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 Er2Si2O7 (Materials Project id mp-7064)

       292      122      131        0      -15        0  
       122      228      123        0       39        0  
       131      123      215        0       -6        0  
         0        0        0       72        0       27  
       -15       39       -6        0       93        0  
         0        0        0       27        0       66  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 165.22 GPaEV = 184.32 GPaGV = 70.133 GPaνV = 0.31407
ReussKR = 161.27 GPaER = 157.08 GPaGR = 58.715 GPaνR = 0.33766
HillKH = 163.25 GPaEH = 170.8 GPaGH = 64.424 GPaνH = 0.32562

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
41.834 GPa 61.037 GPa 96.166 GPa 108.93 GPa 158.81 GPa 499.22 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 111.4 GPa 273.61 GPa 1.1444 TPa–1 2.534 TPa–1 39.374 GPa 106.84 GPa0.0802770.66262Value
Anisotropy 2.456 2.2142 2.714 8.2542Anisotropy
Axis -0.4233
0.8350
0.3515
0.8162
-0.0000
-0.5778
0.9641
0.0000
0.2656
0.0000
1.0000
0.0000
-0.3133
0.7071
-0.6339
-0.2369
0.5130
0.8251
-0.0000
1.0000
-0.0000
0.7324
-0.0001
0.6808
Axis
-0.3133
-0.7071
-0.6339
-0.8717
-0.4872
0.0526
-0.8240
-0.0000
0.5666
0.0001
1.0000
0.0001
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