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 Al9Co2 (Materials Project id mp-16488)

       215       57       46        0       11        0  
        57      212       59        0       -3        0  
        46       59      208        0       16        0  
         0        0        0       72        0       -3  
        11       -3       16        0       62        0  
         0        0        0       -3        0       83  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 106.56 GPaEV = 182.11 GPaGV = 74.933 GPaνV = 0.21515
ReussKR = 105.32 GPaER = 178.13 GPaGR = 73.115 GPaνR = 0.21813
HillKH = 105.94 GPaEH = 180.12 GPaGH = 74.024 GPaνH = 0.21663

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
59.007 GPa 71.235 GPa 83.765 GPa 151.28 GPa 166.12 GPa 320.59 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 132.72 GPa 198.61 GPa 2.6458 TPa–1 3.9574 TPa–1 59.478 GPa 83.765 GPa0.11640.35176Value
Anisotropy 1.496 1.4957 1.408 3.0219Anisotropy
Axis -0.6616
-0.0000
0.7499
0.9846
-0.0000
0.1748
0.7449
-0.0000
0.6671
-0.6671
0.0000
0.7449
-0.0391
0.3539
0.9345
0.0000
1.0000
0.0000
-0.2219
0.5533
0.8029
-0.7493
-0.0002
-0.6622
Axis
-0.8904
-0.4367
0.1281
-0.9690
0.0000
0.2471
-0.8219
-0.5492
0.1513
0.6622
-0.0000
-0.7493
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