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 Ag2BiO3 (Materials Project id mp-23558)

       162       82       88        0        0        0  
        82      114       81        0        0        0  
        88       81      132        0        0        0  
         0        0        0       15        0        0  
         0        0        0        0       19        0  
         0        0        0        0        0       22  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 101.11 GPaEV = 60.667 GPaGV = 21.667 GPaνV = 0.4
ReussKR = 98.073 GPaER = 57.137 GPaGR = 20.364 GPaνR = 0.4029
HillKH = 99.592 GPaEH = 58.903 GPaGH = 21.015 GPaνH = 0.40143

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
15 GPa 19 GPa 22 GPa 41.32 GPa 61.3 GPa 305.38 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 47.317 GPa 91.14 GPa 1.8112 TPa–1 5.2204 TPa–1 15 GPa 28.637 GPa0.217510.58648Value
Anisotropy 1.926 2.8822 1.909 2.6963Anisotropy
Axis -0.0000
0.7523
0.6588
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
1.0000
0.0000
-0.0003
-0.0000
1.0000
0.7071
-0.0003
0.7071
0.0000
0.7190
-0.6950
0.0001
0.6376
0.7704
Axis
0.0000
1.0000
0.0000
0.7071
-0.0005
-0.7071
-1.0000
-0.0000
-0.0000
-0.0001
0.7704
-0.6376
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