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2025-05-10 15:03:39 +08:00
parent e624b0000a
commit d9f27c072a
2 changed files with 63 additions and 41 deletions

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@@ -2,11 +2,18 @@
#import "@preview/tablem:0.2.0": tablem #import "@preview/tablem:0.2.0": tablem
#set par.line(numbering: "1") #set par.line(numbering: "1")
#show figure.caption: it => { #show figure.caption: it => {
set align(left)
set text(10pt) set text(10pt)
show: box.with(width: 80%) align(center, box(align(left, it), width: 80%))
it
} }
#set page(
// paper: "us-letter",
// header: align(right)[
// A fluid dynamic model for
// glacier flow
// ],
numbering: "1/1",
)
#set figure(placement: none)
#show: article.with( #show: article.with(
title: "Article Title", title: "Article Title",
authors: ( authors: (
@@ -34,7 +41,6 @@
// body // body
// }) // })
) )
#set figure(placement: none)
= Introduction = Introduction
@@ -189,19 +195,23 @@ However, the actual visibility of each phonon depends on the magnitudes of its R
// 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。 // 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。 // 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, 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 @nopol. and the results are summarized and compared with experimental results in @nopol.
Some Raman-active phonons are not visible in experiments, Two Raman-active modes are not observed in our experiments,
including E#sub[1] at ~746.91 cm#super[-1] and E#sub[2] at ~764.33 cm#super[-1], including the E#sub[1] mode at 746.91 cm#super[-1] and the E#sub[2] mode at 764.33 cm#super[-1],
causing their Raman intensity are relatively low and located close to strong modes. 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 only visible The A#sub[1] phonon at 812.87 cm#super[-1] is Raman-active
when both the incident and scattered light propagate along the z-direction, in both in-plane (xx and xy) and out-of-plane (zz) polarization configurations,
since its Raman intensity in basal plane is too week to be recognized from the background. but it is only visible when both the incident and scattered light propagate along the z-direction (zz),
We also calculated the linewidthes of these phonons at 300 K and compared them with experimental results, as its Raman intensity in basal plane is too week to be distinguished from the noise.
as summarized in the table. We also calculated the linewidths of these phonons at 300 K and compared them with experimental results,
as summarized in the @nopol.
The atomic vibration amplitudes are listed separately in the Appendix. 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。
// 也就是说,简并的里面有两个或者无数个 phonon但只有一个 mode
#page(flipped: true)[#figure({ #page(flipped: true)[#figure({
let m(n, content) = table.cell(colspan: n, content); let m(n, content) = table.cell(colspan: n, content);
let A1 = [A#sub[1]]; let A1 = [A#sub[1]];
@@ -210,7 +220,7 @@ The atomic vibration amplitudes are listed separately in the Appendix.
// let B2 = [B#sub[2]]; // let B2 = [B#sub[2]];
let E1 = [E#sub[1]]; let E1 = [E#sub[1]];
let E2 = [E#sub[2]]; let E2 = [E#sub[2]];
table(columns: 27, align: center + horizon, inset: (x: 2pt, y: 5pt), table(columns: 27, align: center + horizon, inset: (x: 3pt, y: 5pt),
// [*Direction of Incident & Scattered Light*], // [*Direction of Incident & Scattered Light*],
// m(26)[Any direction (not depend on direction of incident & scattered light)], // m(26)[Any direction (not depend on direction of incident & scattered light)],
[*Number of Phonon*], [*Number of Phonon*],
@@ -225,53 +235,65 @@ The atomic vibration amplitudes are listed separately in the Appendix.
[x], [y], [x], m(2)[y], [x], m(2)[y], m(3)[z], [z], [z], [x], [y], [x], m(2)[y], [x], m(2)[y], m(3)[z], [z], [z],
[*Representation #linebreak() in Group C#sub[6v]*], [*Representation #linebreak() in Group C#sub[6v]*],
m(3, E2), m(3, E2), m(2, E1), B1, B1, m(3, A1), m(2, E1), m(3, E2), m(3, E2), m(3, A1), B1, B1, m(3, E2), m(3, E2), m(2, E1), B1, B1, m(3, A1), m(2, E1), m(3, E2), m(3, E2), m(3, A1), B1, B1,
[*Raman-active or Not*],
m(8)[Raman-active], m(2)[Raman-inactive], m(14)[Raman-active], m(2)[Raman-inactive],
// [*Representation in Group C#sub[2v]*], // [*Representation in Group C#sub[2v]*],
