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 Al4W (Materials Project id mp-30336)

       261       61       47        0        3        0  
        61      224       61        0        1        0  
        47       61      230        0       15        0  
         0        0        0       69        0      -13  
         3        1       15        0       74        0  
         0        0        0      -13        0       69  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 117 GPaEV = 193.06 GPaGV = 78.8 GPaνV = 0.22499
ReussKR = 116.12 GPaER = 186.44 GPaGR = 75.643 GPaνR = 0.23241
HillKH = 116.56 GPaEH = 189.76 GPaGH = 77.221 GPaνH = 0.22867

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
56 GPa 72.392 GPa 82 GPa 163.99 GPa 200.09 GPa 352.53 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 154.53 GPa 240.07 GPa 2.3898 TPa–1 3.3047 TPa–1 56 GPa 100.36 GPa0.0598890.39723Value
Anisotropy 1.554 1.3829 1.792 6.6327Anisotropy
Axis 0.5104
0.7156
0.4770
1.0000
0.0000
0.0087
0.8766
-0.0000
0.4812
-0.4811
-0.0000
0.8766
-0.7071
-0.0000
-0.7071
-0.6184
0.0000
0.7859
0.0282
0.4744
-0.8799
0.1759
0.6490
0.7402
Axis
-0.0000
-1.0000
0.0000
-0.7859
-0.0001
-0.6184
-0.8859
0.4195
0.1978
-0.4231
0.7288
-0.5384
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