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 Al13Os4 (Materials Project id mp-567929)

       229       84      108        0       -2        0  
        84      285      107        0      -19        0  
       108      107      218        0       11        0  
         0        0        0       86        0       -3  
        -2      -19       11        0      114        0  
         0        0        0       -3        0       57  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 147.78 GPaEV = 203.89 GPaGV = 80.267 GPaνV = 0.27005
ReussKR = 146.69 GPaER = 188.96 GPaGR = 73.508 GPaνR = 0.28531
HillKH = 147.24 GPaEH = 196.46 GPaGH = 76.888 GPaνH = 0.27761

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
56.693 GPa 86.307 GPa 97.132 GPa 123.96 GPa 179.33 GPa 445.57 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 144.5 GPa 266.31 GPa 1.863 TPa–1 2.5737 TPa–1 54.444 GPa 112.94 GPa0.0456680.48518Value
Anisotropy 1.843 1.3815 2.074 10.6242Anisotropy
Axis 0.1013
0.0000
-0.9949
0.6973
-0.0000
0.7167
0.0000
1.0000
0.0000
0.9407
-0.0000
0.3391
-0.5344
0.3740
-0.7580
-0.0692
0.0000
0.9976
0.5457
0.3485
0.7621
-0.5466
0.5656
0.6175
Axis
0.6570
-0.3804
-0.6509
-0.9976
0.0000
-0.0692
-0.6281
-0.4318
0.6473
-0.6409
-0.7572
0.1261
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