// // E2 E2 E1 2B1 A1 E1 E2 E2 A1 2B1 // // E2 E2 E1 2B1 A1 E1 E2 E2 A1 2B1
// A2, m(2, A1), A2, m(2, A1), B2, B1, B1, B1, m(3, A1), B2, B1, A2, m(2, A1), A2, m(2, A1), m(3, A1), B1, B1, // A2, m(2, A1), A2, m(2, A1), B2, B1, B1, B1, m(3, A1), B2, B1, A2, m(2, A1), A2, m(2, A1), m(3, A1), B1, B1,
[*Scattering in Polarization #linebreak() (non-zero Raman #linebreak() tenser components)*], [*Scattering in Polarization #linebreak() (non-zero Raman #linebreak() tenser components)*],
// E2 E2 E1 2B1 A1 // E2 E2 E1 2B1 A1
[xy], [xx], [yy], [xy], [xx], [yy], [xz], [yz], [-], [-], [xx], [yy], [zz], [xy], [xx], [yy], [xy], [xx], [yy], [xz], [yz], m(2)[-], [xx], [yy], [zz],
// E1 E2 E2 A1 2B1 // E1 E2 E2 A1 2B1
[xz], [yz], [xy], [xx], [yy], [xy], [xx], [yy], [xx], [yy], [zz], [-], [-], [xz], [yz], [xy], [xx], [yy], [xy], [xx], [yy], [xx], [yy], [zz], m(2)[-],
[*Raman Intensity (a.u.)*], [*Raman Intensity (a.u.)*],
// E2 E2 E1 2B1 A1 // E2 E2 E1 2B1 A1
m(3)[0.17], m(3)[1.13], m(2)[2.43], [0], [0], m(2)[2.83], [1.79], m(3)[0.17], m(3)[1.13], m(2)[2.43], m(2)[0], m(2)[2.83], [1.79],
// E1 E2 E2 A1 2B1 // E1 E2 E2 A1 2B1
m(2)[0.09], m(3)[88.54], m(3)[0.50], m(2)[0.01], [1.78], [0], [0], m(2)[0.09], m(3)[88.54], m(3)[0.50], m(2)[0.01], [1.78], m(2)[0],
[*Visible in Common #linebreak() Raman Experiment*], [*Visible in Common #linebreak() Raman Experiment or Not*],
// E2 E2 E1 2B1 A1 // E2 E2 E1 2B1 A1
m(3)[Yes], m(3)[Yes], m(2)[Yes], [No], [No], m(3)[Yes], m(8)[Visible], m(2)[-], m(3)[Visible],
// E1 E2 E2 A1 2B1 // E1 E2 E2 A1 2B1
m(2)[No], m(3)[Yes], m(3)[No], m(2)[No], [Yes], [No], [No], m(2)[Invisible], m(3)[Visible], m(5)[Invisible], [Visible], m(2)[-],
[*Wavenumber #linebreak() (Simulation) (cm#super[-1])*], [*Wavenumber #linebreak() (Simulation) (cm#super[-1])*],
// E2 E2 E1 2B1 A1 // E2 E2 E1 2B1 A1
m(3)[190.51], m(3)[197.84], m(2)[257.35], [389.96], [397.49], m(3)[591.90], m(3)[190.51], m(3)[197.84], m(2)[257.35], [389.96], [397.49], m(3)[591.90],
// E1 E2 E2 A1 2B1 // E1 E2 E2 A1 2B1
m(2)[746.91], m(3)[756.25], m(3)[764.33], m(3)[812.87], [885.68], [894.13], m(2)[746.91], m(3)[756.25], m(3)[764.33], m(3)[812.87], [885.68], [894.13],
[*Wavenumber #linebreak() (Experiment) (cm#super[-1])*], [*Wavenumber #linebreak() (Experiment) (cm#super[-1])*],
// E2 E2 E1 2B1 A1 // E2 E2 E1 2B1 A1
m(3)[195.5], m(3)[203.3], m(2)[269.7], [-], [-], m(3)[609.5], m(3)[195.5], m(3)[203.3], m(2)[269.7], m(2)[-], m(3)[609.5],
// E1 E2 E2 A1 2B1 // E1 E2 E2 A1 2B1
m(2)[-], m(3)[776], m(3)[-], m(2)[-], [839], [-], [-], m(2)[-], m(3)[776], m(5)[-], [839], m(2)[-],
[*FWHM #linebreak() (Simulation) (cm#super[-1])*], [*FWHM #linebreak() (Simulation) (cm#super[-1])*],
// E2 E2 E1 2B1 A1 // E2 E2 E1 2B1 A1
m(3)[0.08], m(3)[0.09], m(2)[0.08], [-], [-], m(3)[0.61], m(3)[0.08], m(3)[0.09], m(2)[0.08], m(2)[-], m(3)[0.61],
// E1 E2 E2 A1 2B1 // E1 E2 E2 A1 2B1
m(2)[3.97], m(3)[4.62], m(3)[4.01], m(3)[0.89], [-], [-], m(2)[3.97], m(3)[4.62], m(3)[4.01], m(3)[0.89], m(2)[-],
[*FWHM #linebreak() (Experiment) (cm#super[-1])*], [*FWHM #linebreak() (Experiment) (cm#super[-1])*],
// E2 E2 E1 2B1 A1 // E2 E2 E1 2B1 A1
m(3)[1.11], m(3)[1.11], m(2)[1.11], [-], [-], m(3)[591.90], m(3)[1.11], m(3)[1.11], m(2)[1.11], m(2)[-], m(3)[591.90],
// E1 E2 E2 A1 2B1 // E1 E2 E2 A1 2B1
m(2)[-], m(3)[1.11], m(3)[-], m(3)[1.11], [-], [-], m(2)[-], m(3)[1.11], m(3)[-], m(3)[1.11], m(2)[-],
[*Electrical Polarity*], [*Electrical Polarity*],
// E2 E2 E1 2B1 A1 // E2 E2 E1 2B1 A1 E1 E2 E2 A1 2B1
m(3)[None], m(3)[None], m(2)[Weak], [None], [None], m(3)[Weak], m(6)[None], m(2)[Weak], m(2)[None], m(5)[Weak], m(6)[None], m(3)[Weak], m(2)[None],
// E1 E2 E2 A1 2B1
m(2)[Weak], m(3)[None], m(3)[None], m(3)[Weak], [None], [None],
)}, )},
caption: [Weak- and None-polarized phonons near $Gamma$ point], caption: [Weak- and None-polarized phonons near $Gamma$ point],
)<nopol>] )<nopol>]
#figure(
image("/画图/拉曼整体图/main.svg"),
caption: [
(a) Phonon dispersion of 4H-SiC along the A#sym.GammaK 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>
#page(flipped: true)[ #page(flipped: true)[
#figure({ #figure({
let m(n, content) = table.cell(colspan: n, content); let m(n, content) = table.cell(colspan: n, content);

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