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Structural and thermal properties of Ca are examined using a modified embedded-atom method (MEAM) interatomic potential. We developed an MEAM interatomic potential for calcium (Ca) using a first principles method based on density functional theory (DFT). The material parameters, such as the cohesive energy, equilibrium atomic volume, and bulk modulus, are used to determine the MEAM potential parameters. The elastic constants and various point defect energies, such as monovacancy and interstitial defects, are also examined while developing the potential. Several structural properties of Ca, such as different surface formation energies, stacking fault energies, and thermal properties, such as coefficient of thermal expansion, specific heat and melting temperature, are investigated using the potential. We found that the present MEAM potential gives a good overall agreement with DFT calculations and experiments.


The material properties of calcium, such as stacking fault energies, structure of grain boundaries, and dislocation dynamics need large scale atomistic simulations for further investigations. However, because realistic large scale atomistic simulations often require a number of atoms that render these methods impractical, one alternative is to use (semi-)empirical interaction potentials that can be developed efficiently, such that the atomistic approaches that use these potentials can handle systems with more than a million atoms. The embedded-atom method (EAM) was developed to obtain reliable and transferable semiempirical interatomic potentials for metals.[1][2] The modified embedded-atom method (MEAM) was developed by extending the EAM to include angular forces.[3][4] Successful MEAM potentials have been developed for several fcc and hcp metals.[5][6][7][8][9]

The purpose of the present work is twofold: (1) to develop an MEAM potential for Ca based on first-principles calculations using DFT and experimental values, and (2) to study the structural and thermal properties of Ca using the developed potential, thereby also demonstrating the reliability and transferability of the potential. For construction, we will first calculate the equilibrium lattice parameter and cohesive energy for several basic crystal structures, including bcc, fcc and hcp. The results will be compared with those obtained from DFT calculations. Furthermore, several elastic constants, monovacancy energy, interstitial defect energies are calculated. Noting that the calculated values are in good agreement with the DFT or experimental values, we examine the structural and thermal behaviors of Ca. We calculate surface formation energies, stacking fault energies, coefficient of thermal expansion (CTE), specific heat, and melting temperature. Again, we find that our results are in good agreement with their experimental or DFT counterparts.

A detailed description of how to generate a MEAM potential is available in Phys. Rev. B 46, 2727-2742 (1992).

To use these potentials, follow LAMMPS instructions at

Example Run

We use LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) code to test the potentials. It is a open source code available at for more information go to the web site.

The above potential file are in LAMMPS specific format.

To run Lammps with MEAM potentials you need three files (2 potential files as shown above, and one input file). If you want to specify the atomic positions in a separate file, then you need four files.

Input files

To execute the example run you should have Ca.library.meam, Ca.meam, Ca.pos, in the same directory. If your LAMMPS executable is named lmp_exec then you can execute the following command to begin the run.

lmp_exec <

Output files

  • Ca.log.lammps => contains data such as energy pressure temperature etc. of system specified itn the data.meam
  • Ca.dump.meam => contains the resulting structure (atomic positions) after every run of the system


We developed an MEAM semiempirical potential for Ca based on DFT calculations. We showed that the present potential reproduces several important physical properties accurately to match either the experimental or DFT results. Several structural and thermal properties of Ca are also examined with the present MEAM potential.


  1. M.S. Daw, Phys. Rev. B 39 (1989) 7441–7452.
  2. M.S. Daw, M.I. Baskes, Phys. Rev. B 29 (1984) 6443–6453.
  3. M.I. Baskes, J.S. Nelson, A.F. Wright, Phys. Rev. B 40 (1989) 6085–6100.
  4. M.I. Baskes, Phys. Rev. B 46 (1992) 2727–2742.
  5. B.-J. Lee, J.-H. Shim, M.I. Baskes, Phys. Rev. B 68 (2003) 144112.
  6. B. Jelinek, J. Houze, S. Kim, M.F. Horstemeyer, M.I. Baskes, S.-G. Kim, Phys. Rev. B 75 (2007) 054106.
  7. M.I. Baskes, R.A. Johnson, Modelling Simul. Mater. Sci. Eng. 2 (1994) 147–163.
  8. W. Hu, B. Zhang, B. Huang, F. Gao, D.J. Bacon, J. Phys.: Condens. Matter 13 (2001) 1193–1213.
  9. W. Hu, H. Deng, X. Yuan, M. Fukumoto, Eur. Phys. J. B 34 (2003) 429–440.
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