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 PaRh3 (Materials Project id mp-30825)

       318      158      158        0        0        0  
       158      318      158        0        0        0  
       158      158      318        0        0        0  
         0        0        0       94        0        0  
         0        0        0        0       94        0  
         0        0        0        0        0       94  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 211.33 GPaEV = 232.75 GPaGV = 88.4 GPaνV = 0.31645
ReussKR = 211.33 GPaER = 231.48 GPaGR = 87.85 GPaνR = 0.31745
HillKH = 211.33 GPaEH = 232.11 GPaGH = 88.125 GPaνH = 0.31695

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
94 GPa 94 GPa 94 GPa 160 GPa 160 GPa 634 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 213.11 GPa 245.59 GPa 1.5773 TPa–1 1.5773 TPa–1 80 GPa 94 GPa0.258370.36848Value
Anisotropy 1.152 1.0000 1.175 1.4262Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.4330
0.7500
0.5000
0.9239
0.0000
0.3827
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
0.7071
-0.0006
-0.7071
0.0000
1.0000
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