I have come across many articles and publications that calculates their surface energies for certain compounds. The most general and perhaps the common formula used is Esurface=1/2A(Etot-N*Ebulk) where symbols have their usual meaning. But I have found that different articles have different interpretations for these symbols (eg. N= no of atoms while in some cases N= no of slabs) leading to huge differences in resultant surface energies which leads to huge inconsistencies. So, is this surface energy calculation even reliable?
Hi. For your formula to be correct, I think N should actually be N = N_atoms / N_bulkatoms, where N_atoms is the number of atoms you have in your surface calculation while N_bulkatoms is the number of atoms you have in your bulk calculation. So for example if you simply have a chemical element, like Cu, with the fcc (face centered cubic; a.k.a. cpp = cubic close packed) crystal structure, you can have a bulk unit cell containing just one atom, so N_bulkatoms = 1 and then N is simply the number of atoms in the surface calculation. But you may also want to have a nice cube as the bulk unit cell, so you create a unit cell with 4 Cu atoms. Obviously, you get 4 times larger Ebulk for N_bulk=4 compared to what you got with N_bulk=1, but you should also take N = N_atoms / 4 in the formula for surface energy, so the factor of 4 gets compensated. In general, you can interpret N as the number of bulk unit cells needed to get enough atoms to construct the surface unit cell. Things are easy for elements but get trickier for compounds. I believe it is still okay to use the above formula for Esurface as long as the surface stoichiometry is exactly the same as the bulk stoichiometry for the compound you are interested in. Once the stoichiometry changes on surface, things get really complicated and you need to work with chemical potentials and stuff and I am not sure it would be always possible to define Esurf uniquely.
Thank you so much dear sir Martin Ondracek for your informative answer.
In the mean time I would also like to request you to kindly suggest me some literatures regarding the same.
Thank you soo much dear sir Lalmuan Chhana . Siama hi ka zirtir alawm, a thiamlo a.
I am afraid I do not know any good literature on the topic which I could recommend. It's a long time since I studied the subject myself and even back than, I was kind of an autodidact on this topic, figuring it out by combining common sense with information scattered among various papers, rather than by reading some authoritative textbook on the topic.
What I can do is elaborate on my "common-sense argument" why the "N" in the Esurf formula should be what I wrote and not something else. Basically, one should never attempt to calculate the total energy associated with atoms, which is typically not well defined in DFT anyway. Just the differences between energies are meaningful. So, any total energies of atoms that appear in the formula should eventually get subtracted: The number of atoms from the surface slab should be exactly compensated by the number of atoms from the bulk calculation. The factor N has to be chosen so as to ensure this. Then, you get the surface energy as the energy (per unit surface area) needed to create the surface from the bulk. Is the logic clear? This is after all how the surface would be created in reality, for example by cleaving a crystal: Atoms which have previously been inside the bulk would be used to build the surface; no atoms would be created out of nothing or destroyed.
Thank you dear Sir Martin Ondracek for your clear elaboration. I found your reply quite helpful and I hope it also clear some doubts for others that come across this post.
Hello, Martin's answer is right and I will briefly expand on the case when you encounter non-stoichiometric slabs.
As mentioned, you need to take into account the chemical potentials of the elements, and in the chosen range of chemical potential, you will obtain a phase diagram with surface energy plotted against the potential. I used this article as a reference when I did these calculations during my master's. Hope it helps this way.
Article Composition, Structure, and Stability of RuO2(110) as a Func...
Bernard Lalroliana here you can check this new article ont he topic.
https://pubs.rsc.org/en/content/articlelanding/2023/CP/D2CP04460A?utm_medium=email&utm_campaign=pub-CP-vol-25-issue-19&utm_source=toc-alert
Hello, Kindly refer to the provided video for a detailed, step-by-step guide on how to do surface energy calculation: https://youtu.be/yWLRM-83I8g?si=JreNXVu2uJ2uUDBz
Thank you
Hi, below are some references on how to calculate surface energy:
1. Guijian Guan, Shuhua Liu, Yongqing Cai, Michelle Low, M. S. Bharathi, Shuang-Yuan Zhang, Shiqiang Bai, Yong-Wei Zhang, Ming-Yong Han, Destabilization of gold clusters for controlled nanosynthesis: From clusters to polyhedral. Adv. Mater. 26, 3427–3432 (2014)
2. Hejin Yan, Bowen Wang, Xuefei Yan, Qiye Guan, Hongfei Chen, Zheng Shu, Dawei Wen, and Yongqing Cai*, Efficient passivation of surface defects by Lewis base in lead-free tin-based perovskite solar cells. Mater. Today Energy 27, 101038 (2022)
3. Yan Shao, Wei Gao, Hejin Yan, Runlai Li, Ibrahim Abdelwahab, Xiao Chi, Lukas Rogée, Lyuchao Zhuang, Wei Fu, Shu Ping Lau, Siu Fung Yu*, Yongqing Cai*, Kian Ping Loh*, and Kai Leng*, Unlocking surface octahedral tilt in two-dimensional Ruddlesden-Popper perovskites. Nat. Commun. 13, 138 (2022)
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