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 Na2Zr(CuS2)2 (Materials Project id mp-556536)

       106       22       28        0      -18        0  
        22      116       18        0        2        0  
        28       18       62        0        6        0  
         0        0        0        3        0       -1  
       -18        2        6        0       18        0  
         0        0        0       -1        0       26  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 46.667 GPaEV = 61.026 GPaGV = 23.8 GPaνV = 0.28205
ReussKR = 43.511 GPaER = 26.322 GPaGR = 9.4063 GPaνR = 0.39917
HillKH = 45.089 GPaEH = 44.364 GPaGH = 16.603 GPaνH = 0.33601

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
2.9566 GPa 11.437 GPa 26.043 GPa 51.644 GPa 92.694 GPa 146.23 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 10.93 GPa 109.03 GPa 5.1085 TPa–1 12.109 TPa–1 2.9566 GPa 47.98 GPa-0.587061.2207Value
Anisotropy 9.975 2.3705 16.23Anisotropy
Axis -0.0147
0.6918
0.7219
-0.9586
0.0000
0.2846
0.9995
0.0000
-0.0315
0.0315
-0.0000
0.9995
0.0434
-0.0000
0.9991
-0.6721
0.7071
0.2198
0.8765
0.3622
-0.3170
-0.8301
0.4493
0.3301
Axis
-0.0000
1.0000
0.0000
-0.6720
-0.7071
0.2198
-0.4801
0.6108
-0.6296
-0.0898
-0.6921
0.7162
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