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 YbBi2BrO4 (Materials Project id mp-552016)

       134       62       27        0        0        0  
        62      134       27        0        0        0  
        27       27       66        0        0        0  
         0        0        0       10        0        0  
         0        0        0        0       10        0  
         0        0        0        0        0       50  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 62.889 GPaEV = 74.355 GPaGV = 28.533 GPaνV = 0.30295
ReussKR = 52.173 GPaER = 47.985 GPaGR = 17.816 GPaνR = 0.34671
HillKH = 57.531 GPaEH = 61.293 GPaGH = 23.174 GPaνH = 0.32243

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
10 GPa 10 GPa 50 GPa 55.614 GPa 72 GPa 206.39 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 32.531 GPa 126.98 GPa 3.3978 TPa–1 12.371 TPa–1 10 GPa 50 GPa0.0741380.67749Value
Anisotropy 3.903 3.6410 5 9.1383Anisotropy
Axis 0.6686
-0.0001
0.7437
0.7071
0.7071
0.0000
0.2588
0.9659
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0007
-0.0000
0.4777
0.4777
0.7373
0.5646
0.5645
0.6022
Axis
-0.7660
0.6428
-0.0000
-0.0007
1.0000
-0.0000
-0.7071
0.7071
-0.0000
0.4257
0.4258
-0.7984
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