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 Fe2P2O7 (Materials Project id mp-18849)

       134       85       61      -27       38       19  
        85      212      102      -23       -3       -4  
        61      102      151      -16       10       18  
       -27      -23      -16       63       24       -5  
        38       -3       10       24       54      -10  
        19       -4       18       -5      -10       53  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 110.33 GPaEV = 131.67 GPaGV = 50.6 GPaνV = 0.3011
ReussKR = 43.708 GPaER = 56.247 GPaGR = 21.877 GPaνR = 0.28552
HillKH = 77.021 GPaEH = 93.977 GPaGH = 36.239 GPaνH = 0.29664

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
7.7391 GPa 44.281 GPa 80.076 GPa 82.782 GPa 104.53 GPa 347.59 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 14.738 GPa 220.84 GPa -10.789 TPa–1 33.078 TPa–1 7.1454 GPa 85.75 GPa-0.822081.7784Value
Anisotropy 14.98 12Anisotropy
Axis -0.8127
0.2636
0.5197
0.4642
0.6232
-0.6294
0.0112
0.8991
-0.4377
-0.8024
0.2693
0.5326
0.5764
0.4519
-0.6809
-0.2077
0.2543
-0.9446
0.9254
0.0600
0.3742
0.1973
0.8039
-0.5610
Axis
-0.5717
0.8183
0.0591
-0.7667
-0.6420
-0.0042
-0.3702
0.3549
0.8585
-0.7898
0.4694
0.3948
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