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 KZrCuSe3 (Materials Project id mp-9318)

       101        4       17        0        0        0  
         4       15       14        0        0        0  
        17       14      102        0        0        0  
         0        0        0       12        0        0  
         0        0        0        0       26        0  
         0        0        0        0        0       10  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 32 GPaEV = 53.297 GPaGV = 21.8 GPaνV = 0.22241
ReussKR = 13.878 GPaER = 30.583 GPaGR = 13.5 GPaνR = 0.1327
HillKH = 22.939 GPaEH = 42.142 GPaGH = 17.65 GPaνH = 0.19381

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
10 GPa 12 GPa 12.782 GPa 26 GPa 85.124 GPa 120.09 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 13.05 GPa 97.954 GPa-0.35203 TPa–1 65.026 TPa–1 9.1996 GPa 40.443 GPa0.0169780.89793Value
Anisotropy 7.506 4.396 52.8882Anisotropy
Axis 0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
-0.0000
0.7071
0.7071
0.7072
-0.0002
0.7070
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
Axis
0.0000
0.7071
-0.7071
0.7070
-0.0004
-0.7072
-1.0000
0.0000
0.0000
-0.0000
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