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 Zn2AgAu (Materials Project id mp-31171)

       113       96       96        0        0        0  
        96      113       96        0        0        0  
        96       96      113        0        0        0  
         0        0        0       53        0        0  
         0        0        0        0       53        0  
         0        0        0        0        0       53  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 101.67 GPaEV = 94.674 GPaGV = 35.2 GPaνV = 0.3448
ReussKR = 101.67 GPaER = 48.655 GPaGR = 17.129 GPaνR = 0.42024
HillKH = 101.67 GPaEH = 72.292 GPaGH = 26.165 GPaνH = 0.38149

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
17 GPa 17 GPa 53 GPa 53 GPa 53 GPa 305 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 24.809 GPa 135.46 GPa 3.2787 TPa–1 3.2787 TPa–1 8.5 GPa 53 GPa-0.395791.1858Value
Anisotropy 5.46 1.0000 6.235Anisotropy
Axis 1.0000
0.0000
0.0000
-0.5774
0.5774
-0.5773
0.0000
0.0000
1.0000
0.9914
0.0000
0.1305
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
-0.0000
0.7071
-0.7071
Axis
0.7071
-0.0005
-0.7071
0.7660
0.6428
-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