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 GdBO3 (Materials Project id mp-561949)

       200       92       63        0        0        0  
        92      200       63        0        0        0  
        63       63      196        0        0        0  
         0        0        0        8        0        0  
         0        0        0        0        8        0  
         0        0        0        0        0       54  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 114.67 GPaEV = 105.57 GPaGV = 39.2 GPaνV = 0.34656
ReussKR = 114.11 GPaER = 47.528 GPaGR = 16.612 GPaνR = 0.43058
HillKH = 114.39 GPaEH = 77.422 GPaGH = 27.906 GPaνH = 0.38719

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
8 GPa 8 GPa 54 GPa 108 GPa 142.8 GPa 345.2 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 29.632 GPa 168.82 GPa 2.6981 TPa–1 3.3675 TPa–1 8 GPa 66.236 GPa0.0559610.85221Value
Anisotropy 5.697 1.2481 8.28 15.2287Anisotropy
Axis 0.7039
0.0878
0.7049
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.4023
0.5815
-0.7071
-0.3703
0.5051
0.7795
0.3773
0.5826
0.7199
Axis
1.0000
0.0000
-0.0000
0.4024
-0.5815
-0.7071
-0.8065
-0.5913
-0.0000
0.3915
0.6041
-0.6941
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