Consideration of the Poisson effect that couples in-plane and out of plane expansion

[AvonReppert]

udkm1Dsim toolbox is capable of simulating the thermal expansion as a result of the laser heating in a 1D-masses and springs model. The laser induced temperature change is converted to an expansion, which is implemented via spacer sticks in the linear chain that have a length that is determined by the relative temperature change and the linear thermal expansion coefficient.

In most ultrafast laser excitation experiments the pump-laser spotsize is chosen so large that the probed material is homogenously heated and thus all in-plane stresses cancel. This in plane clamping effect leads to an increased out of plane expansion until the in-plane pressure is released. Graphically one could understand this effect in the following schematic:

The one dimensional nature of the simulation however does not take this "poisson" - effect into account and thus underestimates the stress on ultrafast timescales. The expansion should be larger by a factor of: Where C13 and C33 are the elastic constants and the alphas are the in and out-of-plane expansion coefficents. A similar correction factor has been determined by Lee, Hae Ja, et al. "Optically induced lattice dynamics probed with ultrafast x-ray diffraction." Physical Review B 77.13 (2008): 132301. (pre-factor of the second formula of the paper)

So far one can only manually increase the thermal expansion coefficient by the reported value, which then should give a more realistic result on timescales before the in-plane stress release takes place.

This is of course only relevant if one wants to quantitatively model the observed strain for a given absorbed laser fluence and does not use the fluence as a fitting parameter.

[dschick]

I think this is something which should be implemented in a 3d scenario. As you mentioned, one include that in the actual thermal expansion coefficient or fluence.