Hafnia (HfO₂) and zirconia (ZrO₂) are of great interest in the quest for replacing silicon oxide in semiconductor field effect transistors because of their high permittivity. Both exhibit extensive polymorphism and understanding the energetics of their transitions is of major fundamental and practical importance. In this study, we present a systematic thermodynamic summary of the influence of particle size on thermodynamic phase stability in hafnia and zirconia using recently measured enthalpy data from the literature. The amorphous phase is found to be the most energetically stable above 165 and 363 m²/g of surface area for HfO₂ and ZrO₂, respectively. Below 16 and 20.3 m²/g of surface area, respectively, the monoclinic phase is the most energetically stable for HfO₂ and ZrO₂. At intermediate sizes there are closely balanced energetics among monoclinic, tetragonal, and cubic phases. The energy crossovers reflect decreasing surface enthalpy in the order monoclinic, tetragonal, cubic and amorphous for both hafnia and zirconia.

中文翻译：

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尺寸驱动的热力学交叉法在氧化锆和氧化f中的相稳定性

f（HfO ₂）和氧化锆（ZrO ₂）因其高介电常数而在半导体场效应晶体管中寻求替代氧化硅引起了人们的极大兴趣。两者都表现出广泛的多态性，并且理解它们的转变的能量学具有重要的基础和实践意义。在这项研究中，我们使用最近从文献中测得的焓数据，提供了粒径对氧化ha和氧化锆中热力学相稳定性影响的系统热力学总结。对于HfO ₂和ZrO ₂，分别在165和363 m ² / g的表面积上发现无定形相在能量上最稳定。16和20.3 m ^2以下相对于每克表面积/ g，单斜晶相对于HfO ₂和ZrO ₂在能量上最稳定。在中等大小时，单斜晶相，四方晶相和立方晶相之间的能量平衡非常接近。对于哈夫尼亚和氧化锆，能量交换反映出表面焓按单斜晶，四方晶，立方晶和非晶态的顺序递减。