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 HoCu5 (Materials Project id mp-580364)

       161      101      101        0        0        0  
       101      161      101        0        0        0  
       101      101      161        0        0        0  
         0        0        0       21        0        0  
         0        0        0        0       21        0  
         0        0        0        0        0       21  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 121 GPaEV = 69.116 GPaGV = 24.6 GPaνV = 0.4048
ReussKR = 121 GPaER = 67.175 GPaGR = 23.864 GPaνR = 0.40747
HillKH = 121 GPaEH = 68.146 GPaGH = 24.232 GPaνH = 0.40613

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
21 GPa 21 GPa 21 GPa 60 GPa 60 GPa 363 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 59.555 GPa 83.13 GPa 2.7548 TPa–1 2.7548 TPa–1 21 GPa 30 GPa0.297250.52617Value
Anisotropy 1.396 1.0000 1.429 1.7702Anisotropy
Axis 0.5774
0.5773
-0.5774
1.0000
0.0000
0.0000
0.9239
0.0000
0.3827
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.7071
0.0004
-0.7071
0.7071
-0.0000
-0.7071
Axis
-0.7660
-0.6428
0.0000
0.7071
-0.0005
-0.7071
-0.0003
1.0000
0.0003
-0.7071
0.0002
-0.7071
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