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 TiHg (Materials Project id mp-1526)

       170       53       87        0        0        0  
        53      170       87        0        0        0  
        87       87      142        0        0        0  
         0        0        0       75        0        0  
         0        0        0        0       75        0  
         0        0        0        0        0       32  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 104 GPaEV = 136.79 GPaGV = 53.4 GPaνV = 0.28079
ReussKR = 103.95 GPaER = 116.46 GPaGR = 44.34 GPaνR = 0.31327
HillKH = 103.97 GPaEH = 126.75 GPaGH = 48.87 GPaνH = 0.29682

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
32 GPa 52.969 GPa 75 GPa 75 GPa 117 GPa 312.03 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 74.117 GPa 169.43 GPa 2.9647 TPa–1 3.3277 TPa–1 27.679 GPa 75 GPa-0.061250.62018Value
Anisotropy 2.286 1.1224 2.71Anisotropy
Axis 0.0000
0.0000
1.0000
0.7924
0.0000
0.6100
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.5001
0.4998
-0.7071
0.0000
0.0000
1.0000
-0.5009
0.5009
0.7059
-0.4840
0.4840
-0.7290
Axis
0.4999
-0.5002
-0.7071
-0.7660
0.6428
-0.0000
0.4991
-0.4991
0.7083
-0.7071
-0.7071
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