Electron density and electrostatic potential of KMnF₃: a phase-transition study

Three accurate X-ray diffraction experiments (Mo Kα, T = 190, 240 and 298 K) were carried out to track the temperature dependence of the electron density in the cubic perovskite potassium manganese trifluoride, KMnF₃, from room temperature to just above that of the phase transition to the tetragonal structure (186 K), and to correlate the parameters of the critical points with the phase-transition mechanism. The data obtained were approximated by the Hansen–Coppens multipole model expanded up to hexadecupoles; the anharmonicity of the atomic displacements up to the fourth level was considered. Topological analysis shows only two types of chemical bond at room temperature, Mn—F and K—F. However, at low temperature the K—F bonds blocking the rotation of the MnF₆ octahedra are weakened and new Mn—K bonds are formed to keep the crystal structure from disintegrating. The Mn—K bonds become stronger as the temperature approaches 186 K. This rearrangement of chemical bonds can be regarded as a precursor effect, which starts 50–60° above the phase-transition temperature. The effective one-particle potential of the F atom has a single minimum at 298 K and four well separated minima (with a shift of 0.2 Å from the equilibrium position towards the structural holes) at 190 K. Parameters of the critical points of the electron density indicate closed-shell type interactions between K—F and Mn—K pairs, whereas the Mn—F bond can be considered as an intermediate type. The topology of the electrostatic potentials is discussed as well.

Computing details

For all compounds, data collection: MXC(MAC Science) and a program IUANGLE by Tanaka (Tanaka, K.,Kumazawa S., Tsubokawa, M., Maruno, S. & Shirotani, I. (Acta Cryst., A50, 246-252 (1994)); cell refinement: RSLC-3 UNICS system (Sakurai, T. & Kobayashi, K. (1979), Rep. Inst. Phys. Chem. Res. 55, 69-77); data reduction: PROMETHEUS (Zucker et al., 1983); program(s) used to refine structure: MOLDOS96 (J. Protas, 1996).

Figures

(190K) potassium manganese trifluoride

Crystal data

F3MnK	Dx = 3.422 Mg m^−3
Mr = 151.03	Mo Kα radiation, λ = 0.71069 Å
Cubic, Pm3m	Cell parameters from 40 reflections
Hall symbol: -P 4 2 3	θ = 68.5–72.0°
a = 4.1850 (7) Å	µ = 5.76 mm^−1
V = 73.30 (2) Å^3	T = 190 K
Z = 1	Sphere, pale pink
F(000) = 71	0.06 × 0.06 × 0.06 × 0.03 (radius) mm

Data collection

Four-circle diffractometer	165 independent reflections
Radiation source: fine-focus rotating anode	165 reflections with F > 3.0s(F)
Graphite monochromator	Rint = 0.030
Detector resolution: 1.5x1.5 degrees pixels mm^-1	θmax = 74.7°, θmin = 4.9°
integrated intensities data fom ω/2θ scans	h = −9→11
Absorption correction: for a sphere Zucker et al. (1983)	k = −9→11
Tmin = 0.772, Tmax = 0.780	l = −7→10
1058 measured reflections

Refinement

Refinement on F	w = 1/(s**2 + 0.000049F**2)
Least-squares matrix: full	(Δ/σ)max < 0.001
R[F^2 > 2σ(F^2)] = 0.006	Δρmax = 1.90 e Å^−3
wR(F^2) = 0.009	Δρmin = −0.71 e Å^−3
S = 0.99	Extinction correction: Becker-Coppens type 2 isotropic
165 reflections	Extinction coefficient: 0.019 (7)
25 parameters

Special details

Experimental. Multiple diffraction was avoided by ψ-scan. Intensities was measured at equi-temperature region of combinaion of angles ω and χ of four-circle diffractometer

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
F	0.5	0.0	0.0	0.0221 (3)
K	0.5	0.5	0.5	0.01330 (5)*
Mn	0.0	0.0	0.0	0.00525 (3)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
F	0.0054 (2)	0.0304 (2)	0.0304 (2)	0.0	0.0	0.0

Geometric parameters (Å, º)

K—Mn	3.6243 (6)	Mn—F	2.0925 (3)
K—F	2.9592 (5)
Mn—F—K	90.0000	K—Mn—F	54.7356
F—K—Mn	35.2644

