Table 1 The summary of 2D Invar and anti-Invar monolayers

From: Machine learning enables the discovery of 2D Invar and anti-Invar monolayers

Materials

α (10−6 K−1)

E2D (N/m)

D (eV)

h (Å)

type

ZrO2

0.47

151.93

3.67

4.96

ZTE

HfO2

1.80

157.27

4.48

4.98

ZTE

SbSe2

24.49

31.88

9.03

7.13

EPTE

HfBi2

16.99

70.99

13.74

9.63

EPTE

HfSb2

19.81

55.38

10.01

9.28

EPTE

As2

−36.39

51.13

0.81

5.49

ENTE

Ge2

−30.46

43.47

0.85

4.88

ENTE

Sn2

−61.27

23.96

0.74

5.34

ENTE

  1. The calculated thermal expansion coefficients α (at 500 K, except 40 K for As2, 90 K for Ge2, and 80 K for Sn2), in-plane stiffness E2D, bending stiffness D, and effective thickness h (defines as the geometry thickness, see details in our previous work44) for 2D monolayers with ZTE, EPTE and ENTE. The α for ENTE 2D monolayers is the minimal value of α(T) curves.