01The problem问题
Single-crystal particles avoid the grain-boundary cracking that limits polycrystalline NMC. Large single crystals, however, build up high internal stress during fast discharge, because lithium has further to diffuse. The supplier's customer needed at least 2C capability. A full cell qualification costs about 14 weeks per candidate, so qualifying all four was not an option.
单晶颗粒可以避免多晶 NMC 的晶界开裂。但大尺寸单晶在快速放电时，锂的扩散路径更长，内部应力更高。供应商的下游客户要求至少 2C 能力，而每种候选材料的完整电芯认证约需 14 周，无法四种全做。
02What we did我们做了什么
Measure each powder逐一测量粉体
GITT diffusivity versus state of charge, in-situ XRD for the lattice change (the c-axis collapse above 4.1 V), and nanoindentation for fracture strength.
GITT 测扩散系数随 SoC 的变化，原位 XRD 测晶格变化（4.1 V 以上的 c 轴塌缩），纳米压痕测断裂强度。
Model diffusion-induced stress扩散诱导应力建模
Spherical-particle diffusion coupled to elastic stress, with a partial molar volume that depends on state of charge. Crack probability comes from a Weibull model fitted to the measured strength distribution.
球形颗粒扩散耦合弹性应力，偏摩尔体积随 SoC 变化；开裂概率由基于实测强度分布的 Weibull 模型给出。
Screen across operating conditions跨工况筛选
0.25–3C discharge at 25 °C and 45 °C with a 4.3 V upper cut-off, each candidate at its measured size distribution.
在 25 °C 与 45 °C、上限电压 4.3 V 条件下扫描 0.25–3C 放电，每种候选按其实测粒径分布计算。
Validate cheaply低成本验证
Coin cells, not full cells, cycled 300 times and then cross-sectioned by FIB-SEM, with at least 400 particles counted per sample.
用扣式电池而非全电芯循环 300 次，再做 FIB-SEM 截面，每个样品统计至少 400 个颗粒。
03Results结果
- 6 µm and 8 µm dropped before any cell build. Both exceed the fracture onset inside the customer's 2C requirement.
- 6 µm 与 8 µm 在造电芯前即被淘汰——两者都在客户要求的 2C 以内越过开裂阈值。
- The Al/Zr-doped 4.5 µm candidate carries 58 % less peak stress at 1C than the polycrystalline baseline (75 vs 178 MPa), because doping reduces the lattice collapse by about a third.
- Al/Zr 掺杂 4.5 µm 候选在 1C 下峰值应力比多晶基线低 58 %（75 vs 178 MPa），因为掺杂使晶格塌缩减小约三分之一。
- A size window for the next synthesis round: D50 of 3–5 µm, with doping preferred above 4 µm.
- 为下一轮合成给出粒径窗口：D50 3–5 µm；超过 4 µm 时建议掺杂。
04Limits of validity适用边界
The model idealises particles as spheres, which holds for single crystals with an aspect ratio below 1.5. The polycrystalline baseline is represented by an effective secondary particle, so its comparison is valid as a ranking only, not in absolute stress.
模型把颗粒理想化为球体，适用于长径比小于 1.5 的单晶。多晶基线采用等效二次颗粒表示，其对比仅在排序意义上成立，不代表绝对应力值。