K2Ti2(PO4)3

High-Entropy Materials HEA

MP-ID: mp-6696 · Space group: P2_13 (#198)

Materials Project API

Basic Information

Formula

K2Ti2(PO4)3

MP-ID

mp-6696

Elements

Sites

Density

3.0180

g/cm³

Volume

1,009.86

Å³

Cell a

10.0328

Cell b

10.0328

Cell c

10.0328

α Angle

90.00

β Angle

90.00

γ Angle

90.00

Space Group

P2_13

Point Group

Crystal System

Cubic

Bravais Lattice

Stability

Packing Fraction

0.5236

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
15.30	5.7924	14.6	(1,1,1)
19.79	4.4868	10.1	(2,1,0)
21.70	4.0959	14.6	(2,1,1)
26.66	3.3443	6.4	(2,2,1)
28.13	3.1726	100.0	(3,1,0)
29.53	3.0250	23.0	(3,1,1)
30.87	2.8962	1.2	(2,2,2)
32.17	2.7826	15.9	(3,2,0)
33.42	2.6814	52.5	(3,2,1)
36.94	2.4333	7.4	(3,2,2)
39.14	2.3017	3.2	(3,3,1)
40.20	2.2434	2.3	(4,2,0)
41.23	2.1893	2.7	(4,2,1)
42.25	2.1390	4.5	(3,3,2)
44.23	2.0479	10.3	(4,2,2)
45.19	2.0066	3.2	(5,0,0)
46.13	1.9676	11.2	(5,1,0)
47.07	1.9308	2.1	(5,1,1)
48.89	1.8630	12.0	(5,2,0)
49.78	1.8317	3.3	(5,2,1)
51.53	1.7736	1.2	(4,4,0)
52.39	1.7465	10.6	(5,2,2)
53.24	1.7206	2.7	(5,3,0)
54.08	1.6958	3.1	(5,3,1)

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Energy Properties

Formation Energy/atom

-2.96623

eV/atom

Energy/atom

-7.89653

eV/atom

Energy above Hull

0.0061

eV/atom

Uncorrected Energy

-7.4626

eV/atom

Volume/atom

13.29

Å³

c/a Ratio

1.0000

Electronic Properties

Metallic

Metal

Band Gap

Direct Gap

CBM

N/A

Magnetic Properties

Magnetic

Yes

Total Mag. Moment

3.9315

μB

Mag. Ordering

Mag. Sites

Magnetization/Volume

0.003890

μB/Å³

Elastic Properties

Elastic data not available

Feature Analysis

Composition Overview

Element Composition (atomic fraction)

Composition Info

Major / Matrix Element

O · 0.632

Element Family

Metalloid-Nonmetal

Solute Fraction

0.368

Interstitial Fraction

0.158

High-Entropy Alloy Features

Composite Radar (normalized)

Element-Class Share

Mix Entropy ΔS/R

1.0556

HEA criterion (>1.0 = high entropy)

Mix Entropy ΔS

8.7765

J/mol·K

Ω Parameter

0.0507

Ω > 1.1 favors solid solution

Atomic Size Mismatch δr

55.722%

δr < 6.6% favors single-phase solid solution

Electronegativity Diff Δχ

0.9466

smaller = more stable mixing

VEC

3.842

valence electron concentration, affects phase stability

Mix Enthalpy ΔH_mix

-56.137

kJ/mol; negative = exothermic mixing

Entropy Norm

0.7615

SS Former

Phase Tendency

Related Tasks

Related computation task IDs (2)

