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 ErAs (Materials Project id mp-1688)

       189       25       25        0        0        0  
        25      189       25        0        0        0  
        25       25      189        0        0        0  
         0        0        0       41        0        0  
         0        0        0        0       41        0  
         0        0        0        0        0       41  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 79.667 GPaEV = 138.85 GPaGV = 57.4 GPaνV = 0.20951
ReussKR = 79.667 GPaER = 126.6 GPaGR = 51.25 GPaνR = 0.23514
HillKH = 79.667 GPaEH = 132.79 GPaGH = 54.325 GPaνH = 0.22219

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
41 GPa 41 GPa 41 GPa 164 GPa 164 GPa 239 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 104.99 GPa 183.16 GPa 4.1841 TPa–1 4.1841 TPa–1 41 GPa 82 GPa0.0749630.43328Value
Anisotropy 1.745 1.0000 2 5.7800Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7934
0.0000
0.6088
-0.0000
-0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
-0.0000
-0.7071
0.7071
-0.0002
0.7071
Axis
1.0000
0.0002
0.0000
0.7071
-0.0005
-0.7071
0.0000
-1.0000
-0.0000
0.7071
-0.0005
-0.7071
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