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 TiNi (Materials Project id mp-2716)

       209      130      124       -2        6        0  
       130      209      124        2       -6        0  
       124      124      194        0        0        0  
        -2        2        0       36        0       -6  
         6       -6        0        0       36       -2  
         0        0        0       -6       -2       40  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 152 GPaEV = 105.23 GPaGV = 38 GPaνV = 0.38462
ReussKR = 151.58 GPaER = 102.77 GPaGR = 37.047 GPaνR = 0.387
HillKH = 151.79 GPaEH = 104 GPaGH = 37.524 GPaνH = 0.3858

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
31.367 GPa 34.214 GPa 44.633 GPa 76.742 GPa 80.786 GPa 456.26 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 87.6 GPa 121.42 GPa 1.9992 TPa–1 2.599 TPa–1 31.204 GPa 44.619 GPa0.267980.51596Value
Anisotropy 1.386 1.3000 1.43 1.9254Anisotropy
Axis -0.8052
0.0846
0.5869
0.5494
0.7442
-0.3800
0.2588
0.9659
0.0000
0.0000
0.0000
1.0000
0.3582
0.4866
-0.7968
0.8020
-0.0832
-0.5915
0.3480
0.4714
-0.8103
0.1065
0.9943
0.0018
Axis
-0.8051
0.5931
0.0003
0.0991
0.9951
-0.0056
-0.8062
0.5916
-0.0021
-0.7327
0.0772
0.6761
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