Physics and Chemistry of Minerals

, Volume 40, Issue 2, pp 133–143

Phase transitions and proton ordering in hemimorphite: new insights from single-crystal EPR experiments and DFT calculations

Authors

  • Mao Mao
    • Department of Geological SciencesUniversity of Saskatchewan
  • Zucheng Li
    • Department of Geological SciencesUniversity of Saskatchewan
    • Department of Geological SciencesUniversity of Saskatchewan
Original Paper

DOI: 10.1007/s00269-012-0553-5

Cite this article as:
Mao, M., Li, Z. & Pan, Y. Phys Chem Minerals (2013) 40: 133. doi:10.1007/s00269-012-0553-5
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Abstract

Single-crystal electron paramagnetic resonance spectra of gamma-ray-irradiated hemimorphite (Mapimi, Durango, Mexico) after storage at room temperature for 3 months, measured from 4 to 275 K, reveal a hydroperoxy radical HO2 derived from the water molecule in the channel. The EPR spectra of the HO2 radical confirm that hemimorphite undergoes two reversible phase transitions at ~98 and ~21 K and allow determinations of its spin Hamiltonian parameters, including superhyperfine coupling constants of two more-distant protons from the neighboring hydroxyl groups, at 110, 85, 40 and 7 K. These EPR results show that the HO2 radical changes in site symmetry from monoclinic to triclinic related to the ordering and rotation of its precursor water molecule in the channel at <98 K. The monoclinic structure of hemimorphite with completely ordered O–H systems at low temperature has been evaluated by both the EPR spectra of the HO2 radical at <21 K and periodic density functional theory calculations.

Keywords

HemimorphiteZeolite-like mineralSingle-crystal EPRDFTPhase transitionsHO2 radicalProton hyperfine and superhyperfine coupling constantsProton ordering

Introduction

Hemimorphite of the ideal formula Zn4Si2O7(OH)2·H2O, an important ore mineral in non-sulfide Zn deposits and a common constituent in Zn mine tailings, has attracted considerable attention, because of its complex phase transitions (Libowitzky and Rossman 1997; Libowitzky et al. 1998; Kolesov 2006; Dachs and Geiger 2009; Cano et al. 2009; Bissengaliyeva et al. 2010; Seryotkin and Bakakin 2011) and interesting properties for catalytic (Breuer et al. 1999; Yurieva et al. 2001; Catillon-Mucherie et al. 2007) and environmental applications (Walder and Chavez 1995; Schaider et al. 2007; Mao et al. 2010; Mao and Pan 2012).

The zeolite-like structure of hemimorphite at room temperature (RT) and atmospheric pressure belongs to the space group Imm2 and consists of SiO4 and Zn(OH)O3 tetrahedra sharing corners to form a framework with confined H2O molecules in channels along [001] (Barclay and Cox 1960; McDonald and Cruickshank 1967; Hill et al. 1977; Takéuchi et al. 1978; Cooper and Gibbs 1981; Libowitzky et al. 1998; Fig. 1a). The H2O molecule in the center of the channels lies in the (010) plane with the rotation axis along [001] and is held together by the OH groups via four co-planar hydrogen bonds (i.e., “two-dimensional ice”, Fig. 1b; Hill et al. 1977; Takéuchi et al. 1978; Libowitzky et al. 1998; Kolesov 2006).
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Fig. 1

a Crystal structure of hemimorphite at room temperature projected to the (001) plane (data from Takéuchi et al. 1978); and b and c comparison of the positions and orientations of the water molecule and the hydroxyl groups in the (010) plane at RT (Hill et al. 1977) and 20 K (Libowizky et al. 1998). Distances of hydrogen bonds (dashed lines) are marked

Libowitzky and Rossman (1997), on the basis of infrared and optical measurements, demonstrated that hemimorphite undergoes a reversible second-order phase transition at 98(2) K. Subsequently, Kolesov (2006) observed another phase transition at ~20–30 K in a polarized Raman spectroscopic study. Seryotkin and Bakakin (2011) noted that hemimorphite undergoes a phase transition from Imm2 to Pnn2 at a hydrostatic pressure of ~2.5 GPa.

A neutron diffraction study by Libowitzky et al. (1998) showed that the structure of hemimorphite at 20 K belongs to the space group Abm2. These authors noted that, while hemimorphite at RT contains dynamically disordered OH and H2O groups, the Abm2 structure is characterized by an ordered arrangement of nonequivalent OH groups and rotated H2O molecules in the channels (Fig. 1c). In particular, the H2O molecule at 20 K is displaced from the center of the channels, and the <HOH> bond angle increases from 90.5° at RT to 108(2)° at 20 K. Although all OH groups at 20 K remain in the (010) plane, the symmetrically related O3–H3 hydroxyl groups at RT (Fig. 1b) are rotated to give rise to two different O–H vectors at 20 K (Fig. 1c). Libowitzky et al. (1998) suggested the Abm2 structure to contain a sequence of ordered and apparently disordered channels in the same unit cell and proposed two monoclinic structures with ordered O–H systems in the channels at low temperature.

