PrAlGeAu

High-Entropy Materials HEA

MP-ID: mp-3246707 · Space group: Cmcm (#63)

Materials Project API

Basic Information

Formula

PrAlGeAu

MP-ID

mp-3246707

Elements

Sites

Density

8.5328

g/cm³

Volume

170.28

Å³

Cell a

9.4764

Cell b

9.4764

Cell c

4.3051

α Angle

90.00

β Angle

90.00

γ Angle

153.87

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
9.58	9.2310	2.8	(1,-1,0)
19.23	4.6155	12.1	(2,-2,0)
21.29	4.1738	4.4	(1,0,0)
22.79	3.9017	5.8	(1,-1,1)
25.33	3.5164	6.1	(1,-2,0)
25.33	3.5164	6.1	(2,-1,0)
28.35	3.1482	44.1	(2,-2,1)
29.02	3.0770	1.4	(3,-3,0)
29.81	2.9967	100.0	(1,0,1)
32.00	2.7971	32.5	(2,-3,0)
32.00	2.7971	32.5	(3,-2,0)
32.89	2.7234	44.2	(2,-1,1)
35.87	2.5033	19.3	(3,-3,1)
38.38	2.3455	3.7	(2,-3,1)
38.38	2.3455	3.7	(3,-2,1)
39.03	2.3078	2.7	(4,-4,0)
40.15	2.2460	2.0	(3,-4,0)
40.15	2.2460	2.0	(4,-3,0)
41.97	2.1526	32.1	(0,0,2)
42.18	2.1424	31.7	(1,1,0)
44.55	2.0340	32.3	(4,-4,1)
45.55	1.9913	7.3	(3,-4,1)
45.55	1.9913	7.3	(4,-3,1)
46.55	1.9508	2.6	(2,-2,2)

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Energy Properties

Formation Energy/atom

-0.85199

eV/atom

Energy/atom

-26.00024

eV/atom

Energy above Hull

0.0000

eV/atom

Uncorrected Energy

-26.0002

eV/atom

Volume/atom

21.28

Å³

c/a Ratio

0.4543

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Total Mag. Moment

0.0000

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

Pr · 0.250

Element Family

Lanthanide

Solute Fraction

0.750

Interstitial Fraction

0.000

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.3863

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

11.5257

J/mol·K

Ω Parameter

1.1520

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

14.728%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.5183

smaller = more stable mixing

VEC

5.250

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-11.730

kJ/mol; negative = exothermic mixing

Entropy Norm

1.0000

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (1)

aaahcsvj

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-3246707

Reference Citation

The crystal structure and related material properties of PrAlGeAu were obtained from the Materials Project database (MP-ID: mp-3246707, 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

Loading 3D structure…

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Raw CIF Data

# generated using pymatgen
data_PrAlGeAu
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.47637609
_cell_length_b   9.47637692
_cell_length_c   4.30512120
_cell_angle_alpha   90.00000000
_cell_angle_beta   90.00000000
_cell_angle_gamma   153.86779742
_symmetry_Int_Tables_number   1
_chemical_formula_structural   PrAlGeAu
_chemical_formula_sum   'Pr2 Al2 Ge2 Au2'
_cell_volume   170.27877864
_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  0.90268095  0.09731905  0.75000000  1.0
  Pr  Pr1  1  0.09731905  0.90268095  0.25000000  1.0
  Al  Al2  1  0.25024990  0.74975010  0.75000000  1.0
  Al  Al3  1  0.74975010  0.25024990  0.25000000  1.0
  Ge  Ge4  1  0.53581899  0.46418101  0.75000000  1.0
  Ge  Ge5  1  0.46418101  0.53581899  0.25000000  1.0
  Au  Au6  1  0.67350828  0.32649172  0.75000000  1.0
  Au  Au7  1  0.32649172  0.67350828  0.25000000  1.0

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