diff --git a/paper/result/perfect/non-polar/default.typ b/paper/result/perfect/non-polar/default.typ index df82de0..f00a1f2 100644 --- a/paper/result/perfect/non-polar/default.typ +++ b/paper/result/perfect/non-polar/default.typ @@ -75,8 +75,6 @@ E#sub[1]-2 和 E#sub[2]-4 模式位于最强模式 E#sub[2]-3 附近,且具有 使得它们在实验光谱中难以区分。 此外,A#sub[1]-2 模式在基面极化配置(xx 和 yy,仅为 0.01)中具有非常弱的拉曼强度,这导致它在正入射的拉曼实验中通常不可见; 但当偏振沿 z 轴时(1.78)则显示出可观测的强度。 -// E#sub[1]-1 模式在理论上无法在正入射中观察到,但在实验中仍然可以看到一个小峰。 -// 这被认为是因为入射光并非完全沿z轴入射,由于衬底斜切和共聚焦汇聚角。通过向不同方向倾斜衬底,我们可以使这个峰变高或变低,如附图所示,这印证了我们的猜想。 The Raman tensors and frequencies of the negligible-polar phonons were calculated using first-principles methods, and the results were compared with both experimental data and theoretical predictions (@table-nopol). @@ -96,54 +94,29 @@ Additionally, but showed an observable intensity when the polarization is along the z-axis (1.78). Thus, it was not typically observed in normal incidence Raman experiments (cite), but could be clearly detected in edge incidence configurations in our experiments. -// TODO: 这里缺两个引用 -不同方向的入射配置会导致微小但可观测的峰位差异。 +理想情况下不允许存在的效应被观察到。 +这包括不同入射方向下,弱极性峰位的微小移动,以及 E#sub[1]-1 模式在正入射中的可见性。 +在我们的计算中,从正入射到肩入射,E2-3的峰位几乎不变,E2-1与A1-1会有可观测的蓝移,同时E2-2会有可观测的红移。 +实验结果与计算结果基本一致,如图如表所示。 +E1模式在正入射中可以看到,尽管理论上不应该。 +这被认为是因为入射光并非完全沿z轴入射,由于衬底斜切和共聚焦汇聚角。 +不同方向偏振的结果印证了我们的猜想,如图所示。同时,略微倾斜衬底可以使这个峰变高或变低,如附图所示,这印证了我们的猜想。 -微小但可观测的峰位移动应该存在于不同入射配置的峰位中,因为非零的波矢长度。 -在我们的计算中,相比于正入射,肩入射的E2-1与E2-2的间距会减小0.49,同时A1-1会红移0.19。 -在实验中,E2-1与E2-2的间距减少0.36,A1-1红移了xxxx。 - -Minor but observable peak shifts of negligible-polar phonons were expected between different incidence configurations, - due to non-zero wavevector lengths. +Some effects absent in the ideal model were observed experimentally, + including minor but observable peak shifts of negligible-polar phonons between different incidence configurations, + and the observability of the E#sub[1]-1 mode in normal incidence Raman experiments. +The peak shifts were considered caused by the non-zero wavevector lengths of phonons. In our calculations, compared to normal incidence, - the spacing between the E#sub[2]-1 mode and E#sub[2]-2 mode decreased by 0.49 cm#super[-1] under edge incidence, - while the A#sub[1]-1 mode redshifted by 0.19 cm#super[-1]. -In our experiments, the spacing between the E#sub[2]-1 mode and E#sub[2]-2 mode decreased by 0.36 cm#super[-1], - while the A#sub[1]-1 mode redshifted by xxxx cm#super[-1]. + the E#sub[2]-3 mode's frequency remained nearly unchanged, + while the E#sub[2]-1, E#sub[2]-2, A#sub[1]-1 modes exhibited minor but observable shifts. +The experimental results were in good agreement with our calculations, as shown in figure and table. +The visibility of the E#sub[1]-1 mode in normal incidence Raman experiments were attributed to the fact that + the incident light was not perfectly aligned along the z-axis, + due to the substrate's slight tilt and the converging angle of the confocal setup. +This was confirmed by the results under different polarization configurations and different tilt angles, + as shown in figure. #include "figure-nopo-diff.typ" -E1为什么可以被看到。 - -E1在正入射中可以看到,尽管理论上不应该。 -这被认为是因为入射光并非完全沿z轴入射,由于衬底斜切和共聚焦汇聚角。 -通过向不同方向倾斜衬底,我们可以使这个峰变高或变低,如附图所示。 -此外,考虑到斜切方向(x方向),E1模式应该更容易在zxxz和zyxz中看到,而在zyyz中更难看到,这与实验一致。 - -The E#sub[1]-1 mode was observed in normal incidence Raman experiments, despite being theoretically forbidden. -This was attributed to the fact that the incident light was not perfectly aligned along the z-axis, - due to the substrate's slight tilt and the converging angle of the confocal setup. -This was confirmed by tilting the substrate in different directions, - which caused the peak to become more or less pronounced, as shown in the inset figure. -Furthermore, considering the tilt direction (x-direction), - the E#sub[1]-1 mode should be more easily observed in the zxxz and zyxz configurations, - while being more difficult to detect in the zyyz configuration, - which is consistent with our experimental observations. - #include "figure-e1.typ" - -// 其它峰在其它章节中解释。 -// -// 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。 -// 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" - -// TODO: 解释为什么 E1 可以看到 diff --git a/paper/result/perfect/non-polar/figure-nopo-diff.typ b/paper/result/perfect/non-polar/figure-nopo-diff.typ index ab1743e..2537041 100644 --- a/paper/result/perfect/non-polar/figure-nopo-diff.typ +++ b/paper/result/perfect/non-polar/figure-nopo-diff.typ @@ -1,5 +1,5 @@ #figure( - image("/画图/弱极性不同方向偏移/main.svg"), + image("/画图/弱极性不同方向偏移/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, diff --git a/paper/result/perfect/non-polar/table-nopol.typ b/paper/result/perfect/non-polar/table-nopol.typ index 2135b25..32ee172 100644 --- a/paper/result/perfect/non-polar/table-nopol.typ +++ b/paper/result/perfect/non-polar/table-nopol.typ @@ -5,6 +5,9 @@ let m(n, content) = table.cell(colspan: n, content); let m2(content) = table.cell(colspan: 2, content); let m3(content) = table.cell(colspan: 3, content); + let pm = sym.plus.minus; + let m21(content) = table.cell(rowspan: 2, colspan: 1, content); + let m22(content) = table.cell(rowspan: 2, colspan: 2, content); table(columns: 12, align: center + horizon, m2[*Notation of Mode*], [E#sub[2]-1], [E#sub[2]-2], [E#sub[1]-1], m2[A#sub[1]-1], @@ -19,22 +22,31 @@ // E2 E2 E1 A1 E1 E2 E2 A1 [Error (%)], [2.6], [2.7], [4.6], m2[2.9], [-], [2.5], [-], m2[3.1], table.cell(rowspan: 4)[*Raman Tensor*], - [Non-zero components], + [Non-zero components], // E2 E2 E1 A1 [xy, xx, -yy], [xy, xx, -yy], [xz, yz], [xx, yy], [zz], // E1 E2 E2 A1 [xz, yz], [xy, xx, -yy], [xy, xx, -yy], [xx, yy], [zz], - [Analysis result (a.u.)], - // E2 E2 E1 A1 - [$2epsilon_2-2zeta_2-4eta_2$], [$2epsilon_2-2zeta_2$], [$-2epsilon_1-2zeta_1$], [$-2epsilon_5$], [$-2epsilon_6$], - // E1 E2 E2 A1 - [$-2epsilon_1+2zeta_1$], [$bold(8a_2)+2epsilon_2-2zeta_2-4eta_2$], [$-2epsilon_2+2zeta_2$], [$-2zeta_5$], [$-2zeta_6$], - [Calculation result (a.u.)], - // 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 #linebreak() (a.u.)], - // E2 E2 E1 A1 E1 E2 E2 A1 - [0.15], [1.11], [], [1.64], [], [Invisible], [88.54], [Invisible], [Invisible], [], + [Analysis result (a.u.)], + // E2 E2 E1 + [$2epsilon_2-2zeta_2-4eta_2$], [$2epsilon_2-2zeta_2$], [$-2epsilon_1-2zeta_1$], + // A1 E1 E2 + [$-2epsilon_5$], [$-2epsilon_6$], [$-2epsilon_1+2zeta_1$], [$bold(8a_2)+2epsilon_2-2zeta_2-4eta_2$], + // E2 A1 + [$-2epsilon_2+2zeta_2$], [$-2zeta_5$], [$-2zeta_6$], + [Calculation result (a.u.)], + // 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 #linebreak() (a.u.)], + // E2 E2 E1 A1 E1 E2 E2 A1 + [0.15], [1.11], [], [1.64], [], [Invisible], [88.54], [Invisible], [Invisible], [], + table.cell(rowspan: 2)[*Raman Shift of Different Incidence Directions*], + [Calculation result (cm#super[-1])], + // E2 E2 E1 A1 E1 E2 E2 A1 + [0.263], [-0.221], m21[-], m2[-0.188], m21[-], [0.004], m21[-], m22[-], + [Experiment result (cm#super[-1], average #pm standard deviation)], + // E2 E2 A1 E2 + [0.158 #pm 0.060], [-0.245 #pm 0.026], m2[-0.279 #pm 0.016], [0 #linebreak() (used for calibration)], )}, caption: [Negaligible-polarized Phonons at $Gamma$ Point.], )] diff --git a/画图/弱极性不同方向偏移/embed.svg b/画图/弱极性不同方向偏移/embed.svg new file mode 100644 index 0000000..66f6b87 --- /dev/null +++ b/画图/弱极性不同方向偏移/embed.svg @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a0d318a6bbb683f2d7e5492c3062b2e657ab2102e00990c83a12d3d047836c54 +size 101491 diff --git a/画图/弱极性不同方向偏移/main.svg b/画图/弱极性不同方向偏移/main.svg index 81aeb3c..0fae4db 100644 --- a/画图/弱极性不同方向偏移/main.svg +++ b/画图/弱极性不同方向偏移/main.svg @@ -1,3 +1,3 @@ version https://git-lfs.github.com/spec/v1 -oid sha256:cf48e84ef570750a7eb8bf9e0ace4cc2bc3447348d1c7e6f5340c0c20416ca04 -size 14663 +oid sha256:6aaa9c3d8a6147fa37768a54d739851929c3af65336c911526bfa084ed7e8434 +size 1503 diff --git a/画图/弱极性不同方向偏移/plot.ipynb b/画图/弱极性不同方向偏移/plot.ipynb index 7331e99..50f2365 100644 --- a/画图/弱极性不同方向偏移/plot.ipynb +++ b/画图/弱极性不同方向偏移/plot.ipynb @@ -1,3 +1,3 @@ version https://git-lfs.github.com/spec/v1 -oid sha256:cb661f5bf4080c6050a5dc6728696f9b2bcb1eedee6726be32715e7ee32376b9 -size 835000 +oid sha256:88d0344b15bb01e6c4b6f1062bf78ce2a1025390c3f15dcb2ccd03becea83483 +size 855783 diff --git a/画图/弱极性不同方向偏移/拉曼.svg b/画图/弱极性不同方向偏移/拉曼.svg new file mode 100644 index 0000000..beb93ec --- /dev/null +++ b/画图/弱极性不同方向偏移/拉曼.svg @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2927af239730ae14c2dc1bdd65afc2e9f0fc36f7c8894763dedf3e21ec816647 +size 70354 diff --git a/画图/拉曼结果拟合/250923/shift_E21.txt b/画图/拉曼结果拟合/250923/shift_E21.txt index 86fd1be..7fca1a5 100644 --- a/画图/拉曼结果拟合/250923/shift_E21.txt +++ b/画图/拉曼结果拟合/250923/shift_E21.txt @@ -1,2 +1,2 @@ -1.954075029530483505e+02 1.953478857341484627e+02 1.953769267166200905e+02 1.954027970339571993e+02 1.953347589514454796e+02 1.953585750606797262e+02 1.953331279341388722e+02 1.954060267425776658e+02 1.952899705473047050e+02 1.953494452516382864e+02 1.953889540387470731e+02 -1.955143254061939047e+02 1.955314568194222034e+02 1.955552683333574748e+02 1.955481750180620395e+02 1.955953344290883251e+02 1.955747288170350373e+02 1.955405035622480341e+02 1.954405635948803877e+02 1.953860875562799890e+02 1.955043177012716740e+02 1.955407037484820592e+02 +1.955848052701602739e+02 1.955719549975438838e+02 1.955929051638321710e+02 1.956348447216788884e+02 1.954968231689395282e+02 1.955432332739998742e+02 1.955365842761710553e+02 1.956495763564502113e+02 1.955159160392721844e+02 1.956011491541673593e+02 1.956275997529293704e+02 +1.958012278006910094e+02 1.958162272575077907e+02 1.957831178516572948e+02 1.958249159186141810e+02 1.958364298063405897e+02 1.957933101182395603e+02 1.958021374449715495e+02 1.958134637560016813e+02 1.957881271460675521e+02 1.958187264806561529e+02 1.957841759645648096e+02 diff --git a/画图/拉曼结果拟合/250923/shift_E22.txt b/画图/拉曼结果拟合/250923/shift_E22.txt index 3f62fbe..f67b0e5 100644 --- a/画图/拉曼结果拟合/250923/shift_E22.txt +++ b/画图/拉曼结果拟合/250923/shift_E22.txt @@ -1,2 +1,2 @@ -2.033596745420836385e+02 2.033350514440899133e+02 2.033520034103685248e+02 2.033359289059363277e+02 2.033325794937803437e+02 2.033390901492543037e+02 2.033161571980983240e+02 2.033605399415457100e+02 2.033257530283401309e+02 2.033291258845766265e+02 2.033518148664678051e+02 -2.030969863890181841e+02 2.031161714659073425e+02 2.031116343498714230e+02 2.031200227998062076e+02 2.030973971095251045e+02 2.031188254080149420e+02 2.031087887206043661e+02 2.030768375231341452e+02 2.030640772958760749e+02 2.030605849463428854e+02 2.030720189180035788e+02 +2.034024141958410041e+02 2.033769616315146891e+02 2.033951351274238277e+02 2.033767144659590258e+02 2.033742078065036765e+02 2.033807464342712876e+02 2.033596912050411163e+02 2.034018552200704733e+02 2.033676570593588053e+02 2.033706539863660225e+02 2.033939947741981484e+02 +2.031269701456583903e+02 2.031410180043692435e+02 2.031354010942689854e+02 2.031408982509935299e+02 2.031211049500984416e+02 2.031478830793148802e+02 2.031381933050760722e+02 2.031074067250477526e+02 2.030943949028673501e+02 2.030889933216531062e+02 2.030979516775117872e+02