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 B2O3 (Materials Project id mp-717)

       301       87       80        0        0        0  
        87      504       90        0        0        0  
        80       90      495        0        0        0  
         0        0        0      125        0        0  
         0        0        0        0      170        0  
         0        0        0        0        0      140  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 201.56 GPaEV = 373.03 GPaGV = 156.53 GPaνV = 0.19154
ReussKR = 190.62 GPaER = 356.71 GPaGR = 150.12 GPaνR = 0.18812
HillKH = 196.09 GPaEH = 364.87 GPaGH = 153.32 GPaνH = 0.18987

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
125 GPa 140 GPa 170 GPa 258.76 GPa 409.41 GPa 631.83 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 277.31 GPa 469.41 GPa 1.2938 TPa–1 2.5849 TPa–1 125 GPa 204.7 GPa0.0726850.36961Value
Anisotropy 1.693 1.9980 1.638 5.0851Anisotropy
Axis 1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0001
0.7071
0.7071
0.7258
0.4043
-0.5566
-0.0001
0.7086
0.7056
Axis
-0.0000
1.0000
-0.0000
0.0001
0.7071
-0.7071
-0.6864
0.3722
-0.6248
0.0000
0.7056
-0.7086
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