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 Ca2SiO4 (Materials Project id mp-758006)

       184       69       72        0        0        0  
        69      134       68        0        0        0  
        72       68      163        0        0        0  
         0        0        0       54        0        0  
         0        0        0        0       36        0  
         0        0        0        0        0       42  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 99.889 GPaEV = 116.31 GPaGV = 44.533 GPaνV = 0.30593
ReussKR = 97.983 GPaER = 113.21 GPaGR = 43.294 GPaνR = 0.30744
HillKH = 98.936 GPaEH = 114.76 GPaGH = 43.914 GPaνH = 0.30667

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
36 GPa 42 GPa 54 GPa 77.082 GPa 101.95 GPa 301.97 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 95.657 GPa 137.82 GPa 2.4909 TPa–1 4.5987 TPa–1 36 GPa 54 GPa0.172820.44377Value
Anisotropy 1.441 1.8462 1.5 2.5679Anisotropy
Axis 0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0001
0.0002
1.0000
0.4086
0.7067
0.5776
0.7042
0.4467
0.5519
Axis
1.0000
0.0000
-0.0000
-0.0000
1.0000
-0.0002
-0.3047
0.7021
-0.6436
-0.7022
0.3236
0.6342
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