From 42101ec892b2204c8f11b35534316f7db8f464b4 Mon Sep 17 00:00:00 2001 From: chn Date: Mon, 26 May 2025 10:23:32 +0800 Subject: [PATCH] --- test-typst/main.typ | 50 ++++++++++++++++++++++----------------------- 1 file changed, 25 insertions(+), 25 deletions(-) diff --git a/test-typst/main.typ b/test-typst/main.typ index 85a5e78..acb62f3 100644 --- a/test-typst/main.typ +++ b/test-typst/main.typ @@ -269,12 +269,10 @@ The method only takes the vibration directions of each atom in each phonon mode, and the result was summarized in @table-predmode. In the Raman tensors in @table-predmode, $a_i$ corresponding to the change of polarizability caused by movement of the Si atoms in A and C layers, - $epsilon_i$ and $eta_i$ corresponding to the difference between the A/C layers and B layers, - and $eta_i$ corresponding the difference between the Si and C atoms. -The absolute values of $a_i$ is expected to be much larger than that of $epsilon_i$, $eta_i$ and $zeta_i$, + $epsilon_i$, $eta_i$ and $eta_i$ corresponding to the difference between different bilayers and different atoms. +Due to the similarity of environment in different bilayers and around different atoms, + the absolute values of $epsilon_i$, $eta_i$ and $zeta_i$ are expected to be much smaller than that of $a_i$, thus the Raman tensors containing $a_i$ are expected to be much larger than those not containing $a_i$. -It could be seen that, - our prediction is mostly consistent with the first principle calculation and experiment. // Raman Tensor for A1: line1 xx/yy; line2 zz // Raman Tensor for E1: x-dirc xz or y-dirc yx @@ -324,27 +322,29 @@ It could be seen that, placement: none, )] -as well as the frequencies +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 is the most intense phonon mode, + followed by four modes with lesser intensities + (E#sub[2] modes at 195.5 and 203.3, E#sub[1] mode at 269.7, A#sub[1] mode at 609.5). +The Raman scatter of the E#sub[1] mode calculately at 746.91 and E#sub[2] mode calculately at 756.25 + are much weaker than the E#sub[2] mode calculated at 756.25 but located near it, according to our calculation, + thus it could not be distinguished from E#sub[2] mode calculated at 756.25, + which explains why they are not observed in experiments. +Moveever, the A#sub[1] mode calculated at 812.87 + have a very weak Raman intensity in the 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). -, - except for the E#sub[2] mode experimentally at 200 cm#super[-1], which we expected to be at higher frequencies. - -// 我们计算了拉曼活性声子的频率及拉曼张量，并与实验对比，如表如图所示。 -// 其中有几个声子的拉曼活性较弱，有几个比较强。强的都可以在实验上看到；但弱的能否看到则取决于它是否恰好位于强模式的附近。 -// 其中，xxx 和xxx 位于强模式的附近，它们在实验上无法看到；xxx 只在 z 方向入射/散射时可以看到；xxx 则在任意方向都能看到。 -// 我们同样计算了这些声子在 300K 下的展宽，并与实验对比，结果如表所示。原子的振幅另外列于附录中。 -The Raman tensors of these Raman-active phonons were calculated using first-principles methods, - and the results are summarized and compared with experimental results in @table-nopol. -Two Raman-active modes are not observed in our experiments, - including the E#sub[1] mode at 746.91 cm#super[-1] and the E#sub[2] mode at 764.33 cm#super[-1], - due to their relatively low Raman intensities, broad FWHM values, and their proximity to stronger modes. -The A#sub[1] phonon at 812.87 cm#super[-1] is Raman-active - in both in-plane (xx and xy) and out-of-plane (zz) polarization configurations, - but it is only visible when both the incident and scattered light propagate along the z-direction (zz), - as its Raman intensity in basal plane is too week to be distinguished from the noise. -We also calculated the linewidths of these phonons at 300 K and compared them with experimental results, - as summarized in the @table-nopol. -The atomic vibration amplitudes are listed separately in the Appendix. +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. +Besides, there are small peeks at xxx, + which could not be explained in perfect 4H-SiC and will be discussed in the next section. // TODO: 将一部分 phonons 改为 phonon modes // 在论文中我们这样来称呼：phonon 对应某一个特征向量，而 modes 对应于一个子空间。