A (0 0 1) SrTiO₃ single-crystal plate was investigated in a temperature range 300-25 K by means of wide-angle X-ray scattering under vacuum conditions. Depending on the quality of surface preparation, the plate exhibited different structural characteristics and low-temperature phase transition and domain behaviour. At the polished surface of the single-crystal plate, in a cooling cycle a cubic (C-phase, space group Pm3̄m)-tetragonal (T-phase, space group I4/mcm) phase transformation was recorded at a temperature of approximately 105 K equal to the known C-T-phase transition temperature of bulk SrTiO₃. When cooling, the formation of antiphase orientation domains of the T-phase was observed starting at a temperature of 80 K. The volume fraction of the domains changed stepwise with decrease of temperature. At the lowest temperature of 25 K, the domains developed at a time scale of several hours. The unpolished surface remained in a single-domain state down to a temperature of 25 K due to the coexistence of ideal perovskite and defect-distorted regions. Considerable change of profile parameters of the X-ray reflection (full-width at half-maximum and integrated intensity) of non-distorted C-phase were recorded below a temperature of about 90 K referred to the C-T-phase transition. The lowering of the transition temperature is attributed to oxygen deficiency of the unpolished surface. The distorted regions do not exhibit any transition-like anomalies at this temperature.