Download citation
Download citation
link to html
The structure of, and anisotropic thermal motions in, the red semiconductor tetrahedral layer structure of HgI2 have been studied with neutron powder diffraction as a function of temperature from 10 to 293 K. Average thermal displacement parameters Ueq of the two atoms are comparable in size at 10 K, but Ueq(Hg) increases considerably faster with temperature than Ueq(I), the Hg-I bond being highly non-rigid. The anisotropic displacement tensor U(I) is strongly anisotropic with one term about twice as large as the others, while U(Hg) is nearly isotropic. All displacement tensor elements, except U22(I), increase faster with temperature than harmonic quantum oscillator curves indicating a softening of the isolated-atom potentials at large amplitudes. A lattice dynamical model provides arguments that the anisotropic thermal motions of I are dominated by a soft mode with a wavevector at the [½ ½ 0] boundary of the Brillouin zone consisting essentially of coupled librations of the HgI4 tetrahedra, and by translations of the entire layer. The large vibration amplitudes of Hg suggest weak Hg-I force constants compared with the I-I force constants, allowing Hg to move quite freely inside the tetrahedra. The libration mode induces dynamic deformations of the Hg-I bond with twice its frequency. This provides a mechanism for the anharmonicity and may explain the lightening of the color from red to orange upon cooling at ca 80 K.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768107043327/bk5060sup1.cif
Contains datablocks hgi2_n_red, hgi2_n, hgi2_n30k, hgi2_n60k, hgi2_n100k, hgi2_n200k, hgi2_n293k

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108768107043327/bk5060sup2.cif
Contains datablock raidur9

pdf

Portable Document Format (PDF) file https://doi.org/10.1107/S0108768107043327/bk5060sup3.pdf
Supplementary material

Experimental top

Fluka 83379

Computing details top

For all compounds, program(s) used to refine structure: FULLPROF.

