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 Y3Al5O12 (Materials Project id mp-3050)

       304      104      104        0        0        0  
       104      304      104        0        0        0  
       104      104      304        0        0        0  
         0        0        0      104        0        0  
         0        0        0        0      104        0  
         0        0        0        0        0      104  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 170.67 GPaEV = 256 GPaGV = 102.4 GPaνV = 0.25
ReussKR = 170.67 GPaER = 255.92 GPaGR = 102.36 GPaνR = 0.25008
HillKH = 170.67 GPaEH = 255.96 GPaGH = 102.38 GPaνH = 0.25004

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
104 GPa 104 GPa 104 GPa 200 GPa 200 GPa 512 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 250.98 GPa 259.32 GPa 1.9531 TPa–1 1.9531 TPa–1 100 GPa 104 GPa0.236480.26121Value
Anisotropy 1.033 1.0000 1.04 1.1046Anisotropy
Axis 1.0000
0.0000
0.0000
0.5774
0.5773
-0.5774
0.0000
0.0000
1.0000
0.7934
0.0000
0.6088
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
-0.7071
0.0000
0.7071
Axis
0.7071
-0.0005
-0.7071
-0.5000
0.8660
-0.0000
0.7071
-0.0006
-0.7071
-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