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 Mn2N (Materials Project id mp-9981)

       310      124      141        0        0        0  
       124      321      149        0        0        0  
       141      149      327        0        0        0  
         0        0        0      112        0        0  
         0        0        0        0      120        0  
         0        0        0        0        0       88  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 198.44 GPaEV = 257.44 GPaGV = 100.27 GPaνV = 0.28378
ReussKR = 197.89 GPaER = 253.34 GPaGR = 98.449 GPaνR = 0.28663
HillKH = 198.17 GPaEH = 255.39 GPaGH = 99.358 GPaνH = 0.2852

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
88 GPa 112 GPa 120 GPa 170.55 GPa 191.41 GPa 596.04 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 224.7 GPa 282.56 GPa 1.472 TPa–1 1.8729 TPa–1 85.987 GPa 120 GPa0.175920.37205Value
Anisotropy 1.258 1.2723 1.396 2.1149Anisotropy
Axis 0.7320
0.6813
-0.0000
0.7153
-0.0000
0.6988
0.0000
0.0000
1.0000
1.0000
0.0000
0.0000
0.4624
0.5350
-0.7071
0.0000
0.0000
1.0000
-0.6571
0.2627
0.7066
-0.4820
0.3893
0.7850
Axis
-0.4627
-0.5347
-0.7071
-1.0000
0.0000
0.0000
-0.6627
0.2454
-0.7075
-0.5727
-0.8180
0.0540
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