The main purpose of this dissertation is to design, synthesize and grow novel photoelectric functional crystal materials， especially to explore the deep-ultraviolet birefringent crystal and mid-infrared nonlinear optical crystal materials. In this work, we followed the following idea and strategies: (1) introducing the large electronegativity halogen to extend the bandgap; (2) introducing the alkali metal and alkaline earth metal elements which is without the d-d electron transition to explore the UV-DUV materials; (3) employing the cations susceptible to second-order Jahn-Teller (SOJT) effects, octahedrally coordinated d0 transition metals and lone-pair cations (e.g., Pb2+) to enhance the SHG response; (4) follow the anionic group theory, lewis acid theory and dimensional reduction theory to design and synthesize new compounds. 1. Na3Ba2(B3O6)2F: next generation of deep-ultraviolet birefringent materials. We have fully developed a new deep UV birefringent crystal of NBBF. A single crystal of NBBF with dimensions of 35 mm × 35 mm × 9 mm was grown from its stoichiometric melt for the first time in 2 days, a greatly improved crystal growth method. These NBBF crystals achieve desirable optical properties with a large birefringence (Δn = 0.0750?0.2554) from the IR (3.35 μm) to the deep UV (175 nm) range. NBBF melts congruently with no phase transitions and possesses the lowest growth temperature among birefringent materials, which is beneficial for the growth of large, high quality optical single crystals. The good chemical stability and mechanical properties make it easy to process by cutting and polishing. In particular, by comparing its optical, thermal, and mechanical properties with the industrial birefringent materials, we believe that NBBF is an attractive candidate for the next generation of deep UV birefringent materials. 2. Pb17O8Cl18: a promising IR nonlinear optical material with large laser damage threshold synthesized in an open system. We have successfully developed POC as a new promising IR NLO crystal. It is type-I phase matchable with a large powder SHG efficiency of about 4 times that of KDP at 1064 nm and 6 times that of AgGaS2 at 2090 nm. The introduction of the Cl- anion with a large electronegativity and Pb as a relatively heavy element in POC gives rise to the extension of its UV and IR cut-off edge to 0.34 and 13.9 μm, respectively. POC also exhibits high thermal stability. Remarkably, POC could effectively overcome the two main drawbacks of the commercially available IR NLO materials: (a) it shows high LDT of 408 MW/cm2, which is 12.8 times that of the benchmark IR NLO AgGaS2 materials; (b) transparent POC single crystals with sizes up to 7 mm × 2 mm × 2 mm can be obtained in an open system, which can overcome the difficulty to grow high-quality crystals by the conventional Bridgman?Stockbarger technique. Theoretical morphology of POC was studied according to the Bravais–Friedel and Donnay–Harker (BFDH) theory.We therefore believe that POC is a promising IR NLO material and research to grow larger high quality POC single crystals is in progress. 3. Application of dimensional reduction formalism to Pb5(PO4)2P2O7. We have successfully synthesized Pb5(PO4)2P2O7, a novel unitary metal phosphate with two types of discrete P-O groups, which is very rare. We obtained its LT phase and RT phase using the variable-temperature X-ray single crystal diffractions and confirmed the temperature section of phase transition by the the variable-temperature powder X-ray diffractions technique. The synthesis followed the dimensional reduction theory. 4. Synthesis, crystal structure and properties of Pb8M(BO3)6 (M = Mg, Ca). Followed the Lewis acid theory, we have successfully synthesized Pb8M(BO3)6 (M = Mg,Ca) through the substitution of cations with the similar lewis acid strength. Pb8M(BO3)6 (M = Mg,Ca) contain ?[Pb8B6O18]2- double layer, the double layers are connected by Mg2+ (Ca2+) along the c axis. The synthesis of Pb8M(BO3)6 (M = Mg,Ca) is a good example of using the lewis acid theory.