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 BeO (Materials Project id mp-1778)

       235       91       91        0        0        0  
        91      235       91        0        0        0  
        91       91      235        0        0        0  
         0        0        0      192        0        0  
         0        0        0        0      192        0  
         0        0        0        0        0      192  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 139 GPaEV = 321.11 GPaGV = 144 GPaνV = 0.11497
ReussKR = 139 GPaER = 270.79 GPaGR = 115.2 GPaνR = 0.17531
HillKH = 139 GPaEH = 296.61 GPaGH = 129.6 GPaνH = 0.14435

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
144 GPa 144 GPa 192 GPa 192 GPa 192 GPa 417 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 184.2 GPa 394.4 GPa 2.3981 TPa–1 2.3981 TPa–1 72 GPa 192 GPa-0.200890.46503Value
Anisotropy 2.141 1.0000 2.667Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.8660
0.0000
0.5000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.7071
-0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.7660
0.6428
-0.0000
0.7071
-0.0005
-0.7071
-0.0000
-1.0000
-0.0000
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