As part of our single-crystal EPR study of hemimorphite (Mao et al. 2010; Mao and Pan 2012), we observed a proton-associated oxyradical in gamma-ray-irradiated crystals. The single-crystal EPR spectra of this proton-associated oxyradical measured from 4 to 275 K clearly show that hemimorphite undergoes two phase transitions at ~21 and ~98 K, confirming the observations of Libowitzky and Rossman (1997) and Kolesov (2006). Moreover, quantitative determinations of spin Hamiltonian parameters of this oxyradical, including proton hyperfine and superhyperfine coupling constants (Weil and Bolton 2007; Pan and Nilges 2013), on the basis of single-crystal EPR spectra measured at 110, 85, 40 and 7 K, provide new insights into proton ordering associated with the two phase transitions. In addition, the monoclinic structures proposed by Libowitzky et al. (1998) have been evaluated by both the EPR results at 7 K and periodic density functional theory (DFT) calculations.

Sample and experimental methodology

The hemimorphite crystal (~1 mm × 2.5 mm × 3 mm) of Sample #1 (Mapimi, Durango, Mexico) investigated in Mao et al. (2010) was used in this study. Mao et al. (2010) did single-crystal EPR measurements immediately after this crystal was irradiated at RT in a 60Co cell for a dose of ~50 kGy.

In this study, all EPR spectra of the gamma-ray-irradiated hemimorphite, after storage at RT for three months, were collected on a Bruker EMX spectrometer at the Saskatchewan Structural Sciences Centre, University of Saskatchewan. The spectrometer is equipped with an automatic microwave controller, a high-sensitivity ER-4119 cavity, an ER-218G1 goniometer with a precision of 0.2°, and an Oxford Instrument liquid-helium cryostat.

Detailed spectral measurements in three rotation planes approximately parallel to the (010), (100) and (001) crystal faces, at a constant interval of 5° in each plane, were made at 110, 85, 40 and 7 K. Experimental conditions included microwave frequencies of ~9.39 GHz, a modulation frequency of 100 kHz, a modulation amplitude of 0.05 mT, a microwave power of 20 or 2 mW, and spectral resolutions from 0.0039 mT (i.e., 2,048 data points over 8 mT) to ~0.0078 mT (2,048 data points over 16 mT). Calibration of the magnetic field was made by using a Bruker strong pitch with g = 2.0028 as an external standard.

Additional single-crystal spectral measurements were made with B//a in the temperature range from 4 to 275 K (Fig. 2a) and B//b from 4 to 110 K (Fig. 2b), using variable intervals from 1 to 25 K. At each temperature, the crystal in the cavity was allowed to equilibrate for at least an hour before measurements. Experimental conditions for these measurements were similar to those above, except for spectral resolutions of 0.0049 mT (i.e., 2,048 data points over 10 mT) for those with B//b.
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Fig. 2

Representative single-crystal EPR spectra of gamma-ray-irradiated hemimorphite as a function of temperature: aB//~a and microwave frequency ν = 9. 395 GHz; bB//~b and ν = 9. 386 GHz; cB//~ c and ν = 9. 385 GHz; and dB^a = ~45° and ν = 9. 395 GHz. Three centers (I, II and E′) are marked. Question mark notes an unknown center in (d). Four magnetically nonequivalent sites of Center I in (d) are also labeled

DFT computation methodology

All periodical calculations were performed using the supercell approach (Pisani 1996) and the parameter free hybrid DFT method PBE0 (Adamo and Barone 1999) as implemented in the package CRYSTAL06 (Dovesi et al. 2006). Here, PBE stands for both Perdew, Burke and Ernzerhof GGA exchange and correlation functionals that contain no empirical parameters (Perdew et al. 1996). All-electron basis sets used in this study are those known to be well suitable for periodic calculations (Li and Pan 2011) and include the 86-411d31G of Jaffe and Hess (1993) for Zn, standard 6-31G* for O and H, and 8-41G** of Pisani et al. (1992), [1s3sp2d] from primitives (20s13p2d) for Si.

