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-5492)

       150       70       40        0        0        0  
        70      150       40        0        0        0  
        40       40      123        0        0        0  
         0        0        0       40        0        0  
         0        0        0        0       40        0  
         0        0        0        0        0       40  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 80.333 GPaEV = 107.74 GPaGV = 42.2 GPaνV = 0.27648
ReussKR = 77.974 GPaER = 105.95 GPaGR = 41.597 GPaνR = 0.27353
HillKH = 79.154 GPaEH = 106.84 GPaGH = 41.898 GPaνH = 0.27503

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
40 GPa 40 GPa 40 GPa 80 GPa 96.987 GPa 246.01 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 100.66 GPa 113.28 GPa 3.4786 TPa–1 5.8676 TPa–1 40 GPa 46.727 GPa0.181820.41602Value
Anisotropy 1.125 1.6867 1.168 2.2881Anisotropy
Axis 0.6208
0.2449
0.7447
1.0000
0.0002
0.0000
0.2588
0.9659
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5955
0.3812
0.7071
0.0000
0.0000
1.0000
0.7704
0.6376
0.0000
Axis
-0.7660
0.6428
-0.0000
0.5955
0.3812
-0.7071
0.1736
0.9848
-0.0000
-0.6376
0.7704
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