ELATE: Elastic tensor analysis

Welcome to ELATE, the online tool for analysis of elastic tensors, developed by Romain Gaillac and François-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 Li3P7 (Materials Project id mp-28336)

        36       16       19        0        0        0  
        16       34       17        0        0        0  
        19       17       47        0        0        0  
         0        0        0       11        0        0  
         0        0        0        0       16        0  
         0        0        0        0        0       11

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	K_V = 24.556 GPa	E_V = 30.809 GPa	G_V = 11.933 GPa	ν_V = 0.29089
Reuss	K_R = 23.921 GPa	E_R = 29.775 GPa	G_R = 11.518 GPa	ν_R = 0.29254
Hill	K_H = 24.238 GPa	E_H = 30.292 GPa	G_H = 11.726 GPa	ν_H = 0.2917

Eigenvalues of the stiffness matrix

λ₁	λ₂	λ₃	λ₄	λ₅	λ₆
11 GPa	11 GPa	16 GPa	18.92 GPa	23.494 GPa	74.586 GPa

Variations of the elastic moduli

	Young's modulus		Linear compressibility		Shear modulus		Poisson's ratio
	E_min	E_max	β_min	β_max	G_min	G_max	ν_min	ν_max
Value	24.909 GPa	38.118 GPa	8.6264 TPa^–1	17.916 TPa^–1	9.478 GPa	16 GPa	0.14993	0.40956	Value
Anisotropy	1.53		2.0769		1.688		2.7318		Anisotropy
Axis	0.0000 1.0000 0.0000	0.5666 0.0000 0.8240	0.0000 0.0000 1.0000	0.0000 1.0000 0.0000	-0.7071 0.7071 -0.0000	0.0000 0.0000 1.0000	0.7291 -0.0003 0.6845	-0.6900 0.0000 -0.7238	Axis
					-0.7071 -0.7071 -0.0000	-1.0000 0.0000 0.0000	0.6845 -0.0006 -0.7291	-0.0000 -1.0000 -0.0000	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