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 TlPd3 (Materials Project id mp-571030)

       173       99      124        0        0        0  
        99      173      124        0        0        0  
       124      124      159        0        0        0  
         0        0        0       63        0        0  
         0        0        0        0       63        0  
         0        0        0        0        0       42  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 133.22 GPaEV = 119.23 GPaGV = 44.133 GPaνV = 0.35083
ReussKR = 132.94 GPaER = 94.288 GPaGR = 34.118 GPaνR = 0.38179
HillKH = 133.08 GPaEH = 106.9 GPaGH = 39.126 GPaνH = 0.36612

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
31.26 GPa 42 GPa 63 GPa 63 GPa 74 GPa 399.74 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 45.941 GPa 144.09 GPa 1.9206 TPa–1 2.8009 TPa–1 18.271 GPa 63 GPa-0.0332660.80582Value
Anisotropy 3.136 1.4583 3.448Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5587
0.5587
0.6130
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
0.0001
-0.7071
-0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
0.7071
0.7071
-0.0000
Axis
-0.7071
-0.0002
-0.7071
1.0000
0.0001
0.0000
-0.7071
0.7071
-0.0000
0.0001
-0.0001
-1.0000
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