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 KCaF3 (Materials Project id mp-4950)

       101        0        0        0        0        0  
         0      101        0        0        0        0  
         0        0      101        0        0        0  
         0        0        0       24        0        0  
         0        0        0        0       24        0  
         0        0        0        0        0       24

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	K_V = 33.667 GPa	E_V = 77.314 GPa	G_V = 34.6 GPa	ν_V = 0.11726
Reuss	K_R = 33.667 GPa	E_R = 70.058 GPa	G_R = 30.376 GPa	ν_R = 0.15318
Hill	K_H = 33.667 GPa	E_H = 73.743 GPa	G_H = 32.488 GPa	ν_H = 0.13493

Eigenvalues of the stiffness matrix

λ₁	λ₂	λ₃	λ₄	λ₅	λ₆
24 GPa	24 GPa	24 GPa	101 GPa	101 GPa	101 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	58.176 GPa	101 GPa	9.901 TPa^–1	9.901 TPa^–1	24 GPa	50.5 GPa	0	0.3557	Value
Anisotropy	1.736		1.0000		2.104		∞		Anisotropy
Axis	-0.5774 0.5774 -0.5773	0.0000 0.0000 1.0000	0.0000 0.0000 1.0000	-0.0670 0.2500 0.9659	0.0000 0.0000 1.0000	0.7071 -0.0003 0.7071	0.0000 0.0000 1.0000	0.7071 -0.0000 -0.7071	Axis
					0.1735 0.9848 -0.0000	0.7071 -0.0005 -0.7071	1.0000 0.0000 -0.0000	-0.7071 0.0002 -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