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实验与计算对比的文字

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陈浩南
2025-10-24 15:29:46 +08:00
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paper/result/perfect/non-polar/default.typ
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@@ -13,10 +13,11 @@ This approximation is based on the fact that
the dispersion of these phonons is continuous and very close to the #sym.Gamma point, 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. and has been widely adopted in the literature @_n-sic_2008.
Symmetry analysis pointed out that Symmetry analysis pointed out that
these phonons correspond to twelve irreducible representations of the C#sub[6v] point group these phonons correspond to twelve irreducible representations of the C#sub[6v] point group and were named accrodingly
(2A#sub[1] + 4B#sub[1] + 2E#sub[1] + 4E#sub[2], see appendix for details). (A#sub[1]-1 to A#sub[1]-2, B#sub[1]-1 to B#sub[1]-4, E#sub[1]-1 to E#sub[1]-2, and E#sub[2]-1 to E#sub[2]-4,
In which the B#sub[1] representation is Raman inactive, see appendix for details).
while other phonons are potentially observable in Raman experiments. Among which the B#sub[1] representation is Raman inactive,
while other eight modes are potentially observable in Raman experiments.
However, it should be noted that the intensity of Raman scattering from each mode However, it should be noted that the intensity of Raman scattering from each mode
cannot be inferred from symmetry considerations alone. cannot be inferred from symmetry considerations alone.
@@ -39,73 +40,50 @@ Furthermore, the absolute amplitude differences among atoms of the same type wit
and only their vibrational directions were considered. and only their vibrational directions were considered.
This enables a preliminary estimation of the Raman tensor magnitudes prior to expensive first-principles calculations, This enables a preliminary estimation of the Raman tensor magnitudes prior to expensive first-principles calculations,
with the results summarized in @table-nopol. with the results summarized in @table-nopol.
Our analysis gave the result that the E#sub[2]-3 mode Our analysis gave the result that the E#sub[2]-3 mode possess a much higher Raman intensity
should possess a much higher Raman scattering intensity than the others, and should be clearly observable in Raman experiments,
which is consistent with experimental and first-principles calculation results in the following text. while the observability of other modes depends on their frequencies were well-separated or not
and could only be confirmed by further first-principles calculations or experiments.
Our result showed that Our result showed that
the high Raman intensity of this mode arises from the constructive interference of contributions from all bonds, 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. in contrast to other negligible-polar modes where contributions tend to cancel each other out.
#include "table-nopol.typ" #include "table-nopol.typ"
我们做了计算，估计哪些峰可以看到、哪些峰看不到。 实验看到了7个峰，比别人多。
使用第一性原理计算得到了声子频率和拉曼张量的大小。 我们做了实验，看到了其中 7 个峰，比别人的实验要多。
我们的计算表明，E#sub[2]-1 E#sub[2]-2 E#sub[1]-1 A#sub[1]-1 E#sub[2]-3 模式的拉曼强度较高，并且被报道在绝大多数的拉曼实验中可以看到。 为了解释实验结果，我们进行了第一性原理计算。
A#sub[1]-2 被报道在一些实验中可以观测到而在另外一些实验中不可以观测到(cite)。 E#sub[2]-1 E#sub[2]-2 E#sub[1]-1 A#sub[1]-1 E#sub[2]-3 这几个模式在大多数实验中都可以看到，这是因为它们有较高的拉曼强度且位置比较分散。
我们的计算表明它在面内偏振下拉曼散射强度非常弱，但在 z 轴偏振下有可观测的强度； A#sub[1]-2 在一些实验中可以观察到而在另外一些实验中不可以观察到(cite)，这是因为它在面内偏振下拉曼散射强度非常弱，但在 z 轴偏振下有可观测的强度；
因此在正入射拉曼实验中可能难以看到，但在侧入射时通过选取合适的偏振配置应该可以观察到。 因此在我们的正入射拉曼实验中它很难被看到，但在侧入射时通过选取合适的偏振配置应该可以观察到。
E#sub[1]-2 和 E#sub[2]-4 模式位于最强模式 E#sub[2]-3 附近，且具有很弱的拉曼强度（分别为最强模式的0.1%和0.6%），在报道的实验中都不可见。 E#sub[1]-2 和 E#sub[2]-4 距离最强模式 E#sub[2]-3 很近，且具有很弱的拉曼强度，在报道的实验中都不可见。
E#sub[1]-2 与最强模式 E#sub[2]-3 表示不同，我们认为，通过选取合适的偏振配置，可能可以在实验中观察到。 在我们的实验中，通过选取合适的偏振配置和延长积分时间，E#sub[2]-3 被压制后，E#sub[1]-2 也被观察到了。
我们的实验第一次指出了 E#sub[1]-2 峰，并且与计算和理论吻合较好。
The Raman tensors and frequencies of the negligible-polar phonons were calculated using first-principles methods. Raman experiments were established and seven negligible-polar phonon peaks were observed,
The results showed that which is more than all previous experiments (where only five or six peaks were typically reported).
the E#sub[2]-1, E#sub[2]-2, E#sub[1]-1, A#sub[1]-1, and E#sub[2]-3 modes possess relatively high Raman intensities To further understand our experimental results,
The calculated phonon frequencies were in good agreement with experimental values, first-principles calculations were performed,
with a slight underestimation of 2-5%, and the result was compared with experimental data.
