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 Zn3Cu (Materials Project id mp-972042)

       135       72       72        0        0        0  
        72      135       72        0        0        0  
        72       72      170        0        0        0  
         0        0        0       48        0        0  
         0        0        0        0       48        0  
         0        0        0        0        0       32  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 96.889 GPaEV = 106.72 GPaGV = 40.533 GPaνV = 0.31643
ReussKR = 95.838 GPaER = 103.11 GPaGR = 39.037 GPaνR = 0.32068
HillKH = 96.363 GPaEH = 104.92 GPaGH = 39.785 GPaνH = 0.31854

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
32 GPa 48 GPa 48 GPa 63 GPa 85.01 GPa 291.99 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 88.021 GPa 122.1 GPa 2.5381 TPa–1 3.9481 TPa–1 31.5 GPa 48 GPa0.196930.4283Value
Anisotropy 1.387 1.5556 1.524 2.1749Anisotropy
Axis 0.0000
1.0000
0.0000
0.3010
0.3010
0.9049
0.0000
0.0000
1.0000
0.5000
0.8660
0.0000
-0.7071
0.7071
0.0000
-0.0000
0.0000
1.0000
0.7611
0.0001
0.6486
0.7612
-0.0005
-0.6486
Axis
-0.7071
-0.7071
0.0000
-0.7660
0.6428
-0.0000
0.6486
0.0003
-0.7611
0.0006
1.0000
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