Atomic-size dependence of the cohesive energy, bandgap, Young's modulus, and Raman frequency in different MA2Z4: A bond relaxation investigation

Abstract

Understanding the physical mechanism behind atomic-size dependence of the bandgap, phonon frequency, and mechanical strength in various monolayered MA2Z4 is of crucial importance for their electronic and photoelectronic applications. The density functional theory calculation results confirm that these physical quantities gradually decrease with the increasing periodicity of the atomic size (or radius) of the A or Z of MA2Z4. In order to clarify the common origin of the atomic-size dependence of these quantities, we establish these quantities as functions of bond length and bond energy by developing a bond relaxation theory approach. Theoretical reproduction of periodic trends confirms that bond expansion and energy weakening dominate their atomic-size dependence. The proposed approach is not only helpful to understand the physical origins of atomic-size dependence in different MA2Z4 monolayers but also can be extended to study the periodic trends of the related physical properties in other systems.

Strain-induced phase transitions and high carrier mobility in two-dimensional Janus MGeSN2 (M = Ti, Zr, and Hf) structures: first-principles calculations

“…The variation of Young's modulus values is consistent with the X atoms’ changing atomic sizes. These obtained Y 2D values are comparable to those of previously reported 2D Janus materials such as MoGe 2 P 4 with 183.76 N m −1 and MoSi 2 P 4 with 204.80 N m −1 , but they are lower than that of graphene with 336 N m −1 , 56,57 suggesting that the MGeSN 2 structures are more mechanically flexible than the graphene structure. Poisson's ratio ( ν 2D ) of all three monolayers is also in agreement with the lattice constants a , and the ZrGeSN 2 monolayer has the highest value of 0.35, HfGeSN 2 has 0.34 and TiGeSN 2 has 0.31, and these values are higher than the ν 2D values of the other MoS 2 (0.25), MoSi 2 P 4 (0.26), and graphene (0.19) monolayers.…”

Two-dimensional Janus MGeSiP4 (M = Ti, Zr, and Hf) with an indirect band gap and high carrier mobilities: first-principles calculations

“…The change in Y 2D is consistent with the atomic radii of Ti, Zr, and Hf. The Y 2D values of the MGeSiP 4 monolayers are lower than those of other 2D monolayers such as MoSi 2 P 4 (204.80 N m −1 ), MoGe 2 P 4 (183.76 N m −1 ) 43 and graphene (336 N m −1 ), 44 indicating that the 2D Janus MGeSiP 4 monolayers are softer than MoSi 2 P 4 and graphene structures. In other words, the low Young's modulus values suggest that the 2D Janus MGeSiP 4 monolayers are mechanically flexible.…”

“…As shown in 43 and graphene (336 N m À1 ), 44 indicating that the 2D Janus MGeSiP 4 monolayers are softer than MoSi 2 P 4 and graphene structures. In other words, the low Young's modulus values suggest that the 2D Janus MGeSiP 4 monolayers are mechanically flexible.…”

Moderate direct band-gap energies and high carrier mobilities of Janus XWSiP2 (X = S, Se, Te) monolayers via first-principles investigation

“…The highest Y 2D value of the SWSiP 2 is in agreement with the smallest atomic size of the S atom compared to Se and Te. However, these Y 2D values are smaller than those of other reported 2D materials such as the MoGe 2 P 4 monolayer (183.76 N m À1 ), 42 MoSi 2 P 4 (204.80 N m À1 ), and graphene (336 N m À1 ), 43 suggesting the higher mechanical flexibility of these XWSiP 2 materials. The Poisson's ratio n 2D of the XWSiP 2 monolayers can be derived as:…”