论文标题
周期性缺陷对晶格能量最小化器的影响
Effect of periodic arrays of defects on lattice energy minimizers
论文作者
论文摘要
我们考虑互动能量$ e_f [l] $之间的点$ o \ in \ mathbb {r}^d $，$ d \ geq 2 $，以及一个包含$ o $的晶格$ l $，其中相互作用的潜在$ f $假定是辐射的对称性和衰减，并在无限的速度上足够快。当整数sublattices $ k l $删除（定期空缺阵列）或替换（定期替代缺陷阵列）时，我们研究了$ e_f $的最佳结果的保存。我们考虑单独考虑非偏移的（$ o \ in K l $），并转移（$ o \ in in k l $）案例，我们得出了几个一般条件，以确保在新能量（包括缺陷）的新能量中的通用优化器（非）最佳性。此外，在逆权法律和Lennard-Jones型电势的情况下，我们为在固定密度下的最小值结果保存最小化结果提供了不变的周期空缺或替代缺陷的必要条件。提出了不同的应用示例，包括对某些离子样结构的Kagome晶格和能量比较的最佳结果。
We consider interaction energies $E_f[L]$ between a point $O\in \mathbb{R}^d$, $d\geq 2$, and a lattice $L$ containing $O$, where the interaction potential $f$ is assumed to be radially symmetric and decaying sufficiently fast at infinity. We investigate the conservation of optimality results for $E_f$ when integer sublattices $k L$ are removed (periodic arrays of vacancies) or substituted (periodic arrays of substitutional defects). We consider separately the non-shifted ($O\in k L$) and shifted ($O\not\in k L$) cases and we derive several general conditions ensuring the (non-)optimality of a universal optimizer among lattices for the new energy including defects. Furthermore, in the case of inverse power laws and Lennard-Jones type potentials, we give necessary and sufficient conditions on non-shifted periodic vacancies or substitutional defects for the conservation of minimality results at fixed density. Different examples of applications are presented, including optimality results for the Kagome lattice and energy comparisons of certain ionic-like structures.
