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 HfCr2 (Materials Project id mp-569624)

       297      135      141        0        0        0  
       135      297      141        0        0        0  
       141      141      280        0        0        0  
         0        0        0       52        0        0  
         0        0        0        0       52        0  
         0        0        0        0        0       81  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 189.78 GPaEV = 180.96 GPaGV = 67.467 GPaνV = 0.34108
ReussKR = 189.71 GPaER = 174.5 GPaGR = 64.787 GPaνR = 0.3467
HillKH = 189.75 GPaEH = 177.73 GPaGH = 66.127 GPaνH = 0.34389

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
52 GPa 52 GPa 81 GPa 142.6 GPa 162 GPa 569.4 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 154.23 GPa 207.87 GPa 1.7119 TPa–1 1.8473 TPa–1 52 GPa 81 GPa0.237540.48647Value
Anisotropy 1.348 1.0791 1.558 2.0480Anisotropy
Axis 0.6462
0.1927
0.7384
0.7001
0.7140
-0.0000
0.6088
0.7934
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.8329
0.5534
-0.0000
0.7248
0.2635
0.6366
0.3562
0.6450
-0.6761
Axis
0.1735
0.9848
-0.0000
-0.5534
0.8329
-0.0000
-0.3417
0.9398
0.0000
-0.3268
-0.5918
-0.7368
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