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 TmNiGe (Materials Project id mp-21157)

       157       52       34        0        0        0  
        52      181       88        0        0        0  
        34       88      183        0        0        0  
         0        0        0       69        0        0  
         0        0        0        0       55        0  
         0        0        0        0        0       63  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 96.556 GPaEV = 150.21 GPaGV = 60.533 GPaνV = 0.24072
ReussKR = 93.612 GPaER = 145.58 GPaGR = 58.663 GPaνR = 0.24081
HillKH = 95.084 GPaEH = 147.89 GPaGH = 59.598 GPaνH = 0.24076

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
55 GPa 63 GPa 69 GPa 90.293 GPa 134.11 GPa 296.59 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 126.86 GPa 177.13 GPa 2.5067 TPa–1 4.8104 TPa–1 46.413 GPa 69 GPa0.061370.46856Value
Anisotropy 1.396 1.9190 1.487 7.6350Anisotropy
Axis 0.6963
-0.0000
0.7177
-0.0000
0.6806
0.7327
0.0000
1.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.7071
0.7071
-0.0006
-0.0006
1.0000
0.0000
0.0000
1.0000
-0.0004
-0.0002
1.0000
Axis
-0.0000
0.7071
-0.7071
0.0001
1.0000
0.0006
-1.0000
0.0000
0.0000
-0.0000
1.0000
0.0002
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