THE GROWTH OF CRYSTALS AND THE EQUILIBRIUM STRUCTURE OF THEIR SURFACES
THE GROWTH OF CRYSTALS AND THE EQUILIBRIUM STRUCTURE OF THEIR SURFACES
复制标题
DOI：
10.1098/rsta.1951.0006
复制
发表时间：
1951-01-01
影响因子：
--
通讯作者：
FRANK, FC
中科院分区：
文献类型：
--
作者：
BURTON, WK;CABRERA, N;FRANK, FC
第一部分和第二部分涉及晶体生长的理论，第三部分和第四部分涉及与蒸汽平衡的晶体表面的形式（在原子尺度上）。在第一部分中，我们计算的单分子步骤（即不完整的单分子层的晶体的边缘）作为在蒸汽中的过饱和度和扭结的步骤中的平均浓度的函数的前进速率。我们表明，在大多数情况下的增长从蒸汽的单分子步骤的前进速度将是独立的晶体取向，使一个不断增长的封闭步骤将是圆形的。我们还发现了平行的步骤序列的前进速度。在第二部分中，我们发现由此产生的增长率和陡度的增长锥或增长金字塔时，步骤的持久性是由于位错的存在。在涉及几个或多个位错的情况下进行了详细的分析，它表明，它们通常与单个位错的情况下没有什么不同。含有位错的表面的生长速率被证明是成比例的平方的过饱和度为低的值和第一权力为高的值，后者。沃尔默和舒尔茨（1931）对碘晶体从蒸汽中生长速率的观察可以用这种方法来解释。同样的想法从溶液中生长晶体的应用进行了简要的讨论。第三部分涉及步骤的平衡结构，特别是步骤中扭结的统计，取决于温度，结合能参数和晶体学取向。在给定的温度下，在给定的过饱和度下，获得了处于不稳定平衡的二维成核（即在已完成的层上的新单层晶体的"岛"）的形状和尺寸，由此估计了二维成核的校正活化能。在适度低的过饱和度下，这是如此之大，以至于晶体将没有可观察到的生长速率。对于含有两个相反方向的螺旋位错的晶面，当它们的间距小于相应临界核的直径时，激活能仍然很大;但对于任何更大的间距，激活能为零。第四部分把作为一个"合作现象"的温度依赖性的结构的表面aferefect晶体，免费的步骤在绝对零度。它示出，这样的表面保持几乎平坦（保存为单个吸附分子和空置的表面站点），直到达到一个转变温度，在该温度下的表面的粗糙度增加非常迅速（“表面熔化”）。假设表面的分子都处于两个能级中的一个或另一个，Onsager（1944）关于二维铁磁体的结果可以应用而几乎没有变化。转变温度大约等于或高于在两个方向上具有最近邻相互作用的晶面（例如简单立方晶体的（100）面或面心立方晶体的（111）或（100）面）的熔点。当相互作用是在一个方向上的第二最近邻类型（例如，（110）s.c.或f.c.c.晶体），转变温度较低，并且对应于第二最近邻键的表面熔融。通过将Bethe方法（1935）推广到更大的水平数，研究了由假设的两个可用水平的限制引入的误差。这种方法对二能级问题给出了一个反常的结果。计算出的转变温度从两个到三个能级大幅下降，但对于更大的数目几乎保持不变。
Parts I and II deal with the theory of crystal growth, parts III and IV with the form (on the atomic scale) of a crystal surface in equilibrium with the vapour. In part I we calculate the rate of advance of monomolecular steps (i.e. the edges of incomplete monomolecular layers of the crystal) as a function of supersaturation in the vapour and the mean concentration of kinks in the steps. We show that in most cases of growth from the vapour the rate of advance of monomolecularstepswill be independent of their crystallographic orientation, so that a growing closed step will be circular. We also find the rate of advance for parallel sequences of steps. In part II we find the resulting rate of growth and the steepness of the growth cones or growth pyramids when the persistence of steps is due to the presence of dislocations. The cases in which several or many dislocations are involved are analysed in some detail; it is shown that they will commonly differ little from the case of a single dislocation. The rate of growth of a surface containing dislocations is shown to be proportional to the square of the supersaturation for low values and to the first power for high values of the latter. Volmer & Schultze’s (1931) observations on the rate of growth of iodine crystals from the vapour can be explained in this way. The application of the same ideas to growth of crystals from solution is briefly discussed. Part III deals with the equilibrium structure of steps, especially the statistics of kinks in steps, as dependent on temperature, binding energy parameters, and crystallographic orientation. The shape and size of a two-dimensional nucleus (i.e. an ‘island* of new monolayer of crystal on a completed layer) in unstable equilibrium with a given supersaturation at a given temperature is obtained, whence a corrected activation energy for two-dimensional nucleation is evaluated. At moderately low supersaturations this is so large that a crystal would have no observable growth rate. For a crystal face containing two screw dislocations of opposite sense, joined by a step, the activation energy is still very large when their distance apart is less than the diameter of the corresponding critical nucleus; but for any greater separation it is zero. Part IV treats as a ‘co-operative phenomenon’ the temperature dependence of the structure of the surface of aperfectcrystal, free from steps at absolute zero. It is shown that such a surface remains practically flat (save for single adsorbed molecules and vacant surface sites) until a transition temperature is reached, at which the roughness of the surface increases very rapidly (‘surface melting’). Assuming that the molecules in the surface are all in one or other of two levels, the results of Onsager (1944) for two-dimensional ferromagnets can be applied with little change. The transition temperature is of the order of, or higher than, the melting-point for crystal faces with nearest neighbour interactions in both directions (e.g. (100) faces of simple cubic or (111) or (100) faces of face-centred cubic crystals). When the interactions are of second nearest neighbour type in one direction (e.g. (110) faces of s.c. or f.c.c. crystals), the transition temperature is lower and corresponds to a surface melting of second nearest neighbour bonds. The error introduced by the assumed restriction to two available levels is investigated by a generalization of Bethe’s method (1935) to larger numbers of levels. This method gives an anomalous result for the two-level problem. The calculated transition temperature decreases substantially on going from two to three levels, but remains practically the same for larger numbers.