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 TbPt2 (Materials Project id mp-1697)

       228      122      122        0        0        0  
       122      228      122        0        0        0  
       122      122      228        0        0        0  
         0        0        0       89        0        0  
         0        0        0        0       89        0  
         0        0        0        0        0       89  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 157.33 GPaEV = 193.26 GPaGV = 74.6 GPaνV = 0.29528
ReussKR = 157.33 GPaER = 182.84 GPaGR = 69.985 GPaνR = 0.30631
HillKH = 157.33 GPaEH = 188.07 GPaGH = 72.293 GPaνH = 0.30077

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
89 GPa 89 GPa 89 GPa 106 GPa 106 GPa 472 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 142.95 GPa 224.64 GPa 2.1186 TPa–1 2.1186 TPa–1 53 GPa 89 GPa0.104260.4793Value
Anisotropy 1.571 1.0000 1.679 4.5969Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.8660
0.0000
0.5000
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
-0.7071
0.0000
-0.7071
Axis
0.7071
-0.0005
-0.7071
-0.7660
0.6428
-0.0000
0.7071
-0.0006
-0.7071
-0.0000
-1.0000
-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