# Polarized Raman Spectra ofNH4Al(SO4)2·12H2O

Authors: M. Boujelbene; T. Mhiri
Journal: International Journal of Spectroscopy
 (2011)

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## Abstract

The study by spectroscopie Raman relave to compoundNH4Al(SO4)2·12H2O was interpreted and attributed one being based Theory of group and by comparison with others composed. The current studies of the polarised Raman spectra of NH4Al(SO4)2·12H2O give evidence that the disorder is indeed present in the ammonium alum. This is best manifested through the appearance of surplus bands in the spectral regions of vibrations of the sulphate anion.


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## Body

## 1. Experimental

### 1.1. Preparation

AlumNH4Al(SO4)2·12H2O crystals were prepared by the slow evaporation of an aqueous solutions containing stoichiometric amounts of (NH4)2SO4 and Al2(SO4)3·xH2O salts.


### 1.2. Polarised Raman Spectra ofNH4Al(SO4)2·12H2O

#### 1.2.1. Factor Group Analysis

The ammonium alum,NH4Al(SO4)2·12H2O, belongs to a family of compounds with general formula AM(XO4)2·12H2O (A is a univalent metal such as Na, K, Rb, and Cs; M is a trivalent metal: Al, Ce, In, Fe, Cr, Ir etc.; X is S or Se).According to the crystallographic data [1], the ammonium alum crystallizes in the cubic structure Pa-3 (T6h), Z=4. The site symmetry of sulfate is C3, the trivalent cations occupy S6 sites, and the site symmetry of the two crystallographically distinct types of water molecules is C1. In the model the site symmetry of NH4+ is S6. However, X-ray diffraction studies of ammonium alum by with C3 symmetry. Abdeen et al. [2] indicated the unusual situation of two possible orientations of the sulfate ion, and the  site symmetry of NH4+ is C3. Similar suggestions were deduced from neutron diffraction date by Abdeen et al. [3]. Factor group analysis using standard correlation method [4] has been carried out to determine the symmetries of the vibrations and to predict the IR and Raman active modes.Excluding the acoustic modes, 227 normal modes are predicted.These are distributed as follows:(1)Γoptic=42Ag(R)+42Eg(R)+50Fg(R)+46Au(I)+46Eu(I)+51Fu(IR).
The Ag,Eg,andFg modes are Raman active, and Fu mode is infrared active.The Au and Eu modes exposed by Suresh et al. [5] as being IR active are really inactive.The contribution of the different groupments (SO4, NH4, and H2O) and the Al3+ ion to the Raman active vibrations are given in Table 2.Our polarized measurements were conducted on the (001) and (111) faces of the single crystal (Figure1).Photograph showing (a) face (001) and (b) face (111) things ofNH4Al(SO4)2·12H2O.
(a)(b)Analysis of the tensor components shows that, on (001) face, the Fg modes were obtained in the z(xy)z¯ geometry, the z(xx)z¯ geometry gives both the Ag and the Eg modes. Eg mode can be observed when the crystal is oriented as in (111) face and incident and scattered beams are perpendicular -Z(X′Y′)Z¯, and in polarizations parallel -Z(X′X′)Z¯ geometry the Ag, Eg, and Fg modes can be observed.The polarized Raman spectra recorded for these different geometries are shown in Figure2, and the frequencies of the observed bands and their vibrational assignments are given in Tables 1 and 2 (the spectra were collected from 5 to 4000 cm−1).Table 1
Active modes ofNH4Al(SO4)2·12H2O.
External modesInternal modesLSO4,TSO4,TAl,,LH2O,TH2O,LNH4,TNH4SO4NH4H2OActivityν1ν2ν3ν4ν1ν2ν3ν4ν1ν2ν3RamanAg110331110111011222(αxx+αyy+αzz)Eg110331101110111222(2αzz‒αxx-αyy,αxx‒αyy)Fg330993312331233222(αxy,αyz,αxz)Table 2
Correlation table of theAl(H2O)63+ octahedral.
FreeAl(H2O)63+ Oh symmetrySite groups S6 symmetryFactor groups Th6Figure 2
Raman spectra ofNH4Al(SO4)2·12H2O. The geometries and the corresponding mode symmetries are given in each diagram.


