From 3e4902719c756823a8ec9c7e7599cae0f987224f Mon Sep 17 00:00:00 2001 From: chn Date: Fri, 4 Jul 2025 12:01:42 +0800 Subject: [PATCH] --- paper/result/perfect/non-polar/default.typ | 25 +++++++++++----------- paper/todo.typ | 7 +++--- 2 files changed, 16 insertions(+), 16 deletions(-) diff --git a/paper/result/perfect/non-polar/default.typ b/paper/result/perfect/non-polar/default.typ index 46dd076..bd8167a 100644 --- a/paper/result/perfect/non-polar/default.typ +++ b/paper/result/perfect/non-polar/default.typ @@ -13,23 +13,22 @@ This approximation is based on the fact that 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。 -Gamma 点声子满足 C#sub[6v] 点群对称性，18 个模式包含了 2A#sub[1] + 4B#sub[1] + 2E#sub[1] + 4E#sub[2] 共 12 个表示； - 其中简并表示（E1 和 E2）的拉曼张量的形状可以通过进一步考虑在 C#sub[2v] 点群中的表示来确定，如表所示。 +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。 -// Representation of these 18 phonons, and the shape of their Raman tensors could be determined in advance.) -Phonons at the #sym.Gamma point satisfy the C#sub[6v] point group symmetry, - and the 18 negligible-polar phonons correspond to 12 irreducible representations of the C#sub[6v] point group: - 2A#sub[1] + 4B#sub[1] + 2E#sub[1] + 4E#sub[2]. -Phonons belonging to the A#sub[1] and B#sub[1] representations vibrate along the z-axis and are non-degenerate, - while those belonging to the E#sub[1] and E#sub[2] representations vibrate in-plane and are doubly degenerate. -Phonons of the B#sub[1] representation are Raman-inactive, as their Raman tensors vanish. -In contrast, phonons of the other representations are Raman-active, - and the non-zero components of their Raman tensor - can be determined by further considering their representation in the C#sub[2v] point group (see @table-rep). -These Raman-active phonons are potentially be visible in Raman experiment under appropriate polarization configurations. +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 + (2A#sub[1] + 4B#sub[1] + 2E#sub[1] + 4E#sub[2]). +By further considering the doubly degenerate modes of the C#sub[6v] (E#sub[1] and E#sub[2]) + in the C#sub[2v] point group, + the form of the 18 negligible-polar phonons' Raman tensors can be determined, as shown in @table-rep. +Phonons of the B#sub[1] representation in C#sub[6v] have a zero Raman tensor and do not contribute to Raman scattering, + while other phonons have non-zero Raman tensor components, + indicating they may be observable in Raman experiments under appropriate incidence and polarization configurations. However, whether a mode is sufficiently strong to be experimentally visible depends on the magnitudes of its Raman tensor components, which cannot be determined solely from symmetry analysis. diff --git a/paper/todo.typ b/paper/todo.typ index de92242..39c245c 100644 --- a/paper/todo.typ +++ b/paper/todo.typ @@ -16,6 +16,7 @@ - [x] 英文 - [x] 调整语言 - [ ] 坐标轴定义 + - [ ] 偏振 - [x] 模型总述 - [x] 无缺陷和点缺陷的模型大小、结构 - [x] 中文 @@ -48,9 +49,9 @@ - [x] 中文 - [x] 英文 - [x] 调整语言 - - [ ] 表示 - - [ ] 中文 - - [ ] 英文 + - [/] 表示 + - [x] 中文 + - [x] 英文 - [ ] 调整语言 - [ ] 估算拉曼张量 - [ ] 中文