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 YMg2 (Materials Project id mp-11499)

        77       29       23        0        0        0  
        29       77       23        0        0        0  
        23       23       82        0        0        0  
         0        0        0       19        0        0  
         0        0        0        0       19        0  
         0        0        0        0        0       24  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 42.889 GPaEV = 58.824 GPaGV = 23.133 GPaνV = 0.27141
ReussKR = 42.888 GPaER = 57.435 GPaGR = 22.492 GPaνR = 0.2768
HillKH = 42.888 GPaEH = 58.131 GPaGH = 22.812 GPaνH = 0.2741

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
19 GPa 19 GPa 24 GPa 48 GPa 59.33 GPa 128.67 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 52.293 GPa 72.019 GPa 7.7286 TPa–1 7.8596 TPa–1 19 GPa 28.013 GPa0.200790.38064Value
Anisotropy 1.377 1.0169 1.474 1.8957Anisotropy
Axis 0.7229
0.1834
-0.6662
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0847
0.7020
-0.7071
0.5071
-0.0002
0.8619
0.3252
0.5998
-0.7311
Axis
1.0000
0.0000
-0.0000
-0.0846
-0.7020
-0.7071
0.0005
1.0000
-0.0000
0.3485
0.6427
0.6823
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