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 YbBO3 (Materials Project id mp-5364)

       146       65       60       15        0        0  
        65      146       60      -15        0        0  
        60       60       88        0        0        0  
        15      -15        0       37        0        0  
         0        0        0        0       37       15  
         0        0        0        0       15       41  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 83.333 GPaEV = 94.406 GPaGV = 36 GPaνV = 0.31119
ReussKR = 77.333 GPaER = 80.316 GPaGR = 30.264 GPaνR = 0.32691
HillKH = 80.333 GPaEH = 87.383 GPaGH = 33.132 GPaνH = 0.31871

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
23.867 GPa 28.439 GPa 44.704 GPa 54.133 GPa 89.561 GPa 254.3 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 53.877 GPa 133.68 GPa 2.4631 TPa–1 8.0049 TPa–1 23.109 GPa 54.133 GPa0.110560.66708Value
Anisotropy 2.481 3.2500 2.343 6.0335Anisotropy
Axis 0.0000
0.0000
1.0000
-0.7743
0.4496
0.4453
0.2588
0.9659
0.0000
0.0000
0.0000
1.0000
0.0000
0.8534
-0.5212
0.0000
0.7524
0.6587
-0.5022
0.8648
-0.0014
1.0000
0.0002
0.0000
Axis
-0.0000
0.5212
0.8534
-1.0000
0.0000
0.0000
-0.7020
-0.4086
-0.5834
-0.0001
0.5896
0.8077
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