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 CeIn3 (Materials Project id mp-20369)

        88       29       29        0        0        0  
        29       88       29        0        0        0  
        29       29       88        0        0        0  
         0        0        0       38        0        0  
         0        0        0        0       38        0  
         0        0        0        0        0       38  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 48.667 GPaEV = 83.914 GPaGV = 34.6 GPaνV = 0.21262
ReussKR = 48.667 GPaER = 82.877 GPaGR = 34.073 GPaνR = 0.21617
HillKH = 48.667 GPaEH = 83.396 GPaGH = 34.336 GPaνH = 0.2144

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
38 GPa 38 GPa 38 GPa 59 GPa 59 GPa 146 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 73.624 GPa 90.457 GPa 6.8493 TPa–1 6.8493 TPa–1 29.5 GPa 38 GPa0.125870.28807Value
Anisotropy 1.229 1.0000 1.288 2.2887Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
0.5773
0.4330
0.7500
0.5000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0005
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.7660
0.6428
-0.0000
0.7071
-0.0006
-0.7071
0.0003
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