AI 中文总结
本文将经典成核理论重构为几何闭合热力学框架，统一描述跨三类磁体系的纳米颗粒成核，定量复现相关实验结果，为磁场控制纳米颗粒尺寸提供高效计算方法。
AI 中文摘要
合成过程中控制纳米颗粒尺寸仍是纳米科学的核心挑战，尤其对于以外部磁场作为连续控制参数的体系。现有磁场辅助成核的描述通常针对特定材料，或依赖计算量大的原子级方法。本文通过引入原子组装的球堆积表示，将经典成核理论重构为几何闭合的热力学框架，该构建建立了离散原子结构与外加磁场下连续自由能贡献之间的直接联系，得到临界核尺寸的场驱动演化方程。所得理论在单一形式体系内对超顺磁、顺磁和抗磁体系的纳米颗粒成核提供统一描述，定量复现了此前未解决的磁铁矿和镍纳米颗粒的实验观测结果，即平均颗粒尺寸随磁场增大而系统减小、尺寸分布随磁场增大而变窄。在抗磁极限下，该框架恢复了作者此前基于 susceptibility（磁化率）的银纳米颗粒解析描述，其中场依赖的临界半径由诱导磁化对成核自由能的贡献决定。除了对平均颗粒尺寸随磁场增大而减小的建模外，该框架还揭示尺寸分布变窄是场修正自由能景观曲率的自然结果。这些结果确立磁场辅助成核为几何约束的热力学过程，为跨不同磁类材料控制纳米颗粒尺寸提供了计算高效的途径。
英文摘要
Controlling nanoparticle size during synthesis remains a central challenge in nanoscience, particularly in systems where external magnetic fields are used as continuous control parameters. Existing descriptions of magnetic-field-assisted nucleation are typically material-specific or rely on computationally intensive atomistic methods. Here, we reformulate classical nucleation theory as a geometrically closed thermodynamic framework by introducing a sphere-packing representation of atomic assembly. This construction establishes a direct link between discrete atomic structure and continuum free-energy contributions under applied magnetic fields, yielding a field-driven evolution equation for the critical nucleus size. The resulting theory provides a unified description of nanoparticle nucleation across superparamagnetic, paramagnetic, and diamagnetic systems within a single formalism. It quantitatively reproduces previously unresolved experimental observations for magnetite and nickel nanoparticles, namely the systematic reduction of mean particle size and narrowing of size distributions with increasing magnetic field. In the diamagnetic limit, the framework recovers our earlier analytical susceptibility-based description of silver nanoparticles, in which the field-dependent critical radius is governed by the induced-magnetization contribution to the nucleation free energy. Beyond modeling the reduction of mean particle size with increasing magnetic field, the framework reveals that the narrowing of size distributions emerges naturally from the curvature of the field-modified free-energy landscape. These results establish magnetic-field-assisted nucleation as a geometrically constrained thermodynamic process, providing a computationally efficient route for controlling nanoparticle size across distinct magnetic material classes.