#### 1.2.2. Results and Discussions

NH4+ Vibrations
The internal modes of vibration of freeNH4+ ion with Td symmetry have average frequencies at 3033, 1685, 3134, and 1397 cm−1 for ν1(A1), ν2(E), ν3(F2), and ν4(F2) modes, respectively, [6].
The stretching vibrationsNH4+ ion and the water molecule were observed in the 2900 to 3500 cm−1. It was possible to separate the absorption bands observed in the Raman  spectra of  NH4Al(SO4)2·12H2O by comparison with the RbAl(SO4)2·12H2O sample. The differences observed between the two spectra are most likely due to the  NH4+ vibrations. Indeed, the bands observed in the second at 1444 cm−1 in theZ(XX)Z¯ polarisation and at 1453 in the Z(X′Y′)Z¯   polarisation, and not observed in RbAl(SO4)2·12H2O, are most likely assignable to the asymmetric bending (ν4) mode of NH4+. By similar reasoning we can deduce that the band observed in NH4Al(SO4)2·12H2O at 2442/2482 and at 2210/2473 cm−1 in the -z(xx)z¯ and -Z(X′X′)Z¯ polarisation, respectively, corresponds to the combinations of bending modes ν2 with the internal rotation mode ν6. Appearance of these bands indicates that the NH4+ ion does not rotate freely in the crystalline lattice, thus the ammonium ions form hydrogen bonds in the crystals [7–10]. The bands observed in the z(xx)z polarisation at 3134 cm−1 can be assigned to the asymmetric stretching ν3(Ag) vibrations.H2O Vibration
The vibrational frequencies of a free water molecule are at 3756 (ν3), 3652 (ν1), and 1595 cm−1(ν2) [11]. By comparison  with RbAl(SO4)2·12D2O, and (CH3)2NH2Al(SO4)2·6H2O, it was possible to identify the vibrational frequencies of water molecule in NH4Al(SO4)2·12H2O.
From group theoretical predictions, 18 lines (6Ag+6Fg+6Eg) are expected in all orientation (Table 1).
In thez(xx)z¯ orientation six bands are observed at 1620, 1726, 2856, 3103, 3356, and 3400 and are close to those (1678, 1735, 2900, 3085, 3360, and 3412 cm−1) reported by Abdeen et al. [3], RbAl(SO4)2·12H2O  for RbAl(SO4)2·12H2O. In the z(xy)z¯  geometrics (Fg symmetry) five bands are observed at  1617, 1738, 2936, 3365, and 3376 cm−1. Their analogues in RbAl(SO4)2·12H2O appear at 1605, 1632, 2985, 3120, 3330, and 3380 cm−1. In the  Z(X′Y′)Z¯ geometry (Eg symmetry) only three bands (from six predicted) are observed at 2908, 3072, and 3338 cm−1. The bands observed in each orientation at ~1700 cm−1 can be assigned to the HOH bending vibration ν2(H2O). The bands observed in the 2800–3500 cm−1 region are assigned to the symmetric and asymmetric stretching modes of water molecules. The observed bands in the stretching and bending regions show the presence of two distinct water molecules in NH4Al(SO4)2·12H2O. The significant decrease in the frequencies of the stretching modes and the increase in frequencies of the bending modes from the free state values show that water molecules form hydrogen bonds of medium and strong strength [12, 13].
The librational modes of water are characteristic of coordinated water and fall in the 500–900 cm−1 region [14, 15]. This region is complicated by presence of strong absorptions of ν4(SO4) and ν1(Al(H2O)6), and the ν3(Al(H2O)6) is Raman inactive Table 2. The low polarizability of water molecules makes these bands appear weak. Librational modes of water are assigned by comparison with RbAl(SO4)2·12H2O [5], CsAl(SO4)2·12H2O [15], and its partly deuterated analogues. There is no doublet that the bands observed in the 700–900 cm−1 region should be attributed to librations of water molecules, as done in all previous assignments [5–17].Al(H2O)6 Vibrations
The metal cationAl3+ forms an octahedron with surrounding six water molecules. Under Oh symmetry, the ion has six modes of vibration ν1(A1g), ν2(Eg), ν3(F1u), ν4(F1u), ν5(F2g), andν6(F2u). Out of these ν1, ν2, and ν5 are Raman active, ν3 and ν4 IR active, and ν6 inactive in both IR and Raman. Table 2 shows the correlation diagram between the free Al(H2O)6  group vibrations in Oh symmetry and the Al(H2O)6  internal vibrations in Th factor group symmetry through the S6 one in the crystal.
