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 NaSbS2 (Materials Project id mp-5414)

        40       11       17        0        3        0  
        11       30        8        0       -2        0  
        17        8       77        0        6        0  
         0        0        0       11        0       -3  
         3       -2        6        0       16        0  
         0        0        0       -3        0       13  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 24.333 GPaEV = 38.152 GPaGV = 15.4 GPaνV = 0.23869
ReussKR = 20.849 GPaER = 32.619 GPaGR = 13.161 GPaνR = 0.23924
HillKH = 22.591 GPaEH = 35.385 GPaGH = 14.28 GPaνH = 0.23894

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
8.8377 GPa 14.318 GPa 15.162 GPa 23.808 GPa 38.328 GPa 86.545 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 22.995 GPa 71.998 GPa 7.0055 TPa–1 25.753 TPa–1 8.8377 GPa 20.1 GPa0.0209350.49419Value
Anisotropy 3.131 3.6761 2.274 23.6058Anisotropy
Axis 0.3149
0.8296
0.4611
0.1815
0.0000
0.9834
0.1410
0.0000
0.9900
0.0000
1.0000
0.0000
0.5847
0.0002
0.8112
0.5836
0.6036
0.5431
-0.0000
1.0000
0.0000
-0.1764
0.3968
0.9008
Axis
-0.0002
1.0000
-0.0001
0.2765
0.4812
-0.8319
-0.3763
0.0000
-0.9265
-0.5960
0.6853
-0.4186
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