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 Ti3Ni4 (Materials Project id mp-567653)

       220      144      122       -7      -13        0  
       144      220      122        7       13        0  
       122      122      255        0        0        0  
        -7        7        0       34        0       13  
       -13       13        0        0       34       -7  
         0        0        0       13       -7       38  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 163.44 GPaEV = 115.21 GPaGV = 41.667 GPaνV = 0.38252
ReussKR = 163.35 GPaER = 93.847 GPaGR = 33.415 GPaνR = 0.40425
HillKH = 163.4 GPaEH = 104.61 GPaGH = 37.541 GPaνH = 0.39329

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
21.1 GPa 25.386 GPa 50.9 GPa 84.614 GPa 128.56 GPa 490.44 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 60.917 GPa 173.22 GPa 1.9032 TPa–1 2.1094 TPa–1 21.1 GPa 58.796 GPa-0.00629720.79297Value
Anisotropy 2.844 1.1083 2.787Anisotropy
Axis -0.5311
0.6458
0.5485
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.3816
0.9243
-0.0000
-0.6490
-0.1078
0.7531
0.2002
0.5336
0.8217
0.4926
0.0818
-0.8664
-0.1639
0.9865
0.0000
Axis
0.1639
-0.9865
-0.0000
0.2887
0.7693
-0.5699
-0.1639
0.9865
-0.0000
-0.8540
-0.1418
-0.5005
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