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 BaLiAs (Materials Project id mp-10616)

        72       20       12        0        0        0  
        20       72       12        0        0        0  
        12       12       75        0        0        0  
         0        0        0       16        0        0  
         0        0        0        0       16        0  
         0        0        0        0        0       26  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 34.111 GPaEV = 56.87 GPaGV = 23.267 GPaνV = 0.22213
ReussKR = 34.082 GPaER = 53.233 GPaGR = 21.471 GPaνR = 0.23968
HillKH = 34.097 GPaEH = 55.064 GPaGH = 22.369 GPaνH = 0.23084

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
16 GPa 16 GPa 26 GPa 52 GPa 64.52 GPa 102.48 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 45.385 GPa 71.87 GPa 9.5281 TPa–1 10.284 TPa–1 16 GPa 30.459 GPa0.118260.41952Value
Anisotropy 1.584 1.0794 1.904 3.5475Anisotropy
Axis 0.7162
0.1012
0.6906
0.0000
0.0000
1.0000
0.6088
0.7934
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0478
0.4663
-0.8833
0.3207
0.6168
-0.7188
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.0002
-0.7071
-0.9948
0.1020
-0.0000
-0.3315
-0.6378
-0.6952
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