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 K2ZnF4 (Materials Project id mp-9583)

        77       22       30        0        0        0  
        22       77       30        0        0        0  
        30       30       79        0        0        0  
         0        0        0       17        0        0  
         0        0        0        0       17        0  
         0        0        0        0        0       21  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 44.111 GPaEV = 54.521 GPaGV = 21.067 GPaνV = 0.294
ReussKR = 43.949 GPaER = 52.908 GPaGR = 20.359 GPaνR = 0.29936
HillKH = 44.03 GPaEH = 53.716 GPaGH = 20.713 GPaνH = 0.29667

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
17 GPa 17 GPa 21 GPa 45.411 GPa 55 GPa 132.59 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 47.585 GPa 63.893 GPa 6.4773 TPa–1 8.1382 TPa–1 17 GPa 27.5 GPa0.160860.45346Value
Anisotropy 1.343 1.2564 1.618 2.8190Anisotropy
Axis 0.5350
0.5350
-0.6539
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.3827
0.9239
0.0000
0.0000
0.0000
1.0000
0.7071
0.7071
0.0000
0.9649
-0.0001
0.2626
0.7208
-0.0002
0.6931
Axis
-0.1736
0.9848
-0.0000
-0.7071
0.7071
-0.0000
0.0001
1.0000
0.0000
0.6931
-0.0006
-0.7208
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