Embedded atom model

<h2 id="model-simulation">Model simulation</h2>
<p>In a simulation, the potential energy of an atom, 
  
    
      
        i
      
    
    {\displaystyle i}
  
, is given by<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a>
</p>

E
          
            i
          
        
        =
        
          F
          
            α
          
        
        
          (
          
            
              ∑
              
                j
                ≠
                i
              
            
            
              ρ
              
                β
              
            
            (
            
              r
              
                i
                j
              
            
            )
          
          )
        
        +
        
          
            1
            2
          
        
        
          ∑
          
            j
            ≠
            i
          
        
        
          ϕ
          
            α
            β
          
        
        (
        
          r
          
            i
            j
          
        
        )
      
    
    {\displaystyle E_{i}=F_{\alpha }\left(\sum _{j\neq i}\rho _{\beta }(r_{ij})\right)+{\frac {1}{2}}\sum _{j\neq i}\phi _{\alpha \beta }(r_{ij})}
  
,
<p>where 
  
    
      
        
          r
          
            i
            j
          
        
      
    
    {\displaystyle r_{ij}}
  
 is the distance between atoms 
  
    
      
        i
      
    
    {\displaystyle i}
  
 and 
  
    
      
        j
      
    
    {\displaystyle j}
  
, 
  
    
      
        
          ϕ
          
            α
            β
          
        
      
    
    {\displaystyle \phi _{\alpha \beta }}
  
 is a pair-wise potential function, 
  
    
      
        
          ρ
          
            β
          
        
      
    
    {\displaystyle \rho _{\beta }}
  
 is the contribution to the electron charge density from atom 
  
    
      
        j
      
    
    {\displaystyle j}
  
 of type 
  
    
      
        β
      
    
    {\displaystyle \beta }
  
 at the location of atom 
  
    
      
        i
      
    
    {\displaystyle i}
  
, and 
  
    
      
        F
      
    
    {\displaystyle F}
  
 is an embedding function that represents the energy required to place atom 
  
    
      
        i
      
    
    {\displaystyle i}
  
 of type 
  
    
      
        α
      
    
    {\displaystyle \alpha }
  
 into the electron cloud.
</p><p>Since the electron cloud density is a summation over many atoms, usually limited by a cutoff radius, the EAM potential is a multibody potential. For a single element system of atoms, three scalar functions must be specified: the embedding function, a pair-wise interaction, and an electron cloud contribution function.  For a binary alloy, the EAM potential requires seven functions: three pair-wise interactions (A-A, A-B, B-B), two embedding functions, and two electron cloud contribution functions.  Generally these functions are provided in a tabularized format and interpolated by cubic splines.
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Interatomic_potential/EgJjsSeh">Interatomic potential</a></li>
<li><a href="/facts/Lennard-Jones_potential/yXwcgLmh">Lennard-Jones potential</a></li>
<li><a href="/facts/Bond_order_potential/t7gz2J9e">Bond order potential</a></li>
<li><a href="/facts/Force_field_(chemistry)/p9u8nVk8">Force field (chemistry)</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Daw, Murray S.; Mike Baskes (1984). "Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals". Physical Review B. 29 (12). American Physical Society: 6443–6453. Bibcode:1984PhRvB..29.6443D. doi:10.1103/PhysRevB.29.6443. <a href="/wiki/Murray_S._Daw" target="_blank">/wiki/Murray_S._Daw</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Daw, Murray S.; Foiles, Stephen M.; Baskes, Michael I. (1993). "The embedded-atom method: a review of theory and applications". Mat. Sci. Eng. Rep. 9 (7–8): 251. doi:10.1016/0920-2307(93)90001-U. <a href="/w/index.php?title=Stephen_M._Foiles&action=edit&redlink=1" target="_blank">/w/index.php?title=Stephen_M._Foiles&action=edit&redlink=1</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>"Pair - EAM". LAMMPS Molecular Dynamics Simulator. Retrieved 2008-10-01. <a href="http://lammps.sandia.gov/doc/pair_eam.html" target="_blank">http://lammps.sandia.gov/doc/pair_eam.html</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
</ol>

Embedded atom model open-in-new

Embedded atom model