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 TbPPt (Materials Project id mp-7168)

       224      139       69        0        0        0  
       139      224       69        0        0        0  
        69       69      133        0        0        0  
         0        0        0       53        0        0  
         0        0        0        0       53        0  
         0        0        0        0        0       42  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 126.11 GPaEV = 132.18 GPaGV = 49.867 GPaνV = 0.32532
ReussKR = 109.79 GPaER = 125.23 GPaGR = 47.802 GPaνR = 0.3099
HillKH = 117.95 GPaEH = 128.74 GPaGH = 48.834 GPaνH = 0.31809

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
42 GPa 53 GPa 53 GPa 85 GPa 97.179 GPa 398.82 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 106.77 GPa 131.61 GPa 1.6513 TPa–1 5.8054 TPa–1 42 GPa 53 GPa0.165110.55248Value
Anisotropy 1.233 3.5156 1.262 3.3462Anisotropy
Axis 0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.2588
0.9659
0.0000
0.0000
0.0000
1.0000
1.0000
-0.0002
0.0000
0.0000
0.0000
1.0000
-0.4487
0.4488
0.7728
-0.7071
0.7072
0.0000
Axis
0.0002
1.0000
0.0000
0.7660
0.6428
-0.0000
-0.5465
0.5464
-0.6346
-0.7072
-0.7071
-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