Origin of the hardness in the monolayer nanographene

Abstract

In this paper, we investigated the lattice distortion displacement effects (LDDE) on magnetizations versus temperature in a monolayer nanographene (MLNG) by using effective field theory developed by Kaneyoshi. To obtain the LDDE, we used the twinning angle (theta) of the zigzag edge of the MLNG and obtain the M-T curves for theta = 10 degrees-180 degrees with 10 steps. We find that MLNG has a minimum Curie temperature (T-C(min) = 2.738) for a certain critical twinning angle (theta(CTA) = 130) of the zigzag edge of the MLNG. The T-C increases (T-C > T-C(min)) as the theta increases or decreases from the theta(CTA) = 130 degrees (both theta < theta(CTA) and at theta > theta(CTA) cases). Since the hardness is directly proportional with the T-C, the hardness of the MLNG increases for both theta < theta(CTA) and at theta > theta(CTA) cases. Thus, the MLNG has a resistance against to the any changing in the theta(CTA). Therefore, we suggest that the origin of the hardness in nanographene is theta(CTA). (C) 2019 Elsevier B.V. All rights reserved.