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 TbZr (Materials Project id mp-978918)

       104       32       47        0        0        0  
        32      104       47       -0        0        0  
        47       47      120       -0        0        0  
         0       -0       -0       30        0        0  
         0        0        0        0       30        0  
         0        0        0        0        0       36  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 64.444 GPaEV = 83.835 GPaGV = 32.667 GPaνV = 0.28319
ReussKR = 63.309 GPaER = 82.857 GPaGR = 32.319 GPaνR = 0.28187
HillKH = 63.876 GPaEH = 83.346 GPaGH = 32.493 GPaνH = 0.28253

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
30 GPa 30 GPa 36 GPa 61.052 GPa 72 GPa 194.95 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 81.629 GPa 87.515 GPa 3.5288 TPa–1 6.1334 TPa–1 30 GPa 36 GPa0.15880.36545Value
Anisotropy 1.072 1.7381 1.2 2.3014Anisotropy
Axis 0.7988
0.0004
0.6016
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.7889
0.6145
-0.0000
-0.4115
0.9114
0.0000
0.6082
0.2247
0.7613
Axis
0.1736
0.9848
-0.0000
-0.6145
0.7889
0.0000
-0.9114
-0.4115
0.0000
0.7141
0.2638
-0.6484
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