Ho5Zr3(Si3Rh4)4

High-Entropy Materials HEA

MP-ID: mp-3292455 · Space group: P-62m (#189)

Materials Project API

Basic Information

Formula

Ho5Zr3(Si3Rh4)4

MP-ID

mp-3292455

Elements

Sites

Density

8.8799

g/cm³

Volume

576.30

Å³

Cell a

12.9215

Cell b

12.9215

Cell c

3.9856

α Angle

90.00

β Angle

90.00

γ Angle

120.00

Space Group

P-62m

Point Group

-6m2

Crystal System

Hexagonal

Bravais Lattice

Stability

Yes

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
15.84	5.5952	1.4	(2,0,-2,0)
23.70	3.7545	2.4	(1,0,-1,1)
26.27	3.3921	6.8	(2,-1,-1,1)
27.61	3.2304	17.4	(4,-2,-2,0)
28.76	3.1037	1.5	(4,-1,-3,0)
30.83	2.9007	7.7	(3,-1,-2,1)
32.89	2.7234	6.8	(3,0,-3,1)
34.95	2.5673	2.5	(5,-3,-2,0)
34.95	2.5673	2.5	(5,-2,-3,0)
35.78	2.5096	100.0	(4,-2,-2,1)
36.70	2.4488	23.9	(4,-1,-3,1)
36.81	2.4419	14.3	(5,-1,-4,0)
39.35	2.2898	4.2	(4,0,-4,1)
40.30	2.2381	6.8	(5,0,-5,0)
41.95	2.1536	1.4	(3,-6,3,0)
41.95	2.1536	2.8	(6,-3,-3,0)
42.76	2.1148	3.8	(6,-2,-4,0)
42.76	2.1148	1.9	(4,2,-6,0)
43.46	2.0822	5.3	(5,-1,-4,1)
45.11	2.0099	1.4	(5,-6,1,0)
45.11	2.0099	7.0	(6,-1,-5,0)
45.52	1.9928	22.4	(0,0,0,2)
46.54	1.9515	1.8	(5,-5,0,1)
46.54	1.9515	3.5	(5,0,-5,1)

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Energy Properties

Formation Energy/atom

-1.14750

eV/atom

Energy/atom

-21.26197

eV/atom

Energy above Hull

0.0000

eV/atom

Uncorrected Energy

-21.2620

eV/atom

Volume/atom

16.01

Å³

c/a Ratio

0.3084

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Total Mag. Moment

0.0001

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

Rh · 0.444

Element Family

4d-TM

Solute Fraction

0.556

Interstitial Fraction

0.333

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.2079

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

10.0422

J/mol·K

Ω Parameter

1.0017

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

14.338%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.3909

smaller = more stable mixing

VEC

7.194

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-19.797

kJ/mol; negative = exothermic mixing

Entropy Norm

0.8713

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (1)

aaahfimx

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-3292455

Reference Citation

The crystal structure and related material properties of Ho5Zr3(Si3Rh4)4 were obtained from the Materials Project database (MP-ID: mp-3292455, 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_Ho5Zr3(Si3Rh4)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   12.92153885
_cell_length_b   12.92153965
_cell_length_c   3.98556275
_cell_angle_alpha   90.00000000
_cell_angle_beta   90.00000000
_cell_angle_gamma   120.00000547
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Ho5Zr3(Si3Rh4)4
_chemical_formula_sum   'Ho5 Zr3 Si12 Rh16'
_cell_volume   576.30018806
_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  0.18631531  0.18631531  0.50000000  1.0
  Ho  Ho1  1  0.81368469  1.00000000  0.50000000  1.0
  Ho  Ho2  1  1.00000000  0.81368469  0.50000000  1.0
  Ho  Ho3  1  0.33333300  0.66666700  0.00000000  1.0
  Ho  Ho4  1  0.66666700  0.33333300  0.00000000  1.0
  Zr  Zr5  1  0.56210461  0.56210461  0.00000000  1.0
  Zr  Zr6  1  0.43789539  1.00000000  0.00000000  1.0
  Zr  Zr7  1  1.00000000  0.43789539  0.00000000  1.0
  Si  Si8  1  0.81827270  0.81827270  0.00000000  1.0
  Si  Si9  1  0.18172730  0.00000000  0.00000000  1.0
  Si  Si10  1  0.00000000  0.18172730  0.00000000  1.0
  Si  Si11  1  0.17696758  0.47945654  0.50000000  1.0
  Si  Si12  1  0.52054346  0.69751103  0.50000000  1.0
  Si  Si13  1  0.30248897  0.82303242  0.50000000  1.0
  Si  Si14  1  0.69751103  0.52054346  0.50000000  1.0
  Si  Si15  1  0.82303242  0.30248897  0.50000000  1.0
  Si  Si16  1  0.47945654  0.17696758  0.50000000  1.0
  Si  Si17  1  0.35714249  0.35714249  0.00000000  1.0
  Si  Si18  1  0.64285751  1.00000000  0.00000000  1.0
  Si  Si19  1  1.00000000  0.64285751  0.00000000  1.0
  Rh  Rh20  1  0.72297982  0.72297982  0.50000000  1.0
  Rh  Rh21  1  0.27702018  1.00000000  0.50000000  1.0
  Rh  Rh22  1  1.00000000  0.27702018  0.50000000  1.0
  Rh  Rh23  1  0.18066959  0.37266676  0.00000000  1.0
  Rh  Rh24  1  0.62733324  0.80800283  0.00000000  1.0
  Rh  Rh25  1  0.19199717  0.81933041  0.00000000  1.0
  Rh  Rh26  1  0.80800283  0.62733324  0.00000000  1.0
  Rh  Rh27  1  0.81933041  0.19199717  0.00000000  1.0
  Rh  Rh28  1  0.37266676  0.18066959  0.00000000  1.0
  Rh  Rh29  1  0.36561285  0.48982407  0.50000000  1.0
  Rh  Rh30  1  0.51017593  0.87578979  0.50000000  1.0
  Rh  Rh31  1  0.12421021  0.63438715  0.50000000  1.0
  Rh  Rh32  1  0.87578979  0.51017593  0.50000000  1.0
  Rh  Rh33  1  0.63438715  0.12421021  0.50000000  1.0
  Rh  Rh34  1  0.48982407  0.36561285  0.50000000  1.0
  Rh  Rh35  1  0.00000000  0.00000000  0.00000000  1.0

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