The thresholds for the overlap and penetration Coulomb integrals, the overlap for Hartree–Fock (HF) exchange integrals, and the two pseudo-overlaps for HF series were set to 10−8, 10−8, 10−8, 10−8, and 10−18 hartree, respectively, while a tight SCF tolerance of 10−8 hartree was chosen. Also, the extra-large grid (XLGRID) that employs the pruned (75,974) grid for each atom was used, which is much more accurate than the default (55,434) grid in the description of the optimized charge densities (Li and Pan 2011). The Pack–Monkhorst shrink factor was set to 6 for the unit-cell geometry optimizations. The same shrink factor was doubled for the Gilat net to describe the Fermi surface of the system (Dovesi et al. 2006).

Results and discussion

Single-crystal EPR spectra

Single-crystal EPR measurements of the gamma-ray-irradiated hemimorphite after storage at RT for 3 months show that the [AsO4]4− and [AsO4]2− radicals observed in Mao et al. (2010) have faded completely and that two new resonance signals (denoted I and II in Fig. 2) are now resolved at <275 K. It should be noted, however, that Centers I and II are present in the crystal immediately after gamma-ray irradiation but commonly overlap with the [AsO4]2− radical, making them difficult to investigate before the latter is completely decayed. Figure 2 also shows an electron-like center E′ of Cano et al. (2009) and Gallegos et al. (2009), which does not have any detectable hyperfine structures and has not been investigated further in this study.

The 110 K spectra of Center I consist of two strong lines and three weak satellites at B//a (Fig. 2a), and two sets of three lines with the intensity ratio of ~1:2:1 at B//b (Fig. 2b). These spectral features suggest that Center I arises from an unpaired electron (S = 1/2) interacting with one close proton (i = 1/2 and natural isotope abundance of ~100 %) and two more-distant and equivalent protons. The spectrum of Center I at B//c contains a broad multiplet (Fig. 2c). Away from crystallographic axes, the signals of Center I are resolved into at most two sets, indicative of a monoclinic site symmetry (Rae 1969). The average linewidth of Center I at 110 K is ~0.25 mT.

Below 98 K, the EPR spectra of Center I at random orientations consist of four magnetically nonequivalent sets (Fig. 2d), indicative of a triclinic site symmetry (Rae 1969). The average linewidths of Center I at 85 K and 40 K are 0.14 and ~0.12 mT, respectively, which are significantly narrower than that at 110 K and result in better resolved superhyperfine splittings arising from the two more-distant protons in the 40 K spectra (Fig. 2).

The spectra of Center I at <21 K are closely comparable to these above 98 K but differ markedly from those between 22 and 98 K (Fig. 2a, b), providing clear evidence for another phase transition at ~21 K. Repeated EPR measurements showed that this phase transition at ~21 K, similar to that at ~98 K (Libowitzky and Rossman 1997), is reversible. Moreover, the linewidth of Center I increases significantly close to the phase transition at ~21 K (Fig. 2a, b). Lang et al. (1977) reported a similar increase in the EPR linewidth of the substitutional Fe3+ center [FeO4]0 in quartz and the isostructural berlinite (AlPO4) near the αβ phase transition and interpreted it to originate from fluctuations at the phase transition. It is unclear why a similar increase in the EPR linewidth was not observed in spectra close to the phase transition at 98 K (Fig. 2a,b).

The 110 K EPR spectrum of Center II at B//a consists of two strong lines and two weak satellites (Fig. 2a), with an average linewidth of ~0.16 mT. The satellites decrease in intensity when B is rotated away from a and are not resolved at B//b or B//c. This center is resolved into at most two sets in all three rotation planes, indicating a monoclinic site symmetry (Rae 1969). These features suggest that Center II arises from an unpaired electron (S = ½) interacting with one proton. The doublet and the weak satellites represent the “forbidden” and “allowed” proton nuclear transitions, respectively. The EPR spectra of Center II also show clear evidence for the phase transition at ~98 K but become too weak to be detected below 21 K. Also, Center II is invariably lower in intensity than Center I (Fig. 2a, b) and is obscured completely by the latter where they overlap with each other. Therefore, quantitative determinations of the spin Hamiltonian parameters of Center II are not possible, owing to insufficient data points.

