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README.md

heat-conductivity-hnemd

A 350-line C code for heat conductivity calculations using homogeneous nonequilibrium molecular dynamics (HNEMD).

Features and Restrictions

  • This is a small but working MD code, which is particularly useful to beginners who are interested in thermal conductivity calculations using molecular dynamics simulations.

  • A matlab script is provided to show how to properly analyze the computed data.

  • Without proper modifications, this code can only calculate the lattice thermal conductivity of solid argon.

  • This is not intended as a code for doing original research, but is useful for teaching.

Theory

The method used is called the homogeneous nonequilibrium molecular dynamics (HNEMD) method and was proposed by Evans in 1982 [D. J. Evans, Physics Letters A 91, 457 (1982)]. The simulation consists of three steps:

  • The equilibrium stage: The system is equilibrated in an NVT ensemble (It does not matter much whether a true NVT ensemble is used or not here; so the simple velocity-rescaling method is used).
  • The production stage: An external driving force Fe is applied on each particle (the total force on the whole system is then set to zero) and the total heat current J of the system is calculated in an NVT ensemble (again the simple velocity-rescaling method suffices).
  • The post-processing stage: The heat conductivity is calculated as J/T/V/Fe, where T is the temperature and V is the volume of the system.

File organizations

  • The main code is a standalone C code:

    • kappa_hnemd.cpp

  • The following Matlab script in the "20" directory can be used to analyze the data:

    • plot_kappa.m

Unit system

  • I use the following basic units:

    • Length: Angstrom
    • Mass: amu (atomic mass unit)
    • Energy: eV
    • Temperature: K

  • Other units are then derived.

Compile and run

  • Although the code was written in pure C, I used a suffix of .cpp and one can therefore use g++ to compile it. In linux, it can be compiled using, e.g.

    • g++ -O3 kappa_hnemd.cpp -o kappa_hnemd

  • Then, go to the directory "20" and type

    • ../kappa_hnemd < input

    If you want to do a few independent runs using one command, you can execute the "run" script I prepared:

    • ./run

  • The simulation parameters are read in from the file "input". There are only a few parameters to play with. Check the beginning of the main() function in the C code to understand the meanings (and units) of the input parameters.

  • After running the C code, a file named kappa.txt will be generated and one can run the Matlab script to analyze the results. Two figures will show up:

    • The first figure shows the running average of the diagonal thermal conductivity component k_xx, which should be about 1.5 W/mK (LJ argon at 20 K).
    • The second figure shows the running average of the off-diagonal thermal conductivity component k_yx, which should be close to zero (the system is isotropic).

References

  • For the HNEMD method, see D. J. Evans, "Homogeneous NEMD algorithm for thermal conductivity--Application of non-canonical linear response theory", Physics Letters A 91, 457 (1982).

  • For benchmark results for Lennard-Jones argon, see table 1 of A.J.H. McGaughey and M. Kaviany, "Thermal conductivity decomposition and analysis using molecular dynamics simulations. Part I. Lennard-Jones argon", International Journal of Heat and Mass Transfer 47, 1783 (2004).

Contact

  • Zheyong Fan: brucenju(at)gmail.com; zheyong.fan(at)aalto.fi; zheyongfan(at)163.com