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 Ti4O5 (Materials Project id mp-10734)

       466      103      103        0        0        0  
       103      361      134       27        0        0  
       103      134      361      -27        0        0  
         0       27      -27      113        0        0  
         0        0        0        0       56        0  
         0        0        0        0        0       56  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 207.56 GPaEV = 261.89 GPaGV = 101.53 GPaνV = 0.2897
ReussKR = 206.36 GPaER = 219.1 GPaGR = 82.803 GPaνR = 0.32304
HillKH = 206.96 GPaEH = 240.76 GPaGH = 92.168 GPaνH = 0.30611

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
56 GPa 56 GPa 101.39 GPa 238.61 GPa 334.12 GPa 626.88 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 170.17 GPa 423.14 GPa 1.3798 TPa–1 1.7331 TPa–1 56 GPa 160.21 GPa0.104430.61478Value
Anisotropy 2.487 1.2561 2.861 5.8869Anisotropy
Axis 0.6492
0.2927
0.7020
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.9914
-0.1305
0.0000
0.0000
1.0000
0.7071
0.6539
0.2691
-0.7420
0.2551
-0.6199
-0.7325
0.6296
0.2590
Axis
1.0000
0.0000
-0.0000
-0.7071
0.6539
0.2691
-0.0000
-0.9247
-0.3806
-0.6808
-0.6774
-0.2788
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