Optimization of spin Hamiltonian parameters

The spin Hamiltonian used for the description of Center I having hyperfine and superhyperfine interactions with three protons (i = 1, 2, 3) takes the form:
$$ {\mathbf{H}} = \beta_{e} {\mathbf{B}}^{T} {\mathbf{gS}} + \Upsigma \left( {{\mathbf{I}}^{T} {\mathbf{A}}_{i} {\mathbf{S}} - \beta_{n} {\mathbf{B}}^{T} g_{ni} {\mathbf{I}}} \right) $$
(1)
where βe and βn are the electronic (Bohr) and nuclear magnetons, respectively; S and I are the electron-spin and nuclear-spin operators, respectively; T denotes transpose; and the scalar gn value of 5.5856912 is adopted for 1H. Iterative fittings for the Zeeman electron matrix g and the nuclear hyperfine matrices A were made by using the software package EPR-NMR (Brown et al. 2003). The experimental axes x, y, and z were set along the crystallographic axes a, b, and c, respectively.
The total number of line-position data points for the fitting of Center I at 110 K is 5,800, which is reduced to 5,782 after assigning those at crossover regions to a weighing factor of 0.5. The final value of the root-mean-squares of weighted differences (RMSD) is 0.030 mT (Table 1), which is less than half of the average linewidth. The calculated normals of the three rotation planes at ( θ = 5.9°, ϕ = 124.7°), (91.2°, 356.0°), and (87.7°, 87.7°), in comparison with the ideal orientations at (0°, 0°), (90°, 0°), and (90°, 90°), respectively, indicate minor crystal misalignments. Here, θ and ϕ denote the polar and azimuthal angles from c and a, respectively. Spectral simulations by using the best-fit spin Hamiltonian parameters at 110 K (Table 1) reproduce the experimental spectra very well (Fig. 3a).
Table 1

Spin Hamiltonian parameters of the HO2 radical in hemimorphite at different temperatures

 

Matrix Y

k

Principal value (Yk)

Principal direction

RMSD (mT)

θ (°)

ϕ (°)

110 K

 g

2.0092(0)

0

0

1

2.0241(1)

90.0(1)

270.0(1)

0.030

 

2.0242(3)

0

2

2.0141(1)

0.0(1)

344a

  

2.0141(2)

3

2.0092(1)

90.0(1)

0.0(1)

 1HcA/geβe (mT)

−1.074(2)

0

0

1

0.038(1)

0.0(1)

70a

 

−1.670(1)

0

2

−1.074(2)

90.0(1)

0.0(1)

  

0.038(1)

3

−1.670(1)

90.0(1)

270.0(1)

 1Hd1A/geβe (mT)

−0.056(1)

0

−0.263(1)

1

−0.207(1)

90(4)

269(8)

 

−0.207(1)

0

2

−0.194(2)

62.4(1)

359(11)

  

0.309(1)

3

0.447(2)

152.4(1)

0.0(3)

 1Hd2A/geβe (mT)

−0.056(1)

0

0.263(1)

1

−0.207(1)

90(4)

90(8)

 

−0.207(1)

0

2

−0.194(2)

62.4(1)

180(11)

  

0.309(1)

3

0.447(2)

152.4(1)

180.0(3)

85 K

 g

2.0091(1)

0.0033(1)

0.0055(1)

1

2.0272(1)

69.9(1)

73.2(1)

0.069

 

2.0248(1)

0.0036(1)

2

2.0148(1)

40.6(1)

317.8(2)

  

2.0134(1)

3

2.0053(1)

56.4(1)

177.2(2)

 1HcA/geβe (mT)

−1.06(1)

−0.30(1)

0.52(1)

1

−0.08(1)

36.6(6)

330(1)

 

−1.58(1)

−0.34(2)

2

−1.37(1)

54.4(6)

166(2)

  

−0.55(1)

3

−1.74(1)

82(1)

70(1)

 1Hd1A/geβe (mT)

−0.09(1)

0.01 (1)

−0.18(1)

1

−0.16(1)

90(14)

93(37)

 

−0.18(1)

−0.01(1)

2

−0.16(1)

69(1)

3(42)

  

0.32(1)

3

0.39(1)

159.1(6)

4(4)

 1Hd2A/geβe (mT)

−0.04(1)

−0.04(1)

0.30(1)

1

−0.24(1)

98(10)

66(17)

 

−0.23(1)

−0.04(1)

2

−0.21(1)

60(3)

151(23)

  

0.29(1)

3

0.48(1)

149.0(5)

171(2)

40 K

 g

2.0077(1)

0.0080(1)

0.0066(1)

1

2.0359(1)

61.1(1)

67.1(1)

0.062

 

2.0262(1)

0.0011(1)

2

2.0083(1)

42.5(1)

300.0(1)

  

2.0136(1)

3

2.0034(1)

61.8(1)

174.2(1)

 1HcA/geβe (mT)

−1.11(1)

−0.07(1)

0.54(1)

1

−0.03(1)

27.5(2)

348.8(1)

 

−1.72(1)

−0.13(1)

2

−1.38(1)

62.9(6)

179.4(2)

  

−0.32(1)

