We measured germanium-silicon (Ge/Si) ratios in both fluid and solid phases using a series of highly constrained amorphous silica precipitation experiments at 20 °C and neutral pH for a wide range of seed crystal surface areas. Silicon isotope data (δ^30/28Si) for these experiments were previously reported by Fernandez et al. (2019). A distinct lag in the onset of Ge/Si partitioning relative to δ³⁰Si fractionation during active amorphous silica growth indicated that Ge incorporation rates were orders of magnitude slower than silicon precipitation rates. Slow Ge kinetics give the appearance of conservative behavior over short experimental timescales (∼30 days). A major outcome from these observations was the existence of distinct equilibration timescales between Ge/Si and $\mathrm{\delta }$³⁰Si. Further, these experimental results provide the first documented evidence of rate dependent behavior in Ge partition coefficients. Successful application of a modified solid solution model, initially developed for characterizing stable isotope fractionation, indicates that a common fractionation model theory is able to describe both Ge/Si and $\mathrm{\delta }$³⁰Si partitioning. Numerical simulations conducted at longer timescales (1–1000 years) predict eventual Ge incorporation into the mineral surface, but this occurs when the system is in close proximity to equilibrium conditions. These long-term predictions underscore the potential of Ge as a (near)equilibrium tracer in complement to the mixed kinetic and equilibrium signatures recorded by δ³⁰Si. Our findings illustrate the viability of a combined Ge/Si–δ³⁰Si multi-tracer approach for constraining silicate mineral formation across a variety of terrestrial and marine systems.

我们使用一系列高度受限的无定形二氧化硅沉淀实验，在20°C和中性pH值下，对各种晶种表面积进行了测量，从而测量了液相和固相中锗硅（Ge / Si）的比率。这些实验的硅同位素数据（^δ30/28 Si）先前由Fernandez等报道。（2019）。在锗/硅的划分相对发作一个明显滞后δ ³⁰活性的无定形二氧化硅生长期间的Si分馏表明，掺入锗率分别为数量级比硅沉淀速率慢。Ge动力学缓慢，在较短的实验时间内（约30天）表现出保守的行为。这些观察的主要结果是Ge / Si和Si之间存在不同的平衡时间尺度。$\mathrm{\delta }$³⁰ Si。此外，这些实验结果提供了锗分配系数中速率依赖行为的第一个文献证明。最初开发用于表征稳定同位素分馏的改进型固溶体模型的成功应用表明，通用的分馏模型理论能够描述Ge / Si和$\mathrm{\delta }$³⁰ Si分区。在较长的时间尺度（1–1000年）内进行的数值模拟预测，Ge最终会掺入矿物表面，但这会在系统非常接近平衡条件时发生。这些长期预测强调的Ge作为（近）平衡示踪剂在补充由δ记录的混合动力学和平衡签名的电位³⁰的Si。我们的发现说明了结合Ge / Si–δ ³⁰ Si多示踪剂方法来限制各种陆地和海洋系统中硅酸盐矿物形成的可行性。