晶体生长动力学1256

2018年8月2日星期四3时45分44秒
State Key Laboratory of Crystal Materials
12. The Surface Roughening Transition Smooth Int45分44秒
State Key Laboratory of Crystal Materials
2018年8月2日星期四3时45分44秒
State Key Laboratory of Crystal Materials
12. The Surface Roughening Transition
Cooperative Processes （协同过程）
我们所讨论的现象，是由于局部相互作用引起的长程有 序效应，这称为协同过程(cooperative processes)。 很多不同的系统可以用相同的数学描述，产生了定义— —普适类别(universality classes)。在同一个普适类的 系统在临界点附近具有相似的行为： Critical Point Phenomena The Ising Model also describes the properties of a liquid/vapor system near a critical point.
2018年8月2日星期四3时45分44秒
State Key Laboratory of Crystal Materials
12. The Surface Roughening Transition
The Ising Model
The mathematics for the Ising model also apply to an ordering alloy where there is one interaction between atoms of the same kind, and a different interaction between dissimilar atoms. At low temperatures, there is an ordered state. There is a critical temperature above which the occupancy of sites is random.
2018年8月2日星期四3时45分44秒
State Key Laboratory of Crystal Materials
12. The Surface Roughening Transition Rough Interfaces
2018年8月2日星期四3时45分44秒
State Key Laboratory of Crystal Materials
2018年8月2日星期四3时45分44秒
State Key Laboratory of Crystal Materials
12. The Surface Roughening Transition Cooperative Processes
details of local interactions lattice type anisotropy of bond strengths second nearest neighbor interactions whether there is a lattice
12. The Surface Roughening Transition Rough Interface
2018年8月2日星期四3时45分44秒
State Key Laboratory of Crystal Materials
12. The Surface Roughening Transition Rough Interface
2018年8月2日星期四3时45分44秒
State Key Laboratory of Crystal Materials
12. The Surface Roughening Transition The Ising Model
The same mathematical model applies to the KosselStranski model. An atom has one interaction energy with an occupied neighboring crystalline site, and a different interaction energy with neighboring site which is not occupied by an atom of the crystal. This is just like the Ising system, where there is one interaction if the neighboring atom has the same spin, and a different interaction energy if it does not. The Ising Universality Class (普适类别） 这些情况都适用相同的数学，我们就说它们属于普适类（别）
12. The Surface Roughening Transition The Ising Model
In the Ising model, the spins on the atoms point either up or down.
模型假设： The spins interact only with spins on neighboring atoms. There is one interaction energy if the two spins are parallel, and a different interaction if the two spins are anti-parallel. The spins align at a low temperatures, and are random at high temperatures 。
2018年8月2日星期四3时45分44秒
State Key Laboratory of Crystal Materials
12. The Surface Roughening Transition 系统一些性质的行为，如秩序参数(order parameter， 表示秩序程度的物理量，如液体与气体共存时两者的密 度差), 可以用如下的形式描述： The co-existance curve near a critical point:
Cooperative Processes
Here Tc is the critical temperature. b is a critical
exponent (临界指数). 对于多种系统参数，如秩序参数，声速，密度，粘度，扩散系 数，相干长度等等，可以计算或者估计其临界指数。这些系统 参数的临界指数是相关的。 同一个普适类具有相同的临界指数。 临界温度与特定的材料系统及原子间相互作用的细节有关，但 是，临界指数： b is independent of:
This model has been extensively studied in statistical mechanics because it describes critical point behavior.
2018年8月2日星期四3时45分44秒
State Key Laboratory of Crystal Materials
12. The Surface Roughening Transition
Surface roughness The Ising Model Cooperative Processes Monte Carlo Simulations of Crystallization Equilibrium Surface Structure Computer Simulations Growth Morphologies Kinetic Roughening
12. The Surface Roughening Transition The Ising Model 伊辛模型 ,易行模型
这个模型是W Lenz 1920年提出的铁磁性物质居里点模型,伦兹的学生易 行最先找出它在一维空间的准确解,称The Ising Model。 1944年Onsager发表了二维空间Ising Model的精确解。 模型假设：每一个晶格点有一个自旋，自旋只能有+1和-1两种值，只有 最邻近的自旋有交互作用，自旋也可和外加磁场耦合。 The mathematics for the Kossel-Stranki model is identical to the mathematics developed for the ferromagnetic Curie transition. It is simple in principle, but becomes very complex in detail.
2018年8月2日星期四3时45分44秒
State Key Laboratory of Crystal Materials
12. The Surface Roughening Transition The Ising Model
最近临相互作用是短程作用,产生了长程有序的效应。 高温时，热能比相互作用能大，spins are random. 这两个区域存在一个二级相变，温度叫临界点，对铁磁体就是the Curie temperature.
State Key Laboratory of Crystal Materials
2018年8月2日星期四3时45分44秒
12. The Surface Roughening Transition
number of components in the order parameter. dimensionality of the system.
2018年8月2日星期四3时45分44秒
b depends on:
State Key Laboratory of Crystal Materials
12. The Surface Roughening Transition Universality Classes The same critical exponents apply to all members of a Universality class.如：对Ising system中的秩序参数， 其临界指数为0.324。对于b青铜，一种铜锌合金，其秩序参 数的临界指数为0.324，氩的临界点附近沿着共存曲线，气 液两相密度差的临界指数为0.324。这些都属于Ising普适类 ，具有相同的临界指数。 Members of the Ising Universality class: Ferromagnetism Order-disorder Critical point phenomena Kossel-Stranski
2018年8月2日星期四3时45分44秒
State Key Laboratory of Crystal Materials
12. The Surface Roughening Transition
表面粗糙度 在原子尺度上,一些晶体的界面是光滑的,还有一些是粗糙的 ，这对晶体生长过程影响很大。 在原子尺度上的粗糙界面通常有各相同性的性质，在微观 尺度上是圆形的。 光滑界面有各相异性的性质，在微观上或宏观上形成面。 The transition between these two modes is known as the surface roughening transition.