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 YCo3 (Materials Project id mp-2588)

       201      136      115        2       -0        1  
       136      200      113       -1        1       -0  
       115      113      245       -0       -0        2  
         2       -1       -0       39       -1       -0  
        -0        1       -0       -1       38        1  
         1       -0        2       -0        1       33  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 152.67 GPaEV = 112.39 GPaGV = 40.8 GPaνV = 0.37731
ReussKR = 152.32 GPaER = 106.63 GPaGR = 38.541 GPaνR = 0.38333
HillKH = 152.5 GPaEH = 109.51 GPaGH = 39.67 GPaνH = 0.38031

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
32.76 GPa 37.511 GPa 39.488 GPa 64.697 GPa 123.19 GPa 458.35 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 95.683 GPa 167.67 GPa 1.9185 TPa–1 2.4231 TPa–1 31.672 GPa 51.809 GPa0.191660.56773Value
Anisotropy 1.752 1.2630 1.636 2.9622Anisotropy
Axis -0.8548
0.2841
-0.4342
-0.0057
-0.0058
1.0000
0.1039
0.0850
0.9910
-0.5242
0.8514
-0.0181
-0.5371
0.8435
-0.0007
-0.3743
0.5962
-0.7102
-0.5291
0.8486
-0.0016
0.2121
0.9772
0.0044
Axis
-0.8265
-0.5264
-0.1994
0.3632
-0.6104
-0.7039
-0.0344
-0.0234
-0.9991
-0.9750
0.2119
-0.0673
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