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 Ni2P2O7 (Materials Project id mp-18819)

       237       75       91        0       17        0  
        75      217      107        0       26        0  
        91      107      209        0       13        0  
         0        0        0       95        0       18  
        17       26       13        0       63        0  
         0        0        0       18        0       37  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 134.33 GPaEV = 167.92 GPaGV = 65 GPaνV = 0.29167
ReussKR = 128.6 GPaER = 144.92 GPaGR = 55.222 GPaνR = 0.31218
HillKH = 131.47 GPaEH = 156.48 GPaGH = 60.111 GPaνH = 0.30162

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
31.868 GPa 58.084 GPa 100.13 GPa 105.04 GPa 156.81 GPa 406.07 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 93.435 GPa 234.07 GPa 1.2871 TPa–1 3.6529 TPa–1 31.868 GPa 100.13 GPa0.00694460.69829Value
Anisotropy 2.505 2.8380 3.142100.5520Anisotropy
Axis 0.6556
0.7199
-0.2279
-0.2098
0.7239
-0.6572
-0.6711
-0.0000
-0.7414
-0.7414
0.0000
0.6711
-0.9617
-0.0000
0.2742
0.2742
0.0002
0.9617
-0.6009
0.5751
-0.5551
0.7015
0.4842
0.5229
Axis
0.0000
-1.0000
0.0000
-0.0001
1.0000
-0.0002
0.2376
-0.5346
-0.8110
-0.6782
0.6791
0.2809
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