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 Al2SiO5 (Materials Project id mp-4753)

       202       76       94        0        0        0  
        76      268       85        0        0        0  
        94       85      330        0        0        0  
         0        0        0       89        0        0  
         0        0        0        0       78        0  
         0        0        0        0        0      102  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 145.56 GPaEV = 224.14 GPaGV = 90.133 GPaνV = 0.24336
ReussKR = 139.45 GPaER = 217.03 GPaGR = 87.469 GPaνR = 0.24061
HillKH = 142.5 GPaEH = 220.58 GPaGH = 88.801 GPaνH = 0.24201

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
78 GPa 89 GPa 102 GPa 142.15 GPa 209.32 GPa 448.53 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 164.33 GPa 275.97 GPa 1.4688 TPa–1 3.4013 TPa–1 75.63 GPa 105.73 GPa0.10950.38734Value
Anisotropy 1.679 2.3157 1.398 3.5375Anisotropy
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
0.5614
0.4299
0.0962
0.7005
0.7071
0.7307
0.6827
-0.0000
0.0000
0.0000
1.0000
Axis
-0.7071
-0.5614
-0.4300
0.0965
0.7005
-0.7071
-0.6827
0.7307
0.0000
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