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 ZrZn3 (Materials Project id mp-864889)

       142       87       67        0        0        0  
        87      142       67        0        0        0  
        67       67      179        0        0        0  
         0        0        0       46        0        0  
         0        0        0        0       46        0  
         0        0        0        0        0       27  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 100.56 GPaEV = 105.8 GPaGV = 39.933 GPaνV = 0.32465
ReussKR = 100.35 GPaER = 98.468 GPaGR = 36.839 GPaνR = 0.33647
HillKH = 100.45 GPaEH = 102.15 GPaGH = 38.386 GPaνH = 0.33052

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
27 GPa 46 GPa 46 GPa 55 GPa 106.01 GPa 301.99 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 82.953 GPa 139.79 GPa 2.9675 TPa–1 3.4986 TPa–1 27 GPa 46 GPa0.169110.53617Value
Anisotropy 1.685 1.1789 1.704 3.1705Anisotropy
Axis -0.7071
0.7071
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.1294
0.9916
0.0000
1.0000
-0.0002
0.0000
0.0000
-0.0000
1.0000
0.6331
0.6329
0.4457
-0.7071
0.7071
-0.0000
Axis
0.0002
1.0000
0.0000
-0.1734
0.9848
0.0000
0.3151
0.3152
-0.8952
-0.7071
-0.7071
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