One-step custom design of experiment was employed for the simultaneous screening and optimization of raw yield (Y₁) and percent yield (Y₂) with heating temperature, T (190–220 °C) and reaction time, t (1.0–2.5 h) as the predictors in a conventional solvothermal magnetite nanoparticles (NPs) synthesis. Two accurate models capable of explaining 98.3% variability in the data were developed. A strong correlation exists between the actual yields (Y₁, Y₂) and their predicted counterparts (r = 0.99). T, t, Tt and t² terms have a significant synergistic effect on the yields the at α = 0.05. The diagnostic plots depicted the effects in the order t > T > Tt > t². Surface and contour plots show maximum Y₁ (0.295 g) and Y₂ (105%) at T = 219 °C and t = 2.5 h. The optimizer plot shows maximized Y₁ (109.94%) and Y₂ (0.31 g) at the highest predictor values (T = 220 °C, and t = 2.5 h) at composite desirability of 1. NPs characterization using various techniques revealed nanocubes and nanospheres with a mean diameter of 23.9 ± 7.9 nm, the crystallite size of 8.3 ± 1.4–20.4 ± 4.9 nm, a pore size of 9.07–24.47 nm, and surface area of 35.80–93.57 m² g⁻¹. The NPs exhibit stretching Fe–O vibrations at 571 cm⁻¹ for tetrahedral and at 428 cm⁻¹ for octahedral geometries in the infrared spectra and are thermally stable within the range 30–700 °C with low weight loss (8.81–32.92%) typical of mesoporous magnetite phase.

采用一步定制的实验设计，同时筛选和优化了加热温度T（190–220°C）和反应时间t（1.0–2.5 ）时的原始收率（Y ₁）和百分收率（Y ₂）。 h）作为常规溶剂热磁铁矿纳米颗粒（NPs）合成的预测因子。开发了两个能够解释数据中98.3％变异性的准确模型。实际收益率（Y ₁，Y ₂）与预测的收益率（r = 0.99）之间存在很强的相关性。T，t，Tt和t ²项对α= 0.05时的产量具有显着的协同作用。诊断图以t> T> Tt> t ²的顺序描述了这些影响。。表面和轮廓图显示了在T = 219°C和t = 2.5 h时的最大Y ₁（0.295 g）和Y ₂（105％）。优化器图显示了在复合期望值为_1时，在最高预测值（T = 220°C，t = 2.5 h）下，Y ₁（109.94％）和Y ₂（0.31 g）最大化。使用各种技术对NPs的表征揭示了纳米立方体和纳米球，平均直径为23.9±7.9 nm，微晶尺寸为8.3±1.4–20.4±4.9 nm，孔径为9.07–24.47 nm，表面积为35.80–93.57 m ²  g ^-1。NP在四面体的571 cm ^-1和428 cm ^-1处表现出拉伸的Fe–O振动 用于红外光谱中的八面体几何形状，并且在30–700°C的温度范围内具有热稳定性，且介孔磁铁矿相的典型失重较低（8.81–32.92％）。