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 PrAg2 (Materials Project id mp-568654)

        94       65       44        0        0        0  
        65       94       44        0        0        0  
        44       44       55        0        0        0  
         0        0        0       23        0        0  
         0        0        0        0       23        0  
         0        0        0        0        0       14  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 61 GPaEV = 49.164 GPaGV = 18 GPaνV = 0.36567
ReussKR = 52.398 GPaER = 44.874 GPaGR = 16.531 GPaνR = 0.35726
HillKH = 56.699 GPaEH = 47.024 GPaGH = 17.266 GPaνH = 0.36177

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
14 GPa 23 GPa 23 GPa 25.907 GPa 29 GPa 188.09 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 30.648 GPa 51.428 GPa 2.2573 TPa–1 14.57 TPa–1 13.479 GPa 23 GPa0.0661560.57028Value
Anisotropy 1.678 6.4545 1.706 8.6202Anisotropy
Axis 0.0000
0.0000
1.0000
0.8136
-0.0001
0.5815
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.4999
0.5001
0.7071
-0.0000
0.0000
1.0000
-0.4948
0.4946
-0.7145
-0.6081
0.6081
0.5104
Axis
0.5002
0.4998
-0.7071
-0.1736
0.9848
-0.0000
0.5051
-0.5053
-0.6996
-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