Unambiguous assignments of these modes are difficult as they fall in the region of the anion bending modes, librational modes of water molecules, and external modes. However, a few of these modes are assigned by comparison with the bands observed for theAl(H2O)63+ complex in RbAl(SO4)2·12H2O [5] and in similar compounds in (CH3)2NH2Al(SO4)2·6H2O [13]. The medium bands around 530 cm−1 are due to the ν1 mode of the ion. ν2 modes are observed as very weak bands around 400 cm−1. The triply degenerate symmetric bending mode (ν5) is observed with medium intensity in the Raman spectra, around 330 cm−1, being observed at similar frequencies (517, 416 and 386 cm−1) in the spectrum of potassium alum [18].SO42- Vibration
The four internal modes of a freeSO42- ion with tetrahedral, Td symmetry are at ν1(A1) 981 cm−1, ν2(E) 451 cm−1, ν3(F2) 1104 cm−1, and ν4(F2) 613 cm−1 [19]. Table 2 shows resultant of correlation diagram between the free SO4 group vibrations in Td symmetry and the SO4 internal vibrations in Th factor group symmetry through the C3 one in the crystal. In an ordered structure 15 Raman lines are predicted:(i)
7 stretching modes:2ν1(1Ag, 1Fg); 5ν3(1Ag, 1Eg, 3Fg);(ii)
8 deformation modes:3ν2(1Eg,2Fg); 5ν4(1Ag,1Eg,3Fg).In the ordered lattice, group theory analysis (Table 1) predicts two bands arising from the symmetric stretching mode ν1(Ag and Fg modes). This vibration that involves large changes in polarizability is observed as very intense bands at 990 cm−1 and medium bands at 975 cm−1: in the z(xx)z¯ geometry (Ag and Fg symmetry), in the  z(xy)z¯ geometry (Eg symmetry), and in Z(X′X′)Z¯ geometry (Ag, Eg, and Fg symmetry). The two bands should be attributed to Ag component to two types of sulfate anion, as done in all previous assignments (see [5–17]. The two bands with different intensity are also observed in the single crystal Raman spectrum of potassium alum for x(zz)y and x(xy)x orientations at 973 and 989 cm−1 [20]. These last authors assert that the two bands have some Ag symmetry, and there is no indication of a band with Fg symmetry. Although in the studied Raman spectrum of polycrystalline K-alum anly one very strong band is observed below 1000 cm−1 originating from the SO4 symmetry stretching mode ν1(991 cm−1), the weak intensity in the z(xy)z¯ orientation was attributed to spillover of the Ag intensity because the peak positions were identical in both orientations. Intensity ratio of the bands due to the two sites gave a higher value (p1/p2~9.9) than (p1/p2~5) calculated from X-Ray studies [20]. In the Z(X′Y′)Z¯ orientation where only the Eg modes are expected, two very weak bands, with equal intensity, are observed at 986 and 993 cm−1. The presence of two bands for the symmetric stretching mode ν1(Fg) confirms the hypothesis of a disordered structure. The two Fg modes are observed at 985 and 968 cm−1 in the single crystal Raman spectrum of K-Alum [21]. For the symmetric bending mode ν2, three Raman components (1Eg+2Fg) are predicted in all polarization geometries. In the z(xx)z¯ and Z(X′Y′)Z¯ orientations where only the Fg modes are expected, three bands are observed at 440, 460, and at 471 cm−1. Their analogues in RbAl(SO4)2·12H2O and KAl(SO4)2·12H2O  appear at (441, 458 and 480 cm−1) and (441, 458, and 475 cm−1), respectively. Two Eg modes (z(xy)z geometry) are observed at 439 and 460 cm−1. Thus the number of deformation mode ν2 of SO4 shows very clearly the two different orientations of SO42- groupments in this structure.
From group theoretical predictions, five lines(1Ag+1Eg+3Fg) are expected in all orientation for the asymmetric bending mode ν4. In the Z(X′Y′)Z¯ geometry (Eg symmetry) two bands are observed at 614 and 634 cm−1.In the z(xx)z¯ geometry (Ag+Eg symmetry) three bands are observed at 615, 634, and 648 cm−1. The two bands appearing at 615 and 648 cm−1 are assigned to the Ag symmetry. The splitting of the Ag and Eg modes confirms the existence of two types of tetrahedral. In the z(xy)z¯ geometry (Fg symmetry) three bands are observed at 610, 621, and 632 cm−1.
