Er2Ga9Ru2Rh

High-Entropy Materials HEA

MP-ID: mp-3296264 · Space group: Cmcm (#63)

Materials Project API

Basic Information

Formula

Er2Ga9Ru2Rh

MP-ID

mp-3296264

Elements

Sites

Density

9.1975

g/cm³

Volume

457.52

Å³

Cell a

7.4272

Cell b

7.4272

Cell c

9.5633

α Angle

90.00

β Angle

90.00

γ Angle

119.86

Space Group

Cmcm

Point Group

mmm

Crystal System

Orthorhombic

Bravais Lattice

Stability

Yes

Packing Fraction

X-ray Diffraction

Diffraction Pattern

Target / Radiation

X-axis: 2θ (°); Y-axis: relative intensity; Cu Kα ; λ=1.5418 Å

Diffraction Peaks (Top 24)

2θ	d (Å)	I	hkl
13.75	6.4414	1.2	(1,0,-1,0)
13.78	6.4275	2.1	(1,-1,0,0)
16.59	5.3425	2.3	(1,0,-1,1)
23.18	3.8365	1.1	(1,-1,0,2)
25.69	3.4683	5.4	(1,1,-2,1)
25.74	3.4617	5.9	(1,-2,1,1)
25.74	3.4617	5.9	(2,-1,-1,1)
27.70	3.2207	1.1	(0,2,-2,0)
27.70	3.2207	1.1	(2,0,-2,0)
27.76	3.2137	4.8	(2,-2,0,0)
29.26	3.0523	6.7	(0,2,-2,1)
29.26	3.0523	6.7	(2,0,-2,1)
30.44	2.9369	10.4	(1,1,-2,2)
30.48	2.9330	19.2	(2,-1,-1,2)
31.31	2.8570	1.4	(1,0,-1,3)
33.55	2.6713	2.0	(0,2,-2,2)
33.55	2.6713	2.0	(2,0,-2,2)
33.60	2.6673	11.7	(2,-2,0,2)
36.90	2.4361	7.7	(2,1,-3,0)
36.99	2.4301	4.4	(3,-2,-1,0)
37.14	2.4210	48.7	(1,1,-2,3)
37.17	2.4188	100.0	(2,-1,-1,3)
37.62	2.3908	28.3	(0,0,0,4)
38.12	2.3607	3.9	(2,1,-3,1)

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Energy Properties

Formation Energy/atom

-0.64152

eV/atom

Energy/atom

-18.20018

eV/atom

Energy above Hull

0.0000

eV/atom

Uncorrected Energy

-18.2002

eV/atom

Volume/atom

16.34

Å³

c/a Ratio

1.2876

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Total Mag. Moment

0.0014

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.000000

μB/Å³

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

Ga · 0.643

Element Family

PostTransition-Noble

Solute Fraction

0.357

Interstitial Fraction

0.000

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.0285

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

8.5511

J/mol·K

Ω Parameter

4.3710

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

10.029%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.2896

smaller = more stable mixing

VEC

5.429

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-1.926

kJ/mol; negative = exothermic mixing

Entropy Norm

0.7419

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (1)

aaahfodk

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-3296264

Reference Citation

The crystal structure and related material properties of Er2Ga9Ru2Rh were obtained from the Materials Project database (MP-ID: mp-3296264, database version v2026.04.13).

Literature Citation

Horton, M.K., Huck, P., Yang, R.X. et al. Accelerated data-driven materials science with the Materials Project. Nat. Mater. 24, 1522–1532 (2025). https://doi.org/10.1038/s41563-025-02272-0

3D Crystal Structure Rendering

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Raw CIF Data

# generated using pymatgen
data_Er2Ga9Ru2Rh
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.42718152
_cell_length_b   7.42718209
_cell_length_c   9.56327640
_cell_angle_alpha   90.00000000
_cell_angle_beta   90.00000000
_cell_angle_gamma   119.85670817
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Er2Ga9Ru2Rh
_chemical_formula_sum   'Er4 Ga18 Ru4 Rh2'
_cell_volume   457.52066998
_cell_formula_units_Z   2
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Er  Er0  1  0.99746267  0.66804057  0.25000000  1.0
  Er  Er1  1  0.00253733  0.33195943  0.75000000  1.0
  Er  Er2  1  0.66804057  0.99746267  0.25000000  1.0
  Er  Er3  1  0.33195943  0.00253733  0.75000000  1.0
  Ga  Ga4  1  0.12800212  0.12800212  0.25000000  1.0
  Ga  Ga5  1  0.87199788  0.87199788  0.75000000  1.0
  Ga  Ga6  1  0.00523608  0.33524891  0.07752865  1.0
  Ga  Ga7  1  0.99476392  0.66475109  0.92247135  1.0
  Ga  Ga8  1  0.99476392  0.66475109  0.57752865  1.0
  Ga  Ga9  1  0.33524891  0.00523608  0.42247135  1.0
  Ga  Ga10  1  0.00523608  0.33524891  0.42247135  1.0
  Ga  Ga11  1  0.66475109  0.99476392  0.57752865  1.0
  Ga  Ga12  1  0.66475109  0.99476392  0.92247135  1.0
  Ga  Ga13  1  0.33524891  0.00523608  0.07752865  1.0
  Ga  Ga14  1  0.33953153  0.33953153  0.56457770  1.0
  Ga  Ga15  1  0.66046847  0.66046847  0.43542230  1.0
  Ga  Ga16  1  0.66046847  0.66046847  0.06457770  1.0
  Ga  Ga17  1  0.33953153  0.33953153  0.93542230  1.0
  Ga  Ga18  1  0.33559527  0.54823741  0.25000000  1.0
  Ga  Ga19  1  0.66440473  0.45176259  0.75000000  1.0
  Ga  Ga20  1  0.54823741  0.33559527  0.25000000  1.0
  Ga  Ga21  1  0.45176259  0.66440473  0.75000000  1.0
  Ru  Ru22  1  0.67500800  0.32499200  0.00000000  1.0
  Ru  Ru23  1  0.32499200  0.67500800  0.00000000  1.0
  Ru  Ru24  1  0.32499200  0.67500800  0.50000000  1.0
  Ru  Ru25  1  0.67500800  0.32499200  0.50000000  1.0
  Rh  Rh26  1  0.00000000  0.00000000  0.00000000  1.0
  Rh  Rh27  1  0.00000000  0.00000000  0.50000000  1.0

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