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 Ti5Te4 (Materials Project id mp-7498)

       109       38       38        0        0        0  
        38      101       68        4        0        0  
        38       68      101       -4        0        0  
         0        4       -4       39        0        0  
         0        0        0        0       51        0  
         0        0        0        0        0       51  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 66.556 GPaEV = 98.58 GPaGV = 39.333 GPaνV = 0.25314
ReussKR = 66.098 GPaER = 83.993 GPaGR = 32.601 GPaνR = 0.28821
HillKH = 66.327 GPaEH = 91.383 GPaGH = 35.967 GPaνH = 0.27037

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
29.597 GPa 42.403 GPa 51 GPa 51 GPa 77.453 GPa 200.55 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 51.756 GPa 113.6 GPa 4.5709 TPa–1 5.9873 TPa–1 15.81 GPa 51 GPa-0.128420.69058Value
Anisotropy 2.195 1.3099 3.226Anisotropy
Axis 0.0000
0.0853
0.9964
0.6405
0.5874
0.4947
-0.0000
0.9238
-0.3830
1.0000
0.0000
0.0000
0.0001
0.6442
-0.7648
-0.0000
-0.0000
1.0000
-0.7287
0.6823
-0.0584
0.5582
0.8266
-0.0708
Axis
0.0001
-0.7648
-0.6442
-1.0000
-0.0000
-0.0000
-0.6848
-0.7261
0.0621
-0.0000
-0.0853
-0.9964
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