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 LaAl4 (Materials Project id mp-21109)

        89       47       64        0        0        0  
        47       89       64        0        0        0  
        64       64      126        0        0        0  
         0        0        0       31        0        0  
         0        0        0        0       31        0  
         0        0        0        0        0       46  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 72.667 GPaEV = 79.576 GPaGV = 30.2 GPaνV = 0.31749
ReussKR = 67.758 GPaER = 72.387 GPaGR = 27.379 GPaνR = 0.32195
HillKH = 70.212 GPaEH = 75.983 GPaGH = 28.789 GPaνH = 0.31963

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
31 GPa 31 GPa 40.352 GPa 42 GPa 46 GPa 221.65 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 52.774 GPa 89.152 GPa 0.89445 TPa–1 6.932 TPa–1 20.633 GPa 46 GPa-0.128940.57343Value
Anisotropy 1.689 7.7500 2.229Anisotropy
Axis 0.0000
1.0000
0.0000
0.5657
0.5657
0.6000
0.0000
0.0000
1.0000
0.5000
0.8660
0.0000
0.7071
-0.0000
-0.7071
1.0000
-0.0000
0.0000
-0.7071
0.7071
-0.0000
-0.7071
0.7071
-0.0000
Axis
-0.7071
0.0002
-0.7071
0.0000
1.0000
-0.0000
-0.7071
-0.7071
-0.0000
0.0004
0.0003
-1.0000
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