(hgi2_n) top
Crystal data top
HgI2Z = 2
Mr = 454.39Dx = 6.450 Mg m3
Tetragonal, P42/nmcNeutron radiation, λ = 1.371700 Å
Hall symbol: -P 4ac 2aT = 10 K
a = 4.35803 (2) Åred
c = 12.30042 (9) Åcylinder, 52 × 8 mm
V = 233.62 (1) Å3
Data collection top
Neutron
diffractometer
Scan method: step
Radiation source: continuous spallation neutron source2θmin = 4.647°, 2θmax = 164.597°, 2θstep = 0.050°
Refinement top
Rp = 0.031Profile function: 7 (Thompson-Cox-Hastings pseudo-Voigt function convoluted with axial divergence asymmetry function: J. Appl. Cryst. (1994). 27, 892)
Rwp = 0.04128 parameters
Rexp = 0.0250 restraints
RBragg = 0.034Weighting scheme based on measured s.u.'s
χ2 = NOT FOUND
3200 data pointsBackground function: FullProf Background function number -4 (cosine Fourier series for background with 12 background coefficients)
Excluded region(s): none
Crystal data top
HgI2V = 233.62 (1) Å3
Mr = 454.39Z = 2
Tetragonal, P42/nmcNeutron radiation, λ = 1.371700 Å
a = 4.35803 (2) ÅT = 10 K
c = 12.30042 (9) Åcylinder, 52 × 8 mm
Data collection top
Neutron
diffractometer
2θmin = 4.647°, 2θmax = 164.597°, 2θstep = 0.050°
Scan method: step
Refinement top
Rp = 0.031χ2 = NOT FOUND
Rwp = 0.0413200 data points
Rexp = 0.02528 parameters
RBragg = 0.0340 restraints
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
HG10.250000.750000.250000.00125 (19)
I10.250000.250000.39150 (10)0.0011 (5)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
HG10.00133 (16)0.00133 (16)0.0011 (2)0.000000.000000.00000
I10.0024 (5)0.0001 (5)0.0008 (5)0.000000.000000.00000
Geometric parameters (Å, º) top
Hg1—I1i2.7888 (10)Hg1—I1iii2.7888 (10)
Hg1—I1ii2.7888 (10)I1—Hg1iv2.7888 (10)
Hg1—I12.7888 (10)
I1i—Hg1—I1102.77 (5)I1i—Hg1—I1iii112.92 (3)
I1ii—Hg1—I1112.92 (3)I1ii—Hg1—I1iii102.77 (5)
I1iii—Hg1—I1112.92 (3)Hg1iv—I1—Hg1102.77 (5)
I1i—Hg1—I1ii112.92 (3)
Symmetry codes: (i) x+1/2, y+3/2, z; (ii) y+1/2, x+1, z+1/2; (iii) y, x+1/2, z+1/2; (iv) x+1/2, y+1/2, z.
(hgi2_n30k) top
Crystal data top
HgI2Z = 2
Mr = 454.39Dx = 6.456 Mg m3
Tetragonal, P42/nmcNeutron radiation, λ = 1.371700 Å
Hall symbol: -P 4ac 2aT = 30 K
a = 4.35808 (4) Åred
c = 12.30636 (16) Åcylinder, 52 × 8 mm
V = 233.73 (1) Å3
Data collection top
Neutron
diffractometer
Scan method: step
Radiation source: continuous spallation neutron source2θmin = 4.645°, 2θmax = 164.595°, 2θstep = 0.050°
Refinement top
Rp = 0.054Profile function: 7 (Thompson-Cox-Hastings pseudo-Voigt function convoluted with axial divergence asymmetry function: J. Appl. Cryst. (1994). 27, 892)
Rwp = 0.06428 parameters
Rexp = 0.0270 restraints
RBragg = 0.035Weighting scheme based on measured s.u.'s
χ2 = NOT FOUND
3200 data pointsBackground function: FullProf Background function number -4 (cosine Fourier series for background with 12 background coefficients)
Excluded region(s): none
Crystal data top
HgI2V = 233.73 (1) Å3
Mr = 454.39Z = 2
Tetragonal, P42/nmcNeutron radiation, λ = 1.371700 Å
a = 4.35808 (4) ÅT = 30 K
c = 12.30636 (16) Åcylinder, 52 × 8 mm
Data collection top
Neutron
diffractometer
2θmin = 4.645°, 2θmax = 164.595°, 2θstep = 0.050°
Scan method: step
Refinement top
Rp = 0.054χ2 = NOT FOUND
Rwp = 0.0643200 data points
Rexp = 0.02728 parameters
RBragg = 0.0350 restraints
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
HG10.250000.750000.250000.0035 (3)
I10.250000.250000.39144 (18)0.0027 (8)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
HG10.0036 (3)0.0036 (3)0.0032 (5)0.000000.000000.00000
I10.0048 (9)0.0009 (9)0.0025 (8)0.000000.000000.00000
Geometric parameters (Å, º) top
Hg1—I1i2.7889 (13)Hg1—I1iii2.7889 (13)
Hg1—I1ii2.7889 (13)I1—Hg1iv2.7889 (13)
Hg1—I12.7889 (13)
I1i—Hg1—I1102.76 (8)I1i—Hg1—I1iii112.93 (4)
I1ii—Hg1—I1112.93 (4)I1ii—Hg1—I1iii102.76 (8)
I1iii—Hg1—I1112.93 (4)Hg1iv—I1—Hg1102.76 (8)
I1i—Hg1—I1ii112.93 (4)
Symmetry codes: (i) x+1/2, y+3/2, z; (ii) y+1/2, x+1, z+1/2; (iii) y, x+1/2, z+1/2; (iv) x+1/2, y+1/2, z.
