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 TbCu5 (Materials Project id mp-11363)

       135       61       73        0        0        0  
        61      135       73        0        0        0  
        73       73      235        0        0        0  
         0        0        0       40        0        0  
         0        0        0        0       40        0  
         0        0        0        0        0       37  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 102.11 GPaEV = 113.74 GPaGV = 43.267 GPaνV = 0.31436
ReussKR = 94.658 GPaER = 107.94 GPaGR = 41.2 GPaνR = 0.30995
HillKH = 98.384 GPaEH = 110.84 GPaGH = 42.233 GPaνH = 0.31223

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
37 GPa 40 GPa 40 GPa 74 GPa 110.44 GPa 320.56 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 99.003 GPa 180.62 GPa 1.4123 TPa–1 4.576 TPa–1 37 GPa 50.668 GPa0.204650.39866Value
Anisotropy 1.824 3.2400 1.369 1.9480Anisotropy
Axis 0.2902
0.9203
-0.2623
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.8660
0.5000
0.0000
0.9573
0.2890
0.0000
0.3267
0.6271
0.7071
0.4505
0.8928
-0.0000
0.2842
0.3652
0.8865
Axis
-0.2890
0.9573
-0.0000
0.3267
0.6271
-0.7071
0.0000
-0.0000
-1.0000
0.5444
0.6996
-0.4627
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