The asymmetric stretching modeν3 is found in the 1000–1160 cm−1 region. Group theory analysis predicts five bands for this mode (1Ag+1Eg+3Fg). In the x(zz)x geometry (Ag+Eg symmetry) as in the x(zy)x geometry (Fg symmetry) and in the Z(X′Y′)Z¯  geometry (Eg symmetry), three (1107, 1131, and 1189 cm−1), four (1034, 1092, 1102, and 1131 cm−1), and two (1134 and 1189 cm−1) bands are obtained, respectively. The bands observed at 1107 and 1131 cm−1, for the first orientation, can be associated to the Ag mode, and those at 1134 and 1189 cm−1 are attributed to the Eg mode. The four peaks observed in the second orientation are attributed to the Fg mode. In the Z(X′X′)Z¯ geometry (Ag+Eg+Fg) symmetry five bands are observed at 1099, 1101, 1131, 1134, and 1191 cm−1. In the polycrystalline spectrum of Raman are observed in the region of the ν3(SO4) modes, in the IR spectra of various alums [21], where 3ν3(SO4) modes predict [19] two intense doublet at ≈1100–1090 cm−1 and two less intense bands at ≈1070–1200 cm−1. These last were assigned to ν3(SO4) modes of the mirror sulfates [22]. Thus the number of ν3(SO4) modes observed in spectra gives evidence that the disorder is indeed in NH4-alum.
In conclusion, X-Ray diffraction studies indicated that the sulphate groups inNH4+ alum is orientationally disordered. The current studies of the polarised Raman spectra give evidence that the disorder is indeed present in the ammonium alum. This is best manifested through the appearance of surplus bands in the spectral regions of vibrations of the sulphate anion.External Modes
10 Ag, 10 Eg, and 21 Fg lines can be expected in the Raman low-frequency range, corresponding to external modes. Experimentally, 11 lines in the z(xx)z geometry (Ag+Eg symmetry), 5 lines in the Z(X′Y′)Z geometry (Eg symmetry), and 10 lines in the x(zy)x geometry (Fg symmetry) indeed exist (Table 3).  Each external mode may be dominated by the contributions from all cations. However, in certain frequency ranges the external modes may be dominated by contribution from one kind of cation (translations) or groups of atoms (rotation). The external modes are assigned by comparison with attribution proposed in RbAl(SO4)2·12H2O and by considering the fact that the translator and libratory modes of NH4+ ion occur at higher wave numbers than those of the SO42- ions. The librations of both NH4+ and SO42- ions are found to be stronger in intensity than the corresponding translational modes. By relative data comparison to the ammonium and rubidium alum, the bands observed in the 53–61 cm−1 region, at 167, 186, and at ~245 cm−1, can be attributed to the  translations and librations of NH4+ ion, since these bands are not observed in the rubidium alum. By similar reasoning we can confirm the attribution of the band observed at 238 cm−1 in rubidium alum to the Rb–O stretching mode [5–18]. Thus, the other bands observed in the 90–150 cm−1 region can be assigned to translational modes and those in the 150–200 cm−1 region to rotational modes of SO42- [5–21].Table 3
Raman band positions and assignments ofNH4Al(SO4)2·12H2O.
z(xx)z¯z(xy)z¯Z(X′Y′)Z¯Z(X′X′)Z¯AssignmentAg+EgFgEgAg+Eg+Fg11m11m—11mLattice modes14w—14w14w16m——16m39w——39w44w47w48w44w—53w—59w61w59m60m61m—73w—73w80w———120w120m——Trans ofSO42-159s153m—159m—186m167m—193s196193mRota ofSO42-—195m—245wbr228w—246wνNH4–O326w329w320w327w440m440w434w440wν2SO42-460m460m459m458m539wbr471w———581sh——615s610s614s614sν4SO42-621s634s632m—902w913w905wν1SO42-915s986s990s990vs990m993m1099m1094wbr1034m1101m1104s1091m1102m1112s1102s1123s1131m1131m1130m1132m1134mν3SO42-−1190m——1191m————1444sν4NH4+1444s1453s—1540sν2H2O—1621sν2NH4+1750s1620m1617mbr1726m1738wbr2210m—2473m2442w—ν1H2O2482w2908m2920m3072m2856m2936m—3132m3103m——3134s—3338m3350m3356mbr3365s—ν3H2O3400wbr3400mbr3376ss: strong; w: weak; m: medium; sh: shoulder; v: very; br: broad.


