Supplementary Material for

Anisotropic Elastic Modulus, High Poisson’s ratio and Negative Thermal

Expansion of Graphynes and Graphdiynes

Sergio A. Hernandez and Alexandre F. Fonseca

Applied Physics Department, Institute of Physics “Gleb Wataghin”, University of

Campinas - UNICAMP, 13083-859, Campinas, São Paulo, Brazil.

This document contains Figures S1 to S8 with captions and legends.

1. Test of convergence of the calculations of the TEC of GYs and GDYs

Here, we present the results of the tests of convergence of the TEC of all GYs and

GDYs with the system size. Figures S1 and S2 show the results for GYs and GDYs

respectively. We can see that except for some GDYs, the dependence of TEC with size

is very small. But since for some GDYs the TEC converged for sizes about 600 Å, we

adopted system sizes of approximated 600 Å for all structures.

Figure S1. Linear TEC at T = 300 K along x (left) and y (right) directions of all seven

GYs as functions of size. See figure 1 in the main text for the structure of different GYs.

Figure S2. Linear TEC at T = 300 K along x (left) and y (right) directions of all seven

GDYs as functions of size. See figure 1 in the main text for the structure of different

GDYs.

2. Equilibrium lengths and TECs of all GY and GDY structures as functions of the

temperature

Here, Figures S3 and S4 present all equilibrium lengths and TECs of all seven types of

GYs and GDYs along armchair and zigzag directions as functions of temperature

calculated as described in the METHODS Section of the main text.

The curves of the TEC of the structures are calculated from linear regression of the

points shown in Figures S3 and S4 and using equation (1) of the main text. The curves

are presented in Figures S5 and S6. The graphics of TEC versus T are shown in

equivalent scale so as to compare the inclinations of the curves.

Figure S3. Equilibrium lengths along armchair and zigzag directions for all GY

structures as function of temperature. From top left to bottom right: from GY1 to GY7

and graphene.

Figure S4. Equilibrium lengths along armchair and zigzag directions for all GDY

structures as function of temperature. From top left to bottom right: from GDY1 to

GDY7.

Figure S5. Linear TEC along armchair and zigzag directions for all GY structures as

function of temperature. From top left to bottom right: from GY1 to GY7 and graphene.

Figure S6. Linear TEC along armchair and zigzag directions for all GDY structures as

function of temperature. From top left to bottom right: from GDY1 to GYD7.

3. Curves of the variation of the energy for uniaxial and biaxial tensile strains

Here, the variation of Uuniaxial and Ubiaxialwith tensile strain for all structures are shown,

including that of graphene.

Figure S7. Potential energy U versus strain for uniaxial (“+” and “×” symbols) and

biaxial (“*” symbol) in order to obtain the quantities C11, C22 and C12=M−0.5 (C11+C22 )

for the following structures: from top left to bottom right: GY1, GY2, GY3, GY4, GY5,

GY6, GY7 and graphene.

Figure S8. Potential energy U versus strain for uniaxial (“+” and “×” symbols) and

biaxial (“*” symbol) in order to obtain the quantities C11, C22 and C12=M−0.5 (C11+C22 )

for the following structures: from top left to bottom right: GDY1, GDY2, GDY3,

GDY4, GDY5, GDY6, GDY7.