atoms Flashcards
what’s the LJ 6-12 potential
the Lennard Jones 6-12 potential.
V = 4ε [ (σ/r^)12 - (σ/r)^6]
(σ/r^)12 represents the strong force
(σ/r^)6 represents the van der waals force
potential energy per atom
n/2 * ε
n: number of nearest neighbours
ε: binding energy
1/2 : the ε is shared between both atoms in the bond
how does the LJ 6-12 potential change for an ionic bond
the 4ε changes
the (σ/r)^6 loses its power of 6. (not actually lost just replaced as the van der Waals force is tiny compared to the Coulomb force)
whats the unit cell
smallest unit that can form the whole structure by tessalation
draw a diagram to show Bragg scattering
2 rows of parallel particles
2 parallel light rays incident at the centre (one at the top row and one at the bottom row)
θ is the angle between the light ray and the line of particles
draw 2 lines. each is from the top row’s centre particle and is perpendicular to the incident and reflected rays.
θ is also the angle between those lines and the normal to the row of particles.
this makes the distance between the bottom centre particle and the point where those lines intercept the light ray equal to d*sin(θ)
hence the path difference is 2d*sin(θ)
Bragg’s law equation
2dsin(θ) = nλ
d: the particle separation
λ: wavelength
n: an integer (for constructive interference)
θ: angle between light ray and row of particles
whats the scattering angle for Bragg scattering
2θ. (twice the angle between the light ray and the row of particles)
define quasistatic.
a process that happens so slowly that the system is always in instantaneous thermal equilibrium.
show how to relate the fractional volume change to the fractional d-spacing change for Bragg-scattering
nλ = 2d*sin(θ)
d= λ/2sin(θ) (use n= 1 for the scatter angle)
∂d/∂θ = -λcos(θ)/2sin²(θ) = -d/tan(θ)
∂d/d = -∂θ/tan(θ)
V∝d³
V = Ad³ (A is a constant of proportionality)
∂V/∂d = 3Ad²
∂V/V = 3* ∂d/d = -3 *∂θ/tan(θ)
this can be subbed into the Bulk modulus equation
