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 MnAgO2 (Materials Project id mp-996995)

       289       64       43        0       -9        0  
        64      213       33        0      -11        0  
        43       33      108        0      -13        0  
         0        0        0       44        0       -0  
        -9      -11      -13        0       19        0  
         0        0        0       -0        0       17  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 98.889 GPaEV = 122.46 GPaGV = 47.333 GPaνV = 0.2936
ReussKR = 73.452 GPaER = 77.658 GPaGR = 29.332 GPaνR = 0.32379
HillKH = 86.17 GPaEH = 100.15 GPaGH = 38.333 GPaνH = 0.3063

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
16.923 GPa 17 GPa 44 GPa 95.899 GPa 177.4 GPa 338.78 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 45.89 GPa 259.18 GPa-0.34884 TPa–1 10.674 TPa–1 16.93 GPa 91.265 GPa0.00101690.87178Value
Anisotropy 5.648 5.391857.2647Anisotropy
Axis -0.6115
0.0000
-0.7913
1.0000
-0.0000
-0.0097
-0.9013
0.0000
0.4331
-0.4332
0.0000
-0.9013
-0.0564
0.3849
0.9212
-0.7068
0.7071
-0.0209
-0.7118
0.0000
-0.7024
-0.8741
-0.0000
0.4858
Axis
-0.9956
0.0480
-0.0810
-0.7068
-0.7071
-0.0208
-0.0000
-1.0000
-0.0000
-0.4858
0.0000
-0.8741
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