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 Na4P2O7 (Materials Project id mp-27579)

        90       24       33        0        0        0  
        24      105       14        0        0        0  
        33       14       78        0        0        0  
         0        0        0       13        0        0  
         0        0        0        0       22        0  
         0        0        0        0        0       23  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 46.111 GPaEV = 63.664 GPaGV = 25.067 GPaνV = 0.26989
ReussKR = 45.55 GPaER = 56.368 GPaGR = 21.785 GPaνR = 0.29375
HillKH = 45.831 GPaEH = 60.047 GPaGH = 23.426 GPaνH = 0.28164

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
13 GPa 22 GPa 23 GPa 49.971 GPa 83.56 GPa 139.47 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 39.506 GPa 98.19 GPa 5.9327 TPa–1 9.0614 TPa–1 13 GPa 36.997 GPa0.0527380.53023Value
Anisotropy 2.485 1.5274 2.846 10.0540Anisotropy
Axis 0.0000
0.6703
0.7421
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0003
0.0003
1.0000
0.0001
0.7071
-0.7071
0.0000
-0.0000
1.0000
0.0001
0.7464
-0.6655
Axis
0.0000
1.0000
-0.0003
0.0002
-0.7071
-0.7071
-0.0000
-1.0000
-0.0000
0.0001
-0.6655
-0.7464
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