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 SiO2 (Materials Project id mp-572283)

       137       67       67        0        0        0  
        67      128       72        0        0        0  
        67       72      128        0        0        0  
         0        0        0       38        0        0  
         0        0        0        0       60        0  
         0        0        0        0        0       60  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 89.444 GPaEV = 113.55 GPaGV = 44.067 GPaνV = 0.28841
ReussKR = 89.427 GPaER = 104.8 GPaGR = 40.162 GPaνR = 0.30469
HillKH = 89.436 GPaEH = 109.2 GPaGH = 42.114 GPaνH = 0.2965

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
38 GPa 56 GPa 60 GPa 60 GPa 68.649 GPa 268.35 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 79.07 GPa 131.06 GPa 3.5827 TPa–1 3.7998 TPa–1 28 GPa 60 GPa0.0132840.53936Value
Anisotropy 1.658 1.0606 2.143 40.6006Anisotropy
Axis 0.0000
0.0000
1.0000
0.6901
0.5118
0.5118
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0001
0.7071
0.7071
0.0000
0.0000
1.0000
0.7065
-0.0002
0.7077
0.6783
-0.0002
-0.7348
Axis
0.0001
0.7071
-0.7071
-1.0000
0.0000
0.0000
0.7077
-0.0005
-0.7065
0.0001
1.0000
-0.0002
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