aaacatwv aaacywtw

Citation & References

Materials Project Page

https://materialsproject.org/materials/mp-6696

Reference Citation

The crystal structure and related material properties of K2Ti2(PO4)3 were obtained from the Materials Project database (MP-ID: mp-6696, 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_K2Ti2(PO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.03274900
_cell_length_b   10.03274900
_cell_length_c   10.03274900
_cell_angle_alpha   90.00000000
_cell_angle_beta   90.00000000
_cell_angle_gamma   90.00000000
_symmetry_Int_Tables_number   1
_chemical_formula_structural   K2Ti2(PO4)3
_chemical_formula_sum   'K8 Ti8 P12 O48'
_cell_volume   1009.85691003
_cell_formula_units_Z   4
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
  K  K0  1  0.93087200  0.93087200  0.93087200  1.0
  K  K1  1  0.43087200  0.56912800  0.06912800  1.0
  K  K2  1  0.56912800  0.06912800  0.43087200  1.0
  K  K3  1  0.06912800  0.43087200  0.56912800  1.0
  K  K4  1  0.70404600  0.70404600  0.70404600  1.0
  K  K5  1  0.79595400  0.29595400  0.20404600  1.0
  K  K6  1  0.29595400  0.20404600  0.79595400  1.0
  K  K7  1  0.20404600  0.79595400  0.29595400  1.0
  Ti  Ti8  1  0.41266200  0.41266200  0.41266200  1.0
  Ti  Ti9  1  0.58733800  0.91266200  0.08733800  1.0
  Ti  Ti10  1  0.91266200  0.08733800  0.58733800  1.0
  Ti  Ti11  1  0.08733800  0.58733800  0.91266200  1.0
  Ti  Ti12  1  0.85806200  0.64193800  0.35806200  1.0
  Ti  Ti13  1  0.64193800  0.35806200  0.85806200  1.0
  Ti  Ti14  1  0.35806200  0.85806200  0.64193800  1.0
  Ti  Ti15  1  0.14193800  0.14193800  0.14193800  1.0
  P  P16  1  0.37327500  0.54215200  0.72618000  1.0
  P  P17  1  0.87327500  0.95784800  0.27382000  1.0
  P  P18  1  0.62672500  0.04215200  0.77382000  1.0
  P  P19  1  0.95784800  0.27382000  0.87327500  1.0
  P  P20  1  0.77382000  0.62672500  0.04215200  1.0
  P  P21  1  0.27382000  0.87327500  0.95784800  1.0
  P  P22  1  0.54215200  0.72618000  0.37327500  1.0
  P  P23  1  0.72618000  0.37327500  0.54215200  1.0
  P  P24  1  0.04215200  0.77382000  0.62672500  1.0
  P  P25  1  0.45784800  0.22618000  0.12672500  1.0
  P  P26  1  0.22618000  0.12672500  0.45784800  1.0
  P  P27  1  0.12672500  0.45784800  0.22618000  1.0
  O  O28  1  0.24023900  0.52174900  0.80171300  1.0
  O  O29  1  0.74023900  0.97825100  0.19828700  1.0
  O  O30  1  0.75976100  0.02174900  0.69828700  1.0
  O  O31  1  0.97825100  0.19828700  0.74023900  1.0
  O  O32  1  0.69828700  0.75976100  0.02174900  1.0
  O  O33  1  0.19828700  0.74023900  0.97825100  1.0
  O  O34  1  0.52174900  0.80171300  0.24023900  1.0
  O  O35  1  0.80171300  0.24023900  0.52174900  1.0
  O  O36  1  0.02174900  0.69828700  0.75976100  1.0
  O  O37  1  0.47825100  0.30171300  0.25976100  1.0
  O  O38  1  0.30171300  0.25976100  0.47825100  1.0
  O  O39  1  0.25976100  0.47825100  0.30171300  1.0
  O  O40  1  0.35206100  0.49678700  0.58079600  1.0
  O  O41  1  0.85206100  0.00321300  0.41920400  1.0
  O  O42  1  0.64793900  0.99678700  0.91920400  1.0
  O  O43  1  0.00321300  0.41920400  0.85206100  1.0
  O  O44  1  0.91920400  0.64793900  0.99678700  1.0
  O  O45  1  0.41920400  0.85206100  0.00321300  1.0
  O  O46  1  0.70162900  0.52274500  0.95424200  1.0
  O  O47  1  0.49678700  0.58079600  0.35206100  1.0
  O  O48  1  0.99678700  0.91920400  0.64793900  1.0
  O  O49  1  0.50321300  0.08079600  0.14793900  1.0
  O  O50  1  0.08079600  0.14793900  0.50321300  1.0
  O  O51  1  0.14793900  0.50321300  0.08079600  1.0
  O  O52  1  0.47725500  0.45424200  0.79837100  1.0
  O  O53  1  0.97725500  0.04575800  0.20162900  1.0
  O  O54  1  0.52274500  0.95424200  0.70162900  1.0
  O  O55  1  0.04575800  0.20162900  0.97725500  1.0
  O  O56  1  0.08008700  0.31062700  0.23131300  1.0
  O  O57  1  0.23131300  0.08008700  0.31062700  1.0
  O  O58  1  0.31062700  0.23131300  0.08008700  1.0
  O  O59  1  0.18937300  0.76868700  0.58008700  1.0
  O  O60  1  0.73131300  0.41991300  0.68937300  1.0
  O  O61  1  0.68937300  0.73131300  0.41991300  1.0
  O  O62  1  0.26868700  0.91991300  0.81062700  1.0
  O  O63  1  0.76868700  0.58008700  0.18937300  1.0
  O  O64  1  0.81062700  0.26868700  0.91991300  1.0
  O  O65  1  0.58008700  0.18937300  0.76868700  1.0
  O  O66  1  0.91991300  0.81062700  0.26868700  1.0
  O  O67  1  0.41991300  0.68937300  0.73131300  1.0
  O  O68  1  0.02274500  0.54575800  0.29837100  1.0
  O  O69  1  0.29837100  0.02274500  0.54575800  1.0
  O  O70  1  0.54575800  0.29837100  0.02274500  1.0
  O  O71  1  0.95424200  0.70162900  0.52274500  1.0
  O  O72  1  0.79837100  0.47725500  0.45424200  1.0
  O  O73  1  0.45424200  0.79837100  0.47725500  1.0
  O  O74  1  0.20162900  0.97725500  0.04575800  1.0
  O  O75  1  0.58079600  0.35206100  0.49678700  1.0

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