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 LuPd3 (Materials Project id mp-1158)

       176      119      119        0        0        0  
       119      176      119        0        0        0  
       119      119      176        0        0        0  
         0        0        0       77        0        0  
         0        0        0        0       77        0  
         0        0        0        0        0       77  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 138 GPaEV = 151.69 GPaGV = 57.6 GPaνV = 0.31679
ReussKR = 138 GPaER = 123.75 GPaGR = 45.814 GPaνR = 0.35055
HillKH = 138 GPaEH = 137.9 GPaGH = 51.707 GPaνH = 0.33346

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
57 GPa 57 GPa 77 GPa 77 GPa 77 GPa 414 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 79.993 GPa 194.77 GPa 2.4155 TPa–1 2.4155 TPa–1 28.5 GPa 77 GPa-0.0691490.72289Value
Anisotropy 2.435 1.0000 2.702Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.8660
0.0000
0.5000
0.7071
0.0001
-0.7071
-0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.0000
0.7071
-0.7071
Axis
-0.7071
-0.0002
-0.7071
-0.5000
0.8660
-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