Day $4$ : Validation of Kittel's relationship

Problems:

$($a$)$ Use the images below to extract the domain width associated with each film thickness. Make a scatter plot of domain width $D_0$ versus square root of film thickness.

$($b$)$ Plot a straight line fit to show that Kittel's relationship is verified for these barium titanate thin films.

$($c$)$ Use your best fit to extract a value for the domain wall energy density $.$ You will need the additional information that for barium titanate the shear modulus $G=55{10}^{9}Pa,$ and the strains along the a$-$ and c$-$axis are $s_a=1\mathrm{.}001{10}^{-3}$ and $s_c=1\mathrm{.}0035{10}^{-2}$ respectively.

In each of the below four panels the scale is $1cm=200nm$