## Bond Valence Sum(BVS)

### BVS概述

$$v_{\mathrm{i}}=\exp \left(\frac{R_{0}-R_{\mathrm{i}}}{b}\right) \quad V=\sum\left(v_{\mathrm{i}}\right)$$where $$R_{\mathrm{i}}$$ is the length of a bond between the two given atoms and the bond valence is a measure of the strength of the bond. The parameters  $$R_{\mathrm{i}}$$ and $$b$$ in the equation are compiled or tabulated by I. David Brown. The bond valence has the property that its sum around each atom in a compound is equal to the valence (oxidation state) of that atom. The bond valence is frequently used to validate newly determined crystal structures, but it has many other uses in the analysis and modelling of crystal structures.

(1) Bond valence parameters
(2) Bond valence method-Wiki
(3) Bond-valence parameters obtained from a systematic analysis of the inorganic crystal structure database
(4) 基于键价理论的晶体本征性质经验预测方法与模型及应用-whut博士论文

### 应用-稀土发光领域

然后基于这个和BVS，和Refined occupancies，重新计算了两个格位的BVS。The end member compositions cause one site to be overbonded and one site to be underbonded, while the intermediate compositions with varying Sr/Ba ratios are able to balance this and achieve an optimized bonding network with a BVS close to +2 for both sites. This indicates that the intermediate compositions form a highly rigid crystal structure, which will have an influence on the thermal stability of the photoluminescence. 作者后续用测试了固溶样品的德拜温度，也是中间相的德拜温度最高，但是基于DFT计算的结果和测试结果矛盾。

(2) 当x大于1.2的时候，Ga的某一个格位的BVS计算值远小于3，也就是处在一个非常underbonded，结构不够rigidity，换句话说就是不稳定，此时的XRD数据也表明了杂相的出现。
(3) 基于Rietveld refinement的格位占据结果，占据概率的改变可以balance BVS的不平衡。For all the samples, changing the Sc3+/Ga3+ ratio between the Ga1 and Ga2 sites can balance the deviation in their BVS value. Neither Sc/Ga(Ga1) nor Sc/Ga(Ga2) is highly overbonded or underbonded. The occupancy-corrected BVS values are closed to +3 throughout the entire series. This finding indicates that Ga2−xScxO3:Cr3+ can have a rigid structure, which further affects its thermal stability.

Ce3+掺杂的样品在日常环境下的强度衰减很弱，但是Eu2+掺杂的样品衰减很强(放置时间长会变成amorphous)。这说明site stability was improved to a greater extent by the Ce3+ doping than by the Eu2+ doping, which enhanced the chemical stability of the host.

https://pubs.rsc.org/en/content/articlehtml/2021/tc/d0tc04228e

https://pubs.rsc.org/en/content/articlehtml/2015/tc/c5tc00152h

### 应用-电化学领域

Using 3D bond valence sum difference maps (BVS-DMs),  the absolute values of the difference |Δv| between the calculated valence of the magnesium ion at each point on a 3D grid within the unit cell and the ideal valence of 2 are plotted as isosurfaces, such that the plausible diffusion pathways can be graphically visualized, where points less than 1.6 Å away from the oxygen atoms were excluded for the calculation.

The BVS-DMs are generally used to find plausible locations for intercalated ions and to probe ion conduction pathways in inorganic materials. Thus, a threedimensional (3D) BVS-DM calculation was performed using the crystallographic information derived from the XRD Rietveld refinement.

The figure shows BVS-DM isosurfaces at |Δv| = 0.2 valence units (v.u.) for Mg ions. Possible magnesium-ion diffusion pathways are noted within the interlayer, providing additional support for the electrochemical magnesium intercalation into H2V3O8.

### 实现BVS计算的工具

• FullProf Suite中的Bond_str模块，参考这里
• Materials Studio中的3DBVSMAPPER附件，参考这里
• VESTA，参考视频