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 CaIr2 (Materials Project id mp-570436)

       220      134      134        0        0        0  
       134      220      134        0        0        0  
       134      134      220        0        0        0  
         0        0        0       73        0        0  
         0        0        0        0       73        0  
         0        0        0        0        0       73  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 162.67 GPaEV = 162.67 GPaGV = 61 GPaνV = 0.33333
ReussKR = 162.67 GPaER = 153.29 GPaGR = 57.073 GPaνR = 0.34294
HillKH = 162.67 GPaEH = 158 GPaGH = 59.036 GPaνH = 0.33812

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
73 GPa 73 GPa 73 GPa 86 GPa 86 GPa 488 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 118.55 GPa 190.5 GPa 2.0492 TPa–1 2.0492 TPa–1 43 GPa 73 GPa0.132920.52813Value
Anisotropy 1.607 1.0000 1.698 3.9732Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.9239
0.0000
0.3827
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.7071
-0.0001
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.5000
0.8660
-0.0000
-0.7071
0.0002
-0.7071
0.0001
1.0000
0.0001
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