## 1.1. Preparation

AlumNH4Al(SO4)2·12H2O crystals were prepared by the slow evaporation of an aqueous solutions containing stoichiometric amounts of (NH4)2SO4 and Al2(SO4)3·xH2O salts.


## 1.2. Polarised Raman Spectra ofNH4Al(SO4)2·12H2O

### 1.2.1. Factor Group Analysis

The ammonium alum,NH4Al(SO4)2·12H2O, belongs to a family of compounds with general formula AM(XO4)2·12H2O (A is a univalent metal such as Na, K, Rb, and Cs; M is a trivalent metal: Al, Ce, In, Fe, Cr, Ir etc.; X is S or Se).According to the crystallographic data [1], the ammonium alum crystallizes in the cubic structure Pa-3 (T6h), Z=4. The site symmetry of sulfate is C3, the trivalent cations occupy S6 sites, and the site symmetry of the two crystallographically distinct types of water molecules is C1. In the model the site symmetry of NH4+ is S6. However, X-ray diffraction studies of ammonium alum by with C3 symmetry. Abdeen et al. [2] indicated the unusual situation of two possible orientations of the sulfate ion, and the  site symmetry of NH4+ is C3. Similar suggestions were deduced from neutron diffraction date by Abdeen et al. [3]. Factor group analysis using standard correlation method [4] has been carried out to determine the symmetries of the vibrations and to predict the IR and Raman active modes.Excluding the acoustic modes, 227 normal modes are predicted.These are distributed as follows:(1)Γoptic=42Ag(R)+42Eg(R)+50Fg(R)+46Au(I)+46Eu(I)+51Fu(IR).
The Ag,Eg,andFg modes are Raman active, and Fu mode is infrared active.The Au and Eu modes exposed by Suresh et al. [5] as being IR active are really inactive.The contribution of the different groupments (SO4, NH4, and H2O) and the Al3+ ion to the Raman active vibrations are given in Table 2.Our polarized measurements were conducted on the (001) and (111) faces of the single crystal (Figure1).Photograph showing (a) face (001) and (b) face (111) things ofNH4Al(SO4)2·12H2O.
(a)(b)Analysis of the tensor components shows that, on (001) face, the Fg modes were obtained in the z(xy)z¯ geometry, the z(xx)z¯ geometry gives both the Ag and the Eg modes. Eg mode can be observed when the crystal is oriented as in (111) face and incident and scattered beams are perpendicular -Z(X′Y′)Z¯, and in polarizations parallel -Z(X′X′)Z¯ geometry the Ag, Eg, and Fg modes can be observed.The polarized Raman spectra recorded for these different geometries are shown in Figure2, and the frequencies of the observed bands and their vibrational assignments are given in Tables 1 and 2 (the spectra were collected from 5 to 4000 cm−1).Table 1
Active modes ofNH4Al(SO4)2·12H2O.
External modesInternal modesLSO4,TSO4,TAl,,LH2O,TH2O,LNH4,TNH4SO4NH4H2OActivityν1ν2ν3ν4ν1ν2ν3ν4ν1ν2ν3RamanAg110331110111011222(αxx+αyy+αzz)Eg110331101110111222(2αzz‒αxx-αyy,αxx‒αyy)Fg330993312331233222(αxy,αyz,αxz)Table 2
Correlation table of theAl(H2O)63+ octahedral.
FreeAl(H2O)63+ Oh symmetrySite groups S6 symmetryFactor groups Th6Figure 2
Raman spectra ofNH4Al(SO4)2·12H2O. The geometries and the corresponding mode symmetries are given in each diagram.


