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 Cu6Sn5 (Materials Project id mp-1233)

       136       56       58        0       -7        0  
        56      131       56        0        6        0  
        58       56      126        0       -0        0  
         0        0        0       32        0       -1  
        -7        6       -0        0       39        0  
         0        0        0       -1        0       40  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 81.444 GPaEV = 96.552 GPaGV = 37.067 GPaνV = 0.30242
ReussKR = 81.365 GPaER = 95.035 GPaGR = 36.402 GPaνR = 0.30533
HillKH = 81.405 GPaEH = 95.794 GPaGH = 36.735 GPaνH = 0.30387

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
31.877 GPa 36.914 GPa 40.123 GPa 71.104 GPa 79.543 GPa 244.44 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 86.194 GPa 116.05 GPa 3.791 TPa–1 4.3459 TPa–1 31.877 GPa 43.016 GPa0.196920.40387Value
Anisotropy 1.346 1.1464 1.349 2.0510Anisotropy
Axis -0.1108
0.6619
0.7414
0.8733
-0.0000
-0.4872
0.9993
0.0000
-0.0375
0.0375
-0.0002
0.9993
0.1222
-0.0000
0.9925
-0.4756
0.7465
0.4653
-0.0000
1.0000
0.0000
-0.0000
1.0000
0.0000
Axis
-0.0000
1.0000
0.0000
-0.6967
-0.6427
0.3188
-0.7428
-0.0000
0.6695
-0.6695
-0.0000
-0.7428
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