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 Cr2O3 (Materials Project id mp-19399)

       348      142      137       -8        0        0  
       142      348      137        8        0        0  
       137      137      308        0        0        0  
        -8        8        0      136        0        0  
         0        0        0        0      136       -8  
         0        0        0        0       -8      103  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 204 GPaEV = 288.72 GPaGV = 114.2 GPaνV = 0.26411
ReussKR = 203.19 GPaER = 281.54 GPaGR = 110.93 GPaνR = 0.26907
HillKH = 203.6 GPaEH = 285.14 GPaGH = 112.56 GPaνH = 0.26658

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
101.16 GPa 134.22 GPa 137.84 GPa 184.95 GPa 207.78 GPa 613.05 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 231.39 GPa 324.5 GPa 1.5082 TPa–1 1.9051 TPa–1 94.69 GPa 137.84 GPa0.120760.37707Value
Anisotropy 1.402 1.2632 1.456 3.1224Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
0.7839
0.6209
0.9917
0.1289
0.0000
0.0000
0.0000
1.0000
0.0002
0.6745
-0.7382
-0.0000
0.2238
-0.9746
-0.5774
0.3333
0.7453
0.6037
0.3486
0.7169
Axis
-0.0001
-0.7382
-0.6745
-1.0000
-0.0000
-0.0000
-0.6455
0.3726
-0.6667
-0.5000
0.8660
0.0000
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