3

−1.74(1)

85.7(1)

87.2(1)

 1Hd1A/geβe (mT)

−0.17(1)

0.02(1)

−0.23(1)

1

−0.28(1)

64.5(3)

23(1)

 

−0.20(1)

−0.11(1)

2

−0.21(1)

89.4(5)

113(1)

  

0.26(1)

3

0.38(1)

154.5(3)

24.5(4)

 1Hd2A/geβe (mT)

−0.12(1)

0.02(1)

0.33(1)

1

−0.34(1)

63.1(1)

143.7(9)

 

−0.22(1)

−0.10(1)

2

−0.19(1)

80.3(4)

238.6(7)

  

0.30(1)

3

0.49(1)

151.2(2)

166.6(2)

7 K

 g

2.0095(1)

0

0

1

2.0237(1)

90.0(1)

270.0(1)

0.059

 

2.0237(1)

0

2

2.0137(1)

0.0(1)

0a

  

2.0137(1)

3

2.0095(1)

90.0(3)

0.0(1)

 1HcA/geβe (mT)

−1.102(7)

0

0

1

0.015(9)

0.0(4)

214a

 

−1.690(8)

0

2

−1.102(8)

90.0(4)

0.0(1)

  

0.015(9)

3

−1.690(7)

90.0(4)

270.0(1)

 1Hd1A/geβe (mT)

−0.051(5)

0

−0.254(6)

1

−0.199(10)

87(20)

275(39)

 

−0.199(9)

0

2

−0.188(6)

62(2)

7(49)

  

0.281(8)

3

0.418(8)

151.6(5)

0.1(9)

 1Hd2A/geβe (mT)

−0.051(5)

0

0.254(6)

1

−0.199(10)

87(20)

95(39)

 

−0.199(9)

0

2

−0.188(6)

62(2)

187(49)

  

0.281(8)

3

0.418(8)

151.6(5)

180.1(9)

1Hc denotes the proton of the HO2 radical, whereas 1Hd1 and 1Hd2 represent the two more-distant protons

aTilting angles from a (ϕ) are meaningless when the tilting angle from c (θ) is close to zero. The sets of (θ, ϕ) and (180° −θ, 180° +ϕ) are equivalent

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Fig. 3

Comparison of experimental and simulated EPR spectra of Center I: aB^b = ~42° in the (100) plane and ν = 9.387 GHz at 110 K; bB^b = ~50° in the (001) plane and ν = 9.386 GHz at 40 K, and cB^a = ~35° in the (010) plane and ν = 9.386 GHz at 7 K

The total numbers of line-position data points for the fittings of Center I at 85 and 40 K are 2,270 and 4,395, respectively, which are reduced to 2,260 and 4,338.5 after assigning a weighing factor of 0.5 to those at the crossover regions. The relatively smaller number of data points at 85 K is due to the fact that some spectra from the (100) and (001) planes at this temperature were not included owing to low signal-to-noise ratios. The final RMSD values for 85 and 40 K are 0.069 and 0.062 mT, respectively (Table 1), again less than half of the average linewidths in the corresponding spectra. The calculated normals of the three rotation planes are (4.0°, 90.7°), (89.3°, 353.9°) and (91.1°, 90.8°) at 85 K, and (1.3°, 175.9°), (91.3°, 359.1°), and (90.0°, 90.0°) at 40 K. The small differences in the calculated normals of a given rotation plane among the experiments at different temperatures are due to the fact that crystal alignment was adjusted after measurements at each temperature. Spectral simulations confirm that the best-fit spin Hamiltonian parameters at 85 and 40 K (Table 1) also reproduce their respective experimental spectra very well (Fig. 3b).

The apparent similarity in the EPR spectra of Center I below 21 K to those above 98 K led us to use the spin Hamiltonian parameters and crystal orientations obtained from the 110 K spectra as the starting point. The final RMSD value of 0.059 mT (Table 1) is also smaller than half of the experimental linewidth. Spectral simulations show that the EPR spectra measured at 7 K are well reproduced by the best-fit spin Hamiltonian parameters of Center I at this temperature (Fig. 3c).

