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 TmN (Materials Project id mp-1975)

       355       93       93        0        0        0  
        93      355       93        0        0        0  
        93       93      355        0        0        0  
         0        0        0      138        0        0  
         0        0        0        0      138        0  
         0        0        0        0        0      138  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 180.33 GPaEV = 324.5 GPaGV = 135.2 GPaνV = 0.20009
ReussKR = 180.33 GPaER = 324.34 GPaGR = 135.11 GPaνR = 0.20024
HillKH = 180.33 GPaEH = 324.42 GPaGH = 135.16 GPaνH = 0.20017

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
138 GPa 138 GPa 138 GPa 262 GPa 262 GPa 541 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 316.39 GPa 329.86 GPa 1.8484 TPa–1 1.8484 TPa–1 131 GPa 138 GPa0.182550.21415Value
Anisotropy 1.043 1.0000 1.053 1.1731Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.7934
0.0000
0.6088
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0005
0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
0.7071
-0.0006
-0.7071
0.0004
1.0000
0.0004
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