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 Sc3Al (Materials Project id mp-978498)

        86       35       35        0        0        0  
        35       86       35        0        0        0  
        35       35       86        0        0        0  
         0        0        0       45        0        0  
         0        0        0        0       45        0  
         0        0        0        0        0       45  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 52 GPaEV = 90.112 GPaGV = 37.2 GPaνV = 0.21118
ReussKR = 52 GPaER = 84.674 GPaGR = 34.459 GPaνR = 0.22861
HillKH = 52 GPaEH = 87.412 GPaGH = 35.83 GPaνH = 0.21983

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
45 GPa 45 GPa 45 GPa 51 GPa 51 GPa 156 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 65.752 GPa 104.78 GPa 6.4103 TPa–1 6.4103 TPa–1 25.5 GPa 45 GPa0.0137610.40138Value
Anisotropy 1.594 1.0000 1.765 29.1666Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.6088
0.0000
0.7934
0.7071
0.0001
-0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.7071
-0.0001
0.7071
Axis
-0.7071
-0.0002
-0.7071
-1.0000
0.0000
-0.0000
-0.7071
0.0002
-0.7071
0.0001
1.0000
0.0001
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