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 K2SO4 (Materials Project id mp-4529)

        51       18       19        0        0        0  
        18       49       20        0        0        0  
        19       20       50        0        0        0  
         0        0        0        9        0        0  
         0        0        0        0       17        0  
         0        0        0        0        0       16  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 29.333 GPaEV = 37.567 GPaGV = 14.6 GPaνV = 0.28655
ReussKR = 29.326 GPaER = 35.831 GPaGR = 13.82 GPaνR = 0.29636
HillKH = 29.33 GPaEH = 36.702 GPaGH = 14.21 GPaνH = 0.29144

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
9 GPa 16 GPa 17 GPa 29.461 GPa 32.527 GPa 88.011 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 27.252 GPa 42.14 GPa 10.979 TPa–1 11.75 TPa–1 9 GPa 17 GPa0.114090.51403Value
Anisotropy 1.546 1.0702 1.889 4.5053Anisotropy
Axis 0.0000
0.7085
0.7057
0.8087
0.0000
0.5882
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0002
0.0001
1.0000
0.0000
0.0000
1.0000
-0.6628
0.5277
-0.5313
0.0004
0.7057
-0.7085
Axis
-0.0000
1.0000
-0.0001
-1.0000
0.0000
0.0000
-0.7487
-0.4524
0.4847
0.0000
-0.7085
-0.7057
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