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 ReO2 (Materials Project id mp-7228)

       367      255      184        0        0        0  
       255      445      160        0        0        0  
       184      160      484        0        0        0  
         0        0        0      141        0        0  
         0        0        0        0      200        0  
         0        0        0        0        0      247  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 277.11 GPaEV = 411.07 GPaGV = 164.07 GPaνV = 0.25276
ReussKR = 276.03 GPaER = 353.63 GPaGR = 137.44 GPaνR = 0.28648
HillKH = 276.57 GPaEH = 382.72 GPaGH = 150.75 GPaνH = 0.26936

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
141 GPa 142.59 GPa 200 GPa 247 GPa 321.34 GPa 832.07 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 200.89 GPa 518.4 GPa 0.99649 TPa–1 1.4353 TPa–1 73.106 GPa 247 GPa-0.0387080.65367Value
Anisotropy 2.58 1.4403 3.379Anisotropy
Axis 1.0000
0.0000
0.0000
-0.6613
0.7501
-0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
0.0000
1.0000
-0.0000
0.0000
0.7004
-0.0004
0.7138
0.0000
1.0000
0.0000
Axis
-0.7071
-0.7071
-0.0000
0.0000
1.0000
-0.0000
0.7138
0.0003
-0.7004
-1.0000
0.0000
-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