Making a pellet with correct density and thickness: As we know the mean free path of a pellet is: lambda=4*R/3/rou, where R is the particle radius, rou is volume density. We want to make a pellet because our sing crystal sample is too thick to transmit light. Then we want to grind sample to small particles that can transmit light and put them into pellets. The keys are: 1) pellet thickness d should be slightly larger than the mean free path: d > lambda =4*R/3/rou 2) effective thickness (deff) should be small enough so that light can penetrate: deff =d*rou < 1/alpha, where alpha is the absorption coefficient. Thus the correct thickness is: 4R/3/rou < d < 1/alpha/rou is the real condition that we want to meet. There is a implicit condition here: R < 3/alpha/4, which is very important. In conclusion, to make a good pellet: 1) particle size has to be R < 3/alpha/4 2) sample thickness 4R/3/rou < d < 1/alpha/rou, which can be tuned by the volume concentration rou. Example: If we have alpha=1e7 m^{-1}, then the condition of a good pellet is : 1) R < 75 nm. 2) d < 1e7/rou This condition can not be realized because the particle size needs to be very small.

Mean free path as a function of density in volume and particle size:

assuming a unit volume for KCl, then the density will be:

rou=V0, where V0 is the volume of the sample.

Number of particles will be:

Np=V0/V, where V=4pi/3*R^3 is the volume of the particles,

then Np=V0/(4pi/3*R^3)

The mean free path will be:

lambda=1/simga/Np, where sigma=pi*R^2 is the crossection of the particle.

Therefore lambda=4R/3/rou

Example:

rou=0.01, R=1e-6 meter

then the mean free path is:

lambda=1.3e-4 meter which is 0.13 mm.