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 Ni2Ge (Materials Project id mp-17383)

       196      125      133        0        0        0  
       125      264      144        0        0        0  
       133      144      272        0        0        0  
         0        0        0       35        0        0  
         0        0        0        0       38        0  
         0        0        0        0        0       40  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 170.67 GPaEV = 123.08 GPaGV = 44.6 GPaνV = 0.37981
ReussKR = 164.67 GPaER = 117.42 GPaGR = 42.508 GPaνR = 0.38116
HillKH = 167.67 GPaEH = 120.25 GPaGH = 43.554 GPaνH = 0.38047

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
35 GPa 38 GPa 40 GPa 91.728 GPa 124.17 GPa 516.11 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 104.61 GPa 165.01 GPa 1.2602 TPa–1 3.2513 TPa–1 35 GPa 61.915 GPa0.254540.55155Value
Anisotropy 1.577 2.5799 1.769 2.1668Anisotropy
Axis -0.6240
0.5428
0.5621
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
-0.0000
-0.0000
1.0000
-0.0001
0.7071
0.7071
0.7300
-0.0003
-0.6835
-0.0000
0.7100
0.7042
Axis
0.0000
1.0000
0.0000
0.0001
0.7071
-0.7071
0.0004
1.0000
-0.0001
0.0000
0.7042
-0.7100
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