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 SrMg6Mo (Materials Project id mp-1016296)

        63       35       35        0        0        0  
        35       64       15       -0        0        0  
        35       15       64       -0        0        0  
         0       -0       -0       15        0        0  
         0        0        0        0       42       -0  
         0        0        0        0       -0       42  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 40.111 GPaEV = 65.889 GPaGV = 26.867 GPaνV = 0.22622
ReussKR = 38.877 GPaER = 51.158 GPaGR = 19.973 GPaνR = 0.28068
HillKH = 39.494 GPaEH = 58.664 GPaGH = 23.42 GPaνH = 0.25244

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15 GPa 20.86 GPa 42 GPa 42 GPa 49 GPa 121.14 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 31.987 GPa 82.028 GPa 3.5615 TPa–1 11.08 TPa–1 11.351 GPa 42 GPa-0.157260.66691Value
Anisotropy 2.564 3.1111 3.7Anisotropy
Axis 1.0000
0.0000
0.0000
0.6525
0.7578
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.7071
0.5000
0.5000
0.0000
0.0000
1.0000
0.7055
0.5011
-0.5011
-0.7720
0.4494
0.4495
Axis
-0.7071
-0.5000
-0.5000
-1.0000
0.0000
0.0000
-0.7087
0.4989
-0.4989
-0.0000
-0.7071
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