Computational study of structures of diamond and amorphous carbon under extreme heating and cooling

Anastassia Sorkin

Abstract

Carbon is unique among the elements in its ability to form strong chemical bonds with a variety of coordination numbers, including two (e.g. linear chains or carbyne phase), three (e.g. graphite) and four (e.g. diamond). Combining strong bonds with light mass and high melting point, condensed carbon phases have many unique properties that make them technologically important as well as scientifically fascinating. Despite extensive studies over the past few decades, many interesting problems remain unresolved. In particular, the geometric and electronic structures of various disordered carbon phases is an area of research with many unanswered questions.

Amorphous structures are characterized by short range order and the absence of long range order. In amorphous structures, the bond length, the number of nearest neighbor atoms, and the angle between adjacent bonds are close to those in crystalline structures.

There are various methods to obtain amorphous carbon from diamond or from graphite. Two specific amorphous forms of carbon that can be obtained are the diamondlike amorphous carbon, which will be denoted by ta-C, and graphitelike amorphous carbon named a-C. These two structures can be distinguished clearly by their macroscopic and microscopic properties. The former is a hard and dense material, mostly made of distorted sp$^3$ bonds, while the latter has a less dense structure and mainly consists of sp$^2$ bonds.

We apply a tight-binding molecular dynamics method to investigate the formation of ta-C and a-C solids under extreme heating and subsequent cooling. The tight-binding method incorporates electronic structure calculations in the molecular dynamics through an empirical tight-binding Hamiltonian, and bridges the gap between ab initio molecular dynamics and simulations using empirical classical potentials.

The ta-C and a-C networks are obtained by quenching or annealing of liquid carbon with various densities. The first peak of the radial distribution function is very sensitive to the relative concentration of sp, sp$^2$ and sp$^3$ bonding. The structural properties of the amorphous carbon networks generated in this work are in good agreement with those of $a-C$ networks of Wang and Ho [1], computed under similar conditions.

Doping by ion implantation in diamond may result in graphitization and give rise to the onset of electrical conductvity, due to the ability of carbon atoms to form the $sp^2$ and $sp^3$ types of bonds. Increase of electrical conductivity associated with the creation of graphitelike pathways, i.e., with transformation of sp$^3$ to sp$^2$ bonds, was observed by Prawer and Kalish [2] and investigated in computer simulations by Saada [3].

The transfer of energy of a slowing down ion to the diamond network and the intermediate phase involved in this process are the subject of many discussions. There are a few models for the complex mechanism of the ion beam induced transformation of diamond to a conducting form of carbon [7,8] and until now, most of them cannot describe this process completely satisfactorily.

The purpose of this study is to understand the processes which occur in very hot layers of amorphous carbon surrounded of a cold crystal diamond layer or a cold diamond-like carbon layer. These hot layers mimic the ``thermal spike'' induced by heavy ion irradiation. The formation of $ta-C$ structures was observed in these layers after annealing. The radial and angle distribution functions, the statistics of threefold and fourfold bonds, as well as the depth of the bandgap have been investigated. The results confirm that in the hot diamond-like region $sp^2$ bonded atoms appear and the affected region becomes conductive. The structure of the amorphous heated layers depends very strongly on temperature, size of hot layers and structure of initial amorphous sample (in the cases, where the frozen layers are amorphous).

In order to investigate the transformation in details visualizations of the heating of the amorphous carbon layers was carried out.