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 Nd2AlNO3 (Materials Project id mp-546679)

       293       90      118        0        0        0  
        90      293      118        0        0        0  
       118      118      253        0        0        0  
         0        0        0      121        0        0  
         0        0        0        0      121        0  
         0        0        0        0        0      120  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 165.67 GPaEV = 263.32 GPaGV = 106.6 GPaνV = 0.23509
ReussKR = 165.59 GPaER = 253.49 GPaGR = 101.81 GPaνR = 0.24486
HillKH = 165.63 GPaEH = 258.42 GPaGH = 104.21 GPaνH = 0.23996

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
120 GPa 121 GPa 121 GPa 138.91 GPa 203 GPa 497.09 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 180.29 GPa 291.29 GPa 1.9551 TPa–1 2.1289 TPa–1 75.418 GPa 121 GPa0.0641980.43646Value
Anisotropy 1.616 1.0889 1.604 6.7987Anisotropy
Axis 0.0000
0.0000
1.0000
0.5817
0.5817
-0.5686
0.5000
0.8660
0.0000
0.0000
0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.0000
1.0000
-0.7071
0.7071
0.0000
-0.7071
0.7071
-0.0000
Axis
0.7071
-0.0005
-0.7071
1.0000
0.0002
-0.0000
-0.7071
-0.7071
0.0000
0.0004
0.0004
-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