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 Te2Ru (Materials Project id mp-1848)

       249       61       61        0        0        0  
        61      249       61        0        0        0  
        61       61      249        0        0        0  
         0        0        0       68        0        0  
         0        0        0        0       68        0  
         0        0        0        0        0       68  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 123.67 GPaEV = 194.17 GPaGV = 78.4 GPaνV = 0.23832
ReussKR = 123.67 GPaER = 190.18 GPaGR = 76.459 GPaνR = 0.24369
HillKH = 123.67 GPaEH = 192.18 GPaGH = 77.43 GPaνH = 0.241

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
68 GPa 68 GPa 68 GPa 188 GPa 188 GPa 371 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 172.4 GPa 224.99 GPa 2.6954 TPa–1 2.6954 TPa–1 68 GPa 94 GPa0.160140.34633Value
Anisotropy 1.305 1.0000 1.382 2.1627Anisotropy
Axis 0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.9914
0.0000
-0.1305
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0001
0.7071
0.7071
-0.0002
0.7071
Axis
-0.1736
0.9848
-0.0000
-0.7071
-0.0002
-0.7071
0.0001
1.0000
0.0000
0.7071
-0.0005
-0.7071
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