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 Tb2Fe2Si2C (Materials Project id mp-6624)

       208       82       74        0      -47        0  
        82      255       78        0       11        0  
        74       78      217        0        9        0  
         0        0        0       92        0       15  
       -47       11        9        0       92        0  
         0        0        0       15        0       93  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 127.56 GPaEV = 208.92 GPaGV = 85.133 GPaνV = 0.22702
ReussKR = 124.71 GPaER = 189.75 GPaGR = 76.117 GPaνR = 0.24642
HillKH = 126.13 GPaEH = 199.39 GPaGH = 80.625 GPaνH = 0.23653

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
62.173 GPa 77.492 GPa 107.51 GPa 153.96 GPa 170.31 GPa 385.56 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 113.15 GPa 265.07 GPa 1.9657 TPa–1 3.7062 TPa–1 48.183 GPa 113.54 GPa0.0113120.49363Value
Anisotropy 2.343 1.8854 2.356 43.6396Anisotropy
Axis 0.9355
0.0000
0.3534
-0.8382
0.0000
0.5453
0.0000
1.0000
0.0000
0.8548
-0.0000
0.5189
-0.8919
-0.0000
0.4522
-0.3163
0.4815
0.8174
0.4534
-0.0000
0.8913
-0.3231
0.4544
0.8301
Axis
-0.4522
0.0001
-0.8919
-0.9238
-0.3524
-0.1500
-0.8913
0.0000
0.4534
-0.9463
-0.1666
-0.2771
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