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 LiCuO2 (Materials Project id mp-9158)

        72       41       51        0       -3        0  
        41      328       58        0       22        0  
        51       58      162        0       30        0  
         0        0        0       40        0       15  
        -3       22       30        0       36        0  
         0        0        0       15        0       33  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 95.778 GPaEV = 126.17 GPaGV = 49.267 GPaνV = 0.28045
ReussKR = 66.174 GPaER = 79.778 GPaGR = 30.706 GPaνR = 0.29907
HillKH = 80.976 GPaEH = 103 GPaGH = 39.986 GPaνH = 0.28799

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
21.097 GPa 22.104 GPa 51.903 GPa 57.197 GPa 159.1 GPa 359.6 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 42.759 GPa 288.37 GPa 1.3274 TPa–1 11.38 TPa–1 16.556 GPa 85.019 GPa-0.0146280.76759Value
Anisotropy 6.744 8.5730 5.135Anisotropy
Axis -0.9653
-0.0000
-0.2612
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.9939
-0.0000
-0.1103
-0.8998
-0.0001
0.4362
-0.2053
0.7071
-0.6766
-0.4414
0.0000
0.8973
-0.1712
0.0001
0.9852
Axis
-0.4362
0.0002
-0.8998
-0.2054
-0.7071
-0.6767
-0.0000
-1.0000
-0.0000
-0.9852
-0.0001
-0.1712
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