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 MgTi2O5 (Materials Project id mp-28232)

       267       86      145        0        0        0  
        86      242      102        0        0        0  
       145      102      299        0        0        0  
         0        0        0       82        0        0  
         0        0        0        0       51        0  
         0        0        0        0        0       73  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 163.78 GPaEV = 190.37 GPaGV = 72.867 GPaνV = 0.30627
ReussKR = 159.34 GPaER = 182.97 GPaGR = 69.911 GPaνR = 0.30861
HillKH = 161.56 GPaEH = 186.67 GPaGH = 71.389 GPaνH = 0.30743

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
51 GPa 73 GPa 82 GPa 136.76 GPa 172.96 GPa 498.28 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 158.2 GPa 206.01 GPa 1.3691 TPa–1 2.8101 TPa–1 51 GPa 82.646 GPa0.165490.55378Value
Anisotropy 1.302 2.0526 1.621 3.3463Anisotropy
Axis 0.7348
-0.0000
-0.6783
-0.0000
0.2516
-0.9678
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
-0.7734
0.3074
0.5544
0.6711
-0.0000
0.7413
Axis
1.0000
0.0000
-0.0000
-0.7071
0.7071
0.0000
-0.2016
-0.9484
0.2446
0.7413
-0.0002
-0.6711
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