- #1
Hermes Chirino
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The bulk modulus B = - V (∂P/∂V). At constant temperature the pressure is given by P= -∂U/∂V, where U is the total energy. We can write B in terms of the energy per particle u = U/N and volume per particle
v = V/N :
B = v (∂/∂v) (∂u/∂v) Eq (1)
The volume per particle v in a fcc lattice is v = a^3/4, where the side a of the conventional cubic cell is related to the nearest-neighbor separation r by a = √2r. We may therefore write:
v = r^3/√2 ; thus: ∂/∂v = (√2 / 3r^3)(∂/∂r) Eq (2)
And rewrite the bulk modulus as:
B = (√2/9) r (∂/∂r) 1/r^2 (∂/∂r) u Eq (3)
Questions:
How the three equations were derived (and I am very familiar with differential calculus and still not get it)
Thanks, any help will be appreciate !
v = V/N :
B = v (∂/∂v) (∂u/∂v) Eq (1)
The volume per particle v in a fcc lattice is v = a^3/4, where the side a of the conventional cubic cell is related to the nearest-neighbor separation r by a = √2r. We may therefore write:
v = r^3/√2 ; thus: ∂/∂v = (√2 / 3r^3)(∂/∂r) Eq (2)
And rewrite the bulk modulus as:
B = (√2/9) r (∂/∂r) 1/r^2 (∂/∂r) u Eq (3)
Questions:
How the three equations were derived (and I am very familiar with differential calculus and still not get it)
Thanks, any help will be appreciate !