Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Key Laboratory for Matter Microstructure and Function of Hunan Province, School of Physics and Electronics, Hunan Normal University, Changsha 410006, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 11574080, 91833302)
Received Date:30 July 2020
Accepted Date:23 August 2020
Available Online:09 December 2020
Published Online:20 December 2020
Abstract:One-dimensional (1D) carbyne chain has the potential applications in the nanoelectronic devices due to its unique properties. Although some progress of the mechanical and thermal properties of 1D carbyne chain has been made, the physical mechanism of the strain modulation of atomic bond nature remains unclear. In order to explore the strain effects on the mechanical and related physical properties of 1D carbyne chain, we systematically investigate the strain-dependent bond nature of 1D carbyne chain based on the first-principles calculations of density functional theory and generalized gradient approximation. It is found that when the compressive strain is 16%, the bonding nature of 1D carbyne chain is changed, and the bond length alternation of single and triple bonds in 1D carbyne chain tends to zero, which originates from the difference in bond strength between single bond and triple bond. Moreover, 1D carbyne chain can change from semiconductor into metal when the compressive strain is 16% indicated by analyzing the band structure and related differential charge density. When the strain is 17%, the phonon spectrum has an imaginary frequency. Besides, when the ambient temperature is less than 510 K, the heat capacity of 1D carbyne chain decreases with strain increasing. However, more phonon modes will be activated at larger strains when the temperature is higher than 510 K, and the heat capacity is enhanced gradually with strain increasing. Also, the stiffness coefficient of 1D carbyne chain is larger than that of graphene and carbon nanotube. These results conduce to the fundamental understanding of atomic bond nature in 1D carbyne chain under different strains. Keywords:carbyne/ first-principles calculations/ electronic structure/ heat capacity
其中E为应变能, L为c方向晶格常数, $\varepsilon $为应变, 有效半径r为0.82 ?[8]. 用四阶多项式将carbyne链原胞的应变能与应变的关系进行拟合(图2(a)). 得到的抗拉刚度为76.33 eV/?, 进而得出其杨氏模量为36.20 TPa, 这与已有理论结果一致[8]. 通过对比, 发现carbyne链的杨氏模量比石墨烯(1.05 TPa)[18]和碳纳米管(0.97 TPa)[19]高1个数量级. 图 2 (a) Carbyne链单位应变能(两个原子)与应变之间的关系; (b), (c) 分别为拉伸应变和压缩应变所对应的carbyne链键长差值的变化; (d) carbyne链差分电荷密度在拉伸和压缩应变下的变化图 Figure2. (a) Density functional theory calculations of stretching energy per unit cell (two atoms) as a function of strain $\varepsilon $; (b) tensile strain and (c) compressive strain dependence of bond length difference; (d) the charge density of carbyne under the condition of tensile and compressive strains.
Carbyne链是由单三键交替相连的一维单原子碳链. 之前的讨论表明, 由于碳-碳单键和碳-碳三键有不同的抗拉刚度, 导致不同应变下carbyne链的单三键键长差值也会有所不同, 这种现象与弹簧串联时的情况相似. 在此基础上, 我们近似将carbyne链看做是由碳-碳单键和碳-碳三键串联而成的系统, 图4(a)—(c)分析了在拉伸应变下, 碳-碳单键、碳-碳三键以及carbyne链受到的力与c方向长度改变量之间的关系. 为了使模型合理化, 这里的单键系统和三键系统采用两个原子的原胞模型, 通过调节两个碳原子之间的碳键来实现. 可以看到, 结果满足胡克定律. 图中之所以存在改变量为零时力不为零的情况, 主要是因为计算数据存在误差. 进一步计算得出碳-碳单键、碳-碳三键以及carbyne链的劲度系数分别为59.25, 103.18, 39.81 N/m. 串联系统的等效劲度系数${K_{{\rm{carbyne}}}}$为 图 4 (a), (b), (c) 分别为碳-碳单键、碳-碳三键和carbyne链在拉伸应变下外力与c方向长度改变量之间的关系 Figure4. Force of (a) single bond, (b) triple bonds and (c) carbyne chain as a function of length change in the c direction under tensile strain.
图 1 (a) Carbyne链结构示意图; (b) 差分电荷密度图
图 2 (a) Carbyne链单位应变能(两个原子)与应变之间的关系; (b), (c) 分别为拉伸应变和压缩应变所对应的carbyne链键长差值的变化; (d) carbyne链差分电荷密度在拉伸和压缩应变下的变化图
图 3 Carbyne链原胞的能带结构 (a) 未施加应变; (b) 压缩应变为16%.
图 4 (a), (b), (c) 分别为碳-碳单键、碳-碳三键和carbyne链在拉伸应变下外力与c方向长度改变量之间的关系
图 5 Carbyne链原胞的声子谱 (a)—(f) 分别是轴向拉伸应变为0%, 3%, 6%, 9%, 12%, 17%时对应的声子谱.
图 6 轴向拉伸应变下carbyne链热容量随温度的变化