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 BaCuBi (Materials Project id mp-31145)

        79       24       20        0        0        0  
        24       79       20        0        0        0  
        20       20       52        0        0        0  
         0        0        0       23        0        0  
         0        0        0        0       23        0  
         0        0        0        0        0       28  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 37.556 GPaEV = 60.439 GPaGV = 24.533 GPaνV = 0.23178
ReussKR = 35.874 GPaER = 58.835 GPaGR = 23.982 GPaνR = 0.22666
HillKH = 36.715 GPaEH = 59.638 GPaGH = 24.257 GPaνH = 0.22927

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
23 GPa 23 GPa 28 GPa 39.418 GPa 55 GPa 115.58 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 44.233 GPa 68.328 GPa 7.0237 TPa–1 13.828 TPa–1 21.652 GPa 28 GPa0.191770.29995Value
Anisotropy 1.545 1.9688 1.293 1.5641Anisotropy
Axis 0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
0.2430
0.9700
-0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
1.0000
-0.0002
-0.0000
0.3971
-0.0001
0.9178
0.7071
0.7071
0.0000
Axis
0.7071
-0.0005
-0.7071
0.0002
1.0000
-0.0000
0.9178
-0.0007
-0.3971
-0.0000
-0.0000
1.0000
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