The best-fit matrices g and A(1H for the close proton) of Center I at 110 K (Table 1) are similar to those of the hydroperoxy radical HO2 (or HO2·, where ‘·’ denotes the unpaired spin) in various hosts (Table 2; Adrian et al. 1967; Wyard et al. 1968; Catton and Symons 1969; Radhakrishna et al. 1976; Bednarek and Plonka 1987; Plonka et al. 1999, Chumakova et al. 2008). Following Chumakova et al. (2008), the unique g1 axis of the HO2 radical is along the O=O bond direction, and the unique A1 axis is close to the O–H bond direction. The g3 and A2 axes are usually coaxial and normal to the radical plane, although dissymmetry is known and has been attributed to hydrogen bonds between the radical and the host (Chumakova et al. 2008). Matrices g and A(1H for the close proton) of Center I in hemorphite at 110 K are both close to axial in symmetry and coaxial. Therefore, the orientations of the g3 and A2 axes (Table 1) suggest that the HO2 radical at 110 K lies in the (100) mirror plane, hence explaining its monoclinic site symmetry, and those of the unique g1 and A1 axes indicate the O=O and O–H bonds along b and c, respectively. Also, the best-fit matrices A for the two more-distant protons are axial in symmetry as well and have their unique axes oriented at (152.4°, 180°) and (152.4°, 0°), consistent with those from the oxygen atom of the water molecule to the protons of the two nearest hydroxyl groups (Fig. 1b). Therefore, the most plausible model for Center I in hemimorphite at 110 K involves hole trapping on an O=O–H group formed from the water molecule and interacting with two equivalent protons of the nearest hydroxyl groups (Fig. 1b). Hydroperoxy radicals have ~73 % and ~27 % of the unpaired spin localized on the terminal and internal O, respectively (Villamena et al. 2005), and their formations from the H2O molecule are expected to be independent of the proton population.
Table 2

Spin Hamiltonian parameters of the HO2 radical in selected hosts

Host

g1

g2

g3

A1/geβe (mT)

A2/geβe (mT)

A3/geβe (mT)

Refs.

Argon

2.0393

2.0044

2.0044

1.35

0.86

0.86

1

BaCl2·H2O

2.02

2.007

2.007

1.6

0.8

0.8

2

Glassy hydrogen peroxide

2.0356

2.0082

2.0043

−20.1

8.7

−5.3

3

SrCl2·6H2O

2.0355

2.008

2.003

−1.72

−0.6

−1.27

4

Hydrogen peroxide

2.0353

2.0086

2.0042

1.38

0.35

1.55

5

Ice Ih

2.0376

2.0117

2.0025

−0.8

−1.6

−1.3

6

Ice Ih

2.0443

2.0081

2.0022

−0.5

−1.5

−1.1

6

Ice Ih

2.0455

2.0105

2.0023

−0.3

−1.4

−1.0

6

1 Adrian et al. (1967), 2 Radhakrishna et al. (1976), 3 Chumakova et al. (2008), 4 Catton and Symons (1969), 5 Wyard et al. (1968), and 6 Bednarek and Plonka (1987)

The anisotropic components of the superhyperfine coupling constants A for the two more-distant protons (Table 1), using the point-dipole model
$$ T_{z} = \left( { 2\mu_{0} / 4\pi } \right)\left( {g\beta_{e} g_{n} \beta_{n} /{\text{r}}^{ 3} } \right) $$
(2)
where Tz is the traceless part (Tx = Ty = − Tz/2), predict a hole-nucleus distance of 2.33 Å, which is in reasonable agreement with the O5 − H1a and O5 − H1b distances of 1.99 Å (Fig. 1b). This agreement is even better, if one considers the fact that the isotropic component of the hyperfine coupling constant a = −0.9 mT (Table 1) indicates a small portion of the unpaired spin on the proton and therefore provides further support for the formation of the HO2 radical from the water molecule in the channel.

The orientations of the g3 axis (56.4°, 177.2°) and the proton hyperfine A2 axis (54.4°, 166°) of Center I at 85 K suggest that the HO2 radical is now inclined to the (100) plane. Also, the unique g1 and A1 axes are not along b or c, explaining the triclinic site symmetry at this temperature. Moreover, the two protons from the nearest hydroxyl groups (Fig. 1c) are not equivalent either (Table 1). The best-fit spin Hamiltonian parameters of Center I at 40 K also suggest an inclined HO2 radical relative to the (100) plane but differ significantly in both principal values and principal axis directions from those of its counterpart at 85 K (Table 1), indicating a marked thermal effect in this temperature range.

The best-fit spin Hamiltonian parameters of the HO2 radical at 7 K are closely comparable to those at 110 K, except that the superhyperfine coupling constants of the two more-distant protons at 7 K are notably smaller than those at 110 K (Table 1).

Attempts to determine superhyperfine structures of the HO2 radical expected from more-distant protons in the hemimorphite structure (Fig. 1) have been made by use of pulsed electron nuclear double resonance (ENDOR) and electron-spin echo envelope modulation (ESEEM) measurements at temperatures from 4 to 40 K but were not successful, presumably owing to a short spin-relaxation time of this center.

