Byeong-Joo Lee calphad Byeong-Joo Lee Dept. of MSE Pohang University of Science and Technology (POSTECH)[email protected] Atomistic

Byeong-Joo Lee www.postech.ac.kr/~calphad

Byeong-Joo LeeByeong-Joo Lee

Dept. of MSEDept. of MSE

Pohang University Pohang University

of Science and Technologyof Science and Technology

(POSTECH)(POSTECH)

[email protected]@postech.ac.kr

Atomistic SimulationsAtomistic Simulations


More about Molecular Dynamics More about Molecular Dynamics - Lecture Note of Prof. V. Vitek, 2002- Lecture Note of Prof. V. Vitek, 2002


Physical Interpretation of MD using the concept of Statistical Mechanics Physical Interpretation of MD using the concept of Statistical Mechanics

Fluctuations







J. S. Rowlinson: Liquids and liquid mixtures, Butterworth: London, 1969






Physical Interpretation of MD Physical Interpretation of MD - Generalized Einstein Relations- Generalized Einstein Relations

dxtxNxN

xtx ),(1

)]0()([ 2

0

2

x

NDxN

Dt

x

Dt

NtxN

4exp

2),(

20

Consider One dimensional Diffusion

If N0 atoms were concentrated at the origin x=0 at time t=0

Mean-square displacement of atoms

Dtxtx 2)]0()([ 2

Dt

rtrt

6

)]0()([lim

2


Physical Interpretation of MD Physical Interpretation of MD - Green-Kubo Relations- Green-Kubo Relations

)"()'('"2)"()'('")]0()(["

0000

2 tAtAdtdttAtAdtdtAtAmsdtttt

dt

dAtA )(

)0()(2

)]0()([lim

0

2

AAdt

AtAt

Shifting the time origin to t’ :

)'(')0()(0

tAdtAtAt

)0()'"()"()'( AttAtAtA

t

AAdtdtAAdAAddtmsdttttt

1)0()(2")0()(2)0()("2

00

"

00

t

AAdt

AtA t 1)0()(2

)]0()([

0

2


Physical Interpretation of MD Physical Interpretation of MD - Autocorrelations- Autocorrelations






More about MDMore about MD

Additional literature

D. Chandler: Introduction to Modern Statistical Mechanics, 1987, Oxford: Oxford University Press.

M. P. Allen and D. J. Tildesley: Computer Simulation of Liquids, 1987, Oxford: Oxford University Press.

J. P. Boon and S. Yip: Molecular Hydrodynamics, 1980, New York: McGraw-Hill; also Dover Publications, 1991.

J.M. Haile: Molecular Dynamics Simulation Elementary Method, 1992, John Wiley & Sons,

D. Frenkel and B. Smit: Understanding Molecular Simulations, 1996, New York, Academic Press.

Documents

Byeong-Joo Lee calphad Byeong-Joo Lee Dept. of MSE Pohang University of Science and Technology (POSTECH)[email protected] Atomistic