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 AsPd5 (Materials Project id mp-2512)

       210      129      112        0        1        0  
       129      201      125        0      -16        0  
       112      125      222        0       -0        0  
         0        0        0       49        0      -11  
         1      -16       -0        0       33        0  
         0        0        0      -11        0       59  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 151.67 GPaEV = 125.33 GPaGV = 46 GPaνV = 0.36228
ReussKR = 150.82 GPaER = 113.91 GPaGR = 41.449 GPaνR = 0.37412
HillKH = 151.25 GPaEH = 119.64 GPaGH = 43.725 GPaνH = 0.36816

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
28.739 GPa 41.917 GPa 66.083 GPa 76.958 GPa 105.09 GPa 455.21 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 73.957 GPa 160.01 GPa 1.5886 TPa–1 2.6776 TPa–1 26.474 GPa 66.083 GPa0.135910.64161Value
Anisotropy 2.164 1.6855 2.496 4.7208Anisotropy
Axis 0.7425
0.0000
-0.6698
0.6069
0.7353
-0.3016
0.6584
-0.0000
-0.7527
0.7526
0.0001
0.6584
0.5314
0.7071
-0.4665
-0.8408
-0.0000
0.5414
0.0000
1.0000
-0.0000
-0.0000
1.0000
-0.0000
Axis
-0.5314
0.7071
0.4665
0.0000
-1.0000
0.0000
-0.6425
0.0000
-0.7663
-0.7662
0.0000
0.6426
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