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 ZrW2 (Materials Project id mp-675)

       316      165      165        0        0        0  
       165      316      165        0        0        0  
       165      165      316        0        0        0  
         0        0        0       95        0        0  
         0        0        0        0       95        0  
         0        0        0        0        0       95  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 215.33 GPaEV = 230.49 GPaGV = 87.2 GPaνV = 0.3216
ReussKR = 215.33 GPaER = 227.93 GPaGR = 86.104 GPaνR = 0.32358
HillKH = 215.33 GPaEH = 229.21 GPaGH = 86.652 GPaνH = 0.32259

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
95 GPa 95 GPa 95 GPa 151 GPa 151 GPa 646 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 202.8 GPa 248.46 GPa 1.548 TPa–1 1.548 TPa–1 75.5 GPa 95 GPa0.2380.39788Value
Anisotropy 1.225 1.0000 1.258 1.6717Anisotropy
Axis 0.0000
0.0000
1.0000
0.5774
0.5774
0.5773
0.4619
0.8001
0.3827
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
0.7071
-0.0002
0.7071
0.7071
0.0004
-0.7071
Axis
0.7071
-0.0005
-0.7071
-0.5000
0.8660
-0.0000
0.7071
-0.0006
-0.7071
-0.0003
1.0000
0.0003
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