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 Ba2YBiO6 (Materials Project id mp-23137)

       232       56       56        0        0        0  
        56      232       56        0        0        0  
        56       56      232        0        0        0  
         0        0        0       59        0        0  
         0        0        0        0       59        0  
         0        0        0        0        0       59  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 114.67 GPaEV = 175.73 GPaGV = 70.6 GPaνV = 0.24457
ReussKR = 114.67 GPaER = 170.24 GPaGR = 67.958 GPaνR = 0.25255
HillKH = 114.67 GPaEH = 173 GPaGH = 69.279 GPaνH = 0.24855

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
59 GPa 59 GPa 59 GPa 176 GPa 176 GPa 344 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 151.09 GPa 210.22 GPa 2.907 TPa–1 2.907 TPa–1 59 GPa 88 GPa0.150320.37725Value
Anisotropy 1.391 1.0000 1.492 2.5097Anisotropy
Axis 0.5774
0.5774
0.5773
0.0000
0.0000
1.0000
0.5000
0.0000
0.8660
-0.1206
0.9160
0.3827
-0.0000
-0.0000
1.0000
0.7071
0.0001
-0.7071
-0.7071
0.0000
0.7071
0.7071
-0.0000
-0.7071
Axis
1.0000
0.0002
0.0000
-0.7071
-0.0002
-0.7071
-0.0000
-1.0000
0.0000
-0.7071
0.0002
-0.7071
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