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 MnAlFe2 (Materials Project id mp-31185)

       301      144      144        0        0        0  
       144      301      144        0        0        0  
       144      144      301        0        0        0  
         0        0        0      163        0        0  
         0        0        0        0      163        0  
         0        0        0        0        0      163  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 196.33 GPaEV = 317.87 GPaGV = 129.2 GPaνV = 0.23016
ReussKR = 196.33 GPaER = 286.41 GPaGR = 113.94 GPaνR = 0.25686
HillKH = 196.33 GPaEH = 302.31 GPaGH = 121.57 GPaνH = 0.24337

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
157 GPa 157 GPa 163 GPa 163 GPa 163 GPa 589 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 207.8 GPa 383.01 GPa 1.6978 TPa–1 1.6978 TPa–1 78.5 GPa 163 GPa-0.0296590.49259Value
Anisotropy 1.843 1.0000 2.076Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.9241
0.0000
0.3823
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.7071
-0.0001
0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
0.0001
1.0000
0.0001
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