This commit is contained in:
@@ -43,30 +43,34 @@ This approach is founded on the assumption that the change in polarizability ind
|
||||
while other factors (mass, bond length, etc.) only have small contributions.
|
||||
As a result,
|
||||
the phonon modes with the strongest Raman intensities can be predicted
|
||||
prior to first-principles calculations and experiments,
|
||||
and the Raman tensors of the calculated phonon modes can be estimated without additional first-principles computations.
|
||||
prior to first-principles calculations and experiments (appendix),
|
||||
and the Raman tensors of the calculated phonon modes can be estimated
|
||||
before additional first-principles computations.
|
||||
Further details are provided in the appendix.
|
||||
|
||||
The Raman tensors and frequencies of the negligible-polar phonons were calculated using first-principles methods,
|
||||
and the results are compared with experiment and theory (@table-nopol).
|
||||
Calculated frequencies of these phonons are consistent with the experimental results
|
||||
with a low-estimated error of about 2% to 5%, which might be due to the PBE functional used in the calculation (cite).
|
||||
The Raman tensors of these phonons are also consistent with the experimental and theoretical results,
|
||||
where E#sub[2] mode experimentally at 776 cm#super[-1] (mode 8) is the most intense phonon mode,
|
||||
followed by four modes visible in experiment with lesser intensities,
|
||||
including E#sub[2] modes at 195.5 cm#super[-1] (mode 1) and 203.3 cm#super[-1] (mode 2),
|
||||
E#sub[1] mode at 269.7 cm#super[-1] (mode 3), A#sub[1] mode at 609.5 cm#super[-1] (mode 6).
|
||||
The Raman scatter of the E#sub[1] mode calculately at 746.91 cm#super[-1] (mode 7)
|
||||
and E#sub[2] mode calculately at 756.25 cm#super[-1] (mode 9)
|
||||
are much weaker than the most intense mode but located near it, according to our calculation,
|
||||
thus it could not be distinguished from the most intense mode,
|
||||
which explains why they are not observed in experiments.
|
||||
Moreover, the A#sub[1] mode calculated at 812.87 cm#super[-1] (mode 10)
|
||||
have a very weak Raman intensity in the basal plane (xx and yy, only 0.01)
|
||||
and the results are compared with both experimental data and theoretical predictions (@table-nopol).
|
||||
The calculated phonon frequencies show good agreement with experimental data,
|
||||
with a slight underestimation of 2-5%,
|
||||
which may be attributed to the underestimation of forces by PBE functional (cite).
|
||||
The calculated Raman tensors are also consistent with experimental and theoretical results.
|
||||
Among negligible-polar modes, the E#sub[2] mode observed experimentally at 776 cm#super[-1] (mode 8)
|
||||
exhibits the highest Raman intensity,
|
||||
followed by four modes with lower intensities that are also experimentally visible,
|
||||
including the E#sub[2] modes at 195.5 cm#super[-1] (mode 1) and 203.3 cm#super[-1] (mode 2),
|
||||
the E#sub[1] mode at 269.7 cm#super[-1] (mode 3), and the A#sub[1] mode at 609.5 cm#super[-1] (mode 6).
|
||||
The E#sub[1] mode calculated at 746.91 cm#super[-1] (mode 7)
|
||||
and the E#sub[2] mode calculated at 756.25 cm#super[-1] (mode 9)
|
||||
are predicted to have much weaker Raman intensities and are located close to the most intense mode (mode 8),
|
||||
making them indistinguishable in experimental spectra.
|
||||
This explains their absence in experimental observations.
|
||||
Additionally, the A#sub[1] mode calculated at 812.87 cm#super[-1] (mode 10)
|
||||
exhibits very weak Raman intensity in the scattering in basal plane (xx and yy, only 0.01)
|
||||
but an observable intensity in the zz configuration (1.78).
|
||||
Thus, this mode could not be observed in most Raman experiments (cite),
|
||||
but could be observable when incident light propagate not along the z-direction (our experiment),
|
||||
or the incident light wavelength is near the resonance condition (cite).
|
||||
As most Raman experiments are back-scattering along the z-direction with photon energy much less than the band gap,
|
||||
this mode is generally not observed in these experiments (cite),
|
||||
but it may become detectable when the incident light does not propagate along the z-direction (as in our experiment)
|
||||
or when the incident light wavelength is near resonance conditions (cite).
|
||||
|
||||
Besides, there are other peeks in the experiment.
|
||||
The peek at 796 and 980 are caused by strong-polar phonons which will be discussed later.
|
||||
|
||||
@@ -14,8 +14,8 @@
|
||||
m2[*Number of Mode*],
|
||||
// E2 E2 E1 2B1 A1 E1 E2 E2 A1 2B1
|
||||
m2[1], m2[2], m2[3], [4], [5], m2[6], m2[7], m2[8], m2[9], m2[10], [11], [12],
|
||||
// E2 E2 E1 2B1 A1 E1 E2 E2 A1 2B1
|
||||
m2[*Vibration Direction*], [x], [y], [x], [y], [x], [y], m2[z], m2[z], [x], [y], [x], [y], [x], [y], m2[z], m2[z],
|
||||
// E2 E2 E1 2B1 A1 E1 E2 E2 A1 2B1
|
||||
m2[*Vibration Direction*], [x], [y], [x], [y], [x], [y], m(4)[z], [x], [y], [x], [y], [x], [y], m(4)[z],
|
||||
table.cell(rowspan: 2)[*Representation*],
|
||||
[C#sub[6v]], m2(E2), m2(E2), m2(E1), B1, B1, m2(A1), m2(E1), m2(E2), m2(E2), m2(A1), B1, B1,
|
||||
// E2 E2 E1 2B1 A1 E1 E2 E2 A1 2B1
|
||||
@@ -35,8 +35,9 @@
|
||||
// E2 A1 2B1
|
||||
m2[$-2epsilon_2+2zeta_2$], [$-2zeta_5$], [$-2zeta_6$], m2[-],
|
||||
[Calculation result (a.u.)],
|
||||
// TODO: 改正正负号
|
||||
// E2 E2 E1 2B1 A1 E1 E2 E2 A1 2B1
|
||||
m2[0.17], m2[1.13], m2[2.43], m2[0], [2.83], [1.79], m2[0.09], m2[88.54], m2[0.50], [0.01], [1.78], m2[0],
|
||||
m2[0.17], m2[1.13], m2[2.43], m2[-], [2.83], [1.79], m2[0.09], m2[88.54], m2[0.50], [0.01], [1.78], m2[-],
|
||||
[Experiment result (a.u.)],
|
||||
// TODO: 填充
|
||||
// E2 E2 E1 2B1 A1 E1 E2 E2 A1 2B1
|
||||
|
||||
Reference in New Issue
Block a user