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 YAlO3 (Materials Project id mp-3792)

       288      127      118        0        0        0  
       127      316      133        0        0        0  
       118      133      355        0        0        0  
         0        0        0      130        0        0  
         0        0        0        0       94        0  
         0        0        0        0        0      152  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 190.56 GPaEV = 285 GPaGV = 113.93 GPaνV = 0.25073
ReussKR = 189.05 GPaER = 274.45 GPaGR = 109.08 GPaνR = 0.25804
HillKH = 189.8 GPaEH = 279.74 GPaGH = 111.51 GPaνH = 0.25436

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
94 GPa 130 GPa 152 GPa 174.22 GPa 210.71 GPa 574.07 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 223.03 GPa 321.37 GPa 1.4788 TPa–1 2.1212 TPa–1 87.23 GPa 152 GPa0.0556510.37522Value
Anisotropy 1.441 1.4344 1.743 6.7423Anisotropy
Axis 1.0000
0.0000
0.0000
0.6856
0.7280
-0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
0.7071
0.0000
1.0000
-0.0001
0.0000
-0.7084
0.7059
-0.0000
-0.4117
0.7080
-0.5739
Axis
-0.7071
0.7071
0.0000
0.0001
1.0000
-0.0000
-0.7059
-0.7084
-0.0000
-0.7347
0.1148
0.6686
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