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 TmS (Materials Project id mp-1766)

       248       30       30        0        0        0  
        30      248       30        0        0        0  
        30       30      248        0        0        0  
         0        0        0       22        0        0  
         0        0        0        0       22        0  
         0        0        0        0        0       22  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 102.67 GPaEV = 143.87 GPaGV = 56.8 GPaνV = 0.26645
ReussKR = 102.67 GPaER = 87.747 GPaGR = 32.318 GPaνR = 0.35755
HillKH = 102.67 GPaEH = 116.78 GPaGH = 44.559 GPaνH = 0.31042

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
22 GPa 22 GPa 22 GPa 218 GPa 218 GPa 308 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 61.6 GPa 241.53 GPa 3.2468 TPa–1 3.2468 TPa–1 22 GPa 109 GPa0.0338220.72041Value
Anisotropy 3.921 1.0000 4.955 21.3000Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.5624
0.7330
-0.3827
0.9239
0.0000
0.3827
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.0000
0.7071
0.7071
-0.0002
0.7072
Axis
-0.7880
0.6157
-0.0000
-0.7071
-0.0002
-0.7071
-0.0000
-1.0000
-0.0000
0.7072
-0.0005
-0.7071
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