Acoustic vibration is often used to improve the yield of crystals and nanoparticles growing from solutions and melts. As there is still a debate on how acoustic vibration actually works, we have examined the possibility that acoustic pressure can affect the rate of nucleation. Our method is based on an expansion of the free energy of the nucleus in powers of the acoustic pressure. With the assumption that the period of the sound wave is short as compared to the time scale for nucleation, we replace the powers of the acoustic pressure by their time averages, retaining the average of the square of the acoustic pressure as the leading term. By assuming a nucleus having spherical shape, we use the Young-Laplace equation to relate the pressure inside the nucleus to the ambient pressure. Without making further approximations not already standard in classical nucleation theory, we find that the proximate effect of acoustic pressure is to reduce both the size of the critical nucleus as well as the work required to form it from monomers. As the work serves as the activation energy, the ultimate effect of acoustic pressure is to increase the rate of nucleation. If we assume that the atomic structure of the nucleus is the same as that of an ordinary solid, however, we find the compressibility is too small for acoustic vibration effects to be noticeable. If on the other hand, we assume that the structure is similar to that of a loosely bound colloidal particle, then the effects of acoustic vibration become potentially observable.

经常使用声振动来提高从溶液和熔体中生长出来的晶体和纳米颗粒的产率。由于仍然存在关于声振动实际上如何工作的争论，我们已经研究了声压会影响成核速率的可能性。我们的方法基于声压幂中核自由能的扩展。假设声波的周期比成核的时间尺度短，我们用它们的时间平均值代替声压的幂，并保留声压平方的平均值作为前导项。通过假设原子核具有球形形状，我们使用Young-Laplace方程将原子核内部的压力与环境压力相关联。在没有进行经典成核理论尚未成为标准的进一步近似的情况下，我们发现声压的直接作用是减小临界核的尺寸以及由单体形成临界核所需的功。由于功是活化能，声压的最终作用是增加成核速率。如果我们假设原子核的原子结构与普通固体的原子结构相同，那么我们发现可压缩性太小而无法引起声振动效应。另一方面，如果我们假设其结构与松散结合的胶体颗粒的结构相似，则可能会观察到声振动的影响。我们发现，声压的直接作用是减小临界核的尺寸以及由单体形成临界核所需的功。由于功是活化能，声压的最终作用是增加成核速率。如果我们假设原子核的原子结构与普通固体的原子结构相同，那么我们发现可压缩性太小而无法引起声振动效应。另一方面，如果我们假设其结构与松散结合的胶体颗粒的结构相似，则可能会观察到声振动的影响。我们发现，声压的直接作用是减小临界核的尺寸以及由单体形成临界核所需的功。由于功是活化能，声压的最终作用是增加成核速率。如果我们假设原子核的原子结构与普通固体的原子结构相同，那么我们发现可压缩性太小而无法引起声振动效应。另一方面，如果我们假设其结构与松散结合的胶体颗粒的结构相似，则可能会观察到声振动的影响。如果我们假设原子核的原子结构与普通固体的原子结构相同，那么我们发现可压缩性太小而无法引起声振动效应。另一方面，如果我们假设其结构与松散结合的胶体颗粒的结构相似，则可能会观察到声振动的影响。如果我们假设原子核的原子结构与普通固体的原子结构相同，那么我们发现可压缩性太小而无法引起声振动效应。另一方面，如果我们假设其结构与松散结合的胶体颗粒的结构相似，则可能会观察到声振动的影响。