The Relative Thermodynamic Stability of Diamond and Graphite

Abstract

Recent density-functional theory (DFT) calculations raised the possibility that diamond could be degenerate with graphite at very low temperatures. Through high-accuracy calorimetric experiments closing gaps in available data, we reinvestigate the relative thermodynamic stability of diamond and graphite. For T < 400 K, graphite is always more stable than diamond at ambient pressure. At low temperatures, the stability is enthalpically driven, and entropy terms add to the stability at higher temperatures. We also carried out DFT calculations: B86bPBE-25X-XDM//B86bPBE-XDM and PBE0-XDM//PBE-XDM results overlap with the experimental ÀTDS results and bracket the experimental values of DH and DG, displaced by only about 2 the experimental uncertainty. Revised values of the standard thermodynamic functions for diamond are D f H o = À2150 AE 150 J mol À1 , D f S o = 3.44 AE 0.03 J K À1 mol À1 and D f G o = À3170 AE 150 J mol À1 .

Delocalization error: The greatest outstanding challenge in density‐functional theory

“…The most notable examples are , with its bond length stretched far beyond equilibrium, 4,25–28 and analogous stretched ions (, , , etc.). However, similar errors have been identified for many other systems, including charge‐transfer complexes, 29–32 transition states of radical reactions, 33–38 band gaps of semi‐conductors, 39–44 polarizabilities of long‐chain molecules, 45–48 systems with extended conjugation, 49–58 halogen and chalcogen bonds, 59–61 and organic acid/base co‐crystals 62 . These are not the result of separate errors, but rather represent many facets of one single error in common density functionals.…”

“…Energy‐driven errors also occur for systems with extended conjugation, where GGAs overstabilize the delocalized electron density in the π system. In the solid state, this results in overstabilization of graphite relative to diamond, 55 while in molecular calculations it can affect the energy ordering of C 20 isomers, 54 although both of these examples are complicated by the role of London dispersion. A simpler benchmark can be assembled from the work of Woodcock and co‐workers on the relative stabilities of cumulenes and poly‐ynes 50 .…”

Developments in Synthesis and Potential Electronic and Magnetic Applications of Pristine and Doped Graphynes

“…Nevertheless, this structural diversity and versatility of chemical bonding brings an enormous pool of physicochemical properties, reactivities, and so on; crystal structures of over 500 periodic allotropes, known and hypothesized, have been collected 2 of 39 in a unique Sacada database (https://www.sacada.info/) [19]. Despite the long-lasting research of carbon-based materials, some fundamental issues related to the shape of the phase diagram and mutual stability of polymorphs, or even their existence, remain unresolved to this day [20][21][22]; e.g., it has been recently claimed that lonsdaleite is not a genuine allotropic form but a twin of cubic crystals, which raised controversy [23,24]. One illustration of the intensity of the research field of carbon materials can be provided by an inspection of the Web of Science database; this resource lists approximately 114,000 papers using the keyword 'diamond', approximately 147,000 papers discussing 'graphite', and approximately 240,000 papers featuring 'graphene'.…”

Topological Impact of Delocalization on the Stability and Band Gap of Partially Oxidized Graphene

“…Despite the σ−π inseparability of the Hamiltonian, the symmetric contradistinction of πbands from the σ-framework due to network planarity offers easier cognition of the avoided crossings in the frontier bands. Though π-bonds are weak, delocalization stabilizes the sp 2 carbon network, which is evidenced in its allotropes 7 and argues for the high thermodynamic stability of these nanosheets. Electronic effects from the delocalization of πelectrons are described as conjugation, aromaticity, etc.…”