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 ZrC (Materials Project id mp-1009894)

       162      121      121        0        0        0  
       121      162      121        0        0        0  
       121      121      162        0        0        0  
         0        0        0       57        0        0  
         0        0        0        0       57        0  
         0        0        0        0        0       57  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 134.67 GPaEV = 115.12 GPaGV = 42.4 GPaνV = 0.35753
ReussKR = 134.67 GPaER = 92.269 GPaGR = 33.291 GPaνR = 0.38581
HillKH = 134.67 GPaEH = 103.81 GPaGH = 37.845 GPaνH = 0.37152

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
41 GPa 41 GPa 57 GPa 57 GPa 57 GPa 404 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 58.53 GPa 149.86 GPa 2.4752 TPa–1 2.4752 TPa–1 20.5 GPa 57 GPa-0.054350.78751Value
Anisotropy 2.56 1.0000 2.78Anisotropy
Axis 0.0000
1.0000
0.0000
0.5774
0.5774
0.5773
0.9659
0.0000
0.2588
0.1317
0.9830
0.1283
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.7071
0.7071
Axis
-0.7071
-0.0002
-0.7071
0.5000
0.8660
-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