标题： 在锗上蚀刻的自发螺旋图案 显示英文标题

标题： Spontaneous spiral patterns etched on Germanium

摘要： 在有水存在的情况下，锗上的薄金属膜形成了一个显著的图案形成系统。 在这里，我们对锗表面自发蚀刻的螺旋结构进行了分析。 我们获得了螺旋生长动力学的测量结果以及金属膜中局部应变场的测量结果。 两者均表明，图案的近似几何秩序来源于一个奇点（晶体缺陷）的远场。 测量得到的蚀刻轮廓与金属催化腐蚀锗表面的模型在定量上一致。 具体而言，局部蚀刻深度与锗-金属接触线的法向速度成反比。 生长机制结合了裂纹扩展、反应扩散动力学和薄膜机械不稳定性，并说明了缺陷的长程场如何在非平衡生长过程中施加几何秩序。 与其他图案形成系统相关的普遍特征是化学与力学的耦合以及奇点驱动的秩序。 显示英文摘要

摘要： Thin metal film on Germanium, in the presence of water, results in a remarkable pattern forming system. Here we present an analysis of spirals spontaneously etched on the Ge surface. We obtain measurements of the growth dynamics of the spirals and measurements of the local strain field in the metal film. Both indicate that the near geometric order of the pattern originates from the unique far field of a singularity - a crystal defect. The measured engraving profile is found in quantitative agreement with a model of metal catalyzed corrosion of the Ge surface. Specifically, local etch depth is inversely proportional to the normal velocity of the Ge-metal contact line. The growth mechanism combines crack propagation, reaction diffusion dynamics, and thin film mechanical instabilities, and illustrates how a defect's long range field can impose geometric order in a non-equilibrium growth process. General features relevant to other pattern forming systems are the coupling of chemistry and mechanics and the singularity driven order.