碳是生命中不可或缺的元素，具有多種雜化方式（sp、sp²、sp³）。比如，石墨和金剛石這兩種碳的同素異形體中，金剛石為sp³雜化，形成三維碳原子網(wǎng)絡(luò)，而石墨則是sp²雜化，形成層狀結(jié)構(gòu)，層與層之間為范德華力相互作用。

從石墨中發(fā)現(xiàn)石墨烯被認(rèn)為是凝聚態(tài)物理的一項(xiàng)重大突破，然而這些碳同素異形體都不是半導(dǎo)體。C₆₀分子形狀類似足球，由六邊形和五邊形碳原子構(gòu)成，通過sp²雜化與其三個(gè)最近的鄰居形成鍵合。

最近的研究合成了Mg與C₆₀分子結(jié)合的二維六角形結(jié)構(gòu)（Mg₄C₆₀)_n。去除Mg后形成了石墨勒烯（Graphullerene），其碳原子同時(shí)表現(xiàn)出sp²和sp³雜化，暗示了其亞穩(wěn)定性。Mg原子的摻雜對結(jié)構(gòu)的穩(wěn)定性影響很大，但Mg原子在穩(wěn)定結(jié)構(gòu)中的作用及其對材料性能的影響仍有待確定。

來自以色列的本–古里安大學(xué)材料工程系的Guy Makov教授小組，采用從頭算的方法，研究了石墨勒烯的力學(xué)和能量穩(wěn)定性、原子結(jié)構(gòu)、聲子色散曲線和能帶結(jié)構(gòu)。他們的研究證明了石墨勒烯是一種亞穩(wěn)態(tài)半導(dǎo)體，其結(jié)構(gòu)由受應(yīng)變的C₆₀分子通過共價(jià)鍵與鄰近分子相連構(gòu)成。

他們還研究測定了石墨勒烯的鍵長和振動譜，并與孤立C₆₀分子進(jìn)行了對比，發(fā)現(xiàn)了石墨勒烯的特征振動信號。作者揭示了Mg原子的作用，指出加入Mg原子可以使結(jié)構(gòu)的形成能從負(fù)值轉(zhuǎn)為正值，增強(qiáng)結(jié)構(gòu)的能量穩(wěn)定性，并降低電子帶隙。

Fig. 5 Phonon modes.

這些發(fā)現(xiàn)與實(shí)驗(yàn)觀察一致，為進(jìn)一步開發(fā)這類材料的技術(shù)應(yīng)用和合成路線提供了更堅(jiān)實(shí)的理論基礎(chǔ)。該文近期發(fā)布于npj Computational Materials 9: 211 (2023)。

Fig. 6 The electronic density difference between graphullerene with and without Mg atoms.

Editorial Summary

Carbon, an essential element in life, exhibits various hybridizations (sp, sp², sp³) as seen in allotropes like graphite and diamond. Diamond, with sp³ hybridization, forms a three-dimensional carbon network, whereas the sp² hybridization of graphite creates layered structures held together by van der Waals forces. The discovery of graphene from graphite is a significant breakthrough in condensed matter physics. However, these carbon allotropes are not semiconductors. C₆₀molecules, resembling soccer balls made of hexagonal and pentagonal carbon atoms, are bonded through sp² hybridization. Recent studies synthesized a two-dimensional hexagonal structure (Mg₄C₆₀)_ncombining magnesium and C₆₀ molecules. Upon removing Mg, Graphullerene forms, displaying both sp² and sp³ hybridizations, suggesting meta-stability. The doping of Mg atoms significantly impacts the structural stability, yet their role in the stabilized structure and influence on material properties remains to be determined.?

Fig. 7 Electron density of bulk graphullerene.

A group led by Prof. Guy Makov from the Dept. of Materials Engineering, Ben-Gurion University of the Negev, Israel, utilized ab initio calculations to study the mechanical and energy stability, atomic structure, phonon dispersion curves, and band structure of graphullerene. Their research confirms graphullerene as a meta-stable semiconductor, structured by strained C₆₀ molecules covalently bonded to neighbors. They also determined the bond lengths and vibrational spectrum of graphullerene, compared them with isolated C₆₀molecules and identified a characteristic vibrational signature. Moreover, they revealed the role of Mg atoms, noting that their inclusion turns the formation energy from negative to positive, enhancing stability and reducing the electronic band gap. These findings align with experimental observations, laying a solid foundation for further technological applications and synthetic routes of such materials. This article was recently published in npj Computational Materials 9: 211 (2023).

原文Abstract及其翻譯

Structure and properties of graphullerene: a semiconducting two-dimensional C₆₀ Crystal （graphullerene的結(jié)構(gòu)和性質(zhì)：一種半導(dǎo)體性的二維C₆₀?晶體結(jié)構(gòu)）

Uri Argaman?&?Guy Makov?

Abstract Graphullerene is a recently discovered, two-dimensional allotrope of carbon formed from C₆₀?molecules. It has been synthesized in the form (C₆₀Mg₄)_n?and subsequently transformed into (C₆₀)_n?by removal of the Mg atoms. Ab initio calculations are employed to examine the structure and properties of this material. Structurally, graphullerene is composed of strained C₆₀?molecules. Each of these molecules is connected to six neighbors in a hexagonal network with a total of eight chemical bonds. We find this structure to be meta-stable, owing to the strain produced by the covalent bonding of the molecules. However, the inclusion of Mg atoms transforms the cohesion energy from negative to positive values by forming additional C-Mg bonds, creating an energetically stable material. In the absence of Mg, this allotrope is a pure carbon semiconductor with an indirect band gap. Phonon spectrum calculations confirm the dynamical stability of the material and yield its in- and out-of-plane sound velocities. In addition, symmetry breaking of the C₆₀?molecules results in a distribution of bond lengths and creates vibrational modes that serve as a signature of graphullerene.

摘要Graphullerene是最近發(fā)現(xiàn)的一種碳的二維同素異形體，由C₆₀分子組成。它以(C₆₀Mg₄)_n的形式合成，隨后通過去除鎂原子轉(zhuǎn)化為(C₆₀)_n。我們采用從頭算計(jì)算方法來研究這種材料的結(jié)構(gòu)和性質(zhì)。從結(jié)構(gòu)上看，石墨勒烯（Graphullerene）由受應(yīng)力的C₆₀分子組成。每個(gè)分子都與六個(gè)相鄰的分子形成六角形的網(wǎng)絡(luò)，總共有八個(gè)化學(xué)鍵。我們發(fā)現(xiàn)這種結(jié)構(gòu)是亞穩(wěn)定的，這是由于分子間的共價(jià)鍵形成的應(yīng)力導(dǎo)致的。然而，鎂原子的存在通過形成額外的C-Mg鍵將結(jié)合能從負(fù)值轉(zhuǎn)化為正值，從而創(chuàng)造出一個(gè)在能量上穩(wěn)定的材料。在沒有鎂的情況下，這種同素異形體是一種純碳半導(dǎo)體，具有間接帶隙。聲子譜確認(rèn)了材料的動力學(xué)穩(wěn)定性，并得出了其面內(nèi)和面外聲速。此外，C₆₀分子的對稱性破缺導(dǎo)致鍵長分布的出現(xiàn)，并產(chǎn)生了作為石墨勒烯特征的振動模式。