(hgi2_n60k) top
Crystal data top
HgI2Z = 2
Mr = 454.39Dx = 6.447 Mg m3
Tetragonal, P42/nmcNeutron radiation, λ = 1.371700 Å
Hall symbol: -P 4ac 2aT = 60 K
a = 4.35880 (2) Åred
c = 12.31850 (11) Åcylinder, 52 × 8 mm
V = 234.04 (1) Å3
Data collection top
Neutron
diffractometer
Scan method: step
Radiation source: continuous spallation neutron source2θmin = 4.643°, 2θmax = 164.593°, 2θstep = 0.050°
Refinement top
Rp = 0.027Profile function: 7 (Thompson-Cox-Hastings pseudo-Voigt function convoluted with axial divergence asymmetry function: J. Appl. Cryst. (1994). 27, 892)
Rwp = 0.03528 parameters
Rexp = 0.0230 restraints
RBragg = 0.039Weighting scheme based on measured s.u.'s
χ2 = NOT FOUND
3200 data pointsBackground function: FullProf Background function number -4 (cosine Fourier series for background with 12 background coefficients)
Excluded region(s): none
Crystal data top
HgI2V = 234.04 (1) Å3
Mr = 454.39Z = 2
Tetragonal, P42/nmcNeutron radiation, λ = 1.371700 Å
a = 4.35880 (2) ÅT = 60 K
c = 12.31850 (11) Åcylinder, 52 × 8 mm
Data collection top
Neutron
diffractometer
2θmin = 4.643°, 2θmax = 164.593°, 2θstep = 0.050°
Scan method: step
Refinement top
Rp = 0.027χ2 = NOT FOUND
Rwp = 0.0353200 data points
Rexp = 0.02328 parameters
RBragg = 0.0390 restraints
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
HG10.250000.750000.250000.0071 (2)
I10.250000.250000.39120 (12)0.0057 (6)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
HG10.00713 (19)0.00713 (19)0.0071 (3)0.000000.000000.00000
I10.0088 (6)0.0040 (6)0.0043 (5)0.000000.000000.00000
Geometric parameters (Å, º) top
Hg1—I1i2.7884 (10)Hg1—I1iii2.7884 (10)
Hg1—I1ii2.7884 (10)I1—Hg1iv2.7884 (10)
Hg1—I12.7884 (10)
I1i—Hg1—I1102.81 (6)I1i—Hg1—I1iii112.90 (3)
I1ii—Hg1—I1112.90 (3)I1ii—Hg1—I1iii102.81 (6)
I1iii—Hg1—I1112.90 (3)Hg1iv—I1—Hg1102.81 (6)
I1i—Hg1—I1ii112.90 (3)
Symmetry codes: (i) x+1/2, y+3/2, z; (ii) y+1/2, x+1, z+1/2; (iii) y, x+1/2, z+1/2; (iv) x+1/2, y+1/2, z.
(hgi2_n100k) top
Crystal data top
HgI2Z = 2
Mr = 454.39Dx = 6.433 Mg m3
Tetragonal, P42/nmcNeutron radiation, λ = 1.371700 Å
Hall symbol: -P 4ac 2aT = 100 K
a = 4.36032 (3) Åred
c = 12.33737 (15) Åcylinder, 52 × 8 mm
V = 234.56 (1) Å3
Data collection top
Neutron
diffractometer
Scan method: step
Radiation source: continuous spallation neutron source2θmin = 4.640°, 2θmax = 164.590°, 2θstep = 0.050°
Refinement top
Rp = 0.030Profile function: 7 (Thompson-Cox-Hastings pseudo-Voigt function convoluted with axial divergence asymmetry function: J. Appl. Cryst. (1994). 27, 892)
Rwp = 0.03928 parameters
Rexp = 0.0230 restraints
RBragg = 0.049Weighting scheme based on measured s.u.'s
χ2 = NOT FOUND
3200 data pointsBackground function: FullProf Background function number -4 (cosine Fourier series for background with 12 background coefficients)
Excluded region(s): none
Crystal data top
HgI2V = 234.56 (1) Å3
Mr = 454.39Z = 2
Tetragonal, P42/nmcNeutron radiation, λ = 1.371700 Å
a = 4.36032 (3) ÅT = 100 K
c = 12.33737 (15) Åcylinder, 52 × 8 mm
Data collection top
Neutron
diffractometer
2θmin = 4.640°, 2θmax = 164.590°, 2θstep = 0.050°
Scan method: step
Refinement top
Rp = 0.030χ2 = NOT FOUND
Rwp = 0.0393200 data points
Rexp = 0.02328 parameters
RBragg = 0.0490 restraints
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
HG10.250000.750000.250000.0122 (3)
I10.250000.250000.39085 (16)0.0103 (8)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
HG10.0124 (3)0.0124 (3)0.0120 (5)0.000000.000000.00000
I10.0157 (9)0.0078 (8)0.0074 (7)0.000000.000000.00000
Geometric parameters (Å, º) top
Hg1—I1i2.7880 (12)Hg1—I1iii2.7880 (12)
Hg1—I1ii2.7880 (12)I1—Hg1iv2.7880 (12)
Hg1—I12.7880 (12)
I1i—Hg1—I1102.89 (7)I1i—Hg1—I1iii112.86 (4)
I1ii—Hg1—I1112.86 (4)I1ii—Hg1—I1iii102.89 (7)
I1iii—Hg1—I1112.86 (4)Hg1iv—I1—Hg1102.89 (7)
I1i—Hg1—I1ii112.86 (4)
Symmetry codes: (i) x+1/2, y+3/2, z; (ii) y+1/2, x+1, z+1/2; (iii) y, x+1/2, z+1/2; (iv) x+1/2, y+1/2, z.
