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 Y2O3 (Materials Project id mp-2652)

       207      103      103        0        0        0  
       103      207      103        0        0        0  
       103      103      207        0        0        0  
         0        0        0       69        0        0  
         0        0        0        0       69        0  
         0        0        0        0        0       69  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 137.67 GPaEV = 162.18 GPaGV = 62.2 GPaνV = 0.30366
ReussKR = 137.67 GPaER = 159.5 GPaGR = 61.02 GPaνR = 0.30691
HillKH = 137.67 GPaEH = 160.84 GPaGH = 61.61 GPaνH = 0.30528

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
69 GPa 69 GPa 69 GPa 104 GPa 104 GPa 413 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 138.55 GPa 177.37 GPa 2.4213 TPa–1 2.4213 TPa–1 52 GPa 69 GPa0.201150.39749Value
Anisotropy 1.28 1.0000 1.327 1.9761Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.3696
0.8924
0.2588
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
-0.0001
0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
0.7071
-0.0006
-0.7071
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