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 Lu3Al (Materials Project id mp-973266)

        99       39       36        0        0        0  
        39       99       36        0        0        0  
        36       36       77        0        0        0  
         0        0        0       37        0        0  
         0        0        0        0       37        0  
         0        0        0        0        0       30  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 55.222 GPaEV = 79.896 GPaGV = 31.733 GPaνV = 0.25887
ReussKR = 54.284 GPaER = 77.855 GPaGR = 30.871 GPaνR = 0.26096
HillKH = 54.753 GPaEH = 78.876 GPaGH = 31.302 GPaνH = 0.2599

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
30 GPa 37 GPa 37 GPa 48.151 GPa 60 GPa 166.85 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 58.217 GPa 85.059 GPa 5.1033 TPa–1 8.2151 TPa–1 25.468 GPa 37 GPa0.117140.33256Value
Anisotropy 1.461 1.6098 1.453 2.8391Anisotropy
Axis 0.0000
0.0000
1.0000
0.2598
0.7733
0.5783
0.3827
0.9239
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
-0.5608
0.4044
-0.7225
0.7035
0.2350
-0.6708
Axis
0.7071
-0.0005
-0.7071
-0.9397
-0.3420
0.0000
-0.5860
0.4226
0.6914
-0.3169
0.9485
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