this is for holding javascript data
Edwin Quashie added Figure_ref_fig_fit_graph_shows__.tex
over 8 years ago
Commit id: 9fb843d4afa7b5a0779bb7d562341d08cc10b267
deletions | additions
diff --git a/Figure_ref_fig_fit_graph_shows__.tex b/Figure_ref_fig_fit_graph_shows__.tex
new file mode 100644
index 0000000..44add88
--- /dev/null
+++ b/Figure_ref_fig_fit_graph_shows__.tex
...
Figure \ref{fig:fit_graph} shows how we obtained the slopes of Figure \ref{fig:energy_distance}. In Figure \ref{fig:fit_graph} (a), the magenta curve shows the adiabatic potential energy surface (APES) curve at $v = 0 ~\mathrm{a.u.}$; which is obtained due to the Born-Oppenheimer approximation. The oscillations in the curves reflect the periodicity of the $\mathrm{Cu}$ lattice. At $v = 0 ~\mathrm{a.u.}$, there is no transfer of energy, just oscillations of the total energy with a zero slope. To obtain the slope for $v = 0.06 ~\mathrm{a.u.}$ which represents the $S_\text{e}$ at this velocity, we subtract the oscillations of the $v = 0 ~\mathrm{a.u.}$ curve from $v = 0.06$ curve due to the non-adiabatic effect at velocities greater than $0 ~\mathrm{a.u.}$ to obtain the red line curve in Figure \ref{fig:fit_graph} (b) with little oscillations. This subtraction is done to remove the oscillations that result from the periodic lattice. A linear fit , $y = a + bx$ (blue line) gives a slope of $0.00912649$ with an error of $6.377 \times 10^{-6}$. We then proceed to do a linear fit in addition to an oscillatory function $y = a + bx + Acos(wx + \phi)$ (black line) to capture the oscillation part. This oscillation fit gives a slope of $0.00894109$ with an error of $\pm 6.997 \times 10^{-7}$. For higher velocities, a linear fit alone is enough to obtain reasonable error values.
