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 Rh2O3 (Materials Project id mp-1716)

       379      139      204        0        0        0  
       139      374      144        0        0        0  
       204      144      371        0        0        0  
         0        0        0       92        0        0  
         0        0        0        0      131        0  
         0        0        0        0        0       93  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 233.11 GPaEV = 275.39 GPaGV = 105.67 GPaνV = 0.30311
ReussKR = 231.93 GPaER = 267.5 GPaGR = 102.27 GPaνR = 0.30777
HillKH = 232.52 GPaEH = 271.45 GPaGH = 103.97 GPaνH = 0.30543

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
92 GPa 93 GPa 131 GPa 170.67 GPa 251.99 GPa 701.34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 237.97 GPa 337.04 GPa 1.311 TPa–1 1.6769 TPa–1 85.447 GPa 131 GPa0.188050.47688Value
Anisotropy 1.416 1.2790 1.533 2.5359Anisotropy
Axis 0.0000
0.5320
0.8467
0.7197
0.0000
0.6943
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
1.0000
0.0004
-0.0000
1.0000
-0.0003
0.0000
Axis
-0.7071
-0.0002
-0.7071
-1.0000
0.0000
0.0000
-0.0004
1.0000
-0.0000
0.0000
-0.0004
-1.0000
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