(hgi2_n200k) top
Crystal data top
HgI2Z = 2
Mr = 454.39Dx = 6.392 Mg m3
Tetragonal, P42/nmcNeutron radiation, λ = 1.371700 Å
Hall symbol: -P 4ac 2aT = 200 K
a = 4.36525 (7) Åred
c = 12.3889 (2) Åcylinder, 52 × 8 mm
V = 236.08 (1) Å3
Data collection top
Neutron
diffractometer
Scan method: step
Radiation source: continuous spallation neutron source2θmin = 4.629°, 2θmax = 164.579°, 2θstep = 0.050°
Refinement top
Rp = 0.029Profile function: 7 (Thompson-Cox-Hastings pseudo-Voigt function convoluted with axial divergence asymmetry function: J. Appl. Cryst. (1994). 27, 892)
Rwp = 0.03728 parameters
Rexp = 0.0230 restraints
RBragg = 0.072Weighting scheme based on measured s.u.'s
χ2 = NOT FOUND
3200 data pointsBackground function: FullProf Background function number -4 (cosine Fourier series for background with 12 background coefficients)
Excluded region(s): none
Crystal data top
HgI2V = 236.08 (1) Å3
Mr = 454.39Z = 2
Tetragonal, P42/nmcNeutron radiation, λ = 1.371700 Å
a = 4.36525 (7) ÅT = 200 K
c = 12.3889 (2) Åcylinder, 52 × 8 mm
Data collection top
Neutron
diffractometer
2θmin = 4.629°, 2θmax = 164.579°, 2θstep = 0.050°
Scan method: step
Refinement top
Rp = 0.029χ2 = NOT FOUND
Rwp = 0.0373200 data points
Rexp = 0.02328 parameters
RBragg = 0.0720 restraints
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
HG10.250000.750000.250000.0272 (5)
I10.250000.250000.39038 (19)0.0218 (12)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
HG10.0276 (5)0.0276 (5)0.0264 (7)0.000000.000000.00000
I10.0342 (14)0.0148 (12)0.0164 (11)0.000000.000000.00000
Geometric parameters (Å, º) top
Hg1—I1i2.7910 (15)Hg1—I1iii2.7910 (15)
Hg1—I1ii2.7910 (15)I1—Hg1iv2.7910 (15)
Hg1—I12.7910 (15)
I1i—Hg1—I1102.90 (9)I1i—Hg1—I1iii112.86 (5)
I1ii—Hg1—I1112.86 (5)I1ii—Hg1—I1iii102.90 (9)
I1iii—Hg1—I1112.86 (5)Hg1iv—I1—Hg1102.90 (9)
I1i—Hg1—I1ii112.86 (5)
Symmetry codes: (i) x+1/2, y+3/2, z; (ii) y+1/2, x+1, z+1/2; (iii) y, x+1/2, z+1/2; (iv) x+1/2, y+1/2, z.
(hgi2_n293k) top
Crystal data top
HgI2Z = 2
Mr = 454.39Dx = 6.352 Mg m3
Tetragonal, P42/nmcNeutron radiation, λ = 1.371700 Å
Hall symbol: -P 4ac 2aT = 293 K
a = 4.3704 (3) Åred
c = 12.4368 (10) Åcylinder, 52 × 8 mm
V = 237.54 (3) Å3
Data collection top
Neutron
diffractometer
Scan method: step
Radiation source: continuous spallation neutron source2θmin = 4.625°, 2θmax = 164.575°, 2θstep = 0.050°
Refinement top
Rp = 0.063Profile function: 7 (Thompson-Cox-Hastings pseudo-Voigt function convoluted with axial divergence asymmetry function: J. Appl. Cryst. (1994). 27, 892)
Rwp = 0.07228 parameters
Rexp = 0.0330 restraints
RBragg = 0.086Weighting scheme based on measured s.u.'s
χ2 = NOT FOUND
3200 data pointsBackground function: FullProf Background function number -4 (cosine Fourier series for background with 12 background coefficients)
Excluded region(s): none
Crystal data top
HgI2V = 237.54 (3) Å3
Mr = 454.39Z = 2
Tetragonal, P42/nmcNeutron radiation, λ = 1.371700 Å
a = 4.3704 (3) ÅT = 293 K
c = 12.4368 (10) Åcylinder, 52 × 8 mm
Data collection top
Neutron
diffractometer
2θmin = 4.625°, 2θmax = 164.575°, 2θstep = 0.050°
Scan method: step
Refinement top
Rp = 0.063χ2 = NOT FOUND
Rwp = 0.0723200 data points
Rexp = 0.03328 parameters
RBragg = 0.0860 restraints
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
HG10.250000.750000.250000.042 (2)
I10.250000.250000.3898 (6)0.033 (5)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
HG10.0418 (18)0.0418 (18)0.042 (3)0.000000.000000.00000
I10.052 (5)0.022 (4)0.026 (5)0.000000.000000.00000
Geometric parameters (Å, º) top
Hg1—I1i2.793 (4)Hg1—I1iii2.793 (4)
Hg1—I1ii2.793 (4)I1—Hg1iv2.793 (4)
Hg1—I12.793 (4)
I1i—Hg1—I1103.0 (3)I1i—Hg1—I1iii112.81 (13)
I1ii—Hg1—I1112.81 (13)I1ii—Hg1—I1iii103.0 (3)
I1iii—Hg1—I1112.81 (13)Hg1iv—I1—Hg1103.0 (3)
I1i—Hg1—I1ii112.81 (13)
Symmetry codes: (i) x+1/2, y+3/2, z; (ii) y+1/2, x+1, z+1/2; (iii) y, x+1/2, z+1/2; (iv) x+1/2, y+1/2, z.

