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 SbPbClO2 (Materials Project id mp-23138)

       147       59       69        0        0        0  
        59      102       50        0        0        0  
        69       50      208        0        0        0  
         0        0        0       34        0        0  
         0        0        0        0       26        0  
         0        0        0        0        0       33  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 90.333 GPaEV = 98.13 GPaGV = 37.2 GPaνV = 0.31895
ReussKR = 82.341 GPaER = 89.37 GPaGR = 33.875 GPaνR = 0.31911
HillKH = 86.337 GPaEH = 93.75 GPaGH = 35.538 GPaνH = 0.31902

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
26 GPa 33 GPa 34 GPa 61.309 GPa 112.07 GPa 283.63 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 75.486 GPa 169.26 GPa 2.1276 TPa–1 7.0376 TPa–1 26 GPa 50.74 GPa0.127020.55547Value
Anisotropy 2.242 3.3078 1.952 4.3731Anisotropy
Axis 0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.0000
1.0000
-0.0000
0.6139
0.0001
-0.7894
Axis
-1.0000
0.0000
0.0000
0.7071
-0.0005
-0.7071
-0.0000
0.0000
1.0000
-0.7894
-0.0002
-0.6139
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