Monoclinic structures optimized by DFT calculations

The two monoclinic structures of space groups Cc and Ic with completely ordered O–H systems suggested by Libowitzky et al. (1998) differ only in the choice of the origin. Our DFT calculations for these monoclinic structures started with their unit-cell parameters and atomic fractional coordinates transformed from those of the Abm2 structure by using the relationships described in Libowitzky et al. (1998). Our calculations show that both monoclinic structures converged readily and are, as expected, almost identical in the calculated energies. These structures are characterized by an angle of 29° between the plane of the water molecule and the (010) plane and have the protons of the two closest hydroxyl groups markedly different in distance to the water molecule (1.67 Å vs. 2.48 Å).

Another monoclinic structure with completely ordered O–H systems evaluated by DFT calculations was derived from the orthorhombic one of space group Imm2 (Hill et al. 1977) by using the matrix (1, 0, 0/0, 1, 0/0, −1, 2). The resulting structure of space group Im converged readily as well but is energetically slightly less favorable than its Cc and Ic counterparts (i.e., ΔE = 2.8 kcal/mol). The most salient feature of the Im structure is that its water molecule is parallel to the (010) plane and has two equivalent protons from the nearest hydroxyl groups (r = 2.06 Å).

Phase transitions and proton ordering in hemimorphite

Our single-crystal EPR spectra of the HO2 radical, measured in the temperature range from 4 to 275 K (Fig. 2), provide unambiguous evidence that hemimorphite undergoes two reversible phase transitions at ~98 and ~21 K (Libowitzky and Rossman 1997; Kolesov 2006). Moreover, quantitatively determined proton hyperfine and superhyperfine coupling constants of this radical at 110, 85, 40 and 7 K provide detailed information about the locations and orientations of the water molecule and the hydroxyl groups in hemimorphite at these temperatures.

Specifically, the observed EPR spectra and the best-fit spin Hamiltonian parameters of the HO2 radical at 110 K are consistent with the location of the water molecule at the center of the channel and the presence of two equivalent protons from the nearest hydroxyl groups (Fig. 1b). The reduction in the observed site symmetry of the HO2 radical below ~98 K supports the suggestion of Libowitzky et al. (1998) that the precursor water molecule is displaced (and rotated) away from the center of the channel. In particular, the angles of the inclined HO2 radical relative to the c axis at ~34° and 29° from EPR data at 85 K and 40 K, respectively, are closely comparable to the magnitude of rotation for the water molecule in the Abm2 structure from the neutron diffraction experiment of Libowitzkt et al. (1998). In addition, the distinct superhyperfine coupling constants of the two more-distant protons confirm that the two nearest hydroxyl groups are symmetrically nonequivalent below the ~98 K phase transition (Fig. 1c; Libowitzky et al. 1998). Moreover, the notable differences in both the experimental spectra (Fig. 2) and the best-fit spin Hamiltonian parameters at 85 and 40 K (Table 1) suggest a significant thermal effect on the ordering and rotation of the water molecule in the channel in this temperature range.

The EPR spectra of the HO2 radical below the ~21 K phase transition and the best-fit spin Hamiltonian parameters at 7 K (Table 1) confirm the suggestion of Libowitzky et al. (1998) that the hemimorphite structure with completely ordered O–H systems at low temperature is monoclinic. However, our EPR data do not support the Cc or Ic structures proposed by Libowitzky et al. (1998). Specifically, the HO2 radical in the Cc and Ic structures is expected to be located at a general position, which gives rise to fourfold splitting from both the monoclinic crystal symmetry and the {010} crystal twinning (cf. Libowitzky et al. 1998). Also, the two protons from the nearest hydroxyl groups to a HO2 radical in these structures are magnetically nonequivalent. Therefore, the Cc and Ic structures are incompatible with the observed EPR spectra of the HO2 radical at <21 K (Fig. 2). The Im structure (Table 3), on the other hand, predicts that the HO2 radical in the (100) mirror plane has no magnetic site splitting but can account for the observed splittings in the EPR spectra at <21 K (Fig. 2) by the {010} crystal twinning. Also, the two protons from the nearest hydroxyl groups are equivalent to the HO2 radical in the (100) mirror plane. Moreover, the increased distance from the water molecule to the protons of the nearest hydroxyl groups in the optimized Im structure can explain the smaller proton superhyperfine coupling constants at 7 K relative to those at 110 K (Table 1).
Table 3

Unit-cell parameters and atomic fractional coordinates of monoclinic hemimorphite optimized by DFT calculations

