基本统计力学原理及物理量的计算

原子层次模拟：分子动力学方法（II）

Property calculations

p y

MD simulation is “omnipotent” at the level of classical atoms. All properties that p p p are well-posed in classical mechanics and statistical mechanics can in principle be computed.

accuracy (time and size of model system)

reliability (interatomic potentials)

computational efficiency (serial or parallel computing, HPC).

Categories

1.Structural characterization. Examples include radial distribution function,

d i t t f t t

dynamic structure factor, etc.

2.Equation of state. Examples include free-energy functions, phase diagrams,

static response functions like thermal expansion coefficient, etc.

3.Transport. Examples include viscosity, thermal conductivity (electronic

3Transport Examples include viscosity thermal conductivity(electronic contribution excluded), correlation functions, diffusivity, etc.

4.Non-equilibrium response. Examples include plastic deformation, pattern

formation etc

formation, etc.

5.…

1、Temperature （T ）

根据能量均分定系统的温度由体系的动能确定

2B f

2N

i i k NVT m v k T

E N <>==∑根据能量均分定理，系统的温度由体系的动能确定2Boltzmann constant

NVT ensemble

Ar fcc crystal @ T ~ 80 K

crystal@T80K

normal distribution

()

(Gaussian)

3、Mean Square Displacement

(MSD)

r(0)

r(t)

Mean Square Displacement

For each particle,the probability to find another particle within the shell r to r +Δr is measured by

2()41

P r g r r r

N ρ

πΔ=

⋅Δ−r

Δr

fcc lattice

~3.63 Å(RT) Cu, a

PDFs for liquid and glass