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 Mn3Zn (Materials Project id mp-973181)

       206      188      140        0        0        0  
       188      206      140        0        0        0  
       140      140      285        0        0        0  
         0        0        0      102        0        0  
         0        0        0        0      102        0  
         0        0        0        0        0      165  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 181.44 GPaEV = 229.63 GPaGV = 89.067 GPaνV = 0.28907
ReussKR = 180.92 GPaER = 93.233 GPaGR = 32.965 GPaνR = 0.41411
HillKH = 181.18 GPaEH = 164.57 GPaGH = 61.016 GPaνH = 0.34861

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18 GPa 102 GPa 102 GPa 134.15 GPa 165 GPa 544.85 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 33.639 GPa 295.38 GPa 1.5597 TPa–1 1.9839 TPa–1 9 GPa 165 GPa-0.649211.4159Value
Anisotropy 8.781 1.2719 18.33Anisotropy
Axis 1.0000
0.0000
0.0000
0.6458
0.6458
0.4074
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.7071
0.7071
-0.0000
-1.0000
-0.0000
0.0000
0.5794
0.0001
0.8151
0.0000
0.6101
-0.7923
Axis
-0.7071
-0.7071
0.0000
0.0000
-1.0000
0.0000
0.8151
0.0003
-0.5794
-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