To study non-ideal mixing in an entropy stabilized system, the entropy stabilized oxides HfTiO₄ and ZrTiO₄ were mixed to form the single phase (Hf-Zr)TiO₄ system. HfTiO₄ and ZrTiO₄ are entropy stabilized relative to their constituent oxides (HfO₂, ZrO₂, and TiO₂). Oxide-melt solution calorimetry (OSMC) was performed to determine enthalpies of formation relative to the constituent oxides (ΔH_f,ox) for 11 compositions in the (Hf-Zr)TiO₄ system. ΔH_f,ox for HfTiO₄ was determined to be 22.81 $\pm 2.61$$\pm 2.61$ kJ/mol. ΔH_f,ox for ZrTiO₄ was measured to be 20.79 $\pm$$\pm$ 2.67 kJ/mol which is in good agreement with literature values. Positive ΔH_f,ox values for HfTiO₄ and ZrTiO₄ demonstrates entropy stabilization. X-ray absorption spectroscopy (XAS) data shows that Ti is locally segregated from the Hf and Zr. ΔH_f,ox values for mixed HfTiO₄-ZrTiO₄ samples were used to calculate enthalpies of mixing relative to the HfTiO₄ and ZrTiO₄ end points ($\Delta H_{mix})$$\Delta H_{mix})$. $\Delta H_{mix}$$\Delta H_{mix}$ was determined to be most exothermic ($\Delta H_{mix}$$\Delta H_{mix}$ = -5.3 kJ/mol) at a composition of (Hf_.5Zr_.5)TiO₄. Negative $\Delta H_{mix}$$\Delta H_{mix}$suggests that Hf and Zr experience further ordering upon mixing of HfTiO₄ and ZrTiO₄. X-ray powder diffraction (XRPD) experiments show that the (Hf-Zr)TiO₄ system forms a single-phase product across the composition range with pbcn symmetry (space group #60) and does not form any ordered super structures, as noted by the lack of superlattice reflections. X-ray powder diffraction (XRPD) data additionally reveals that the (Hf-Zr)TiO₄ system has a highly anisotropic positive excess volume, with the majority of the excess volume resulting from changes in the b-lattice parameter. X-ray absorption spectroscopy (XAS) results demonstrate that mixing between Hf and Zr on the local level is non-ideal but cannot ascertain if ordering or segregation occurs. High-resolution transmission electron microscopy (HR-TEM) experiments are needed to fully elucidate the local structure in the (Hf-Zr)TiO₄ system. Using the (Hf-Zr)TiO₄ system as case study, this work shows that mixing in entropy stabilized systems is not always ideal and can give rise to complex local structures that can have interesting and unexpected effects on the chemical and physical properties, such as the large excess expansion along the b-direction.

中文翻译：

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熵稳定 （Hf-Zr）TiO4 系统中的过量热化学性质和局部结构


为了研究熵稳定体系中的非理想混合，将熵稳定氧化物 HfTiO ₄ 和 ZrTiO ₄ 混合形成单相 （Hf-Zr）TiO ₄ 体系。HfTiO ₄ 和 ZrTiO ₄ 相对于它们的组成氧化物（HfO ₂ 、ZrO ₂ 和 TiO ₂ ）是熵稳定的。进行氧化物熔融量热法 （OSMC） 以确定 （Hf-Zr）TiO ₄ 系统中 11 种成分相对于组成氧化物 （ΔH _f,ox ） 的形成焓。HfTiO 的 ΔH _f,ox 确定为 22.81 $\pm 2.61$ kJ/mol。ZrTiO ₄ 的 ΔH _f,ox 测量为 20.79 $\pm$ 2.67 kJ/mol，与文献值吻合较好。 ₄ HfTiO ₄ 和 ZrTiO ₄ 的正 ΔH _f,ox 值表明熵稳定。X 射线吸收光谱 （XAS） 数据显示，Ti 与 Hf 和 Zr 局部分离。混合 HfTiO -ZrTiO 样品的 ΔH _f,ox 值用于计算相对于 HfTiO ₄ 和 ZrTiO ₄ 终点的混合焓 （ $\Delta H_{mix})$ . _{4 4} $\Delta H_{mix}$ 被确定为 （Hf _.5 Zr _.5 ）TiO ₄ 的成分最放热 （ $\Delta H_{mix}$ = -5.3 kJ/mol）。否定表明 $\Delta H_{mix}$ Hf 和 Zr 在 HfTiO ₄ 和 ZrTiO ₄ 混合时经历进一步的排序。X 射线粉末衍射 （XRPD） 实验表明，（Hf-Zr）TiO ₄ 系统在 pbcn 对称性（空间群 #60）的成分范围内形成单相产物，并且没有形成任何有序的超结构，如缺乏超晶格反射所指出的那样。 X 射线粉末衍射 （XRPD） 数据还显示，（Hf-Zr）TiO ₄ 系统具有高度各向异性的正过量体积，其中大部分过量体积是由 b 晶格参数的变化引起的。X 射线吸收光谱 （XAS） 结果表明，Hf 和 Zr 在局部水平上的混合并不理想，但无法确定是否发生有序或偏析。需要高分辨率透射电子显微镜 （HR-TEM） 实验来充分阐明 （Hf-Zr）TiO ₄ 系统中的局部结构。以 （Hf-Zr）TiO ₄ 系统为例，这项工作表明，在熵稳定系统中混合并不总是理想的，并且会产生复杂的局部结构，这些结构可能会对化学和物理性质产生有趣和意想不到的影响，例如沿 b 方向的大过量膨胀。