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 Al13(CrSi)4 (Materials Project id mp-505572)

       223       57       57        0        0        0  
        57      223       57        0        0        0  
        57       57      223        0        0        0  
         0        0        0       56        0        0  
         0        0        0        0       56        0  
         0        0        0        0        0       56  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 112.33 GPaEV = 167.25 GPaGV = 66.8 GPaνV = 0.25186
ReussKR = 112.33 GPaER = 162.15 GPaGR = 64.377 GPaνR = 0.25942
HillKH = 112.33 GPaEH = 164.71 GPaGH = 65.588 GPaνH = 0.25562

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
56 GPa 56 GPa 56 GPa 166 GPa 166 GPa 337 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 144.06 GPa 199.79 GPa 2.9674 TPa–1 2.9674 TPa–1 56 GPa 83 GPa0.157790.38268Value
Anisotropy 1.387 1.0000 1.482 2.4253Anisotropy
Axis 0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.0000
-0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0002
0.0000
-0.7071
-0.0002
-0.7071
-0.0000
-1.0000
-0.0000
-0.7071
0.0002
-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