pair_style meam/c command¶
pair_style meam/c pair_coeff * * ../potentials/library.meam Si ../potentials/si.meam Si pair_coeff * * ../potentials/library.meam Ni Al NULL Ni Al Ni Ni
The behavior of the MEAM potential for alloy systems has changed as of November 2010; see description below of the mixture_ref_t parameter
Style meam/c computes pairwise interactions for a variety of materials using modified embedded-atom method (MEAM) potentials (Baskes). Conceptually, it is an extension to the original EAM potentials which adds angular forces. It is thus suitable for modeling metals and alloys with fcc, bcc, hcp and diamond cubic structures, as well as covalently bonded materials like silicon and carbon. Style meam/c is a translation of the (now obsolete) meam code from Fortran to C++. It is functionally equivalent to meam but more efficient, and thus meam has been removed from LAMMPS after the 12 December 2018 release.
In the MEAM formulation, the total energy E of a system of atoms is given by:
where F is the embedding energy which is a function of the atomic electron density \(\rho\), and \(\phi\) is a pair potential interaction. The pair interaction is summed over all neighbors J of atom I within the cutoff distance. As with EAM, the multi-body nature of the MEAM potential is a result of the embedding energy term. Details of the computation of the embedding and pair energies, as implemented in LAMMPS, are given in (Gullet) and references therein.
The various parameters in the MEAM formulas are listed in two files which are specified by the pair_coeff command. These are ASCII text files in a format consistent with other MD codes that implement MEAM potentials, such as the serial DYNAMO code and Warp. Several MEAM potential files with parameters for different materials are included in the “potentials” directory of the LAMMPS distribution with a “.meam” suffix. All of these are parameterized in terms of LAMMPS metal units.
Note that unlike for other potentials, cutoffs for MEAM potentials are not set in the pair_style or pair_coeff command; they are specified in the MEAM potential files themselves.
Only a single pair_coeff command is used with the meam style which specifies two MEAM files and the element(s) to extract information for. The MEAM elements are mapped to LAMMPS atom types by specifying N additional arguments after the second filename in the pair_coeff command, where N is the number of LAMMPS atom types:
MEAM library file
Elem1, Elem2, …
MEAM parameter file
N element names = mapping of MEAM elements to atom types
See the pair_coeff doc page for alternate ways to specify the path for the potential files.
As an example, the potentials/library.meam file has generic MEAM settings for a variety of elements. The potentials/SiC.meam file has specific parameter settings for a Si and C alloy system. If your LAMMPS simulation has 4 atoms types and you want the first 3 to be Si, and the fourth to be C, you would use the following pair_coeff command:
pair_coeff * * library.meam Si C sic.meam Si Si Si C
The first 2 arguments must be * * so as to span all LAMMPS atom types. The first filename is the element library file. The list of elements following it extracts lines from the library file and assigns numeric indices to these elements. The second filename is the alloy parameter file, which refers to elements using the numeric indices assigned before. The arguments after the parameter file map LAMMPS atom types to elements, i.e. LAMMPS atom types 1,2,3 to the MEAM Si element. The final C argument maps LAMMPS atom type 4 to the MEAM C element.
If the second filename is specified as NULL, no parameter file is read, which simply means the generic parameters in the library file are used. Use of the NULL specification for the parameter file is discouraged for systems with more than a single element type (e.g. alloys), since the parameter file is expected to set element interaction terms that are not captured by the information in the library file.
If a mapping value is specified as NULL, the mapping is not performed. This can be used when a meam potential is used as part of the hybrid pair style. The NULL values are placeholders for atom types that will be used with other potentials.
If the second filename is NULL, the element names between the two filenames can appear in any order, e.g. “Si C” or “C Si” in the example above. However, if the second filename is not NULL (as in the example above), it contains settings that are Fortran-indexed for the elements that precede it. Thus you need to insure you list the elements between the filenames in an order consistent with how the values in the second filename are indexed. See details below on the syntax for settings in the second file.
The MEAM library file provided with LAMMPS has the name potentials/library.meam. It is the “meamf” file used by other MD codes. Aside from blank and comment lines (start with #) which can appear anywhere, it is formatted as a series of entries, each of which has 19 parameters and can span multiple lines:
elt, lat, z, ielement, atwt, alpha, b0, b1, b2, b3, alat, esub, asub, t0, t1, t2, t3, rozero, ibar
The “elt” and “lat” parameters are text strings, such as elt = Si or Cu and lat = dia or fcc. Because the library file is used by Fortran MD codes, these strings may be enclosed in single quotes, but this is not required. The other numeric parameters match values in the formulas above. The value of the “elt” string is what is used in the pair_coeff command to identify which settings from the library file you wish to read in. There can be multiple entries in the library file with the same “elt” value; LAMMPS reads the first matching entry it finds and ignores the rest.
