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 CrIr3 (Materials Project id mp-12083)

       521      200      200        0        0        0  
       200      521      200        0        0        0  
       200      200      521        0        0        0  
         0        0        0      259        0        0  
         0        0        0        0      259        0  
         0        0        0        0        0      259  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 307 GPaEV = 531.96 GPaGV = 219.6 GPaνV = 0.2112
ReussKR = 307 GPaER = 508.94 GPaGR = 207.95 GPaνR = 0.2237
HillKH = 307 GPaEH = 520.51 GPaGH = 213.78 GPaνH = 0.21742

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
259 GPa 259 GPa 259 GPa 321 GPa 321 GPa 921 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 410.04 GPa 606.46 GPa 1.0858 TPa–1 1.0858 TPa–1 160.5 GPa 259 GPa0.0455560.36639Value
Anisotropy 1.479 1.0000 1.614 8.0425Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
0.5773
0.8660
0.0000
0.5000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.7071
-0.0005
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
-0.7071
0.0002
-0.7071
0.0004
1.0000
0.0004
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