HoEr9(RuPb3)2

High-Entropy Materials HEA

MP-ID: mp-3292623 · Space group: P312 (#149)

Materials Project API

Basic Information

Formula

HoEr9(RuPb3)2

MP-ID

mp-3292623

Elements

Sites

Density

10.9249

g/cm³

Volume

473.56

Å³

Cell a

9.1981

Cell b

9.1981

Cell c

6.4632

α Angle

90.00

β Angle

90.00

γ Angle

120.00

Space Group

P312

Point Group

Crystal System

Trigonal

Bravais Lattice

Stability

Packing Fraction

0.7405

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
22.32	3.9829	1.6	(2,-2,0,0)
23.74	3.7472	4.3	(2,-1,-1,1)
27.60	3.2316	15.1	(0,0,0,2)
29.67	3.0108	14.6	(3,-1,-2,0)
29.84	2.9946	2.5	(1,0,-1,2)
32.82	2.7292	100.0	(3,-1,-2,1)
33.76	2.6553	26.8	(3,0,-3,0)
33.76	2.6553	13.4	(3,-3,0,0)
33.90	2.6441	81.2	(2,-1,-1,2)
35.78	2.5095	2.1	(2,0,-2,2)
35.78	2.5095	4.1	(2,-2,0,2)
39.18	2.2995	1.6	(4,-2,-2,0)
40.85	2.2093	3.0	(4,-1,-3,0)
40.97	2.2029	4.2	(3,-1,-2,2)
41.69	2.1665	9.0	(4,-2,-2,1)
43.28	2.0906	18.1	(4,-1,-3,1)
45.55	1.9915	2.4	(4,0,-4,0)
48.59	1.8736	16.4	(4,-2,-2,2)
52.00	1.7585	4.2	(5,-2,-3,1)
52.21	1.7521	4.6	(2,1,-3,3)
52.21	1.7521	22.9	(3,-1,-2,3)
52.65	1.7383	5.1	(5,-1,-4,0)
52.65	1.7383	5.1	(5,-4,-1,0)
54.09	1.6954	5.8	(4,0,-4,2)

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Energy Properties

Formation Energy/atom

-0.62519

eV/atom

Energy/atom

-41.00131

eV/atom

Energy above Hull

0.0005

eV/atom

Uncorrected Energy

-41.0013

eV/atom

Volume/atom

26.31

Å³

c/a Ratio

0.7027

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Total Mag. Moment

0.0005

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

Er · 0.500

Element Family

Lanthanide

Solute Fraction

0.500

Interstitial Fraction

0.000

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.1175

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

9.2908

J/mol·K

Ω Parameter

3.5488

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

7.560%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.5273

smaller = more stable mixing

VEC

8.833

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

3.894

kJ/mol; negative = exothermic mixing

Entropy Norm

0.8061

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (1)

aaahfitj

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-3292623

Reference Citation

The crystal structure and related material properties of HoEr9(RuPb3)2 were obtained from the Materials Project database (MP-ID: mp-3292623, 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_HoEr9(RuPb3)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.19809625
_cell_length_b   9.19809558
_cell_length_c   6.46321452
_cell_angle_alpha   90.00000000
_cell_angle_beta   90.00000000
_cell_angle_gamma   119.99999537
_symmetry_Int_Tables_number   1
_chemical_formula_structural   HoEr9(RuPb3)2
_chemical_formula_sum   'Ho1 Er9 Ru2 Pb6'
_cell_volume   473.56008548
_cell_formula_units_Z   1
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
  Ho  Ho0  1  0.33333300  0.66666700  0.50000000  1.0
  Er  Er1  1  0.99997270  0.76378424  0.75009026  1.0
  Er  Er2  1  0.23621576  0.00002730  0.24990974  1.0
  Er  Er3  1  0.76381154  0.00002730  0.75009026  1.0
  Er  Er4  1  0.99997270  0.23618846  0.24990974  1.0
  Er  Er5  1  0.66666700  0.33333300  0.50000000  1.0
  Er  Er6  1  0.76381154  0.76378424  0.24990974  1.0
  Er  Er7  1  0.23621576  0.23618846  0.75009026  1.0
  Er  Er8  1  0.33333300  0.66666700  0.00000000  1.0
  Er  Er9  1  0.66666700  0.33333300  0.00000000  1.0
  Ru  Ru10  1  0.00000000  0.00000000  0.00000000  1.0
  Ru  Ru11  1  0.00000000  0.00000000  0.50000000  1.0
  Pb  Pb12  1  0.40300305  0.40273344  0.24958546  1.0
  Pb  Pb13  1  0.99973038  0.40273344  0.75041454  1.0
  Pb  Pb14  1  0.99973038  0.59699695  0.24958546  1.0
  Pb  Pb15  1  0.59726656  0.00026962  0.24958546  1.0
  Pb  Pb16  1  0.40300305  0.00026962  0.75041454  1.0
  Pb  Pb17  1  0.59726656  0.59699695  0.75041454  1.0

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