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 ErN (Materials Project id mp-19830)

       343       85       85        0        0        0  
        85      343       85        0        0        0  
        85       85      343        0        0        0  
         0        0        0      133        0        0  
         0        0        0        0      133        0  
         0        0        0        0        0      133  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 171 GPaEV = 313.82 GPaGV = 131.4 GPaνV = 0.19413
ReussKR = 171 GPaER = 313.76 GPaGR = 131.37 GPaνR = 0.19419
HillKH = 171 GPaEH = 313.79 GPaGH = 131.39 GPaνH = 0.19416

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
133 GPa 133 GPa 133 GPa 258 GPa 258 GPa 513 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 309.24 GPa 316.85 GPa 1.9493 TPa–1 1.9493 TPa–1 129 GPa 133 GPa0.183890.20224Value
Anisotropy 1.025 1.0000 1.031 1.0998Anisotropy
Axis 0.0000
1.0000
0.0000
0.5774
0.5774
0.5773
0.9659
0.0000
0.2588
0.4330
0.7500
0.5000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0004
0.7071
Axis
0.7071
-0.0005
-0.7071
0.5000
0.8660
-0.0000
0.7071
-0.0006
-0.7071
0.0003
1.0000
0.0003
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