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 TcO2 (Materials Project id mp-33137)

       407      206      172        0       -3        0  
       206      353      222        0       27        0  
       172      222      348        0      -24        0  
         0        0        0      208        0       64  
        -3       27      -24        0       94        0  
         0        0        0       64        0      156  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 256.44 GPaEV = 323.62 GPaGV = 125.47 GPaνV = 0.28967
ReussKR = 255.59 GPaER = 255.15 GPaGR = 95.661 GPaνR = 0.33362
HillKH = 256.02 GPaEH = 289.95 GPaGH = 110.56 GPaνH = 0.31124

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
70.001 GPa 112.92 GPa 148.22 GPa 213.81 GPa 251.08 GPa 769.97 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 146.53 GPa 450.56 GPa 1.1307 TPa–1 1.5614 TPa–1 48.197 GPa 251.08 GPa-0.108730.67094Value
Anisotropy 3.075 1.3810 5.209Anisotropy
Axis 0.4792
-0.0000
0.8777
0.4195
0.7203
0.5524
0.0000
1.0000
0.0000
-0.1646
-0.0000
-0.9864
0.3479
0.7071
0.6156
0.5584
0.0002
0.8296
0.3735
0.7086
0.5986
0.4404
0.8672
-0.2324
Axis
-0.3479
0.7071
-0.6156
-0.0002
1.0000
-0.0001
-0.3646
0.7055
-0.6077
-0.4770
0.0067
-0.8789
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