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 TmCo3B2 (Materials Project id mp-5714)

       389      106      165        0        0        0  
       106      389      165        0        0        0  
       165      165      334        0        0        0  
         0        0        0      131        0        0  
         0        0        0        0      131        0  
         0        0        0        0        0      142  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 220.44 GPaEV = 317.22 GPaGV = 125.87 GPaνV = 0.26016
ReussKR = 220.44 GPaER = 306.96 GPaGR = 121.05 GPaνR = 0.26792
HillKH = 220.44 GPaEH = 312.11 GPaGH = 123.46 GPaνH = 0.26403

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
131 GPa 131 GPa 142 GPa 167.66 GPa 283 GPa 661.34 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 224 GPa 335.52 GPa 1.4881 TPa–1 1.5242 TPa–1 93.341 GPa 142 GPa0.0778860.45554Value
Anisotropy 1.498 1.0242 1.521 5.8487Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5894
0.5894
0.5524
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
-0.0003
0.7071
1.0000
0.0007
0.0000
0.7071
0.7071
0.0000
-0.7071
0.7071
0.0000
Axis
0.7071
-0.0005
-0.7071
-0.0007
1.0000
0.0000
-0.7071
0.7071
-0.0000
-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