Space group

Im

Ic

Unit-cell parameter

a = 8.448 Å, b = 11.899 Å, c = 10.132 Å, α = 115.2°

a = 8.154 Å, b = 12.004 Å, c = 10.262 Å, α = 115.3°

x/a

y/b

z/c

x/a

y/b

z/c

Zn1

0.29558

−0.33931

0.09284

0.29162

−0.33750

0.09524

Zn2

−0.29558

−0.33931

0.09284

−0.28996

−0.34770

0.09517

Zn3

0.20481

−0.16003

−0.06742

0.21325

−0.15566

−0.06358

Zn4

−0.20481

−0.16003

−0.06742

−0.20987

−0.15814

−0.05854

Zn5

−0.29506

0.33990

−0.06718

−0.29013

0.34186

−0.05854

Zn6

0.29506

0.33990

−0.06718

0.28675

0.34434

−0.06358

Zn7

−0.20495

0.16016

0.09260

−0.21004

0.15230

0.09517

Zn8

0.20495

0.16016

0.09260

0.20838

0.16250

0.09524

Si1

0

−0.14528

−0.30633

−0.00026

−0.14470

−0.2998

Si2

0

0.14531

−0.16100

−0.00548

0.14129

−0.15793

Si3

0

0.14542

0.33871

0.00548

0.14129

0.34207

Si4

0

−0.14541

0.19367

0.00026

−0.14470

0.20020

O1

0.16031

−0.20514

−0.27413

0.16274

−0.20818

−0.27021

O2

−0.16031

−0.20514

−0.27413

−0.16571

−0.20139

−0.26335

O3

0.16039

0.20512

−0.06902

0.15027

0.21237

−0.05863

O4

−0.16039

0.20512

−0.06902

−0.17930

0.19033

−0.07350

O5

0

−0.16095

−0.47322

−0.00527

−0.15897

−0.46444

O6

0

0.16131

0.18760

0.00257

0.15298

0.19048

O7

0

0.00002

−0.18457

0.00875

−0.00135

−0.17811

O8

0.16032

−0.20511

0.22607

0.16571

−0.20139

0.23665

O9

−0.16032

−0.20511

0.22607

−0.16274

−0.20818

0.22979

O10

0

0.00007

0.31473

−0.00875

−0.00135

0.32189

O11

0

0.16090

−0.31226

−0.00257

0.15298

−0.30952

O12

0

−0.16173

0.02645

0.00527

−0.15897

0.03556

O13

0.16043

0.20514

0.43070

0.34973

−0.28763

−0.05863

O14

−0.16043

0.20514

0.43070

−0.32070

−0.30967

−0.07350

O15

−0.30969

0.00031

−0.47327

−0.32301

0.00424

−0.48938

O16

0.30969

0.00031

−0.47327

0.32293

−0.00327

−0.45083

O17

−0.50000

0.00212

−0.22159

0.48306

−0.01262

−0.23138

O18

0.31052

0.00002

0.02667

0.32301

0.00424

0.01062

O19

−0.31052

0.00002

0.02667

−0.32293

−0.00327

0.04917

O20

−0.50000

−0.00554

0.27671

0.01694

0.48738

−0.23138

H1

−0.38375

0.00161

−0.39978

0.36951

−0.00253

−0.36139

H2

0.38375

0.00161

−0.39978

−0.36951

−0.00253

0.13861

H3

0.41136

0.00093

−0.16132

0.06619

−0.49789

0.04438

H4

−0.41136

0.00093

−0.16132

0.43381

0.00211

0.04438

H5

0.38230

−0.00030

0.10110

0.41653

−0.00412

−0.14801

H6

−0.38230

−0.00030

0.10110

0.08347

0.49588

−0.14801

H7

0.41138

−0.00142

0.33949

−0.41765

0.03281

−0.19229

H8

−0.41138

−0.00142

0.33949

0.41765

0.03281

0.30771

Note that all atoms, including symmetrically equivalent ones, are listed for comparison

Acknowledgments

We thank Dr. Milan Rieder and two reviewers for incisive criticisms and helpful suggestions, Dr. Mark J. Nilges of the Illinois EPR Research Center for attempts of pulsed ENDOR and ESEEM measurements, Prof. Jin-Xiao Mi for assistance with matrix transformation, and the Natural Science and Engineering Research Council (NSERC) of Canada for financial support of this study. DFT calculations in this research have been enabled by the use of Westgrid computing resources, which are funded in part by the Canadian Foundation for Innovation, Alberta Innovation and Science, BC Advanced Education, and the participating research institutions. Westgrid equipment is provided by IBM, Hewlett Packard and SGI.

Copyright information

© Springer-Verlag Berlin Heidelberg 2012