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 HoPd3 (Materials Project id mp-1979)

       172      110      110        0        0        0  
       110      172      110        0        0        0  
       110      110      172        0        0        0  
         0        0        0       70        0        0  
         0        0        0        0       70        0  
         0        0        0        0        0       70  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 130.67 GPaEV = 143.31 GPaGV = 54.4 GPaνV = 0.3172
ReussKR = 130.67 GPaER = 124.87 GPaGR = 46.567 GPaνR = 0.34073
HillKH = 130.67 GPaEH = 134.17 GPaGH = 50.483 GPaνH = 0.32886

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
62 GPa 62 GPa 70 GPa 70 GPa 70 GPa 392 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 86.184 GPa 178.18 GPa 2.551 TPa–1 2.551 TPa–1 31 GPa 70 GPa0.00462970.63657Value
Anisotropy 2.067 1.0000 2.258137.4990Anisotropy
Axis 1.0000
0.0000
0.0000
-0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.4330
0.7500
0.5000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.0000
0.7071
0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
-0.7071
0.0002
-0.7071
-1.0000
0.0000
-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