最近捷报频传，又收到了一篇Carbon论文接受的消息。这篇文章是关于石墨烯晶界的Kapitza热阻的分子动力学模拟的。论文题目为Kapitza thermal resistance across individual grain boundaries in graphene。
论文链接：http://www.sciencedirect.com/science/article/pii/S0008622317309351
论文亮点：
1）用相场晶体（Phase field crystal）法产生了从0度到60度夹角的高质量晶界。一共13个长800纳米、宽25纳米的样品。我以后会在Zenodo公开这些样品的坐标文件。
2）用非平衡分子动力学（NEMD）方法计算了所有样品的Kapitza热阻，其中用到的MD程序是我写的GPUMD 程序（https://github.com/brucefan1983/GPUMD）。我以后会在程序手册中给一个具体例子。
3）对经典结果进行了量子修正，解释了之前NEMD结果和量子输运（Landauer-Buttiker方法）结果的差别。该量子修正不同于很多人印象中的那个修正温度的方法，而是一个新的方法，比较适合于缺陷散射（例如这里的晶界散射）起主导的情形。
4）该文与之前被Nano Letters接受的论文（http://pubs.acs.org/doi/abs/10.1021/acs.nanolett.7b01742）是互为补充的：那里研究具有很多晶粒的多晶石墨烯，而这里研究单独的晶界。相关结论也是融洽的。实际上，我们本来准备只写一篇论文发表的，但我（博士后）和Carbon的第一作者（博士在读）都很需要第一作者的论文，所以就写了两篇文章。现在回想一下，如果只写一篇论文，可能很难做到在一篇文章中专注于一个中心思想。
本文投稿、审稿的大致过程：
Carbon不像Nano Letters 那么高傲，所以给编辑的Cover Letter不用搞得太酷。我们的稿子在编辑手里待了一个星期就送审了。大概过了一个月就收到了两个审稿意见。第一个审稿人一看就是个同行，问了几个他/她感兴趣的问题，并建议增加几个参考文献。对于这些问题，我们觉得回答一下即可，没有必要做出任何修改。这相当于免费给审稿人上上课。至于增加参考文献，我们一般并不反对，但我们会仔细核实审稿人建议的参考文献是否真的相关。例如，我们发现第一个审稿人在第三点评论中指出的参考文献和我们的文章关系不是那么密切，就没有引用。第二个审稿人建议直接接受，我们只要感谢即可。很有意思的是，我们最近两篇接受的文章都有一个审稿人认为非常完美，不用做任何修改。知道为什么吗？因为我们的文章一般要修改半年才投稿，不会出现任何写作上的问题，哪怕是一个标点符号。稿子修回后进行了二审。第一个审稿人说很满意，于是顺利接受。不要以为当审稿人说“作者应该xxx”时你真的就应该那么做。对有些你不同意的评论，只要有力地论述自己正确的观点即可。可以说，对这篇Carbon论文我们没有作任何修改，除了增加几个参考文献。
审稿意见和我们的回复如下：
Ms. Ref. No.: CARBON-D-17-02212
Title: Kapitza thermalresistance across individual grain boundaries in graphene
Dear Dr. Prof. XXX,
Thank you for a rapid processing of our manuscript exclusively submitted for publication in Carbon. We hereby submit a revised version of the manuscript “Kapitza thermal resistance across individual grain boundaries in graphene” by Khatereh Azizi, Petri Hirvonen, Zheyong Fan, Ari Harju, Ken R. Elder, Tapio Ala-Nissila, and S. Mehdi Vaez Allaei (Manuscript Ref. No.: Carbon-D-17-02212). We thank the reviewers for their constructive criticism that has helped us to improve the manuscript. Since the changes to the manuscript are relatively minor we hope that our work can now be accepted for publication.
Yours Sincerely,
Zheyong Fan
On behalf of the co-authors
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Reply to the First Referee -- Carbon-D-17-02212
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Reviewer#1: The authors reported a theoretical study on Kapitza resistance of bicrystalline graphene with different GB tilt angles using non-equilibrium molecular dynamic simulations. Kapitza resistance is a crucial quantity that is widely used to describe thermal transport across interfaces or GBs based on Fourier's law. The authors reveal that the Kapitza resistance strongly depends on the tilt angle of which the value could be varied up to one order of magnitude; yet the line tension of GB do not show significant dependence. They also demonstrate that the quantum correction to the classical MD results is of substantial importance, which should be applied in order to get more reasonable values. Finally, the Landauer-Butticker formula was employed to demonstrate that the corrected results are comparable with the quantum mechanics level calculations. Overall, to me, this is a good theoretical work, and the manuscript is well written and clear, rendering people can easily understand their contributions. For simulation part, the results are reproducible (I have done the same simulation for 21.78 GB, and got similar result of un-corrected Kapitza resistance); however, the authors should address the following concerning before I can recommend it a publication in Carbon.
