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 LiMg2 (Materials Project id mp-865939)

        43       21       24        0        0        0  
        21       43       24        0        0        0  
        24       24       44        0        0        0  
         0        0        0       37        0        0  
         0        0        0        0       37        0  
         0        0        0        0        0       35  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 29.778 GPaEV = 60.176 GPaGV = 25.867 GPaνV = 0.16319
ReussKR = 29.714 GPaER = 44.511 GPaGR = 17.8 GPaνR = 0.25034
HillKH = 29.746 GPaEH = 52.624 GPaGH = 21.833 GPaνH = 0.20515

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
18.616 GPa 22 GPa 35 GPa 37 GPa 37 GPa 89.384 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 26 GPa 77.511 GPa 9.6154 TPa–1 12.019 TPa–1 9.6847 GPa 37 GPa-0.298480.70826Value
Anisotropy 2.981 1.2500 3.82Anisotropy
Axis 0.0000
0.0000
1.0000
0.5698
0.5697
0.5923
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
-0.7071
0.7071
0.0000
0.7071
0.7071
-0.0000
Axis
0.7071
-0.0005
-0.7071
-0.9397
-0.3420
0.0000
-0.7071
-0.7071
-0.0000
0.0005
-0.0005
-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