Other parameters in the MEAM library file correspond to single-element potential parameters:
lat = lattice structure of reference configuration z = number of nearest neighbors in the reference structure ielement = atomic number atwt = atomic weight alat = lattice constant of reference structure esub = energy per atom (eV) in the reference structure at equilibrium asub = "A" parameter for MEAM (see e.g. (Baskes))
The alpha, b0, b1, b2, b3, t0, t1, t2, t3 parameters correspond to the standard MEAM parameters in the literature (Baskes) (the b parameters are the standard beta parameters). Note that only parameters normalized to t0 = 1.0 are supported. The rozero parameter is an element-dependent density scaling that weights the reference background density (see e.g. equation 4.5 in (Gullet)) and is typically 1.0 for single-element systems. The ibar parameter selects the form of the function G(Gamma) used to compute the electron density; options are
0 => G = sqrt(1+Gamma) 1 => G = exp(Gamma/2) 2 => not implemented 3 => G = 2/(1+exp(-Gamma)) 4 => G = sqrt(1+Gamma) -5 => G = +-sqrt(abs(1+Gamma))
If used, the MEAM parameter file contains settings that override or complement the library file settings. Examples of such parameter files are in the potentials directory with a “.meam” suffix. Their format is the same as is read by other Fortran MD codes. Aside from blank and comment lines (start with #) which can appear anywhere, each line has one of the following forms. Each line can also have a trailing comment (starting with #) which is ignored.
keyword = value keyword(I) = value keyword(I,J) = value keyword(I,J,K) = value
The indices I, J, K correspond to the elements selected from the MEAM library file numbered in the order of how those elements were selected starting from 1. Thus for the example given before
pair_coeff * * library.meam Si C sic.meam Si Si Si C
an index of 1 would refer to Si and an index of 2 to C.
The recognized keywords for the parameter file are as follows:
rc = cutoff radius for cutoff function; default = 4.0 delr = length of smoothing distance for cutoff function; default = 0.1 rho0(I) = relative density for element I (overwrites value read from meamf file) Ec(I,J) = cohesive energy of reference structure for I-J mixture delta(I,J) = heat of formation for I-J alloy; if Ec_IJ is input as zero, then LAMMPS sets Ec_IJ = (Ec_II + Ec_JJ)/2 - delta_IJ alpha(I,J) = alpha parameter for pair potential between I and J (can be computed from bulk modulus of reference structure re(I,J) = equilibrium distance between I and J in the reference structure Cmax(I,J,K) = Cmax screening parameter when I-J pair is screened by K (I<=J); default = 2.8 Cmin(I,J,K) = Cmin screening parameter when I-J pair is screened by K (I<=J); default = 2.0 lattce(I,J) = lattice structure of I-J reference structure: fcc = face centered cubic bcc = body centered cubic hcp = hexagonal close-packed dim = dimer dia = diamond (interlaced fcc for alloy) dia3= diamond structure with primary 1NN and secondary 3NN interaction b1 = rock salt (NaCl structure) c11 = MoSi2 structure l12 = Cu3Au structure (lower case L, followed by 12) b2 = CsCl structure (interpenetrating simple cubic) ch4 = methane-like structure, only for binary system lin = linear structure (180 degree angle) zig = zigzag structure with a uniform angle tri = H2O-like structure that has an angle nn2(I,J) = turn on second-nearest neighbor MEAM formulation for I-J pair (see for example (Lee)). 0 = second-nearest neighbor formulation off 1 = second-nearest neighbor formulation on default = 0 attrac(I,J) = additional cubic attraction term in Rose energy I-J pair potential default = 0 repuls(I,J) = additional cubic repulsive term in Rose energy I-J pair potential default = 0 zbl(I,J) = blend the MEAM I-J pair potential with the ZBL potential for small atom separations (ZBL) default = 1 theta(I,J) = angle between three atoms in line, zigzag, and trimer reference structures in degrees default = 180 gsmooth_factor = factor determining the length of the G-function smoothing region; only significant for ibar=0 or ibar=4. 99.0 = short smoothing region, sharp step 0.5 = long smoothing region, smooth step default = 99.0 augt1 = integer flag for whether to augment t1 parameter by 3/5*t3 to account for old vs. new meam formulations; 0 = don't augment t1 1 = augment t1 default = 1 ialloy = integer flag to use alternative averaging rule for t parameters, for comparison with the DYNAMO MEAM code 0 = standard averaging (matches ialloy=0 in DYNAMO) 1 = alternative averaging (matches ialloy=1 in DYNAMO) 2 = no averaging of t (use single-element values) default = 0 mixture_ref_t = integer flag to use mixture average of t to compute the background reference density for alloys, instead of the single-element values (see description and warning elsewhere in this doc page) 0 = do not use mixture averaging for t in the reference density 1 = use mixture averaging for t in the reference density default = 0 erose_form = integer value to select the form of the Rose energy function (see description below). default = 0 emb_lin_neg = integer value to select embedding function for negative densities 0 = F(rho)=0 1 = F(rho) = -asub*esub*rho (linear in rho, matches DYNAMO) default = 0 bkgd_dyn = integer value to select background density formula 0 = rho_bkgd = rho_ref_meam(a) (as in the reference structure) 1 = rho_bkgd = rho0_meam(a)*Z_meam(a) (matches DYNAMO) default = 0
Rc, delr, re are in distance units (Angstroms in the case of metal units). Ec and delta are in energy units (eV in the case of metal units).
