Department of Chemistry, Mount Holyoke College, 50 College Street, South Hadley, Massachusetts 01075, USA.
J Chem Phys. 2010 Jun 7;132(21):214709. doi: 10.1063/1.3447377.
When BaZrO(3) is doped with Y in 12.5% of Zr sites, density functional theory with the PBE functional predicts octahedral distortions within a cubic phase yielding a greater variety of proton binding sites than undoped BaZrO(3). Proton binding sites, transition states, and normal modes are found and used to calculate transition state theory rate constants. The binding sites are used to represent vertices in a graph. The rate constants connecting binding sites are used to provide weights for graph edges. Vertex and color coding are used to find proton conduction pathways in BaZr(0.875)Y(0.125)O(3). Many similarly probable proton conduction pathways which can be periodically replicated to yield long range proton conduction are found. The average limiting barriers at 600 K for seven step and eight step periodic pathways are 0.29 and 0.30 eV, respectively. Inclusion of a lattice reorganization barrier raises these to 0.42 and 0.33 eV, respectively. The majority of the seven step pathways have an interoctahedral rate limiting step while the majority of the eight step pathways have an intraoctahedral rate limiting step. While the average limiting barrier of the seven step periodic pathway including a lattice reorganization barrier is closer to experiment, how to appropriately weight different length periodic pathways is not clear. Likely, conduction is influenced by combinations of different length pathways. Vertex and color coding provide useful ways of finding the wide variety of long range proton conduction pathways that contribute to long range proton conduction. They complement more traditional serial methods such as molecular dynamics and kinetic Monte Carlo.
当 BaZrO(3) 中的 Zr 位掺杂 12.5%的 Y 时，基于 PBE 泛函的密度泛函理论预测立方相中会出现八面体畸变，从而产生比未掺杂 BaZrO(3) 更多种类的质子结合位。找到了质子结合位、过渡态和正则模态，并用于计算过渡态理论速率常数。结合位用于表示图中的顶点。连接结合位的速率常数用于为图边提供权重。顶点和颜色编码用于在 BaZr(0.875)Y(0.125)O(3)中找到质子传导途径。找到了许多具有相似可能性的质子传导途径，这些途径可以周期性复制以产生长程质子传导。在 600 K 下，七个和八个重复周期的质子传导途径的平均限制势垒分别为 0.29 和 0.30 eV。考虑晶格重排势垒后，这些值分别提高到 0.42 和 0.33 eV。大多数七个重复周期的途径具有八面体间的限速步骤，而大多数八个重复周期的途径具有八面体内部的限速步骤。虽然包括晶格重排势垒的七个重复周期途径的平均限制势垒更接近实验值，但如何为不同长度的周期性途径赋予适当的权重尚不清楚。很可能，传导受到不同长度途径的组合影响。顶点和颜色编码提供了一种有用的方法来找到对长程质子传导有贡献的多种长程质子传导途径。它们补充了更传统的串行方法，如分子动力学和动力学蒙特卡罗。
