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 NdPbAu2 (Materials Project id mp-865597)

        81       69       69        0        0        0  
        69       81       69        0        0        0  
        69       69       81        0        0        0  
         0        0        0       34        0        0  
         0        0        0        0       34        0  
         0        0        0        0        0       34  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 73 GPaEV = 61.95 GPaGV = 22.8 GPaνV = 0.35856
ReussKR = 73 GPaER = 33.753 GPaGR = 11.86 GPaνR = 0.42294
HillKH = 73 GPaEH = 48.178 GPaGH = 17.33 GPaνH = 0.39

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
12 GPa 12 GPa 34 GPa 34 GPa 34 GPa 219 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 17.52 GPa 88.292 GPa 4.5662 TPa–1 4.5662 TPa–1 6 GPa 34 GPa-0.353981.1534Value
Anisotropy 5.04 1.0000 5.667Anisotropy
Axis 0.0000
0.0000
1.0000
-0.5774
0.5774
-0.5773
0.2566
0.9577
0.1305
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.0000
1.0000
0.7071
0.0001
-0.7071
0.0000
0.7071
-0.7071
Axis
-0.7071
-0.0002
-0.7071
0.7660
0.6428
-0.0000
-0.7071
-0.0002
-0.7071
-1.0000
0.0000
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