调整一些细节

paper/result/perfect/default.typ

@@ -34,6 +34,9 @@ These phonons were categorized into two groups according to their electrical pol
     where atoms of the same species vibrate in phase,
     resulting in strong electrical polarization and observable effects in Raman spectra
     (colored lines in @figure-discont).
+The categorized is also illustrated and compared with Raman experiment in @fig-raman.
+
+#include "figure-raman.typ"
 
 #include "non-polar/default.typ"
 #include "polar/default.typ"

paper/result/perfect/figure-discont.typ

@@ -3,6 +3,7 @@
   caption: [
     (a) Phonon dispersion of 4H-SiC along the A–#sym.Gamma–K high-symmetry path.
     (b) Magnified view of the boxed region in (a).
+    (c) Magnified view of the boxed region in (b).
       The orange dashed lines mark the phonon wavevectors involved in Raman scattering
         with green laser light under normal and edge incidence configurations.
   ],

paper/result/perfect/non-polar/default.typ

@@ -1,27 +1,28 @@
 === Phonons with Negligible Polarities
 
-用 gamma 点的声子来近似。
+对弱极性声子的理论分析，首先使用 Gamma 点的声子来近似，然后再讨论不同入射方向导致的差异。
+使用Gamma 点的声子来近似，基于这样的事实：这些声子的色散曲线在 Gamma 点附近连续且非常接近 Gamma 点，并且已经被广泛使用 @_n-sic_2008。
 
-Gamma 点的声子被用于近似参与拉曼散射的弱极性声子，无论入射配置。
-这个近似是因为这些声子的色散曲线在 Gamma 点附近连续且非常接近 Gamma 点，并且已经被广泛使用。
-
-Phonons at the #sym.Gamma point were employed to approximate negligible-polar phonons for all incidence configurations.
+Negligible-polar phonons were theoretically analyzed,
+  starting with the approximation using phonons at the #sym.Gamma point,
+  followed by a discussion of variations arising from non-zero wavevectors
+    (e.g. different incidence configurations in Raman experiments).
 This approximation is based on the fact that
     the dispersion of these phonons is continuous and very close to the #sym.Gamma point,
   and has been widely adopted in the literature @_n-sic_2008.
 
 18 个声子属于 12 个表示。拉曼张量的形状可以确定，大小不能。
 
-这些声子的拉曼张量的形状可以通过对称性分析来确定。
+使用对称性分析来从理论上研究声子。
 18 个 Gamma 点的弱极性声子包含了 C#sub[6v] 点群的12 个不可约表示（2A#sub[1] + 4B#sub[1] + 2E#sub[1] + 4E#sub[2]）。
 通过进一步考虑 C#sub[6v] 中简并表示（E1 和 E2）在 C#sub[2v] 中的表示，所有声子的拉曼张量的非零分量可以确定，如表所示。
 其中，B#sub[1] 模式具有零拉曼张量，不参与拉曼散射；
   其它表示的模式具有非零拉曼张量分量，可能可以在适当的偏振配置下在拉曼实验中观察到。
 然而，模式是否足够强以在实验中可见取决于其拉曼张量分量的大小，而仅通过对称性分析无法确定这些大小。
 
-The form of the Raman tensors (i.e., which components are non-zero) could be determined by symmetry analysis.
-The 18 negligible-polar phonons at the #sym.Gamma point
-  correspond to twelve irreducible representations of the C#sub[6v] point group
+Symmetry analysis was utilized
+  to theoretically investigate the properties of 18 negligible-polar phonons at the #sym.Gamma point.
+These phonons correspond to twelve irreducible representations of the C#sub[6v] point group
   (2A#sub[1] + 4B#sub[1] + 2E#sub[1] + 4E#sub[2]).
 By further decomposing the doubly degenerate modes (E#sub[1] and E#sub[2] of C#sub[6v] group)
     in the C#sub[2v] point group,
@@ -30,7 +31,7 @@ Phonons of the B#sub[1] representation in C#sub[6v] possess zero Raman tensors
     and thus do not contribute to Raman scattering,
   while other phonons have non-zero Raman tensor components,
   making them potentially observable in Raman experiments under appropriate incidence and polarization configurations.
-It should be noted, however, that the observability in Raman experiment depends not only on the tensor form,
+It should be noted, however, that the observability in Raman experiment depends not only on the form of Raman tensor,
   but also on the magnitude of its Raman tensor components,
   which cannot be inferred from symmetry considerations alone.
 