Experimental details

(hgi2_n)(hgi2_n30k)(hgi2_n60k)(hgi2_n100k)
Crystal data
Chemical formulaHgI2HgI2HgI2HgI2
Mr454.39454.39454.39454.39
Crystal system, space groupTetragonal, P42/nmcTetragonal, P42/nmcTetragonal, P42/nmcTetragonal, P42/nmc
Temperature (K)103060100
a, c (Å)4.35803 (2), 12.30042 (9)4.35808 (4), 12.30636 (16)4.35880 (2), 12.31850 (11)4.36032 (3), 12.33737 (15)
V3)233.62 (1)233.73 (1)234.04 (1)234.56 (1)
Z2222
Radiation typeNeutron, λ = 1.371700 ÅNeutron, λ = 1.371700 ÅNeutron, λ = 1.371700 ÅNeutron, λ = 1.371700 Å
Specimen shape, size (mm)Cylinder, 52 × 8Cylinder, 52 × 8Cylinder, 52 × 8Cylinder, 52 × 8
Data collection
DiffractometerNeutron
diffractometer
Neutron
diffractometer
Neutron
diffractometer
Neutron
diffractometer
Specimen mounting????
Data collection mode????
Scan methodStepStepStepStep
2θ values (°)2θmin = 4.647 2θmax = 164.597 2θstep = 0.0502θmin = 4.645 2θmax = 164.595 2θstep = 0.0502θmin = 4.643 2θmax = 164.593 2θstep = 0.0502θmin = 4.640 2θmax = 164.590 2θstep = 0.050
Refinement
R factors and goodness of fitRp = 0.031, Rwp = 0.041, Rexp = 0.025, RBragg = 0.034, χ2 = NOT FOUNDRp = 0.054, Rwp = 0.064, Rexp = 0.027, RBragg = 0.035, χ2 = NOT FOUNDRp = 0.027, Rwp = 0.035, Rexp = 0.023, RBragg = 0.039, χ2 = NOT FOUNDRp = 0.030, Rwp = 0.039, Rexp = 0.023, RBragg = 0.049, χ2 = NOT FOUND
No. of data points3200320032003200
No. of parameters28282828


(hgi2_n200k)(hgi2_n293k)
Crystal data
Chemical formulaHgI2HgI2
Mr454.39454.39
Crystal system, space groupTetragonal, P42/nmcTetragonal, P42/nmc
Temperature (K)200293
a, c (Å)4.36525 (7), 12.3889 (2)4.3704 (3), 12.4368 (10)
V3)236.08 (1)237.54 (3)
Z22
Radiation typeNeutron, λ = 1.371700 ÅNeutron, λ = 1.371700 Å
Specimen shape, size (mm)Cylinder, 52 × 8Cylinder, 52 × 8
Data collection
DiffractometerNeutron
diffractometer
Neutron
diffractometer
Specimen mounting??
Data collection mode??
Scan methodStepStep
2θ values (°)2θmin = 4.629 2θmax = 164.579 2θstep = 0.0502θmin = 4.625 2θmax = 164.575 2θstep = 0.050
Refinement
R factors and goodness of fitRp = 0.029, Rwp = 0.037, Rexp = 0.023, RBragg = 0.072, χ2 = NOT FOUNDRp = 0.063, Rwp = 0.072, Rexp = 0.033, RBragg = 0.086, χ2 = NOT FOUND
No. of data points32003200
No. of parameters2828

Computer programs: FULLPROF.

 

Follow Acta Cryst. B
Sign up for e-alerts
Follow Acta Cryst. on Twitter
Follow us on facebook
Sign up for RSS feeds