Pr4SnB4Rh9

High-Entropy Materials HEA

MP-ID: mp-3293137 · Space group: P6_3/mmc (#194)

Materials Project API

Basic Information

Formula

Pr4SnB4Rh9

MP-ID

mp-3293137

Elements

Sites

Density

9.6885

g/cm³

Volume

566.19

Å³

Cell a

5.5925

Cell b

5.5925

Cell c

20.9036

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
25.57	3.4839	1.1	(0,0,0,6)
31.64	2.8282	9.7	(1,0,-1,6)
31.64	2.8282	4.9	(1,-1,0,6)
32.01	2.7962	10.0	(1,1,-2,0)
32.01	2.7962	10.0	(1,-2,1,0)
32.01	2.7962	10.0	(2,-1,-1,0)
33.16	2.7012	8.0	(1,1,-2,2)
33.16	2.7012	8.0	(1,-2,1,2)
33.16	2.7012	8.0	(2,-1,-1,2)
34.32	2.6130	24.5	(0,0,0,8)
35.31	2.5419	100.0	(1,0,-1,7)
35.31	2.5419	50.0	(1,-1,0,7)
36.44	2.4655	9.9	(1,1,-2,4)
36.44	2.4655	9.9	(1,-2,1,4)
36.44	2.4655	9.9	(2,-1,-1,4)
37.13	2.4216	16.3	(0,2,-2,0)
37.13	2.4216	16.3	(2,0,-2,0)
37.13	2.4216	16.2	(2,-2,0,0)
37.38	2.4055	60.9	(0,2,-2,1)
37.38	2.4055	60.9	(2,0,-2,1)
37.38	2.4055	61.0	(2,-2,0,1)
38.15	2.3591	2.0	(0,2,-2,2)
38.15	2.3591	2.0	(2,0,-2,2)
38.15	2.3591	2.0	(2,-2,0,2)

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Energy Properties

Formation Energy/atom

-0.79561

eV/atom

Energy/atom

-22.40524

eV/atom

Energy above Hull

0.0000

eV/atom

Uncorrected Energy

-22.4052

eV/atom

Volume/atom

15.73

Å³

c/a Ratio

3.7378

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Total Mag. Moment

0.0022

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

3.4549

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

23.375%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.4535

smaller = more stable mixing

VEC

6.056

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-5.480

kJ/mol; negative = exothermic mixing

Entropy Norm

0.8480

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (1)

aaahfjnd

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-3293137

Reference Citation

The crystal structure and related material properties of Pr4SnB4Rh9 were obtained from the Materials Project database (MP-ID: mp-3293137, 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_Pr4SnB4Rh9
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.59247875
_cell_length_b   5.59248040
_cell_length_c   20.90359474
_cell_angle_alpha   90.00000000
_cell_angle_beta   90.00000000
_cell_angle_gamma   119.99990633
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Pr4SnB4Rh9
_chemical_formula_sum   'Pr8 Sn2 B8 Rh18'
_cell_volume   566.18822342
_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  0.66666777  0.33333223  0.52625455  1.0
  Pr  Pr1  1  0.33333223  0.66666777  0.47374545  1.0
  Pr  Pr2  1  0.33333223  0.66666777  0.02625455  1.0
  Pr  Pr3  1  0.66666777  0.33333223  0.97374545  1.0
  Pr  Pr4  1  0.66670664  0.33329336  0.67498911  1.0
  Pr  Pr5  1  0.33329336  0.66670664  0.32501089  1.0
  Pr  Pr6  1  0.33329336  0.66670664  0.17498911  1.0
  Pr  Pr7  1  0.66670664  0.33329336  0.82501089  1.0
  Sn  Sn8  1  0.00000000  0.00000000  0.50000000  1.0
  Sn  Sn9  1  0.00000000  0.00000000  0.00000000  1.0
  B  B10  1  0.00005751  0.99994249  0.67591086  1.0
  B  B11  1  0.99994249  0.00005751  0.32408914  1.0
  B  B12  1  0.99994249  0.00005751  0.17591086  1.0
  B  B13  1  0.00005751  0.99994249  0.82408914  1.0
  B  B14  1  0.66660930  0.33339070  0.32512330  1.0
  B  B15  1  0.33339070  0.66660930  0.67487670  1.0
  B  B16  1  0.33339070  0.66660930  0.82512330  1.0
  B  B17  1  0.66660930  0.33339070  0.17487670  1.0
  Rh  Rh18  1  0.16706058  0.33395986  0.75000000  1.0
  Rh  Rh19  1  0.16707286  0.83292714  0.75000000  1.0
  Rh  Rh20  1  0.66604014  0.83293942  0.75000000  1.0
  Rh  Rh21  1  0.83293942  0.66604014  0.25000000  1.0
  Rh  Rh22  1  0.83292714  0.16707286  0.25000000  1.0
  Rh  Rh23  1  0.33395986  0.16706058  0.25000000  1.0
  Rh  Rh24  1  0.16661704  0.33309228  0.60897759  1.0
  Rh  Rh25  1  0.16661650  0.83338350  0.60897433  1.0
  Rh  Rh26  1  0.66690772  0.83338296  0.60897759  1.0
  Rh  Rh27  1  0.83338296  0.66690772  0.39102241  1.0
  Rh  Rh28  1  0.83338350  0.16661650  0.39102567  1.0
  Rh  Rh29  1  0.33309228  0.16661704  0.39102241  1.0
  Rh  Rh30  1  0.83338296  0.66690772  0.10897759  1.0
  Rh  Rh31  1  0.83338350  0.16661650  0.10897433  1.0
  Rh  Rh32  1  0.33309228  0.16661704  0.10897759  1.0
  Rh  Rh33  1  0.16661704  0.33309228  0.89102241  1.0
  Rh  Rh34  1  0.16661650  0.83338350  0.89102567  1.0
  Rh  Rh35  1  0.66690772  0.83338296  0.89102241  1.0

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