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 MnS (Materials Project id mp-2065)

       109       29       29        0        0        0  
        29      109       29        0        0        0  
        29       29      109        0        0        0  
         0        0        0       39        0        0  
         0        0        0        0       39        0  
         0        0        0        0        0       39  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 55.667 GPaEV = 95.637 GPaGV = 39.4 GPaνV = 0.21366
ReussKR = 55.667 GPaER = 95.625 GPaGR = 39.394 GPaνR = 0.2137
HillKH = 55.667 GPaEH = 95.631 GPaGH = 39.397 GPaνH = 0.21368

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
39 GPa 39 GPa 39 GPa 80 GPa 80 GPa 167 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 94.85 GPa 96.812 GPa 5.988 TPa–1 5.988 TPa–1 39 GPa 40 GPa0.206930.22221Value
Anisotropy 1.021 1.0000 1.026 1.0738Anisotropy
Axis -0.5774
0.5774
0.5773
-0.0000
-0.0000
1.0000
0.0000
0.0000
1.0000
-0.0670
0.2500
0.9659
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.0000
0.7071
0.7071
-0.0002
0.7071
Axis
0.9397
0.3420
-0.0000
-0.7071
-0.0002
-0.7071
-0.0000
-1.0000
0.0000
0.7071
-0.0006
-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