In the presented work, the features of mechanical stiffness of carbon nanoparticles (nanodiamonds and fullerenes) in a wide range of sizes are considered. The enhancement of nanodiamonds stiffness (comparing to bulk diamond) is studied and explained in the terms of average bond stiffness 〈k〉 0 . It is shown that 〈k〉 0 can be useful in the description of various carbon nanostructures and gives reliable estimates of their incompressibility. Moreover, we found that 〈k〉 0 can be well estimated based only on relaxed atomic geometry.
IntroductionDiamond crystal is well-known for the variety of its extraordinary properties. In particular, diamond is famous for the unique mechanical stiffness having the highest bulk modulus and being referred to as the hardest crystalline material [1]. Search for superhard materials still draws close attention of materials scientists and attempts to find materials superior to diamond by stiffness, already counting successful studies of carbon nanotubes [2-4], ultrahard fullerites [5-7] and graphene [8,9], continue to this day. Nanodiamonds (ND) represent small (several nm in size) diamond particles. From general considerations, it can be supposed that size effects in such particles should lead to modification of the original diamond properties. Structural, electronic and magnetic properties of nanodiamonds attract significant interest and have been studying for decades [10,11]. Special attention was also * Corresponding author. Tel. +7 495 638-4415. E-mail: PBSorokin@tisnum.ru (Pavel Sorokin) 2 given to nanocrystalline diamond [12,13] due to its exceptional mechanical stiffness by which it can even exceed single crystal diamond. Nevertheless, the mechanical properties of single nanodiamonds -structural units of a nanocrystalline diamond -mainly remained unexplored until recently. However, the latest experimental evidence of nanodiamonds ultrastiffness [14,15] indicates that their mechanical properties also deserve detailed study.Conventionally, mechanical stiffness is characterized by bulk modulus B0 as a measure of incompressibility. However, the calculation of elastic moduli for nanostructures can be puzzling due to the ambiguity of volume on the nanoscale. This problem was widely discussed for carbon nanotubes (CNTs) and fullerenes, and many different ways to determine their volume were proposed. Most often CNTs were described as hollow structures with a certain shell thickness t.The ad hoc convention is to set t = 3.4 Å [16,17] as a value of interlayer spacing in graphite. The alternative approach proposed by Yakobson [18] is based on continuum shell elasticity theory and gives the value of t = 0.66 Å. Later, many other approaches for finding shell thickness t were examined [16,17,19]. As for fullerenes, Ruoff et. al were the first to estimate B0 of C60 molecule as 843 GPa [20] and 826 GPa [21]. In both cases, C60 was considered as a homogenous elastic solid. With the same assumption, Peón-Escalante et. al [22] theoretically predicted B0 = 874 GPa, but a spherical shell model of C60 ...
