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 YAlNi (Materials Project id mp-13095)

       126       56       92        0        0        0  
        56      126       92        0        0        0  
        92       92      106        0        0        0  
         0        0        0       56        0        0  
         0        0        0        0       56        0  
         0        0        0        0        0       35  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 93.111 GPaEV = 98.64 GPaGV = 37.267 GPaνV = 0.32344
ReussKR = 90.923 GPaER = 43.164 GPaGR = 15.189 GPaνR = 0.42088
HillKH = 92.017 GPaEH = 71.857 GPaGH = 26.228 GPaνH = 0.36985

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
8.4566 GPa 35 GPa 56 GPa 56 GPa 70 GPa 279.54 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 12.989 GPa 120.97 GPa-0.84602 TPa–1 5.9222 TPa–1 5.4234 GPa 56 GPa-0.523151.3164Value
Anisotropy 9.313 10.33Anisotropy
Axis 0.0000
0.0000
1.0000
0.7942
0.1078
0.5980
0.0000
0.0000
1.0000
0.1283
0.9917
0.0000
0.7071
-0.0003
0.7071
-0.0000
0.0000
1.0000
-0.6734
0.7071
-0.2158
0.1518
0.9884
0.0000
Axis
0.7071
-0.0005
-0.7071
-0.5000
0.8660
-0.0000
-0.7241
-0.6896
0.0000
0.0000
0.0000
-1.0000
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