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-25372)

       247       88       65       -6        0        0  
        88      247       65        6        0        0  
        65       65      185        0        0        0  
        -6        6        0       50        0        0  
         0        0        0        0       50       -6  
         0        0        0        0       -6       80  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 123.89 GPaEV = 169.73 GPaGV = 66.733 GPaνV = 0.27167
ReussKR = 120.28 GPaER = 160.57 GPaGR = 62.846 GPaνR = 0.2775
HillKH = 122.08 GPaEH = 165.15 GPaGH = 64.79 GPaνH = 0.27454

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
48.845 GPa 49.343 GPa 81.155 GPa 141.36 GPa 159.66 GPa 378.64 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 131.21 GPa 207.66 GPa 2.2419 TPa–1 3.83 TPa–1 48.831 GPa 81.155 GPa0.132080.41888Value
Anisotropy 1.583 1.7083 1.662 3.1715Anisotropy
Axis -0.0000
0.6775
-0.7355
0.8495
0.5195
-0.0924
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.1654
0.0960
-0.9815
0.0000
0.9820
-0.1891
0.5082
0.2960
-0.8088
-0.6190
0.3648
-0.6955
Axis
-0.5005
-0.8657
-0.0003
-1.0000
0.0000
0.0000
-0.5029
0.8643
0.0003
0.5993
-0.3530
-0.7185
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