Pr4ZnB4Rh9

High-Entropy Materials HEA

MP-ID: mp-3296301 · Space group: P6_3/mmc (#194)

Materials Project API

Basic Information

Formula

Pr4ZnB4Rh9

MP-ID

mp-3296301

Elements

Sites

Density

9.6040

g/cm³

Volume

552.74

Å³

Cell a

5.5497

Cell b

5.5497

Cell c

20.7230

α Angle

90.00

β Angle

90.00

γ Angle

120.00

Space Group

P6_3/mmc

Point Group

6/mmm

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
17.12	5.1808	1.0	(0,0,0,4)
25.79	3.4538	3.7	(0,0,0,6)
31.91	2.8047	12.2	(0,1,-1,6)
31.91	2.8047	12.2	(1,0,-1,6)
31.91	2.8047	12.3	(1,-1,0,6)
32.26	2.7749	10.0	(1,1,-2,0)
32.26	2.7749	10.0	(1,-2,1,0)
32.26	2.7748	10.0	(2,-1,-1,0)
33.43	2.6804	6.9	(1,1,-2,2)
33.43	2.6804	6.9	(1,-2,1,2)
33.43	2.6804	6.9	(2,-1,-1,2)
34.63	2.5904	27.3	(0,0,0,8)
35.62	2.5206	60.2	(0,1,-1,7)
35.62	2.5206	60.2	(1,0,-1,7)
35.62	2.5206	60.2	(1,-1,0,7)
36.74	2.4461	9.2	(1,1,-2,4)
36.74	2.4461	18.5	(2,-1,-1,4)
37.42	2.4031	24.5	(0,2,-2,0)
37.42	2.4031	24.5	(2,0,-2,0)
37.42	2.4031	24.3	(2,-2,0,0)
37.68	2.3871	76.0	(0,2,-2,1)
37.68	2.3871	76.0	(2,0,-2,1)
37.68	2.3871	76.3	(2,-2,0,1)
39.52	2.2803	9.9	(1,0,-1,8)

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Energy Properties

Formation Energy/atom

-0.75807

eV/atom

Energy/atom

-21.48795

eV/atom

Energy above Hull

0.0000

eV/atom

Uncorrected Energy

-21.4880

eV/atom

Volume/atom

15.35

Å³

c/a Ratio

3.7341

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Total Mag. Moment

0.0013

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 · 0.500

Element Family

4d-TM

Solute Fraction

0.500

Interstitial Fraction

0.222

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.1756

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

9.7742

J/mol·K

Ω Parameter

2.5334

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

23.396%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.4588

smaller = more stable mixing

VEC

6.500

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-7.513

kJ/mol; negative = exothermic mixing

Entropy Norm

0.8480

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (1)

aaahfoev

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-3296301

Reference Citation

The crystal structure and related material properties of Pr4ZnB4Rh9 were obtained from the Materials Project database (MP-ID: mp-3296301, 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_Pr4ZnB4Rh9
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.54968863
_cell_length_b   5.54969008
_cell_length_c   20.72304043
_cell_angle_alpha   90.00000000
_cell_angle_beta   90.00000000
_cell_angle_gamma   119.99987637
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Pr4ZnB4Rh9
_chemical_formula_sum   'Pr8 Zn2 B8 Rh18'
_cell_volume   552.74140126
_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
  Pr  Pr0  1  0.66667143  0.33332857  0.52257419  1.0
  Pr  Pr1  1  0.33332857  0.66667143  0.47742581  1.0
  Pr  Pr2  1  0.33332857  0.66667143  0.02257419  1.0
  Pr  Pr3  1  0.66667143  0.33332857  0.97742581  1.0
  Pr  Pr4  1  0.66674308  0.33325692  0.67378520  1.0
  Pr  Pr5  1  0.33325692  0.66674308  0.32621480  1.0
  Pr  Pr6  1  0.33325692  0.66674308  0.17378520  1.0
  Pr  Pr7  1  0.66674308  0.33325692  0.82621480  1.0
  Zn  Zn8  1  0.00000000  0.00000000  0.50000000  1.0
  Zn  Zn9  1  0.00000000  0.00000000  0.00000000  1.0
  B  B10  1  0.00006241  0.99993759  0.67463059  1.0
  B  B11  1  0.99993759  0.00006241  0.32536941  1.0
  B  B12  1  0.99993759  0.00006241  0.17463059  1.0
  B  B13  1  0.00006241  0.99993759  0.82536941  1.0
  B  B14  1  0.66660934  0.33339066  0.32651109  1.0
  B  B15  1  0.33339066  0.66660934  0.67348891  1.0
  B  B16  1  0.33339066  0.66660934  0.82651109  1.0
  B  B17  1  0.66660934  0.33339066  0.17348891  1.0
  Rh  Rh18  1  0.16681798  0.33341221  0.75000000  1.0
  Rh  Rh19  1  0.16680656  0.83319344  0.75000000  1.0
  Rh  Rh20  1  0.66658779  0.83318202  0.75000000  1.0
  Rh  Rh21  1  0.83318202  0.66658779  0.25000000  1.0
  Rh  Rh22  1  0.83319344  0.16680656  0.25000000  1.0
  Rh  Rh23  1  0.33341221  0.16681798  0.25000000  1.0
  Rh  Rh24  1  0.16570708  0.33123176  0.60654144  1.0
  Rh  Rh25  1  0.16570163  0.83429837  0.60654103  1.0
  Rh  Rh26  1  0.66876824  0.83429292  0.60654144  1.0
  Rh  Rh27  1  0.83429292  0.66876824  0.39345856  1.0
  Rh  Rh28  1  0.83429837  0.16570163  0.39345897  1.0
  Rh  Rh29  1  0.33123176  0.16570708  0.39345856  1.0
  Rh  Rh30  1  0.83429292  0.66876824  0.10654144  1.0
  Rh  Rh31  1  0.83429837  0.16570163  0.10654103  1.0
  Rh  Rh32  1  0.33123176  0.16570708  0.10654144  1.0
  Rh  Rh33  1  0.16570708  0.33123176  0.89345856  1.0
  Rh  Rh34  1  0.16570163  0.83429837  0.89345897  1.0
  Rh  Rh35  1  0.66876824  0.83429292  0.89345856  1.0

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