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 YbGa2 (Materials Project id mp-2178)

       118       33       21        0        0        0  
        33      118       21        0        0        0  
        21       21       88        0        0        0  
         0        0        0       61        0        0  
         0        0        0        0       61        0  
         0        0        0        0        0       43  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 52.667 GPaEV = 113.25 GPaGV = 49.6 GPaνV = 0.14162
ReussKR = 51.053 GPaER = 108.94 GPaGR = 47.599 GPaνR = 0.14436
HillKH = 51.86 GPaEH = 111.1 GPaGH = 48.6 GPaνH = 0.14296

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
43 GPa 61 GPa 61 GPa 76.207 GPa 85 GPa 162.79 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 82.159 GPa 119 GPa 5.4006 TPa–1 8.7861 TPa–1 40.022 GPa 61 GPa-0.0527030.25657Value
Anisotropy 1.448 1.6269 1.524Anisotropy
Axis 0.0000
0.0000
1.0000
0.5766
0.5766
0.5789
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7127
0.0001
-0.7015
0.8974
-0.0003
-0.4411
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
-0.7015
-0.0001
-0.7127
0.0004
1.0000
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