@@ -43,18 +44,24 @@ It should be noted, however, that the observability in Raman experiment depends
   每个原子对拉曼张量的贡献主要取决于第一近邻原子（它们的贡献记为 $a_i$），更远的原子则归结为小量（记为 $epsilon_i$ $eta_i$ $zeta_i$)。
   此外，我们忽略了同一个振动模式中，同种原子振幅的绝对值的差异，只考虑它们振动方向的不同。
 因此，拉曼张量的大小可以在进一步的第一性原理计算之前给出，结果总结在表中。
-我们的结果表明，756 附近的峰应该比其它峰具有更强的拉曼强度。
+我们的结果表明，756 附近的峰应该比其它峰具有更强的拉曼强度，这与实验一致。
+我们的研究表明，这个峰的高拉曼强度来自于所有键的贡献的相长干涉，这与其他弱极性模式不同（他们的贡献相互抵消）。
 
-A method to rapidly estimate the magnitudes of the Raman tensors was proposed (see appendix for details).
-This approach is founded on the symmetry analysis and incorporates the assumption
+A method to estimate the magnitudes of the Raman tensors of each mode from their vibration patterns (eigenvectors)
+  was proposed (see appendix for details).
+This approach was founded on the symmetry analysis and incorporates the assumption
   that the primary contribution from each atom to the Raman tensor arises from its nearest neighbors (denoted as $a_i$),
   while contributions from more distant atoms are much smaller (denoted as $epsilon_i$, $eta_i$, and $zeta_i$).
-Furthermore, we neglect the absolute amplitude differences among atoms of the same type within a phonon mode,
-  considering only their vibrational directions.
+Furthermore, the absolute amplitude differences among atoms of the same type within a phonon mode was neglected,
+  and only their vibrational directions were considered.
 This enables a preliminary estimation of the Raman tensor magnitudes prior to detailed first-principles calculations,
   with the results summarized in @table-nopol.
-Our analysis indicates that the E#sub[2] mode at 756.25 cm#super[-1] in simulation (mode 8)
-  should possess a much higher Raman intensity than the others.
+Our analysis gave the result that the E#sub[2] mode at 756.25 cm#super[-1] in simulation (mode 8)
+  should possess a much higher Raman intensity than the others,
+  which is consistent with experimental observations.
+Our result showed that
+  the high Raman intensity of this mode arises from the constructive interference of contributions from all bonds,
+  in contrast to other negligible-polar modes where contributions tend to cancel each other out.
 
 #include "table-nopol.typ"
 
@@ -117,6 +124,6 @@ Besides, there are small peeks at xxx,
 // 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。
 // 也就是说，简并的里面有两个或者无数个 phonon，但只有一个 mode
 
-#include "figure-raman.typ"
+// #include "figure-raman.typ"
 
 // TODO: 解释为什么 E1 可以看到

paper/result/perfect/non-polar/figure-raman.typ

@@ -1,11 +0,0 @@
-#figure(
-  image("/画图/拉曼整体图/embed.svg"),
-  caption: [
-    (a) Phonon dispersion of 4H-SiC along the A–#sym.Gamma–K high-symmetry path.
-      Gray lines represent negligible-polar phonon modes,
-      while colored lines indicate strong-polar phonon modes.
-    (b) Magnified view of the boxed region in (a).
-      The orange dashed lines mark the phonon wavevectors involved in Raman scattering
-        with incident light along the z- and y-directions.
-  ]
-)<raman>

