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 Ti2Ga3 (Materials Project id mp-30673)

       154       56       56        0        0        0  
        56      170       51       -0        0        0  
        56       51      170        0        0        0  
         0       -0        0       55        0        0  
         0        0        0        0       91        0  
         0        0        0        0        0       91  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 91.111 GPaEV = 166.17 GPaGV = 69.467 GPaνV = 0.19603
ReussKR = 91.023 GPaER = 157.95 GPaGR = 65.225 GPaνR = 0.21079
HillKH = 91.067 GPaEH = 162.08 GPaGH = 67.346 GPaνH = 0.20336

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
55 GPa 91 GPa 91 GPa 101.51 GPa 119 GPa 273.49 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 125.62 GPa 183.75 GPa 3.53 TPa–1 3.9262 TPa–1 51.776 GPa 91 GPa-0.0115250.34084Value
Anisotropy 1.463 1.1122 1.758Anisotropy
Axis 1.0000
0.0000
0.0000
0.6620
-0.0000
0.7495
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.7071
0.5000
-0.5000
-0.0000
0.0000
1.0000
0.7068
0.5002
-0.5002
-0.7104
0.4976
0.4976
Axis
-0.7071
0.5000
-0.5000
-1.0000
0.0000
-0.0000
-0.7074
0.4998
-0.4998
0.0000
-0.7071
0.7071
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