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 BaGeF6 (Materials Project id mp-14006)

        77       34       31        2        0        0  
        34       77       31       -2        0        0  
        31       31      109        0        0        0  
         2       -2        0       18        0        0  
         0        0        0        0       18        2  
         0        0        0        0        2       22  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 50.556 GPaEV = 59.31 GPaGV = 22.733 GPaνV = 0.30447
ReussKR = 49.644 GPaER = 55.855 GPaGR = 21.278 GPaνR = 0.31248
HillKH = 50.1 GPaEH = 57.586 GPaGH = 22.006 GPaνH = 0.30843

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
17.172 GPa 17.684 GPa 22.828 GPa 43.316 GPa 66.148 GPa 153.85 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 46.348 GPa 91.685 GPa 4.8148 TPa–1 7.6643 TPa–1 17.113 GPa 29.783 GPa0.168780.49242Value
Anisotropy 1.978 1.5918 1.74 2.9175Anisotropy
Axis 0.0000
0.8174
0.5760
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
0.2588
0.9659
0.0000
0.3492
0.2066
0.9140
0.5110
0.4339
0.7420
0.4694
0.2797
0.8375
-0.4992
0.3011
0.8125
Axis
-0.5077
0.8615
-0.0007
0.5958
0.4434
-0.6696
-0.5098
0.8603
-0.0015
-0.6979
0.4160
-0.5830
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