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 CaAl2(SiO4)2 (Materials Project id mp-758658)

       133       76       49       11       14       13  
        76      140       61        2        4        1  
        49       61      126        7        6        1  
        11        2        7       43       -1       -7  
        14        4        6       -1       38        9  
        13        1        1       -7        9       67  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 85.667 GPaEV = 112.27 GPaGV = 43.8 GPaνV = 0.28158
ReussKR = 80.752 GPaER = 99.907 GPaGR = 38.61 GPaνR = 0.2938
HillKH = 83.209 GPaEH = 106.1 GPaGH = 41.205 GPaνH = 0.28748

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
33.176 GPa 37.299 GPa 59.487 GPa 71.311 GPa 85.366 GPa 260.36 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 68.799 GPa 164.44 GPa 1.6555 TPa–1 6.4493 TPa–1 25.253 GPa 72.306 GPa0.0133190.56183Value
Anisotropy 2.39 3.8957 2.863 42.1829Anisotropy
Axis -0.8426
-0.0607
0.5351
0.7794
0.5899
0.2110
0.3012
0.8614
0.4090
0.5992
0.1626
-0.7839
0.7232
0.6858
-0.0817
0.9740
-0.0443
-0.2221
0.6744
0.7136
-0.1894
0.2313
0.7779
0.5843
Axis
-0.5691
0.6587
0.4921
0.1102
0.9495
0.2939
-0.5833
0.6723
0.4559
-0.9570
0.0739
0.2805
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