which might be attributed to the known tendency of the PBE functional underestimating interatomic forces (cite). Our calculation showed that the mode of E#sub[2]-1, E#sub[2]-2, E#sub[1]-1, A#sub[1]-1 and E#sub[2]-3
The calculated Raman tensors were also consistent with both experimental and theoretical results. had relatively high Raman intensities and well-separated frequencies,
Among negligible-polar modes, the E#sub[2]-3 mode showed the highest Raman intensity, making them observed in our experiments as well as most previous experiments.
followed by four modes with lower intensities that were also visible in normal incidence Raman experiments, The A#sub[1]-2 mode had only a very weak Raman intensity with in-plane polarization (e.g., zyy#overline[z]),
including the E#sub[2]-1 mode, the E#sub[2]-2 mode, the E#sub[1]-1 mode, and the A#sub[1]-1 mode. while showed an observable intensity when the polarization is along the z-axis (e.g., xzzx).
The E#sub[1]-2 mode and E#sub[2]-4 mode were not visible in our Raman experiments, Thus, it could be observed clearly in our edge incidence experiments (xzzx),
as they were located close to the most intense E#sub[2]-3 mode (only about 10 cm#super[-1] away) but hardly seen in normal incidence configurations.
with very weak Raman intensities (only 0.1% and 0.6% of the E#sub[2]-3 mode, respectively). This peek was reported to be observable in some experiments (cite) but not in others (cite),
Additionally, our calculation provided an explanation for this discrepancy.
the A#sub[1]-2 mode had only a very weak Raman intensity under the incident light with in-plane polarization The E#sub[1]-2 and E#sub[2]-4 modes are calculated
(only 0.01), to be located close to the most intense E#sub[2]-3 mode (< 10 cm#super[-1] away)
but showed an observable intensity when the polarization is along the z-axis (1.78). and exhibit very weak Raman intensities (only 0.1% and 0.6% of the E#sub[2]-3 mode, respectively),
Thus, it was not typically observed in normal incidence Raman experiments (cite), making them hard to observe in reported experiments.
but could be clearly detected in edge incidence configurations in our experiments. However, in our experiments,
with edge incidence configuration (zxy#overline[z]) and extended integration time,
the E#sub[2]-3 peek was suppressed and the E#sub[1]-2 mode was also observed.
我们做了实验，比别人多看到了几个峰；和计算结果比对良好。 Our experiments reported the E#sub[1]-2 peak for the first time,
and the experimental results were in good agreement with both calculations and theoretical analysis.
拉曼散射实验在衬底上进行，并与第一性原理计算结果进行了比较。
在我们的实验中，除了 E#sub[2]-4 以外的弱极性模式对应的拉曼散射峰都被观察到，多于其它实验；
这包括 A#sub[1]-2 在 xzzx 下可以观察到，
以及 E#sub[1]-2 在 xzyx 下通过额外延长积分时间而观察到。
计算的声子频率与实验数据有很好的吻合，误差在 2-5% 之间，这个误差可能是由于 PBE 泛函对原子间力的低估（cite）。
计算的拉曼张量也与实验和理论结果基本一致。
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).
The calculated phonon frequencies were in good agreement with experimental values,
with a slight underestimation of 2-5%,
which might be attributed to the known tendency of the PBE functional underestimating interatomic forces (cite).
The calculated Raman tensors were also consistent with both experimental and theoretical results.
Among negligible-polar modes, the E#sub[2]-3 mode showed the highest Raman intensity,
followed by four modes with lower intensities that were also visible in normal incidence Raman experiments,
including the E#sub[2]-1 mode, the E#sub[2]-2 mode, the E#sub[1]-1 mode, and the A#sub[1]-1 mode.
The E#sub[1]-2 mode and E#sub[2]-4 mode were not visible in our Raman experiments,
as they were located close to the most intense E#sub[2]-3 mode (only about 10 cm#super[-1] away)
with very weak Raman intensities (only 0.1% and 0.6% of the E#sub[2]-3 mode, respectively).
Additionally,
the A#sub[1]-2 mode had only a very weak Raman intensity under the incident light with in-plane polarization
(only 0.01),
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.
#include "figure-raman.typ" #include "figure-raman.typ"

6
paper/result/perfect/non-polar/table-nopol.typ
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@@ -48,6 +48,10 @@
// E2 E2 A1 E2 // E2 E2 A1 E2
[0.228 #pm 0.051], [-0.260 #pm 0.025], m2[-0.279 #pm 0.016], [0 #linebreak() (used for calibration)], [0.228 #pm 0.051], [-0.260 #pm 0.025], m2[-0.279 #pm 0.016], [0 #linebreak() (used for calibration)],
)}, )},
caption: [Negaligible-polarized Phonons at $Gamma$ Point.], caption: [
Negaligible-polarized Phonons at $Gamma$ Point.
The calculated phonon frequencies had a slight underestimation of 2-5% comparing to experimental values,
which might be attributed to the known tendency of the PBE functional underestimating interatomic forces (cite).
],
)<table-nopol>] )<table-nopol>]