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 DyPO4 (Materials Project id mp-5767)

       347       98       98        0        0        0  
        98      246       32        0        0        0  
        98       32      246        0        0        0  
         0        0        0       19        0        0  
         0        0        0        0       70        0  
         0        0        0        0        0       70  

Average properties

Averaging schemeBulk modulusYoung's modulusShear modulusPoisson's ratio
VoigtKV = 143.89 GPaEV = 186.3 GPaGV = 72.533 GPaνV = 0.28421
ReussKR = 133.2 GPaER = 131.31 GPaGR = 49.153 GPaνR = 0.33571
HillKH = 138.55 GPaEH = 159.22 GPaGH = 60.843 GPaνH = 0.30846

Eigenvalues of the stiffness matrix

λ1 λ2 λ3 λ4 λ5 λ6
19 GPa 70 GPa 70 GPa 169.68 GPa 214 GPa 455.32 GPa

Variations of the elastic moduli

Young's modulusLinear compressibility Shear modulusPoisson's ratio
EminEmax βminβmaxGminGmax νminνmax
Value 64.92 GPa 277.91 GPa 1.0614 TPa–1 3.223 TPa–1 19 GPa 107 GPa-0.074060.79268Value
Anisotropy 4.281 3.0366 5.632Anisotropy
Axis 0.0000
0.7071
0.7071
1.0000
0.0000
0.0000
1.0000
0.0000
0.0000
0.0000
0.3827
0.9239
0.0002
0.0001
1.0000
0.0000
0.7071
-0.7071
0.7457
0.4711
-0.4711
-0.6893
0.5123
0.5123
Axis
-0.0000
1.0000
-0.0001
0.0000
-0.7071
-0.7071
-0.6663
0.5273
-0.5273
-0.0000
-0.7071
0.7071
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