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 SrAl2O4 (Materials Project id mp-3094)

       130       39       53        0       -0        0  
        39      138       66        0        4        0  
        53       66      157        0       -7        0  
         0        0        0       40        0       -3  
        -0        4       -7        0       53        0  
         0        0        0       -3        0       46  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 82.333 GPaEV = 115.48 GPaGV = 45.6 GPaνV = 0.26623
ReussKR = 80.457 GPaER = 112.76 GPaGR = 44.519 GPaνR = 0.26642
HillKH = 81.395 GPaEH = 114.12 GPaGH = 45.059 GPaνH = 0.26633

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
38.757 GPa 47.243 GPa 50.91 GPa 81.393 GPa 95.602 GPa 250.1 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 106.08 GPa 138.46 GPa 2.7253 TPa–1 5.2431 TPa–1 38.611 GPa 53.984 GPa0.130570.40185Value
Anisotropy 1.305 1.9238 1.398 3.0777Anisotropy
Axis -0.5325
0.8424
-0.0830
-0.5744
0.0000
0.8186
-0.0046
-0.0000
1.0000
1.0000
0.0000
0.0046
0.1928
0.7071
0.6803
0.9839
-0.0000
-0.1786
0.0001
1.0000
0.0000
0.0182
0.0000
0.9998
Axis
-0.1928
0.7071
-0.6803
-0.1786
0.0001
-0.9839
-0.9691
0.0001
0.2467
0.0000
1.0000
-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