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 Er2SiO5 (Materials Project id mp-16993)

       175      112       35        0      -44        0  
       112      270      106        0       -4        0  
        35      106      201        0       -2        0  
         0        0        0       76        0      -10  
       -44       -4       -2        0       29        0  
         0        0        0      -10        0       57  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 128 GPaEV = 152.52 GPaGV = 58.6 GPaνV = 0.3014
ReussKR = 81.305 GPaER = 89.12 GPaGR = 33.826 GPaνR = 0.31731
HillKH = 104.65 GPaEH = 120.85 GPaGH = 46.213 GPaνH = 0.30754

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
13.016 GPa 52.707 GPa 80.293 GPa 97.351 GPa 160.58 GPa 404.05 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 26.934 GPa 190.75 GPa -1.8468 TPa–1 14.959 TPa–1 13.366 GPa 84.385 GPa-0.35331.4072Value
Anisotropy 7.082 6.314Anisotropy
Axis -0.8220
-0.0000
-0.5694
0.0524
0.6839
0.7277
0.0000
1.0000
0.0000
-0.8182
-0.0000
-0.5749
-0.9839
0.0001
0.1789
0.8222
-0.0000
0.5692
-0.9732
0.0001
0.2301
-0.3164
0.8156
0.4845
Axis
-0.1789
-0.0001
-0.9839
-0.5692
0.0000
0.8222
-0.2301
-0.0001
-0.9732
-0.8344
0.0037
-0.5512
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