the system need to be carried out. APPE cell has been fabricated for the measurements that can be used to measure the thermal properties of solid samples from ~ 90 K to ~ 350 K. The cell has been calibrated using standard samples and the accuracy of the technique is found to be of the order of± 1%.In this thesis, we have taken up work n photopyroelectric investigation of thermal parameters of ferroelectric crystals such as Glycine phosphite (NH3CH2COOH3P03), Triglycine sulfate and Thiourea as well as mixed valence perovskites samples such as Lead doped Lanthanum Manganate (Lal_xPb~Mn03) Calcium doped (Lal_xCaxMnOJ) and Nickel doped Lanthanum Stroncium Cobaltate (Lao~Sro5Ni,Col_x03).The three ferroelectric crystals are prepared by the slow evaporation technique and the mixed valence perovskites by solid state reaction technique.Mixed valence perovskites, with the general formula RI_xA~Mn03 (R = La. Nd or Pr and A = Ba, Ca, Sr or Pb) have been materials of intense experimental and theoretical studies over the past few years. These materials show . colossal magneloresis/ance' (CMR) in samples with 0.2 < x < 0.5 in such a doping region, resistivity exhibits a peak at T = T p' the metal - insulator transition temperature. The system exhibits metallic characteristics with d %T > Oabove Tp (wherep is the resistivity) and insulating characteristics with d % T < 0 above T p. Despite intensive investigations on the CMR phenomena and associated electrical properties. not much work has been done on the variation of thermal properties of these samples. We have been quite successful in finding out the nature of anomaly associated with thermal properties when the sample undergoes M-I transition.The ferroelectric crystal showing para-ferroelectric phase transitions - Glycine phosphite. Thiourea and Triglycine sulfate - are studied in detail in order to see how well the PPE technique enables one to measure the thermal parameters during phase transitions. It is seen that the phase transition gets clearly reflected in the variation of thermal parameters. The anisotropy in thermal transport along different crystallographic directions are explained in terms of the elastic anisotropy and lattice contribution to the thermal conductivity. Interesting new results have been obtained on the above samples and are presented in three different chapters of the thesis.In summary. we have carried investigations of the variations of the thermal parameters during phase transitions employing photopyroelectric technique. The results obtained on different systems are important not only in understanding the physics behind the transitions but also in establishing the potentiality of the PPE tool. The full potential of PPE technique for the investigation of optical and thermal properties of materials still remains to be taken advantage of by workers in this field.

Some Lattice Problems In Fuzzy Set Theory And Fuzzy Topology

It is believed that every fuzzy generalization should be formulated in such a way that it contain the ordinary set theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9] with an arbitrary complete and distributive lattice as the membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy topologies on a set. It is proved that in general, the lattice of fuzzy topologies is not complemented. Complements of some fuzzy topologies are found out. It is observed that (L,X) is not uniquely complemented. However, a complete analysis of the problem of complementation in the lattice of fuzzy topologies is yet to be found out