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 Er2Al3Si2 (Materials Project id mp-12004)

       174       54       35        0       -2        0  
        54      161       64        0        5        0  
        35       64      157        0        4        0  
         0        0        0       86        0        5  
        -2        5        4        0       65        0  
         0        0        0        5        0       64  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 88.667 GPaEV = 157.87 GPaGV = 65.6 GPaνV = 0.20326
ReussKR = 88.257 GPaER = 152.36 GPaGR = 62.838 GPaνR = 0.21229
HillKH = 88.462 GPaEH = 155.12 GPaGH = 64.219 GPaνH = 0.20774

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
62.917 GPa 64.443 GPa 87.083 GPa 92.078 GPa 133.86 GPa 266.62 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 125.16 GPa 189.04 GPa 3.2546 TPa–1 4.2816 TPa–1 46.916 GPa 87.083 GPa0.0678890.3885Value
Anisotropy 1.51 1.3156 1.856 5.7225Anisotropy
Axis 0.0000
1.0000
0.0000
0.2147
0.6868
0.6944
0.0000
1.0000
0.0000
0.4448
0.0000
-0.8956
-0.0544
0.7071
-0.7050
0.2118
0.0002
0.9773
-0.3726
-0.0000
-0.9280
0.3929
-0.0000
0.9196
Axis
-0.0544
-0.7071
-0.7050
-0.0001
1.0000
-0.0002
0.9280
0.0000
-0.3726
-0.0000
1.0000
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