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 ZrNCl (Materials Project id mp-568592)

       141       60        1        0        0        0  
        60      141        1       -0        0        0  
         1        1        3        0        0        0  
         0       -0        0        1        0        0  
         0        0        0        0        1        0  
         0        0        0        0        0       40  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 45.444 GPaEV = 59.624 GPaGV = 23.267 GPaνV = 0.28133
ReussKR = 2.9606 GPaER = 4.8918 GPaGR = 1.9973 GPaνR = 0.22461
HillKH = 24.203 GPaEH = 32.28 GPaGH = 12.632 GPaνH = 0.27771

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
1 GPa 1 GPa 2.9899 GPa 40 GPa 81 GPa 201.01 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 2.6628 GPa 115.36 GPa 3.3278 TPa–1 331.11 TPa–1 1 GPa 40.5 GPa0.00497510.60526Value
Anisotropy 43.32 99.5000 40.5121.6578Anisotropy
Axis 0.3541
0.3541
0.8656
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.0000
1.0000
0.0000
0.0000
1.0000
-0.7071
0.7071
-0.0000
0.0000
0.0000
1.0000
0.9392
-0.0004
0.3432
Axis
1.0000
0.0000
-0.0000
-0.7071
-0.7071
-0.0000
-0.7660
0.6428
0.0000
0.3432
-0.0005
-0.9392
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