Introduction Strontium zirconate titanate is an important dielectric material with a high dielectric constant and a low dielectric loss. Also, as a semiconductor catalytic material, it has an application potential in the fields of photocracking water and photodegradation of organic matter. However, as a semiconductor catalytic material, SrTixZr(1-x)O3 has a wide band gap and a low carrier migration rate. Element substitution is commonly performed via ion doping at the B site (i.e., Ti element site) in the lattice. The resulting lattice defects inhibit photogenerated electron-hole recombination and narrow the band gap, thereby improving the catalytic efficiency. At present, the doping of transition metal elements such as Nb, Co, Rh, Fe and Ce is beneficial to reducing the band gap and promoting its response to visible light. Little studies have been reported to explain the morphology of single crystal particles by theoretical calculations. In this paper, SrTixZr(1-x)O3 single crystal nanoparticles with different Ti/Zr molar ratios were synthesized by a hydrothermal method. The micro-morphology, crystal size and light response characteristics of SrTixZr(1-x)O3 single crystal nanoparticles were investigated. In addition, the micro-morphology of SrTixZr(1-x)O3 single crystal nanoparticles was also revealed based on the first-principles calculation.Methods Strontium chloride hexahydrate (SrCl2·6H2O) and titanium tetrachloride (TiCl4) from Sinopharm Chemical Reagent Co., Ltd., China, were used as raw materials, respectively. Zirconium tetrachloride (ZrCl4) and lithium hydroxide (LiOH) from Shanghai McLean Biochemical Technology Co., Ltd., China, were used as zirconium source and pH regulator. SrTixZr(1-x)O3 nano-single crystal particles with different molar ratios of titanium to zirconium were prepared by a hydrothermal method at 180 ℃ for 12 h.The phase composition, microstructure and element distribution of the samples were determined by X-ray diffractometer and thermal field emission scanning electron microscope with energy dispersive spectrometer. The light response characteristics of the samples were characterized by UV-visible spectrophotometer. Based on the first-principles density functional theory (DFT), 3 kinds of SrTi0.25Zr0.75O3, 6 kinds of SrTi0.5Zr0.5O3 and 3 kinds of SrTi0.75Zr0.25O3 2×2×2 supercell configurations were designed and calculated.Results and discussion SrTixZr(1-x)O3 nano-single crystal exhibits a perovskite structure. The diffraction peak becomes wider when element Zr gradually replaces elemen Ti. SrCO3 as an impurity phase can be removed by calcining at 1 200 ℃. The hydrothermal reaction synthesized SrTiO3 with a cubic phase shows a regular hexahedron morphology. Most of SrZrO3 crystals with an orthorhombic phase are flat octahedron morphology. The particles basically tend to be regular hexahedron morphology when Ti:Zr= 1:3 and 3:1. However, the lattice distortion effect of SrTixZr(1-x)O3 crystal reaches the maximum, and some of the morphologies are star-shaped when Ti:Zr=1:1.The lattice parameters of SrTixZr(1-x)O3 unit cell configuration were calculated by first-principles density functional theory. In SrTi0.5Zr0.5O3 system, the configurations (iv), (viii) and (ix) are transformed into orthorhombic crystals, and the maximum lattice constant c reaches 9.5 ?. The ground state energies of configurations (iii), (v) and (xii) are 2.538, 1.530 eV and 0.949 eV, respectively. Based on the principle of energy minimization, the crystal grows preferentially according to these configurations. Thus, SrTixZr(1-x)O3 (x=0.25, 0.75) grains exhibit a uniform hexahedral morphology. The octahedral dip angle, bond lengths and angles of four configurations (iii), (v), (ix) and (vii) are selected to analyze the symmetry change and lattice distortion of the crystals. The octahedral bond angles are more than 179.9° in the three lowest ground state energy configurations, which maintain a structural symmetry. However, Ti(Zr)O6 octahedron tilt angles of the configuration (ix) are mainly concentrated at 145°-153°. The Ti(Zr)—O bond lengths are distributed in the range of 1.711-2.926 ?. This indicates that equimolar Ti/Zr causes the lattice distortion due to the change of bond length and angle. The lattice distortion promotes the formation of star-like morphology. The light response characteristics show that the band gap of SrTixZr(1-x)O3 nano-single crystal particles decreases with the increase of Ti4+ proportion. The band gaps of SrTi0.25Zr0.75O3, SrTi0.5Zr0.5O3 and SrTi0.75Zr0.25O3 are 3.70, 3.47 eV and 3.34 eV, respectively, which are consistent with those obtained via the first-principles calculations.Conclusions Perovskite structure SrTixZr(1-x)O3 nano-single crystal particles with different Ti/Zr molar ratios were synthesized by a hydrothermal method. SrTi0.25Zr0.75O3 and SrTi0.75Zr0.25O3 both were transformed into a hexahedral morphology. A special star-shaped polyhedron morphology appeared in SrTi0.5Zr0.5O3 sample. The lattice parameters and energy band structure of SrTixZr(1-x)O3 were obtained via the first-principles calculations. The lattice distortion effect appeared as Ti/Zr=1. There were lattice parameters of three configurations in the supercell lattice arrangement are a=b≠c, where c can be up to 9.570 ?. The actual crystal growth process of the SrTi0.5Zr0.5O3 system was partially carried out according to these arrangements. The heterogeneous nucleation mechanism was induced by different crystal configurations and the lattice distortion, which promoted the formation of star-shaped grains. The band gap change rule of the samples was verified by ultraviolet-visible spectrophotometer. The increase of element Ti ratio led to the decrease of the band gap since the energy level of Ti 3d orbital was lower than that of Zr 4d orbital.