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 V3O5 (Materials Project id mp-622497)

       327      130      112        0      -11        0  
       130      320      111        0        3        0  
       112      111      314        0       -6        0  
         0        0        0       84        0        6  
       -11        3       -6        0       60        0  
         0        0        0        6        0       86  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 185.22 GPaEV = 224.62 GPaGV = 86.533 GPaνV = 0.29788
ReussKR = 184.57 GPaER = 216.11 GPaGR = 82.81 GPaνR = 0.30485
HillKH = 184.9 GPaEH = 220.38 GPaGH = 84.672 GPaνH = 0.30135

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
59.122 GPa 78.917 GPa 91.083 GPa 194.11 GPa 211.43 GPa 556.34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 162.09 GPa 260.42 GPa 1.5872 TPa–1 2.0846 TPa–1 59.277 GPa 104.12 GPa0.159470.52525Value
Anisotropy 1.607 1.3134 1.756 3.2938Anisotropy
Axis 0.7268
-0.0000
0.6868
-0.9955
-0.0000
0.0945
0.8746
-0.0000
-0.4849
-0.4849
0.0000
-0.8746
0.0292
0.0004
0.9996
-0.6862
-0.0002
0.7274
-0.6187
0.0000
0.7857
0.6869
0.0001
-0.7268
Axis
0.9996
-0.0002
-0.0292
-0.7274
0.0000
-0.6862
-0.0000
-1.0000
0.0000
-0.7268
-0.0000
-0.6869
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