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 ReN (Materials Project id mp-1019052)

       691      206      206        0        0        0  
       206      691      206        0        0        0  
       206      206      691        0        0        0  
         0        0        0      147        0        0  
         0        0        0        0      147        0  
         0        0        0        0        0      147  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 367.67 GPaEV = 475.72 GPaGV = 185.2 GPaνV = 0.28435
ReussKR = 367.67 GPaER = 451.96 GPaGR = 174.49 GPaνR = 0.29512
HillKH = 367.67 GPaEH = 463.89 GPaGH = 179.84 GPaνH = 0.28971

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
147 GPa 147 GPa 147 GPa 485 GPa 485 GPa 1103 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 389.14 GPa 596.38 GPa 0.90662 TPa–1 0.90662 TPa–1 147 GPa 242.5 GPa0.164110.44953Value
Anisotropy 1.533 1.0000 1.65 2.7393Anisotropy
Axis -0.5774
0.5774
0.5773
1.0000
0.0000
0.0000
0.9662
0.0000
0.2578
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0000
-0.0000
0.7071
-0.0005
-0.7071
0.0000
1.0000
-0.0000
-0.7071
0.0002
-0.7071
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