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 Ho2O3 (Materials Project id mp-812)

       219      108      108        0        0        0  
       108      219      108        0        0        0  
       108      108      219        0        0        0  
         0        0        0       73        0        0  
         0        0        0        0       73        0  
         0        0        0        0        0       73  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 145 GPaEV = 171.92 GPaGV = 66 GPaνV = 0.3024
ReussKR = 145 GPaER = 169.25 GPaGR = 64.824 GPaνR = 0.30546
HillKH = 145 GPaEH = 170.58 GPaGH = 65.412 GPaνH = 0.30393

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
73 GPa 73 GPa 73 GPa 111 GPa 111 GPa 435 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 147.66 GPa 187.53 GPa 2.2989 TPa–1 2.2989 TPa–1 55.5 GPa 73 GPa0.203230.39293Value
Anisotropy 1.27 1.0000 1.315 1.9334Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
-0.1206
0.9160
0.3827
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.7071
-0.0004
-0.7071
Axis
-0.7071
-0.0002
-0.7071
0.5000
0.8660
-0.0000
-0.7071
0.0002
-0.7071
0.0002
1.0000
-0.0003
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