ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and Fran├žois-Xavier Coudert at CNRS / Chimie ParisTech.
If you use the software in published results (paper, conference, etc.), please cite the corresponding paper (J. Phys. Condens. Matter, 2016, 28, 275201) and give the website URL.

ELATE is open source software. Any queries or comments are welcome at

Summary of the properties

Input: stiffness matrix (coefficients in GPa) of In2Bi (Materials Project id mp-23188)

        51       46       27        0        0        0  
        46       51       27        0        0        0  
        27       27       61        0        0        0  
         0        0        0       14        0        0  
         0        0        0        0       14        0  
         0        0        0        0        0        2  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 40.333 GPaEV = 28.221 GPaGV = 10.2 GPaνV = 0.38338
ReussKR = 40.171 GPaER = 13.174 GPaGR = 4.5573 GPaνR = 0.44534
HillKH = 40.252 GPaEH = 20.861 GPaGH = 7.3787 GPaνH = 0.41362

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2 GPa 5 GPa 14 GPa 14 GPa 36.786 GPa 121.21 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 7.5849 GPa 45.969 GPa 7.625 TPa–1 9.6434 TPa–1 2 GPa 14 GPa-0.397211.1802Value
Anisotropy 6.061 1.2647 7Anisotropy
Axis 0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0002
0.0000
-0.0000
0.0000
1.0000
-0.4086
0.4087
0.8161
-0.4582
0.4582
-0.7616
Axis
0.0002
1.0000
0.0000
-0.5000
0.8660
-0.0000
-0.5771
0.5770
-0.5780
-0.7071
-0.7071
-0.0000
Second axis

Spatial dependence of Young's modulus



Young's modulus in (xy) plane

Young's modulus in (xz) plane

Young's modulus in (yz) plane

Spatial dependence of linear compressibility



linear compressibility in (xy) plane

linear compressibility in (xz) plane

linear compressibility in (yz) plane

Spatial dependence of shear modulus



Shear modulus in (xy) plane

Shear modulus in (xz) plane

Shear modulus in (yz) plane

Spatial dependence of Poisson's ratio



Poisson's ratio in (xy) plane

Poisson's ratio in (xz) plane

Poisson's ratio in (yz) plane