Folie 1

1
Continuum limit of the linear monatomic chain
3D continuum theory of elastic media yields
where the bulk modulus B and the elastic energy
density UEelast/V are related by
with
In 1D we used the atomistic approach with k?0
with D, m and a the spring constant, the mass of
the respective atom and the lattice constant
We now show the equivalence of both expressions
2
Density of the 1D chain
Elastic energy density of the chain provides bulk
modulus