A method for diffraction-based identification of amorphous sp 2 carbon materials

Diffraction-based characterization of amorphous sp2 carbon: sensitivity to domain-like packing of nanostructures

“…In [5], we found that the fraction of carbon atoms, which belong to the intact C 60 fullerenes, in the total number of carbon atoms (we excluded the contribution of gas impurities of N, O and H from our quantitative analysis) in the S 25 and S 600 samples is equal to 59 % and 49 %, respectively. For the samples annealed at high temperatures, this fraction is significantly lower.…”

“…In [5], we suggested a method for estimating the structural properties of amorphous sp 2 carbon and applied it to the samples studied in [1]. This method enabled us to quantify the Diffraction-based characterization of amorphous sp 2 carbon... 227 structural properties of the samples in terms of the average size and curvature of the sp 2 carbon structures (graphene-like flakes of 14 -285 carbon atoms) as well as to estimate the fraction of the intact C 60 fullerenes in the samples for each annealing temperature.…”

“…The main features of the method [5] are as follows: (i) we consider the fitting of the neutron or x-ray powder diffraction patterns for the scattering wave vector's modulus q in the range of a few to several tens of inverse nanometers (the inverse problems are formulated similar to that suggested in [6]); (ii) the sp 2 -structured component of a sample, including the flat and curved carbon flakes with graphene-like arrangement of atoms, is described with a limited number, N str , of structural blocks of a limited number of atoms, N atom ; (iii) the above structural blocks in a sample are packed heterogeneously, in the domains of linear size exceeding 10 nm (for q in the above-mentioned range, the interference of scattering by such separate domains may be neglected), with various average atomic density and various types of spatial ordering of structural blocks, defined by the total potential energy of the ensemble, U tot ; (iv) packing of structural blocks in a domain is modeled using the rigid body molecular dynamics (RBMD) [7] with the Lennard-Jones potential of atom pair interactions in the neighboring rigidbody structural blocks with variable distance R opt at which the potential reaches its minimum. The simulation starts with a random distribution of blocks and the highest value of U tot , and the simulation ends with an ordered steady state which naturally possesses the lowest value of U tot for given initial conditions.…”

“…In [5], we interpreted the neutron powder diffraction patterns from [1] for the amorphous C 60 fullerene obtained by mechanical grinding and subsequent annealing in vacuum at various temperatures (600, 800, 850, 900 and 1000…”

“…The set of the candidate structural blocks of the total number of N str = 36 included the C 60 fullerene molecules and the sp 2 carbon flakes with graphene-like atom arrangements of various curvatures and sizes. The sensitivity of the results to the mutual positions of these structures was analyzed in [5] in the two limiting cases: (A) any domain (taken as an ensemble ranging in number from a few dozens to several thousand nanostructures) containing only identical structural blocks (mono-structural domains) and (B) all the domains are the identical mixtures of many different structural blocks with the structural content of blocks taken from the solution of the inverse problem in the case "A" (multi-structural domains). All the domains in both cases, "A" and "B", have multiple variants of number of N var , which are generated by the variance of the R opt value (which determines the average density of atoms in the domain) and of the U tot value (which determines both the density and the mutual spatial orientation of structural blocks).…”