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 MgSO4 (Materials Project id mp-7572)

        96       29       40        0        0        0  
        29      133       50        0        0        0  
        40       50      201        0        0        0  
         0        0        0       41        0        0  
         0        0        0        0       50        0  
         0        0        0        0        0       50  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 74.222 GPaEV = 120.35 GPaGV = 48.933 GPaνV = 0.22975
ReussKR = 66.089 GPaER = 113.81 GPaGR = 46.914 GPaνR = 0.21298
HillKH = 70.156 GPaEH = 117.11 GPaGH = 47.924 GPaνH = 0.22179

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
41 GPa 50 GPa 50 GPa 78.267 GPa 108.03 GPa 243.71 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 85.03 GPa 172.76 GPa 2.1436 TPa–1 8.0242 TPa–1 40.652 GPa 55.922 GPa0.076640.39324Value
Anisotropy 2.032 3.7433 1.376 5.1310Anisotropy
Axis 1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
0.5970
0.3788
0.2028
0.6774
0.7071
0.7238
0.5850
-0.3658
0.0005
0.6000
0.8000
Axis
-0.7071
0.5971
0.3789
0.2030
0.6773
-0.7071
-0.6900
0.6139
-0.3835
0.0003
0.8000
-0.6000
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