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 TiZnN2 (Materials Project id mp-1016108)

       238      125      113        0        0        0  
       125      230      118        0        0        0  
       113      118      213        0        0        0  
         0        0        0       57        0        0  
         0        0        0        0       53        0  
         0        0        0        0        0       59  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 154.78 GPaEV = 148.64 GPaGV = 55.467 GPaνV = 0.33994
ReussKR = 154.14 GPaER = 148.13 GPaGR = 55.281 GPaνR = 0.33983
HillKH = 154.46 GPaEH = 148.39 GPaGH = 55.374 GPaνH = 0.33988

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
53 GPa 57 GPa 59 GPa 102.81 GPa 113.27 GPa 464.92 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 138.08 GPa 157.93 GPa 1.9458 TPa–1 2.5703 TPa–1 51.584 GPa 59 GPa0.287360.37903Value
Anisotropy 1.144 1.3209 1.144 1.3190Anisotropy
Axis 0.3627
0.0000
0.9319
0.8265
0.5629
-0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
-0.0704
0.7071
0.7036
1.0000
0.0005
0.0000
0.0000
0.0000
1.0000
-1.0000
-0.0000
0.0001
Axis
-0.0704
-0.7071
0.7036
-0.0005
1.0000
0.0000
-1.0000
0.0000
0.0000
0.0000
-1.0000
0.0001
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