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 Ca(CdP)2 (Materials Project id mp-9570)

       114       39       30        2        0        0  
        39      114       30       -2        0        0  
        30       30       89        0        0        0  
         2       -2        0       31        0        0  
         0        0        0        0       31        2  
         0        0        0        0        2       38  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 57.222 GPaEV = 86.25 GPaGV = 34.533 GPaνV = 0.24879
ReussKR = 56.005 GPaER = 84.882 GPaGR = 34.024 GPaνR = 0.2474
HillKH = 56.613 GPaEH = 85.566 GPaGH = 34.279 GPaνH = 0.2481

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
30.469 GPa 30.819 GPa 38.531 GPa 67.859 GPa 75.181 GPa 174.14 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 75.447 GPa 97.309 GPa 4.9928 TPa–1 7.87 TPa–1 30.443 GPa 38.531 GPa0.174670.30644Value
Anisotropy 1.29 1.5763 1.266 1.7543Anisotropy
Axis 0.0000
0.5573
0.8303
0.8252
0.5516
0.1219
0.1305
0.9914
0.0000
0.0000
0.0000
1.0000
0.2312
0.1364
0.9633
0.0000
0.9665
0.2567
0.4097
0.2434
0.8792
-1.0000
0.0000
-0.0000
Axis
-0.5033
0.8641
-0.0016
-1.0000
0.0001
-0.0000
-0.5077
0.8615
-0.0019
-0.0000
-0.8389
-0.5443
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