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 PrH2 (Materials Project id mp-24095)

       110       60       60        0        0        0  
        60      110       60        0        0        0  
        60       60      110        0        0        0  
         0        0        0       54        0        0  
         0        0        0        0       54        0  
         0        0        0        0        0       54  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 76.667 GPaEV = 107.4 GPaGV = 42.4 GPaνV = 0.26652
ReussKR = 76.667 GPaER = 95.362 GPaGR = 36.885 GPaνR = 0.29269
HillKH = 76.667 GPaEH = 101.44 GPaGH = 39.643 GPaνH = 0.27947

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
50 GPa 50 GPa 54 GPa 54 GPa 54 GPa 230 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 67.647 GPa 131.2 GPa 4.3478 TPa–1 4.3478 TPa–1 25 GPa 54 GPa-0.0162530.55432Value
Anisotropy 1.939 1.0000 2.16Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
-0.7071
-0.0000
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.5000
0.8660
-0.0000
-0.7071
0.0002
-0.7071
0.0000
-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