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 TbCo5 (Materials Project id mp-1200)

       189      121      113        0        0        3  
       121      190      113        0        0       -4  
       113      113      268        0        0       -0  
         0        0        0       48        0        0  
         0        0        0        0       48        0  
         3       -4       -0        0        0       38  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 149 GPaEV = 127.09 GPaGV = 46.8 GPaνV = 0.35784
ReussKR = 146.2 GPaER = 120.38 GPaGR = 44.166 GPaνR = 0.36277
HillKH = 147.6 GPaEH = 123.74 GPaGH = 45.483 GPaνH = 0.36028

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
37.214 GPa 48 GPa 48 GPa 69.28 GPa 128.04 GPa 450.46 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 98.958 GPa 185.75 GPa 1.4649 TPa–1 2.7252 TPa–1 32.154 GPa 56.362 GPa0.193870.5402Value
Anisotropy 1.877 1.8603 1.753 2.7864Anisotropy
Axis 0.2766
0.9610
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.8457
0.5336
-0.0000
-0.4931
0.8700
0.0000
-0.3498
0.6145
0.7071
-0.9605
0.2784
-0.0000
-0.9605
0.2783
0.0000
Axis
-0.8700
-0.4931
0.0000
-0.3496
0.6146
-0.7071
-0.0000
-0.0000
1.0000
-0.2783
-0.9605
-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