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 Zr6Ga2Co (Materials Project id mp-22167)

       179       76       76        0        0        0  
        76      179       76        0        0        0  
        76       76      172        0        0        0  
         0        0        0       48        0        0  
         0        0        0        0       48        0  
         0        0        0        0        0       51  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 109.56 GPaEV = 129.14 GPaGV = 49.533 GPaνV = 0.30354
ReussKR = 109.52 GPaER = 129.03 GPaGR = 49.486 GPaνR = 0.30365
HillKH = 109.54 GPaEH = 129.08 GPaGH = 49.51 GPaνH = 0.3036

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
48 GPa 48 GPa 51 GPa 98.286 GPa 103 GPa 328.71 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 126 GPa 133.05 GPa 2.9714 TPa–1 3.1881 TPa–1 48 GPa 51.5 GPa0.287810.32213Value
Anisotropy 1.056 1.0729 1.073 1.1192Anisotropy
Axis 0.3573
0.3572
-0.8630
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.7071
0.7071
-0.0000
0.7902
-0.0005
-0.6129
0.7901
0.0002
0.6130
Axis
0.1735
0.9848
-0.0000
-0.7071
0.7071
0.0000
0.0006
1.0000
-0.0000
0.6130
0.0004
-0.7901
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