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 Ti3O5 (Materials Project id mp-1147)

       217      145       91        0       -3        0  
       145      392      131        0       16        0  
        91      131      280        0       32        0  
         0        0        0       74        0       -4  
        -3       16       32        0       90        0  
         0        0        0       -4        0       58  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 180.33 GPaEV = 207.26 GPaGV = 79.2 GPaνV = 0.30845
ReussKR = 162.37 GPaER = 191.38 GPaGR = 73.409 GPaνR = 0.30356
HillKH = 171.35 GPaEH = 199.33 GPaGH = 76.304 GPaνH = 0.30613

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
57.056 GPa 74.944 GPa 80.793 GPa 136.51 GPa 197.13 GPa 564.57 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 148.62 GPa 273.92 GPa 0.61961 TPa–1 3.3711 TPa–1 57.056 GPa 99.948 GPa0.0667390.56187Value
Anisotropy 1.843 5.4407 1.752 8.4189Anisotropy
Axis 0.9817
-0.0000
0.1906
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.9276
-0.0000
-0.3735
0.9733
-0.0000
0.2297
0.2954
0.0001
-0.9554
0.8883
0.0000
-0.4594
0.0000
1.0000
-0.0000
Axis
0.0000
1.0000
0.0000
-0.9554
-0.0003
-0.2954
-0.4594
-0.0000
-0.8883
-0.9856
0.0000
-0.1691
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