The structure of orange HgI₂. I. Polytypic layer structure

The metastable orange crystals of HgI comprise three different crystal structures, all of which are built from corner-linked HgI supertetrahedra. Two of them are end members with the maximum degree of order (MDO) of a polytypic layer structure; the third shows a three-dimensional linkage. This paper presents the determination from X-ray diffraction data of the tetragonal polytypic structures and their stacking disorder. Diffraction patterns show sharp Bragg reflections and rods of diffuse intensity with pronounced maxima. In a first step, the diffuse intensity was neglected and all maxima were treated as Bragg reflections. The crystal was supposed to be a conglomerate of the two MDO structures diffracting independently, and their parameters and volume ratio were refined against the single data set. The geometries and anisotropic displacement parameters of the layers in the two structures are shown to be nearly identical. Layer contacts in the two stacking modes are identical. The structures are fractal complications of the stable red form of HgI. In a second step, the stacking disorder has been quantitatively analyzed with a Markov chain model. Two probabilities describing next-nearest-layer interactions were visually adjusted to observed intensity profiles extracted from image-plate detector data. Results consistently show that the crystal comprises nearly equal volumes of MDO structures with an average domain thickness of about 5 layers or 30 Å.

Computing details

For both compounds, data collection: Kuma CrysAlis; cell refinement: Kuma CrysAlis; data reduction: Kuma CrysAlis; program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: STACK (Birkedal et al., 1998); molecular graphics: Cerius2; software used to prepare material for publication: Cerius2, Bruker SHELXTL.

Figures

(I)

Crystal data

HgI2	Melting point: 529 K
Mr = 454.39	Mo Kα radiation, λ = 0.71073 Å
Tetragonal, I41/amd	Cell parameters from 618 reflections
a = 8.7863 (5) Å	θ = 14.3–24.1°
c = 24.667 (3) Å	µ = 45.09 mm^−1
V = 1904.3 (4) Å^3	T = 200 K
Z = 16	Truncated pyramid, orange
F(000) = 2976	0.10 × 0.10 × 0.02 mm
Dx = 6.340 Mg m^−3

Data collection

Kuma CCD diffractometer	585 independent reflections
Radiation source: fine-focus sealed tube	585 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.073
Detector resolution: 17.07 pixels mm^-1	θmax = 26.6°, θmin = 3.7°
ω scans	h = 0→7
Absorption correction: analytical based on the shape of the crystal	k = 0→10
Tmin = 0.017, Tmax = 0.411	l = 0→30
843 measured reflections

Refinement

Refinement on F	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.065	Secondary atom site location: difference Fourier map
wR(F^2) = 0.131	w = 1/[σ^2(Yo^2) + (0.0303P)^2 + 4.60896P] where P = (Yo + 2Yc)/3
S = 1.07	(Δ/σ)max < 0.001
585 reflections	Δρmax = not computed with STACK e Å^−3
20 parameters	Δρmin = not computed with STACK e Å^−3

Special details

Refinement. STACK program allows the refinement of several structures against a single data-set. It has been used for the refinement of two structures that are end-members with maximum degree of order (MDO) of a polytypic layer structure. See the text for more details.

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

	x	y	z	Uiso*/Ueq
Hg	0.74792 (15)	0.25	0.06232 (1)	0.0315 (2)
I1	0.50	0.75	0.25752 (9)	0.0249 (6)
I2	0.76416 (14)	0.51416 (14)	0.125	0.0331 (3)
I3	0.50	0.25	0.25758 (12)	0.0333 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Hg	0.0266 (4)	0.0360 (4)	0.0318 (2)	0.0	0.0003 (3)	0.0
I1	0.0304 (11)	0.0261 (10)	0.0182 (9)	0.0	0.0	0.0
I2	0.0313 (4)	0.0313 (4)	0.0364 (6)	−0.0034 (4)	0.0001 (2)	−0.0001 (2)
I3	0.0335 (12)	0.0355 (12)	0.0308 (12)	0.0	0.0	0.0

(II)

Crystal data

HgI2	Melting point: 529 K
Mr = 454.39	Mo Kα radiation, λ = 0.71073 Å
Tetragonal, P42/nmc	Cell parameters from 618 reflections
a = 8.7863 (5) Å	θ = 14.3–24.1°
c = 12.334 (3) Å	µ = 45.09 mm^−1
V = 952.2 (2) Å^3	T = 200 K
Z = 8	Truncated pyramid, orange
F(000) = 1488	0.10 × 0.10 × 0.02 mm
Dx = 6.340 Mg m^−3

Data collection

Kuma CCD diffractometer	570 independent reflections
Radiation source: fine-focus sealed tube	570 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.073
Detector resolution: 17.07 pixels mm^-1	θmax = 26.6°, θmin = 3.7°
ω scans	h = 0→7
Absorption correction: analytical based on the shape of the crystal	k = 0→10
Tmin = 0.017, Tmax = 0.411	l = 0→30
843 measured reflections

Refinement

Refinement on F	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.066	Secondary atom site location: difference Fourier map
wR(F^2) = 0.133	w = 1/[σ^2(Yo^2) + (0.0303P)^2 + 4.60896P] where P = (Yo + 2Yc)/3
S = 1.07	(Δ/σ)max < 0.001
570 reflections	Δρmax = not computed with STACK e Å^−3
20 parameters	Δρmin = not computed with STACK e Å^−3

Special details

Refinement. STACK program allows the refinement of several structures against a single data-set. It has been used for the refinement of two structures that are end-members with maximum degree of order (MDO) of a polytypic layer structure. See the text for more details.

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

	x	y	z	Uiso*/Ueq
Hg	0.50043 (19)	0.75	0.12481 (13)	0.0399 (5)
I1	0.25	0.25	0.5165 (3)	0.0343 (10)
I2	0.51381 (17)	0.01381 (17)	0.25	0.0292 (4)
I3	0.25	0.75	0.5136 (3)	0.0316 (9)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Hg	0.0367 (7)	0.0446 (7)	0.0385 (11)	0.0	−0.0008 (3)	0.0
I1	0.058 (2)	0.0146 (13)	0.0301 (14)	0.0	0.0	0.0
I2	0.0302 (7)	0.0302 (7)	0.0272 (8)	−0.0029 (5)	0.0008 (3)	−0.0008 (3)
I3	0.0454 (18)	0.0282 (16)	0.0211 (14)	0.0	0.0	0.0