Ti5Cr(PO4)6

High-Entropy Materials HEA

MP-ID: mp-776640 · Space group: R3 (#146)

Materials Project API

Basic Information

Formula

Ti5Cr(PO4)6

MP-ID

mp-776640

Elements

Sites

Density

3.1868

g/cm³

Volume

448.72

Å³

Cell a

8.4752

Cell b

8.4752

Cell c

8.4752

α Angle

61.90

β Angle

61.90

γ Angle

61.90

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
20.38	4.3584	84.6	(1,0,-1)
20.98	4.2342	13.5	(2,1,1)
24.24	3.6724	100.0	(2,0,1)
24.24	3.6724	50.0	(2,1,0)
25.15	3.5411	21.9	(2,0,0)
29.41	3.0370	13.4	(2,2,0)
31.66	2.8259	25.0	(2,0,-1)
32.58	2.7483	6.1	(2,1,-1)
33.37	2.6855	47.2	(3,1,2)
33.37	2.6855	23.6	(3,2,1)
35.68	2.5163	41.9	(2,-1,-1)
36.05	2.4917	4.9	(3,1,0)
38.46	2.3404	2.4	(3,2,0)
42.71	2.1171	11.0	(4,2,2)
43.60	2.0758	1.4	(1,-1,3)
43.60	2.0758	2.8	(3,1,-1)
44.37	2.0416	1.0	(4,1,2)
44.76	2.0247	2.4	(3,3,0)
44.98	2.0154	6.5	(4,3,2)
47.76	1.9043	40.1	(4,3,1)
48.86	1.8639	7.7	(4,1,0)
49.09	1.8559	3.0	(2,2,-2)
49.65	1.8362	9.0	(2,0,4)
49.65	1.8362	18.0	(4,2,0)

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Energy Properties

Formation Energy/atom

-2.88660

eV/atom

Energy/atom

-8.45255

eV/atom

Energy above Hull

0.0841

eV/atom

Uncorrected Energy

-7.9390

eV/atom

Volume/atom

12.46

Å³

c/a Ratio

1.0000

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Yes

Total Mag. Moment

5.9428

μB

Mag. Ordering

FiM

Mag. Sites

Magnetization/Volume

0.013240

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

0.9427

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

7.8372

J/mol·K

Ω Parameter

0.0420

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

40.275%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.7601

smaller = more stable mixing

VEC

4.222

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-78.229

kJ/mol; negative = exothermic mixing

Entropy Norm

0.6800

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (3)

aaabzkey aaadryjp aaadzqoc

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-776640

Reference Citation

The crystal structure and related material properties of Ti5Cr(PO4)6 were obtained from the Materials Project database (MP-ID: mp-776640, 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_Ti5Cr(PO4)6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.47521192
_cell_length_b   8.47521192
_cell_length_c   8.47521254
_cell_angle_alpha   61.89505494
_cell_angle_beta   61.89505494
_cell_angle_gamma   61.89505687
_symmetry_Int_Tables_number   1
_chemical_formula_structural   Ti5Cr(PO4)6
_chemical_formula_sum   'Ti5 Cr1 P6 O24'
_cell_volume   448.72414678
_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  0.99718800  0.99718800  0.99718800  1.0
  Ti  Ti1  1  0.50040600  0.50040600  0.50040600  1.0
  Ti  Ti2  1  0.85842800  0.85842800  0.85842800  1.0
  Ti  Ti3  1  0.64119000  0.64119000  0.64119000  1.0
  Ti  Ti4  1  0.36003800  0.36003800  0.36003800  1.0
  Cr  Cr5  1  0.14177200  0.14177200  0.14177200  1.0
  P  P6  1  0.95849800  0.25079300  0.53949200  1.0
  P  P7  1  0.53949200  0.95849800  0.25079300  1.0
  P  P8  1  0.75385900  0.45532600  0.04191400  1.0
  P  P9  1  0.45532600  0.04191400  0.75385900  1.0
  P  P10  1  0.04191400  0.75385900  0.45532600  1.0
  P  P11  1  0.25079300  0.53949200  0.95849800  1.0
  O  O12  1  0.88541700  0.68339300  0.49786500  1.0
  O  O13  1  0.68339300  0.49786500  0.88541700  1.0
  O  O14  1  0.94262800  0.09352500  0.73899300  1.0
  O  O15  1  0.49786500  0.88541700  0.68339300  1.0
  O  O16  1  0.99244000  0.18528200  0.38500600  1.0
  O  O17  1  0.75853900  0.40712900  0.55936300  1.0
  O  O18  1  0.73899300  0.94262800  0.09352500  1.0
  O  O19  1  0.55936300  0.75853900  0.40712900  1.0
  O  O20  1  0.82130100  0.61343400  0.00048600  1.0
  O  O21  1  0.40712900  0.55936300  0.75853900  1.0
  O  O22  1  0.90856100  0.25632200  0.05657400  1.0
  O  O23  1  0.61343400  0.00048600  0.82130100  1.0
  O  O24  1  0.38500600  0.99244000  0.18528200  1.0
  O  O25  1  0.09352500  0.73899300  0.94262800  1.0
  O  O26  1  0.59671500  0.44218400  0.24030000  1.0
  O  O27  1  0.18528200  0.38500600  0.99244000  1.0
  O  O28  1  0.44218400  0.24030000  0.59671500  1.0
  O  O29  1  0.25632200  0.05657400  0.90856100  1.0
  O  O30  1  0.24030000  0.59671500  0.44218400  1.0
  O  O31  1  0.00048600  0.82130100  0.61343400  1.0
  O  O32  1  0.50162100  0.11412900  0.31989100  1.0
  O  O33  1  0.05657400  0.90856100  0.25632200  1.0
  O  O34  1  0.31989100  0.50162100  0.11412900  1.0
  O  O35  1  0.11412900  0.31989100  0.50162100  1.0

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