The thesis begins with a brief introduction and relevant literature references. The novelty of synthesis, methodology and results of the work reported in the thesis and highlighted subsequently. The thesis consist of three parts, Part A of the thesis consist of five chapters describing new methods of synthesis of orthovanadates, mainly dealing with the structure and photocatalytic properties of synthesized materials. Part B of the thesis consist of two chapters dealing with an unique crystallization methodology for subliming and low melting organic compounds and the crystal structure determination via single crystal X-ray diffraction. Part C consists of one chapter presenting the ab-initio approach of structure determination via powder X-ray diffraction methods. Chapter 1 of the thesis presents the synthesis of three zircon type lanthanide orthovanadates, LnVO4 (Ln = Ce, Pr and Nd) via a new solution based approach at room temperature and photodegradation of a variety of water pollutants have been investigated. Chapter 2 describes the importance of microwave synthesis to produce nano particles of the zircon type lanthanide orthovanadates LnVO4. The importance of the surface area in photocatalysis is evaluated. Chapter 3 consist of the synthesis of a series of new compounds, Ln0.95φ0.05Mo0.15V0.85O4 (Ln = Ce, Pr and Nd) via solid state method. The photocatalytic activities of these compounds are investigated both under UV exposure and sunlight. Chapter 4 presents the synthesis of MxCe1-xVO4+ (M = Li, Ca and Fe) with x = 0.1, 0.25 and 0.05 respectively. Different kinds of dyes and organics are degraded under UV radiation and the specificity towards the same are evaluated. Chapter 5 describes a comparative photocatalytic conversion of cyclohexane and benzene to cyclohexanol, cyclohexanone and phenol respectively by LnVO4, LnMo0.15V0.85O4 and MxCe1-xVO4+ (Ln = Ce, Pr and Nd, M= Li, Ca and Fe with x = 0.1, 0.25 and 0.05 respectively). Kinetics of above photoconversions are established by proposing a mechanism and determining the rate constants. Chapter 6 describes the development of a novel apparatus for the crystallization of anhydrous adenine, whose structure has not been solved over the last few decades. The crystal structure is solved via single crystal X-ray diffraction. Chapter 7 presents a modified design for crystallization of low melting organic compounds and co-crystals. A new polymorph of anhydrous thymine has been grown with this apparatus and its structure has been analyzed and compared with the known form of thymine. Chapter 8 presents the ab-initio approach of structure determination via powder X-ray diffraction methods. The methodology of using the direct space approach for the determination of the crystal structure of N-(2-fluorophenyl) benzamide (a drug intermediate), which could not yield good quality single crystals, is outlined.