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 YbSe (Materials Project id mp-286)

       121       17       17        0        0        0  
        17      121       17        0        0        0  
        17       17      121        0        0        0  
         0        0        0       28        0        0  
         0        0        0        0       28        0  
         0        0        0        0        0       28  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 51.667 GPaEV = 90.779 GPaGV = 37.6 GPaνV = 0.20717
ReussKR = 51.667 GPaER = 84.335 GPaGR = 34.34 GPaνR = 0.22795
HillKH = 51.667 GPaEH = 87.584 GPaGH = 35.97 GPaνH = 0.21747

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
28 GPa 28 GPa 28 GPa 104 GPa 104 GPa 155 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 71.148 GPa 116.81 GPa 6.4516 TPa–1 6.4516 TPa–1 28 GPa 52 GPa0.0831590.40811Value
Anisotropy 1.642 1.0000 1.857 4.9076Anisotropy
Axis -0.5774
0.5774
-0.5773
1.0000
0.0000
0.0000
0.8660
0.0000
0.5000
0.0000
0.0000
1.0000
-0.0000
-0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.0000
0.7071
0.7071
-0.0002
0.7071
Axis
1.0000
0.0002
0.0000
-0.7071
-0.0002
-0.7071
-0.0000
-1.0000
0.0000
0.7071
-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