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 Cr3Ru (Materials Project id mp-1272)

       411      191      191        0        0        0  
       191      411      191        0        0        0  
       191      191      411        0        0        0  
         0        0        0       87        0        0  
         0        0        0        0       87        0  
         0        0        0        0        0       87  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 264.33 GPaEV = 257.38 GPaGV = 96.2 GPaνV = 0.33772
ReussKR = 264.33 GPaER = 254.37 GPaGR = 94.94 GPaνR = 0.33962
HillKH = 264.33 GPaEH = 255.87 GPaGH = 95.57 GPaνH = 0.33867

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
87 GPa 87 GPa 87 GPa 220 GPa 220 GPa 793 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 235.2 GPa 289.8 GPa 1.261 TPa–1 1.261 TPa–1 87 GPa 110 GPa0.270220.41852Value
Anisotropy 1.232 1.0000 1.264 1.5488Anisotropy
Axis 0.5774
0.5773
-0.5774
1.0000
0.0000
0.0000
0.8660
0.0000
0.5000
0.0000
0.0000
1.0000
-0.0000
-0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
-0.0001
0.7071
0.7071
-0.0002
0.7071
Axis
1.0000
0.0002
0.0000
0.7071
-0.0005
-0.7071
0.0000
1.0000
0.0000
0.7071
-0.0005
-0.7071
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