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 Mg2P2O7 (Materials Project id mp-5427)

       223       54       74        0       15        0  
        54      206       91        0       21        0  
        74       91      200        0       12        0  
         0        0        0       95        0       14  
        15       21       12        0       66        0  
         0        0        0       14        0       37  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 118.56 GPaEV = 169 GPaGV = 66.933 GPaνV = 0.26242
ReussKR = 114.44 GPaER = 148.82 GPaGR = 57.987 GPaνR = 0.28325
HillKH = 116.5 GPaEH = 158.97 GPaGH = 62.46 GPaνH = 0.27257

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
33.798 GPa 62.408 GPa 98.202 GPa 109.42 GPa 164.72 GPa 358.45 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 97.967 GPa 227.67 GPa 1.7 TPa–1 3.8957 TPa–1 33.798 GPa 98.202 GPa0.00497440.63395Value
Anisotropy 2.324 2.2915 2.906127.4416Anisotropy
Axis -0.6681
0.7189
0.1921
0.1759
0.7230
0.6681
-0.6350
0.0000
-0.7725
-0.7725
-0.0000
0.6351
-0.9748
0.0000
0.2230
-0.2230
0.0000
-0.9748
-0.2957
0.5300
0.7947
0.6825
0.4859
0.5460
Axis
-0.0000
-1.0000
0.0000
-0.0000
-1.0000
-0.0000
-0.5661
0.5729
-0.5927
-0.6865
0.6826
0.2506
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