TiCr3(PO4)6

High-Entropy Materials HEA

MP-ID: mp-773127 · Space group: R3 (#146)

Materials Project API

Basic Information

Formula

TiCr3(PO4)6

MP-ID

mp-773127

Elements

Sites

Density

2.7576

g/cm³

Volume

465.88

Å³

Cell a

8.8090

Cell b

8.8090

Cell c

8.8090

α Angle

58.42

β Angle

58.42

γ Angle

58.42

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
14.40	6.1512	41.9	(1,1,0)
20.17	4.4020	52.2	(2,1,1)
20.66	4.2989	23.6	(1,0,-1)
24.04	3.7013	100.0	(2,1,0)
24.46	3.6386	5.4	(2,2,2)
29.03	3.0756	43.8	(2,2,0)
32.07	2.7912	15.4	(2,0,-1)
32.23	2.7773	29.0	(3,2,1)
35.90	2.5014	8.1	(3,1,0)
36.19	2.4820	11.5	(2,-1,-1)
41.01	2.2010	1.3	(4,2,2)
42.80	2.1126	5.8	(4,3,2)
43.30	2.0894	1.5	(4,2,1)
43.92	2.0614	3.9	(3,1,-1)
44.17	2.0504	1.4	(4,1,1)
44.66	2.0292	2.1	(3,0,-1)
46.34	1.9591	10.9	(4,3,1)
47.05	1.9315	2.4	(3,2,-1)
47.05	1.9315	4.8	(3,-1,2)
48.33	1.8833	3.0	(4,4,2)
49.24	1.8507	10.4	(4,2,0)
49.68	1.8350	4.5	(2,2,-2)
50.14	1.8193	1.6	(4,4,4)
53.09	1.7250	11.6	(5,3,2)

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Energy Properties

Formation Energy/atom

-2.45107

eV/atom

Energy/atom

-7.98338

eV/atom

Energy above Hull

0.0660

eV/atom

Uncorrected Energy

-7.3221

eV/atom

Volume/atom

13.70

Å³

c/a Ratio

1.0000

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Yes

Total Mag. Moment

0.8827

μB

Mag. Ordering

FiM

Mag. Sites

Magnetization/Volume

0.001890

μB/Å³

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

O · 0.706

Element Family

Metalloid-Nonmetal

Solute Fraction

0.294

Interstitial Fraction

0.176

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

0.8699

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

7.2323

J/mol·K

Ω Parameter

0.1431

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

35.851%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.6881

smaller = more stable mixing

VEC

4.353

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-17.388

kJ/mol; negative = exothermic mixing

Entropy Norm

0.6275

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (2)

aaabzisw aaadznpq

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-773127

Reference Citation

The crystal structure and related material properties of TiCr3(PO4)6 were obtained from the Materials Project database (MP-ID: mp-773127, 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_TiCr3(PO4)6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.80901793
_cell_length_b   8.80901793
_cell_length_c   8.80901820
_cell_angle_alpha   58.42045675
_cell_angle_beta   58.42045675
_cell_angle_gamma   58.42045446
_symmetry_Int_Tables_number   1
_chemical_formula_structural   TiCr3(PO4)6
_chemical_formula_sum   'Ti1 Cr3 P6 O24'
_cell_volume   465.88332985
_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  0.85952400  0.85952400  0.85952400  1.0
  Cr  Cr1  1  0.14286100  0.14286100  0.14286100  1.0
  Cr  Cr2  1  0.35722100  0.35722100  0.35722100  1.0
  Cr  Cr3  1  0.64288100  0.64288100  0.64288100  1.0
  P  P4  1  0.03397500  0.46481300  0.75074100  1.0
  P  P5  1  0.46481300  0.75074100  0.03397500  1.0
  P  P6  1  0.75074100  0.03397500  0.46481300  1.0
  P  P7  1  0.25417400  0.96692200  0.53037400  1.0
  P  P8  1  0.53037400  0.25417400  0.96692200  1.0
  P  P9  1  0.96692200  0.53037400  0.25417400  1.0
  O  O10  1  0.13740400  0.50475700  0.28332400  1.0
  O  O11  1  0.28332400  0.13740400  0.50475700  1.0
  O  O12  1  0.06275400  0.28088400  0.92282600  1.0
  O  O13  1  0.50475700  0.28332400  0.13740400  1.0
  O  O14  1  0.21730600  0.43382100  0.57845000  1.0
  O  O15  1  0.00581800  0.63759300  0.77832600  1.0
  O  O16  1  0.28088400  0.92282600  0.06275400  1.0
  O  O17  1  0.43382100  0.57845000  0.21730600  1.0
  O  O18  1  0.57845000  0.21730600  0.43382100  1.0
  O  O19  1  0.22459100  0.99224600  0.36024500  1.0
  O  O20  1  0.07945800  0.93961300  0.71183300  1.0
  O  O21  1  0.36024500  0.22459100  0.99224600  1.0
  O  O22  1  0.63759300  0.77832600  0.00581800  1.0
  O  O23  1  0.92282600  0.06275400  0.28088400  1.0
  O  O24  1  0.77832600  0.00581800  0.63759300  1.0
  O  O25  1  0.42743500  0.78495100  0.55765300  1.0
  O  O26  1  0.55765300  0.42743500  0.78495100  1.0
  O  O27  1  0.71183300  0.07945800  0.93961300  1.0
  O  O28  1  0.99224600  0.36024500  0.22459100  1.0
  O  O29  1  0.78495100  0.55765300  0.42743500  1.0
  O  O30  1  0.49038100  0.72200000  0.86284100  1.0
  O  O31  1  0.93961300  0.71183300  0.07945800  1.0
  O  O32  1  0.72200000  0.86284100  0.49038100  1.0
  O  O33  1  0.86284100  0.49038100  0.72200000  1.0

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