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 SrBi3 (Materials Project id mp-23159)

        52       37       37        0        0        0  
        37       52       37        0        0        0  
        37       37       52        0        0        0  
         0        0        0       19        0        0  
         0        0        0        0       19        0  
         0        0        0        0        0       19  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 42 GPaEV = 38.769 GPaGV = 14.4 GPaνV = 0.34615
ReussKR = 42 GPaER = 32.311 GPaGR = 11.777 GPaνR = 0.37178
HillKH = 42 GPaEH = 35.57 GPaGH = 13.088 GPaνH = 0.35885

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15 GPa 15 GPa 19 GPa 19 GPa 19 GPa 126 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 21.236 GPa 49.531 GPa 7.9365 TPa–1 7.9365 TPa–1 7.5 GPa 19 GPa-0.0222450.72737Value
Anisotropy 2.332 1.0000 2.533Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5773
-0.5774
0.9659
0.0000
0.2588
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.0000
0.7071
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.7660
0.6428
-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