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 Mg3Cr (Materials Project id mp-978277)

        57       42       46        0        0        0  
        42       57       46        0        0        0  
        46       46       52        0        0        0  
         0        0        0       47        0        0  
         0        0        0        0       47        0  
         0        0        0        0        0       31  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 48.222 GPaEV = 68.544 GPaGV = 27.133 GPaνV = 0.2631
ReussKR = 48.211 GPaER = 26.854 GPaGR = 9.5418 GPaνR = 0.40716
HillKH = 48.216 GPaEH = 48.823 GPaGH = 18.338 GPaνH = 0.33124

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
6.3317 GPa 15 GPa 31 GPa 47 GPa 47 GPa 144.67 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 9.2525 GPa 94.273 GPa 6.5502 TPa–1 7.6419 TPa–1 3.7005 GPa 47 GPa-0.571971.3778Value
Anisotropy 10.19 1.1667 12.7Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5745
0.5745
-0.5830
0.0589
0.9983
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.6840
0.6840
0.2535
0.7071
0.7071
0.0000
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
-0.7071
0.7071
0.0000
0.0001
-0.0001
-1.0000
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