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-557837)

        79      -20       24        0       -4        0  
       -20       83      -12        0      -30        0  
        24      -12       62        0       -6        0  
         0        0        0       31        0        3  
        -4      -30       -6        0       36        0  
         0        0        0        3        0       25  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 23.111 GPaEV = 68.258 GPaGV = 33.867 GPaνV = 0.0077519
ReussKR = 15.793 GPaER = 51.548 GPaGR = 26.96 GPaνR = -0.043988
HillKH = 19.452 GPaEH = 59.98 GPaGH = 30.413 GPaνH = -0.013913

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
17.763 GPa 23.757 GPa 32.243 GPa 44.934 GPa 81.115 GPa 116.19 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 38.74 GPa 84.381 GPa 2.58 TPa–1 31.711 TPa–1 20.89 GPa 62.4 GPa-0.660450.40603Value
Anisotropy 2.178 12.2910 2.987Anisotropy
Axis 0.5593
0.6550
0.5080
-0.7978
0.0000
0.6030
0.7371
-0.0000
-0.6758
0.6758
-0.0000
0.7371
0.8775
0.3949
-0.2722
-0.5606
0.7071
-0.4309
0.0000
1.0000
0.0000
0.8264
-0.0001
-0.5631
Axis
-0.0010
0.5691
0.8223
-0.5606
-0.7071
-0.4309
-0.7288
0.0000
-0.6848
-0.5631
0.0002
-0.8264
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