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 BaCdGe (Materials Project id mp-11816)

        71        9       12        0        0        0  
         9       71       12        0        0        0  
        12       12       34        0        0        0  
         0        0        0       24        0        0  
         0        0        0        0       24        0  
         0        0        0        0        0       31  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 26.889 GPaEV = 57.836 GPaGV = 25.333 GPaνV = 0.14151
ReussKR = 24.32 GPaER = 53.056 GPaGR = 23.344 GPaνR = 0.1364
HillKH = 25.604 GPaEH = 55.447 GPaGH = 24.339 GPaνH = 0.13908

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
24 GPa 24 GPa 28.417 GPa 31 GPa 62 GPa 85.583 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 30.4 GPa 66.425 GPa 9.0461 TPa–1 23.026 TPa–1 17.296 GPa 31 GPa0.0444520.32775Value
Anisotropy 2.185 2.5455 1.792 7.3732Anisotropy
Axis 0.0000
0.0000
1.0000
1.0000
0.0001
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.1873
0.9823
0.0000
-0.0869
0.6832
0.7250
0.7827
0.6224
-0.0000
Axis
-0.7071
-0.0002
-0.7071
-0.9823
-0.1873
-0.0000
0.0915
-0.7193
0.6887
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