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 Zr2Rh (Materials Project id mp-571664)

       155       93       93        0        0        0  
        93      158      155        0        0        0  
        93      155      158        0        0        0  
         0        0        0       15        0        0  
         0        0        0        0        6        0  
         0        0        0        0        0        6

Average properties

Averaging scheme	Bulk modulus	Young's modulus	Shear modulus	Poisson's ratio
Voigt	K_V = 128.11 GPa	E_V = 40.71 GPa	G_V = 14.067 GPa	ν_V = 0.44704
Reuss	K_R = 124.37 GPa	E_R = 13.578 GPa	G_R = 4.5817 GPa	ν_R = 0.4818
Hill	K_H = 126.24 GPa	E_H = 27.3 GPa	G_H = 9.3242 GPa	ν_H = 0.46396

Eigenvalues of the stiffness matrix

λ₁	λ₂	λ₃	λ₄	λ₅	λ₆
3 GPa	6 GPa	6 GPa	15 GPa	80.576 GPa	387.42 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	5.9119 GPa	99.735 GPa	1.9861 TPa^–1	4.0683 TPa^–1	1.5 GPa	28.462 GPa	-0.021019	0.98653	Value
Anisotropy	16.87		2.0484		18.97		∞		Anisotropy
Axis	0.0000 0.0000 1.0000	1.0000 0.0000 0.0000	0.0000 0.0000 1.0000	1.0000 0.0000 0.0000	-0.0000 0.7071 0.7071	0.7071 0.5000 -0.5000	0.7673 -0.0006 0.6413	-0.6197 0.7848 -0.0000	Axis
					0.0001 0.7071 -0.7071	-0.7071 0.5000 -0.5000	0.6413 -0.0010 -0.7673	0.0000 0.0000 -1.0000	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