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 Rb3CuO2 (Materials Project id mp-28568)

        36       19       16        0        2        0  
        19       34       20        0        1        0  
        16       20       39        0       -5        0  
         0        0        0        9        0        0  
         2        1       -5        0        9        0  
         0        0        0        0        0       13  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 24.333 GPaEV = 25.92 GPaGV = 9.8 GPaνV = 0.32246
ReussKR = 24.265 GPaER = 23.499 GPaGR = 8.7775 GPaνR = 0.3386
HillKH = 24.299 GPaEH = 24.717 GPaGH = 9.2888 GPaνH = 0.33047

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
6.8311 GPa 9 GPa 13 GPa 14.838 GPa 23.252 GPa 73.079 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 15.407 GPa 32.336 GPa 12.378 TPa–1 15.398 TPa–1 5.8981 GPa 13.509 GPa0.0328470.63257Value
Anisotropy 2.099 1.2440 2.29 19.2580Anisotropy
Axis 0.4813
0.0000
0.8766
-0.3865
0.0000
0.9223
-0.4558
-0.0000
0.8901
0.8901
0.0000
0.4558
0.3585
0.7071
0.6095
0.3722
0.3464
0.8611
-0.6583
0.7062
0.2607
0.6256
0.6949
-0.3545
Axis
-0.3586
0.7071
-0.6094
-0.8651
-0.2066
0.4570
-0.6623
-0.7079
0.2453
-0.4012
-0.1031
-0.9101
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