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,
+  $epsilon_i$, $eta_i$ and $eta_i$ corresponding to the difference between different bilayers and different atoms.
-  and $eta_i$ corresponding the difference between the Si and C atoms.
+Due to the similarity of environment in different bilayers and around different atoms,
-The absolute values of $a_i$ is expected to be much larger than that of $epsilon_i$, $eta_i$ and $zeta_i$,
+  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,
 )<table-predmode>]
 
-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).
 
-,
+Besides, there are other peeks in the experiment.
-  except for the E#sub[2] mode experimentally at 200 cm#super[-1], which we expected to be at higher frequencies.
+The peek at 796 and 980 are caused by strong-polar phonons which will be discussed later.
-
+Besides, there are small peeks at xxx,
-// 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。
+  which could not be explained in perfect 4H-SiC and will be discussed in the next section.
-// 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.
 
 // 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。