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 NdCoSi (Materials Project id mp-21890)

       180       58       70        0        0        0  
        58      180       70        0        0        0  
        70       70       82        0        0        0  
         0        0        0       37        0        0  
         0        0        0        0       37        0  
         0        0        0        0        0       63  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 93.111 GPaEV = 113.29 GPaGV = 43.667 GPaνV = 0.29721
ReussKR = 79.639 GPaER = 91.048 GPaGR = 34.766 GPaνR = 0.30946
HillKH = 86.375 GPaEH = 102.18 GPaGH = 39.216 GPaνH = 0.30283

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
33.968 GPa 37 GPa 37 GPa 63 GPa 122 GPa 286.03 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 40.824 GPa 124.81 GPa 1.2351 TPa–1 10.086 TPa–1 21.176 GPa 63 GPa-0.0307260.87989Value
Anisotropy 3.057 8.1667 2.975Anisotropy
Axis 0.0000
0.0000
1.0000
-0.6732
0.6731
0.3060
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
1.0000
-0.0002
-0.0000
0.7071
0.7071
0.0000
0.7071
0.7071
-0.0000
Axis
0.7071
-0.0005
-0.7071
0.0002
1.0000
-0.0000
-0.7071
0.7071
-0.0000
0.0000
0.0000
1.0000
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