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 TePdI (Materials Project id mp-29748)

        69       13       13        0        0        0  
        13       44       12        0        0        0  
        13       12       44        0        0        0  
         0        0        0       10        0        0  
         0        0        0        0        8        0  
         0        0        0        0        0        8  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 25.889 GPaEV = 33.701 GPaGV = 13.133 GPaνV = 0.28304
ReussKR = 24.831 GPaER = 28.644 GPaGR = 10.952 GPaνR = 0.30774
HillKH = 25.36 GPaEH = 31.19 GPaGH = 12.042 GPaνH = 0.29502

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
8 GPa 8 GPa 10 GPa 32 GPa 43 GPa 82 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 23.038 GPa 62.964 GPa 8.5082 TPa–1 15.882 TPa–1 8 GPa 20.549 GPa0.105990.5791Value
Anisotropy 2.733 1.8667 2.569 5.4636Anisotropy
Axis 0.5991
0.5662
-0.5662
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
-0.0000
0.7071
0.7071
-0.7654
0.6435
-0.0000
Axis
1.0000
0.0000
-0.0000
0.7071
-0.0006
-0.7071
-1.0000
-0.0000
0.0000
-0.6435
-0.7654
0.0001
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