In-situ lattice structure analysis in sp2 hybridization of stable carbon isotopes: Precision modelling of temperature

Quantum temperature measurement in graphene thermal applications is intrinsically coupled to the crystal structure, phonon frequency, and kinetic isotope effect. Precision temperature measurement is a vital technology to characterize the thermal performance of quantum systems. Heat in nanoscale devices is typically modelled in terms of phonon properties by the nonequilibrium function for high temperature and by the transport theory formalism for low temperature that dealt with phonon interaction at the molecular level. In this paper, we investigate the lattice structure of isotope-12 pristine graphite and isotope-13 multi walled carbon nanotubes through the measured 2θ value at the peak of maximum intensity by in-situ X-ray diffractometer from 50 °C steps up to 1200 °C and confined the quantum well system into the hexagonal lattice volume. The likelihood states of the �-nearly free electron in the carbon atom and the electron-phonon probability distribution function are used to identify the system's thermal state region. By performing realistic quantum harmonic oscillator relations that account for the contribution of electron-phonon coupling and atomic mass, we achieved a precision temperature measurement of the quantum system despite the native disorder in sp2 hybridization of different carbon allotropes and introduced a new technique for differentiating carbon isotopes. © 2021 Elsevier B.V.