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 BaPt (Materials Project id mp-31498)

        70       36       34        0        0        0  
        36       70       34        0        0        0  
        34       34      106        0        0        0  
         0        0        0       17        0        0  
         0        0        0        0       17        0  
         0        0        0        0        0       17  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 50.444 GPaEV = 52.214 GPaGV = 19.667 GPaνV = 0.32749
ReussKR = 49.033 GPaER = 49.472 GPaGR = 18.573 GPaνR = 0.33184
HillKH = 49.739 GPaEH = 50.844 GPaGH = 19.12 GPaνH = 0.32963

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
17 GPa 17 GPa 17 GPa 34 GPa 57.917 GPa 154.08 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 45.537 GPa 84.189 GPa 4.2582 TPa–1 8.0681 TPa–1 17 GPa 24.911 GPa0.184550.42009Value
Anisotropy 1.849 1.8947 1.465 2.2763Anisotropy
Axis -0.2263
0.8267
0.5151
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.5955
0.3812
0.7071
0.9331
0.3595
-0.0000
0.0764
0.5694
-0.8185
Axis
-0.1736
0.9848
-0.0000
0.5955
0.3812
-0.7071
-0.0000
0.0000
-1.0000
-0.1087
-0.8113
-0.5745
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