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 ScPd (Materials Project id mp-2781)

       156       93       93        0        0        0  
        93      156       93        0        0        0  
        93       93      156        0        0        0  
         0        0        0       44        0        0  
         0        0        0        0       44        0  
         0        0        0        0        0       44

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	K_V = 114 GPa	E_V = 105.02 GPa	G_V = 39 GPa	ν_V = 0.34646
Reuss	K_R = 114 GPa	E_R = 102.53 GPa	G_R = 37.973 GPa	ν_R = 0.3501
Hill	K_H = 114 GPa	E_H = 103.78 GPa	G_H = 38.486 GPa	ν_H = 0.34827

Eigenvalues of the stiffness matrix

λ₁	λ₂	λ₃	λ₄	λ₅	λ₆
44 GPa	44 GPa	44 GPa	63 GPa	63 GPa	342 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	86.53 GPa	116.95 GPa	2.924 TPa^–1	2.924 TPa^–1	31.5 GPa	44 GPa	0.22164	0.46402	Value
Anisotropy	1.352		1.0000		1.397		2.0936		Anisotropy
Axis	1.0000 0.0000 0.0000	0.5774 0.5774 0.5773	0.2053 0.7663 0.6088	0.8660 0.0000 0.5000	0.7071 -0.0003 0.7071	0.0000 0.0000 1.0000	0.7071 -0.0000 -0.7071	-0.7071 -0.0000 0.7071	Axis
					0.7071 -0.0005 -0.7071	-0.9397 -0.3420 0.0000	-0.7071 0.0002 -0.7071	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