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 Ba (Materials Project id mp-122)

        12        7        7        0        0        0  
         7       12        7        0        0        0  
         7        7       12        0        0        0  
         0        0        0       10        0        0  
         0        0        0        0       10        0  
         0        0        0        0        0       10  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 8.6667 GPaEV = 16.545 GPaGV = 7 GPaνV = 0.18182
ReussKR = 8.6667 GPaER = 11.607 GPaGR = 4.5455 GPaνR = 0.27679
HillKH = 8.6667 GPaEH = 14.172 GPaGH = 5.7727 GPaνH = 0.22747

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
5 GPa 5 GPa 10 GPa 10 GPa 10 GPa 26 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 6.8421 GPa 21.667 GPa 38.462 TPa–1 38.462 TPa–1 2.5 GPa 10 GPa-0.29730.75676Value
Anisotropy 3.167 1.0000 4Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.8660
0.0000
0.5000
0.7071
0.0001
-0.7071
-0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.7071
0.7071
Axis
-0.7071
-0.0002
-0.7071
-0.5000
0.8660
-0.0000
-0.7071
-0.0002
-0.7071
-1.0000
0.0000
-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