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 DyNi2 (Materials Project id mp-421)

       224      164      164        0        0        0  
       164      224      164        0        0        0  
       164      164      224        0        0        0  
         0        0        0       51        0        0  
         0        0        0        0       51        0  
         0        0        0        0        0       51  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 184 GPaEV = 118.64 GPaGV = 42.6 GPaνV = 0.39253
ReussKR = 184 GPaER = 111.48 GPaGR = 39.844 GPaνR = 0.39902
HillKH = 184 GPaEH = 115.07 GPaGH = 41.222 GPaνH = 0.39577

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
51 GPa 51 GPa 51 GPa 60 GPa 60 GPa 552 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 85.361 GPa 140.06 GPa 1.8116 TPa–1 1.8116 TPa–1 30 GPa 51 GPa0.183530.59777Value
Anisotropy 1.641 1.0000 1.7 3.2570Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.2500
0.9330
0.2588
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
-0.0000
-0.7071
0.0000
0.7071
0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-0.0000
-0.7071
0.0002
-0.7071
-1.0000
0.0000
0.0000
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