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 Rb5Au3O2 (Materials Project id mp-29920)

        26       14       10        0        0        0  
        14       34       10        0        0        0  
        10       10       35        0        0        0  
         0        0        0        9        0        0  
         0        0        0        0        9        0  
         0        0        0        0        0       13  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 18.111 GPaEV = 25.905 GPaGV = 10.267 GPaνV = 0.26161
ReussKR = 17.877 GPaER = 24.877 GPaGR = 9.8088 GPaνR = 0.26807
HillKH = 17.994 GPaEH = 25.392 GPaGH = 10.038 GPaνH = 0.26481

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
9 GPa 9 GPa 13 GPa 15.148 GPa 25.24 GPa 54.612 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 19.156 GPa 31.48 GPa 14.368 TPa–1 23.946 TPa–1 7.7831 GPa 13 GPa0.15390.48148Value
Anisotropy 1.643 1.6667 1.67 3.1286Anisotropy
Axis 1.0000
0.0000
0.0000
0.6079
0.7940
0.0000
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
-0.7071
0.6824
0.1854
1.0000
-0.0000
0.0001
-0.6686
0.5445
-0.5064
0.0000
1.0000
-0.0000
Axis
-0.7071
-0.6824
-0.1853
0.0000
1.0000
-0.0000
-0.7119
-0.6654
0.2244
-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