Reply: We thank the Referee for the positive comments.
1. The formula of Kapitza resistance (R=dT/J) can be achieved based on the fact that Fourier's law is valid, which means that the thermal transport is in the diffusive regime and the characteristic length of system should be much larger than the coherent length and elastic MFP of phonons. Under this regime, the classical treatment is valid when the elastic MFP (could be the distance between scattered by two GBs) larger than the coherent length (could be the distance between subjecting two phonon-phonon scatterings in dilute phonon gas). These statements can be found in books "Chapter 1: Phase-Coherent Transport in Nanotechnology. Volume 3: Information Technology I" and "Nanoscale Energy Transport and Conversion". In other words, the quantum treatment should be applied once the coherent length larger than elastic MFP. The authors should carefully clarify in their manuscript.
Reply: The quantum corrections we applied here do not refer to phonon scattering but to phonon population. Classical molecular dynamics MD simulations can affect heat transport in two different ways: one is to overestimate the phonon population (related to the specific heat) and the other is to overestimate phonon scattering rates of some branches. In the calculations of the Kapitza resistance, only the first effect is relevant and we have thus only applied quantum corrections to the specific heat in a mode-to-mode way. This results in good agreement with the results obtained from the quantum mechanical Landauer-Buttiker calculations in the harmonic regime, reinforcing the fact that phonon-scattering is not essential here.
2. The NEMD simulation obtains the heat flux by extracting thecumulative heat fluctuation from both hot and cold reservoirs. In myexperience, the calculating heat flux is quite sensitive to the number of atomsin the reservoirs. The author should show the convergence test for heat fluxwith respect to the size of reservoir.
Reply: The calculated heat flux should not depend on the size of the reservoirs according to energy conservation if steady state has been fully achieved. That said, we have used relatively large reservoirs, which are of size 25 nm x 5 nm, with about 5000 atoms. There are two complementary methods to calculate the steady-state heat flux: one is to use the reservoir energies (as referred to by the Referee) and the other is to directly calculate the heat flux from one to another adjacent block of atoms in the direction of heat transport. In our calculations, these two methods give the same heat flux. More technical details can be found from [Z. Fan et al. “Thermal conductivity decomposition in two-dimensional materials: Application to graphene”, Phys. Rev. B 95, 144309 (2017)].
3. The authors claim that the Kapitza resistance will not be affected too much by the line tension of GB. Similar result can be found in this reference (DOI:10.1016/j.commatsci.2012.12.037). They demonstrate that at high temperature, different configurations of GB (reflecting different line tension) have no significant impact on Kapitza conductance, but they do not explain the reason behind. The authors are encouraged to give a more qualitative explanation for this part.
Reply: We thank the Referee for bringing this reference to our attention. We have checked this reference but found that this paper did not study the Kapitza conductance. Instead it focused on mechanical properties and the overall thermal conductivity of some finite graphene sheets with GBs under shear strain. Also, we did not claim in our manuscript that "the Kapitza resistance will not be affected too much by the line tension of GB". What we stated in the manuscript is: "At small and large tilt angles, where the defect density is relatively small, there is aclear linear dependence of R on both γ and ρ. However, at intermediate tilt angles (2θ ≈ 30 degrees), where the defect density is relatively large, the linear dependences become less clear, especially between R and γ, which may indicate increased interactions between the defects.”.
4.The structure of bicrystalline graphene was first studied by Steven Louie's group (DOI:10.1103/PhysRevB.81.195420) and then was complementary by T.-H. Liuet al. (DOI:10.1016/j.carbon.2011.01.063) in graphene and Y. Liu et al(DOI:10.1021/nl100988r) in nanocorn. These early contributions should be cited in manuscript.
Reply: We thank the Referee for bringing these references to our attention.
Action: We have added citations to these references in the Introduction.
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Reply to the Second Referee -- Carbon-D-17-02212
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Reviewer #2: This article presents a study of heat transport across grain boundaries in graphene. The main result obtained is the Kapitza thermal resistance and its dependence on the tilt angle, the grain boundary line tension and the defect density. The article also analyzes quantum effects in the calculation of the resistance and finds good agreement with Landauer-Bütticker theory results. The authors have performed a very complete study on the thermal resistance in graphene. The article is well-written; then ew results obtained are presented in a clear way. I recommend publication.
Reply: We thank the Referee for recommending publication of our manuscript in Carbon.
