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 SbO2 (Materials Project id mp-230)

       178       30       69        0        0        0  
        30      207       59        0        0        0  
        69       59      160        0        0        0  
         0        0        0       47        0        0  
         0        0        0        0       82        0  
         0        0        0        0        0       34  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 95.667 GPaEV = 145.58 GPaGV = 58.4 GPaνV = 0.24638
ReussKR = 95.536 GPaER = 131.54 GPaGR = 51.767 GPaνR = 0.27052
HillKH = 95.602 GPaEH = 138.63 GPaGH = 55.084 GPaνH = 0.25833

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
34 GPa 47 GPa 82 GPa 92.61 GPa 164.91 GPa 287.48 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 96.758 GPa 188.78 GPa 3.3158 TPa–1 3.7347 TPa–1 34 GPa 82 GPa0.0245960.5027Value
Anisotropy 1.951 1.1263 2.412 20.4383Anisotropy
Axis 0.7347
0.6784
0.0000
0.7649
-0.0000
0.6442
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.0002
0.0000
0.0000
0.0000
1.0000
-1.0000
-0.0000
-0.0001
0.4967
0.6676
0.5546
Axis
0.0002
1.0000
0.0000
-1.0000
0.0000
0.0000
0.0000
-1.0000
0.0000
-0.5896
0.7285
-0.3488
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