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 ZrTi2 (Materials Project id mp-1008568)

       168       84       61        0        0        0  
        84      168       61        0        0        0  
        61       61      202        0        0        0  
         0        0        0       47        0        0  
         0        0        0        0       47        0  
         0        0        0        0        0       42  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 105.56 GPaEV = 128.05 GPaGV = 49.333 GPaνV = 0.29781
ReussKR = 105.49 GPaER = 124.44 GPaGR = 47.735 GPaνR = 0.3034
HillKH = 105.52 GPaEH = 126.25 GPaGH = 48.534 GPaνH = 0.3006

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
42 GPa 47 GPa 47 GPa 84 GPa 137.18 GPa 316.82 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 117.85 GPa 172.47 GPa 2.9911 TPa–1 3.2442 TPa–1 42 GPa 59.237 GPa0.169580.43842Value
Anisotropy 1.463 1.0846 1.41 2.5853Anisotropy
Axis -0.5868
0.6615
0.4670
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
1.0000
-0.0002
-0.0000
0.6074
0.3621
0.7071
0.4327
0.9015
-0.0000
0.3887
0.9214
0.0000
Axis
0.0002
1.0000
-0.0000
0.6074
0.3621
-0.7071
-0.0000
-0.0000
-1.0000
-0.9214
0.3887
-0.0000
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