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 LiCoS2 (Materials Project id mp-753946)

       185       54       36       -4        0        0  
        54      185       36        4        0        0  
        36       36       93        0        0        0  
        -4        4        0       35        0        0  
         0        0        0        0       35       -4  
         0        0        0        0       -4       66  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 79.444 GPaEV = 123.3 GPaGV = 49.667 GPaνV = 0.24132
ReussKR = 69.875 GPaER = 110.05 GPaGR = 44.464 GPaνR = 0.23751
HillKH = 74.66 GPaEH = 116.68 GPaGH = 47.065 GPaνH = 0.23953

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
34.492 GPa 34.668 GPa 66.508 GPa 77 GPa 131.33 GPa 255 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 81.731 GPa 163.15 GPa 2.903 TPa–1 8.5052 TPa–1 34.486 GPa 66.508 GPa0.11330.34983Value
Anisotropy 1.996 2.9298 1.929 3.0877Anisotropy
Axis -0.0000
0.3418
-0.9398
0.8422
0.5350
-0.0670
0.9239
0.3827
0.0000
0.0000
0.0000
1.0000
-0.1101
-0.0641
0.9918
-0.0000
0.9920
-0.1259
-0.5296
0.3093
-0.7899
-0.6947
0.4373
-0.5711
Axis
-0.4996
0.8663
0.0005
-1.0000
-0.0000
0.0000
-0.5040
-0.8637
-0.0003
-0.4823
0.3058
0.8209
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