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 TbCl2F (Materials Project id mp-560119)

       100       41       52        0        3        0  
        41       62       52        0      -12        0  
        52       52      108        0        5        0  
         0        0        0       47        0       -9  
         3      -12        5        0       11        0  
         0        0        0       -9        0       23  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 62.222 GPaEV = 65.051 GPaGV = 24.533 GPaνV = 0.32576
ReussKR = 46.779 GPaER = 27.535 GPaGR = 9.8208 GPaνR = 0.40189
HillKH = 54.5 GPaEH = 46.632 GPaGH = 17.177 GPaνH = 0.3574

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
3.5041 GPa 20 GPa 34.565 GPa 50 GPa 52.734 GPa 190.2 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 9.7675 GPa 97.311 GPa -15.953 TPa–1 24.394 TPa–1 3.13 GPa 50 GPa-0.771511.3755Value
Anisotropy 9.963 15.97Anisotropy
Axis -0.6598
0.0000
0.7514
0.1387
0.6639
-0.7349
0.6292
0.0000
-0.7773
0.0000
1.0000
0.0000
-0.4635
0.7071
0.5340
-0.3162
0.0000
0.9487
0.8310
-0.0000
0.5563
0.7582
-0.0001
0.6520
Axis
-0.4635
-0.7071
0.5341
-0.0000
-1.0000
0.0000
0.0000
1.0000
0.0000
0.6520
-0.0000
-0.7582
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