paper/result/perfect/non-polar/table-nopol.typ

@@ -12,7 +12,7 @@
       [Simulation (cm#super[-1])],
         // E2     E2        E1        A1          E1        E2        E2        A1
         [190.51], [197.84], [257.35], m2[591.90], [746.91], [756.25], [764.33], m2[812.87],
-      [Experiment (cm#super[-1])],
+      [Experiment (cm#super[-1], averaged)],
         // E2    E2       E1       A1         E1           E2     E2           A1
         [195.5], [203.3], [269.7], m2[609.5], [Invisible], [776], [Invisible], m2[839],
       //           E2     E2     E1     A1       E1   E2     E2   A1
@@ -33,10 +33,12 @@
       // TODO: 改正正负号
       // E2   E2      E1      A1              E1      E2       E2      A1
       [0.17], [1.13], [2.43], [2.83], [1.79], [0.09], [88.54], [0.50], [0.01], [1.78],
-    [Experiment result (a.u.)],
+    [Experiment result #linebreak() (a.u., averaged)],
       // TODO: 填充
       // E2 E2 E1 A1      E1           E2  E2           A1
       [], [], [], [], [], [Invisible], [], [Invisible], [Invisible], [],
   )},
   caption: [Negaligible-polarized Phonons at $Gamma$ Point.],
 )<table-nopol>]
+// TODO: 从多个方向的实验中取得平均值。
+

paper/result/perfect/non-polar/table-rep.typ

@@ -12,14 +12,10 @@
     table.cell(rowspan: 2)[*Representation*],
       [C#sub[6v]], A1, B1, m2(E1), m2(E2),
       [C#sub[2v]], A1, B1, B2, B1, A2, A1,
-    table.cell(rowspan: 2, colspan: 2)[*Vibration Direction*],
-      [out-of-plane], [out-of-plane], m2[in-plane], m2[in-plane],
-      [z], [z], [x], [y], [x], [y],
+    m2[*Vibration Direction*], [z], [z], [x], [y], [x], [y],
     m2[*Raman Tensor*],
-      [$mat(a,,;,a,;,,b)$], [$0$], [$mat(,,a;,,;a,,;)$], [$mat(,,;,,a;,a,;)$], [$mat(,a,;a,,;,,;)$], [$mat(a,,;,-a,;,,;)$],
-    m2[*Raman visibility*],
-      [xx/yy: $a^2$ #linebreak() zz: $b^2$ #linebreak() others: 0], [0],
-      m2[xz/yz: $a^2$ #linebreak() others: 0], m2[xx/xy/yy: $a^2$ #linebreak() others: 0],
+      [$mat(a,,;,a,;,,b)$], [$0$],
+      [$mat(,,a;,,;a,,;)$], [$mat(,,;,,a;,a,;)$], [$mat(,a,;a,,;,,;)$], [$mat(a,,;,-a,;,,;)$],
   )},
   caption: [
     Irreducible representations and raman tensors of phonons in 4H-SiC.

slide/main.typ

@@ -168,3 +168,19 @@
 - 在不同入射方向下，极性模式最多会呈现出三个峰。
 
 // TODO: 拟合时不考虑fano共振，结果有些不好。是否将它考虑进去再拟合？
+
+= 其他
+
+== 缺陷
+
+- 比对各个峰的结果，得到：（我们只看 E2 模式的 yy 和 xy，以及 A1 的 yy）
+  - 半高宽/高度/积分来看，似乎富C的样品缺陷更多（更宽、更矮）。这是一个合理的现象。
+  - 富C的E1 xy有非常明显的蓝移，但因为暂时不知道来源，所以暂时不分析（需要其它方向的实验）。
+  - 细节来说，富C的E2 xy有明显红移，A1几乎没有移动，E2 yy有红移但很少。
+  - 主E2，yy和xy不同。xy的高度几乎只受到生长环境的影响，xx的高度则还会受到掺杂浓度的影响。xy的宽度会明显受到生长环境的影响，yy的宽度则不变。次高的E2也有类似的规律。
+  - 以上规律中，积分主要受到高度的影响，所以不单独分析（或者使用积分来分析，或许更合适）。
+
+== 拟合 LOPC
+
+有很多可调的参数。我们首先固定一些参数，以便于拟合。
+