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 CeAl3 (Materials Project id mp-567305)

        99       33       35        0        0        0  
        33       99       35        0        0        0  
        35       35      157        0        0        0  
         0        0        0       73        0        0  
         0        0        0        0       73        0  
         0        0        0        0        0       33  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 62.333 GPaEV = 123.16 GPaGV = 52.6 GPaνV = 0.1707
ReussKR = 59.719 GPaER = 109.99 GPaGR = 46.096 GPaνR = 0.19304
HillKH = 61.026 GPaEH = 116.61 GPaGH = 49.348 GPaνH = 0.18153

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
33 GPa 66 GPa 73 GPa 73 GPa 93.449 GPa 195.55 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 84.236 GPa 150.26 GPa 3.3928 TPa–1 6.6762 TPa–1 33 GPa 73 GPa-0.0542830.35974Value
Anisotropy 1.784 1.9677 2.212Anisotropy
Axis 0.9914
0.1305
0.0000
0.4802
0.1325
0.8671
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.9573
0.2890
0.0000
0.0000
0.0000
1.0000
0.5206
0.4647
-0.7162
0.3099
0.5980
-0.7391
Axis
-0.2890
0.9573
-0.0000
0.5000
0.8660
-0.0000
-0.5343
-0.4770
-0.6979
-0.8878
0.4601
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