diff --git a/test-typst/section/perfect/non-polar/default.typ b/test-typst/section/perfect/non-polar/default.typ index ad0d880..5e2ffe0 100644 --- a/test-typst/section/perfect/non-polar/default.typ +++ b/test-typst/section/perfect/non-polar/default.typ @@ -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. diff --git a/test-typst/section/perfect/non-polar/table-nopol.typ b/test-typst/section/perfect/non-polar/table-nopol.typ index fb1de6b..f949762 100644 --- a/test-typst/section/perfect/non-polar/table-nopol.typ +++ b/test-typst/section/perfect/non-polar/table-nopol.typ @@ -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