Each keyword represents a quantity which is either a scalar, vector, 2d array, or 3d array and must be specified with the correct corresponding array syntax. The indices I,J,K each run from 1 to N where N is the number of MEAM elements being used.
Thus these lines
rho0(2) = 2.25 alpha(1,2) = 4.37
set rho0 for the second element to the value 2.25 and set alpha for the alloy interaction between elements 1 and 2 to 4.37.
The augt1 parameter is related to modifications in the MEAM formulation of the partial electron density function. In recent literature, an extra term is included in the expression for the third-order density in order to make the densities orthogonal (see for example (Wang), equation 3d); this term is included in the MEAM implementation in lammps. However, in earlier published work this term was not included when deriving parameters, including most of those provided in the library.meam file included with lammps, and to account for this difference the parameter t1 must be augmented by 3/5*t3. If augt1=1, the default, this augmentation is done automatically. When parameter values are fit using the modified density function, as in more recent literature, augt1 should be set to 0.
The mixture_ref_t parameter is available to match results with those of previous versions of lammps (before January 2011). Newer versions of lammps, by default, use the single-element values of the t parameters to compute the background reference density. This is the proper way to compute these parameters. Earlier versions of lammps used an alloy mixture averaged value of t to compute the background reference density. Setting mixture_ref_t=1 gives the old behavior. WARNING: using mixture_ref_t=1 will give results that are demonstrably incorrect for second-neighbor MEAM, and non-standard for first-neighbor MEAM; this option is included only for matching with previous versions of lammps and should be avoided if possible.
The parameters attrac and repuls, along with the integer selection parameter erose_form, can be used to modify the Rose energy function used to compute the pair potential. This function gives the energy of the reference state as a function of interatomic spacing. The form of this function is:
astar = alpha * (r/re - 1.d0) if erose_form = 0: erose = -Ec*(1+astar+a3*(astar**3)/(r/re))*exp(-astar) if erose_form = 1: erose = -Ec*(1+astar+(-attrac+repuls/r)*(astar**3))*exp(-astar) if erose_form = 2: erose = -Ec*(1 +astar + a3*(astar**3))*exp(-astar) a3 = repuls, astar < 0 a3 = attrac, astar >= 0
Most published MEAM parameter sets use the default values attrac=repulse=0. Setting repuls=attrac=delta corresponds to the form used in several recent published MEAM parameter sets, such as (Valone)
The default form of the erose expression in LAMMPS was corrected in March 2009. The current version is correct, but may show different behavior compared with earlier versions of lammps with the attrac and/or repuls parameters are non-zero. To obtain the previous default form, use erose_form = 1 (this form does not seem to appear in the literature). An alternative form (see e.g. (Lee2)) is available using erose_form = 2.
Mixing, shift, table, tail correction, restart, rRESPA info¶
For atom type pairs I,J and I != J, where types I and J correspond to two different element types, mixing is performed by LAMMPS with user-specifiable parameters as described above. You never need to specify a pair_coeff command with I != J arguments for this style.
This pair style does not support the pair_modify shift, table, and tail options.
This pair style does not write its information to binary restart files, since it is stored in potential files. Thus, you need to re-specify the pair_style and pair_coeff commands in an input script that reads a restart file.
This pair style can only be used via the pair keyword of the run_style respa command. It does not support the inner, middle, outer keywords.
The meam/c style is provided in the USER-MEAMC package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
The maximum number of elements, that can be read from the MEAM library file, is determined at compile time. The default is 5. If you need support for more elements, you have to change the define for the constant ‘maxelt’ at the beginning of the file src/USER-MEAMC/meam.h and update/recompile LAMMPS. There is no limit on the number of atoms types.
(Baskes) Baskes, Phys Rev B, 46, 2727-2742 (1992).
(Gullet) Gullet, Wagner, Slepoy, SANDIA Report 2003-8782 (2003). This report may be accessed on-line via this link.
(Lee) Lee, Baskes, Phys. Rev. B, 62, 8564-8567 (2000).
(Lee2) Lee, Baskes, Kim, Cho. Phys. Rev. B, 64, 184102 (2001).
(Valone) Valone, Baskes, Martin, Phys. Rev. B, 73, 214209 (2006).
(Wang) Wang, Van Hove, Ross, Baskes, J. Chem. Phys., 121, 5410 (2004).
(ZBL) J.F. Ziegler, J.P. Biersack, U. Littmark, “Stopping and Ranges of Ions in Matter”, Vol 1, 1985, Pergamon Press.