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Four studies of point defects RbTiOPO4 and KTiOAsO4 crystals are described in this dissertation. In the first study, electron paramagnetic resonance (EPR) and electronnuclear double resonance (ENDOR) are used to characterize the complex hyperfine patterns exhibited by the primary radiation-induced trapped hole center in single crystals of RbTiOPO4 (commonly referred to as RTP). These defects are produced at 77 K by irradiating with x rays, and they are destroyed by raising the temperature above approximately 170 K. In this center, the hole resides on a bridging oxygen ion located between two titanium ions and is stabilized by a nearby rubidium vacancy. Hyperfine splittings from interactions with one rubidium neighbor and one phosphorus neighbor are resolved in the EPR spectra. The ENDOR spectra show one larger phosphorus interaction and four smaller phosphorus interactions. Principal values and principal axis directions for this larger phosphorus interaction are obtained from the ENDOR angular dependence. In the second study, the dominant Ti3+ trapped electron center in flux-grown RbTiOPO4 crystals is characterized using EPR and ENDOR. This center is produced during an x-ray irradiation at room temperature when a Ti4+ ion traps an electron and becomes a Ti3+ ion, and it is best studied in the 30 to 40 K range. The EPR spectrum contains a three-line hyperfine pattern from two nearly equivalent neighboring 31P nuclei, along with hyperfine lines from the 47,49Ti nuclei. The g matrix, determined from the angular dependence of the EPR spectrum, has principal values of 1.819, 1.889, and 1.947. Hyperfine matrices for four 31P nuclei are obtained from the angular dependence of the ENDOR spectrum (two of these are resolved in the EPR spectrum). The proposed model for this defect is a Ti3+ ion adjacent to an oxygen vacancy. Analogies are made to a similar Ti3+ center in KTiOPO4 (KTP) crystals. In the third study, the primary trapped hole and trapped electron centers in single crystals of KTiOAsO4 (KTA) are investigated using EPR and ENDOR. Only preliminary results are reported. Forbidden transitions arising from significant nuclear electric quadrupole interactions at one or more neighboring 75As nuclei (I = 3/2, 100% abundant) may be important in explaining the observed complex hyperfine patterns. Analogous effects are not present in the EPR and ENDOR spectra of similar point defects in KTP crystals because the 31P nuclei (I = 1/2) do not have a nuclear electric quadrupole moment. In the fourth study, EPR is used to identify and characterize Pt + (5d9) ions in fluxgrown KTA. The platinum is present as an unintentionally impurity. In the as-grown crystals, Pt0 (5d10) atoms substitute for K+ ions. When the crystals are irradiated with x rays at room temperature or 77 K, the Pt 0 atoms trap holes and convert to Pt+ ions. Once formed, these Pt+ ions are stable for weeks at room temperature. The EPR spectrum of the Pt+ ions is best observed in the 20 to 30 K range. Principal values and principal-axis directions for the g matrix and the 195Pt hyperfine matrix are obtained from a complete set of EPR angular dependence data. These principal values are 1.509, 1.898, and 2.859 for the g matrix and 96.2 MHz, 316.8 MHz, and 616.5 MHz for the 195Pt hyperfine matrix. Formation of the Pt+ ions is accompanied by a gray coloration that may affect device performance when KTA crystals are used in nonlinear optical applications.