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 Ag2SO4 (Materials Project id mp-5625)

        45       58       37        0        0        0  
        58      119       59        0        0        0  
        37       59       55        0        0        0  
         0        0        0       15        0        0  
         0        0        0        0       12        0  
         0        0        0        0        0        9  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 58.556 GPaEV = 32.468 GPaGV = 11.533 GPaνV = 0.40759
ReussKR = 36.998 GPaER = 26.154 GPaGR = 9.4612 GPaνR = 0.38218
HillKH = 47.777 GPaEH = 29.343 GPaGH = 10.497 GPaνH = 0.39764

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
9 GPa 11.35 GPa 12 GPa 15 GPa 20.306 GPa 187.34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 14.092 GPa 39.941 GPa -9.4958 TPa–1 24.921 TPa–1 6.1532 GPa 15 GPa0.0751790.92825Value
Anisotropy 2.834 2.438 12.3473Anisotropy
Axis 1.0000
0.0000
0.0000
0.0000
0.9262
-0.3770
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.7071
-0.0000
-0.7071
-0.0000
-0.0000
1.0000
0.7161
-0.0002
0.6980
-0.0000
0.9323
0.3617
Axis
-0.7071
0.0002
-0.7071
0.0000
1.0000
0.0000
0.6980
-0.0005
-0.7161
-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