(240K) potassium manganese trifluoride

Crystal data

F3MnK	Dx = 3.417 Mg m^−3
Mr = 151.03	Mo Kα radiation, λ = 0.71069 Å
Cubic, Pm3m	Cell parameters from 40 reflections
Hall symbol: -P 4 2 3	θ = 68.3–71.9°
a = 4.1869 (5) Å	µ = 5.76 mm^−1
V = 73.40 (2) Å^3	T = 240 K
Z = 1	Sphere, pale pink
F(000) = 71	0.06 × 0.06 × 0.06 × 0.03 (radius) mm

Data collection

Four-circle diffractometer	156 independent reflections
Radiation source: fine-focus rotating anode	156 reflections with F > 3.0s(F)
Graphite monochromator	Rint = 0.028
Detector resolution: 1.5x1.5 degrees pixels mm^-1	θmax = 74.6°, θmin = 4.9°
integrated intensities data fom ω/2θ scans	h = −10→11
Absorption correction: for a sphere Zucker et al. (1983)	k = −10→10
Tmin = 0.772, Tmax = 0.780	l = −11→10
1001 measured reflections

Refinement

Refinement on F	w = 1/(s**2 + 0.000049F**2)
Least-squares matrix: full	(Δ/σ)max < 0.001
R[F^2 > 2σ(F^2)] = 0.006	Δρmax = 0.70 e Å^−3
wR(F^2) = 0.010	Δρmin = −0.41 e Å^−3
S = 1.02	Extinction correction: Becker-Coppens type 2 isotropic
156 reflections	Extinction coefficient: 0.003 (7)
25 parameters

Special details

Experimental. Multiple diffraction was avoided by ψ-scan. Intensities was measured at equi-temperature region of combinaion of angles ω and χ of four-circle diffractometer

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
F	0.5	0.0	0.0	0.0231 (5)
K	0.5	0.5	0.5	0.01619 (5)*
Mn	0.0	0.0	0.0	0.00631 (4)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
F	0.0068 (2)	0.0313 (3)	0.0313 (3)	0.0	0.0	0.0

Geometric parameters (Å, º)

K—Mn	3.6260 (4)	Mn—F	2.0935 (3)
K—F	2.9606 (4)
Mn—F—K	90.0000	K—Mn—F	54.7356
F—K—Mn	35.2644

(298K) potassium manganese trifluoride

Crystal data

F3MnK	Dx = 3.411 Mg m^−3
Mr = 151.03	Mo Kα radiation, λ = 0.71069 Å
Cubic, Pm3m	Cell parameters from 29 reflections
Hall symbol: -P 4 2 3	θ = 68.3–71.9°
a = 4.1893 (2) Å	µ = 5.75 mm^−1
V = 73.52 (1) Å^3	T = 298 K
Z = 1	Sphere, pale pink
F(000) = 71	0.06 × 0.06 × 0.06 × 0.03 (radius) mm

Data collection

Four-circle diffractometer	146 independent reflections
Radiation source: fine-focus rotating anode	146 reflections with F > 3.0s(F)
Graphite monochromator	Rint = 0.027
Detector resolution: 1.5x1.5 degrees pixels mm^-1	θmax = 74.5°, θmin = 4.9°
integrated intensities data fom ω/2θ scans	h = −5→11
Absorption correction: for a sphere Zucker et al. (1983)	k = −11→11
Tmin = 0.772, Tmax = 0.780	l = −8→11
1145 measured reflections

Refinement

Refinement on F	w = 1/(s**2 + 0.000025F**2)
Least-squares matrix: full	(Δ/σ)max < 0.001
R[F^2 > 2σ(F^2)] = 0.005	Δρmax = 0.92 e Å^−3
wR(F^2) = 0.008	Δρmin = −0.33 e Å^−3
S = 0.99	Extinction correction: Becker-Coppens type 2 isotropic
146 reflections	Extinction coefficient: 0.009 (5)
25 parameters

Special details

Experimental. Multiple diffraction was avoided by ψ-scan. Intensities was measured at equi-temperature region of combinaion of angles ω and χ of four-circle diffractometer

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
F	0.5	0.0	0.0	0.0253 (5)
K	0.5	0.5	0.5	0.01963 (7)*
Mn	0.0	0.0	0.0	0.00756 (3)*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
F	0.0080 (3)	0.0340 (3)	0.0340 (3)	0.0	0.0	0.0

Geometric parameters (Å, º)

K—Mn	3.6280 (2)	Mn—F	2.0947 (1)
K—F	2.9623 (1)
Mn—F—K	90.0000	K—Mn—F	54.7356
F—K—Mn	35.2644