TiMn3Cr2(PO4)6

High-Entropy Materials HEA

MP-ID: mp-776109 · Space group: R3 (#146)

Materials Project API

Basic Information

Formula

TiMn3Cr2(PO4)6

MP-ID

mp-776109

Elements

Sites

Density

3.3127

g/cm³

Volume

444.37

Å³

Cell a

8.4587

Cell b

8.4587

Cell c

8.4587

α Angle

61.71

β Angle

61.71

γ Angle

61.71

Space Group

Point Group

Crystal System

Trigonal

Bravais Lattice

Stability

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
14.63	6.0547	2.0	(1,1,0)
20.47	4.3383	68.3	(1,0,-1)
21.02	4.2265	7.6	(2,1,1)
24.32	3.6598	100.0	(2,1,0)
25.25	3.5265	13.0	(2,0,0)
29.51	3.0274	5.2	(2,2,0)
31.81	2.8131	13.8	(2,0,-1)
32.73	2.7365	2.3	(2,-1,1)
32.73	2.7365	1.1	(2,1,-1)
33.44	2.6799	63.5	(3,2,1)
35.85	2.5047	37.4	(2,-1,-1)
36.18	2.4826	3.9	(3,1,0)
38.60	2.3327	1.8	(3,0,2)
42.79	2.1133	7.1	(4,2,2)
43.80	2.0670	1.8	(3,1,-1)
44.49	2.0363	1.1	(4,2,1)
44.91	2.0182	4.5	(3,0,3)
45.04	2.0126	3.7	(4,3,2)
47.88	1.8999	24.0	(4,3,1)
49.06	1.8568	5.2	(4,1,0)
49.32	1.8476	1.1	(2,-2,2)
49.83	1.8299	26.0	(4,2,0)
53.33	1.7178	2.0	(3,0,-2)
53.80	1.7039	3.8	(4,4,4)

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Energy Properties

Formation Energy/atom

-2.55733

eV/atom

Energy/atom

-8.27765

eV/atom

Energy above Hull

0.0821

eV/atom

Uncorrected Energy

-7.5696

eV/atom

Volume/atom

12.34

Å³

c/a Ratio

1.0000

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Yes

Total Mag. Moment

19.0002

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.042760

μB/Å³

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

O · 0.667

Element Family

Metalloid-Nonmetal

Solute Fraction

0.333

Interstitial Fraction

0.167

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.0361

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

8.6144

J/mol·K

Ω Parameter

0.1887

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

36.466%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.7527

smaller = more stable mixing

VEC

4.528

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-17.849

kJ/mol; negative = exothermic mixing

Entropy Norm

0.6438

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (2)

aaabzkjr aaadzryv

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-776109

Reference Citation

The crystal structure and related material properties of TiMn3Cr2(PO4)6 were obtained from the Materials Project database (MP-ID: mp-776109, 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_TiMn3Cr2(PO4)6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.45865203
_cell_length_b   8.45865203
_cell_length_c   8.45865208
_cell_angle_alpha   61.71215832
_cell_angle_beta   61.71215832
_cell_angle_gamma   61.71216293
_symmetry_Int_Tables_number   1
_chemical_formula_structural   TiMn3Cr2(PO4)6
_chemical_formula_sum   'Ti1 Mn3 Cr2 P6 O24'
_cell_volume   444.36839143
_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
  Ti  Ti0  1  0.85297400  0.85297400  0.85297400  1.0
  Mn  Mn1  1  0.14656400  0.14656400  0.14656400  1.0
  Mn  Mn2  1  0.35393500  0.35393500  0.35393500  1.0
  Mn  Mn3  1  0.64560200  0.64560200  0.64560200  1.0
  Cr  Cr4  1  0.99972400  0.99972400  0.99972400  1.0
  Cr  Cr5  1  0.50121900  0.50121900  0.50121900  1.0
  P  P6  1  0.55057200  0.25083200  0.94941200  1.0
  P  P7  1  0.94941200  0.55057200  0.25083200  1.0
  P  P8  1  0.25083200  0.94941200  0.55057200  1.0
  P  P9  1  0.74976400  0.04946900  0.44969300  1.0
  P  P10  1  0.04946900  0.44969300  0.74976400  1.0
  P  P11  1  0.44969300  0.74976400  0.04946900  1.0
  O  O12  1  0.32030200  0.09865600  0.51862800  1.0
  O  O13  1  0.51862800  0.32030200  0.09865600  1.0
  O  O14  1  0.90651800  0.06483100  0.24801800  1.0
  O  O15  1  0.09865600  0.51862800  0.32030200  1.0
  O  O16  1  0.82841200  0.98868700  0.61101300  1.0
  O  O17  1  0.60156500  0.24937800  0.44596200  1.0
  O  O18  1  0.06483100  0.24801800  0.90651800  1.0
  O  O19  1  0.24937800  0.44596200  0.60156500  1.0
  O  O20  1  0.39627300  0.17778500  0.98994000  1.0
  O  O21  1  0.44596200  0.60156500  0.24937800  1.0
  O  O22  1  0.75458100  0.09052100  0.93090500  1.0
  O  O23  1  0.98994000  0.39627300  0.17778500  1.0
  O  O24  1  0.98868700  0.61101300  0.82841200  1.0
  O  O25  1  0.24801800  0.90651800  0.06483100  1.0
  O  O26  1  0.56794300  0.40149100  0.74514500  1.0
  O  O27  1  0.61101300  0.82841200  0.98868700  1.0
  O  O28  1  0.74514500  0.56794300  0.40149100  1.0
  O  O29  1  0.93090500  0.75458100  0.09052100  1.0
  O  O30  1  0.40149100  0.74514500  0.56794300  1.0
  O  O31  1  0.17778500  0.98994000  0.39627300  1.0
  O  O32  1  0.89782400  0.48737400  0.67848800  1.0
  O  O33  1  0.09052100  0.93090500  0.75458100  1.0
  O  O34  1  0.48737400  0.67848800  0.89782400  1.0
  O  O35  1  0.67848800  0.89782400  0.48737400  1.0

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