### 1.2.2. Results and Discussions

NH4+ Vibrations
The internal modes of vibration of freeNH4+ ion with Td symmetry have average frequencies at 3033, 1685, 3134, and 1397 cm−1 for ν1(A1), ν2(E), ν3(F2), and ν4(F2) modes, respectively, [6].
The stretching vibrationsNH4+ ion and the water molecule were observed in the 2900 to 3500 cm−1. It was possible to separate the absorption bands observed in the Raman  spectra of  NH4Al(SO4)2·12H2O by comparison with the RbAl(SO4)2·12H2O sample. The differences observed between the two spectra are most likely due to the  NH4+ vibrations. Indeed, the bands observed in the second at 1444 cm−1 in theZ(XX)Z¯ polarisation and at 1453 in the Z(X′Y′)Z¯   polarisation, and not observed in RbAl(SO4)2·12H2O, are most likely assignable to the asymmetric bending (ν4) mode of NH4+. By similar reasoning we can deduce that the band observed in NH4Al(SO4)2·12H2O at 2442/2482 and at 2210/2473 cm−1 in the -z(xx)z¯ and -Z(X′X′)Z¯ polarisation, respectively, corresponds to the combinations of bending modes ν2 with the internal rotation mode ν6. Appearance of these bands indicates that the NH4+ ion does not rotate freely in the crystalline lattice, thus the ammonium ions form hydrogen bonds in the crystals [7–10]. The bands observed in the z(xx)z polarisation at 3134 cm−1 can be assigned to the asymmetric stretching ν3(Ag) vibrations.H2O Vibration
The vibrational frequencies of a free water molecule are at 3756 (ν3), 3652 (ν1), and 1595 cm−1(ν2) [11]. By comparison  with RbAl(SO4)2·12D2O, and (CH3)2NH2Al(SO4)2·6H2O, it was possible to identify the vibrational frequencies of water molecule in NH4Al(SO4)2·12H2O.
From group theoretical predictions, 18 lines (6Ag+6Fg+6Eg) are expected in all orientation (Table 1).
In thez(xx)z¯ orientation six bands are observed at 1620, 1726, 2856, 3103, 3356, and 3400 and are close to those (1678, 1735, 2900, 3085, 3360, and 3412 cm−1) reported by Abdeen et al. [3], RbAl(SO4)2·12H2O  for RbAl(SO4)2·12H2O. In the z(xy)z¯  geometrics (Fg symmetry) five bands are observed at  1617, 1738, 2936, 3365, and 3376 cm−1. Their analogues in RbAl(SO4)2·12H2O appear at 1605, 1632, 2985, 3120, 3330, and 3380 cm−1. In the  Z(X′Y′)Z¯ geometry (Eg symmetry) only three bands (from six predicted) are observed at 2908, 3072, and 3338 cm−1. The bands observed in each orientation at ~1700 cm−1 can be assigned to the HOH bending vibration ν2(H2O). The bands observed in the 2800–3500 cm−1 region are assigned to the symmetric and asymmetric stretching modes of water molecules. The observed bands in the stretching and bending regions show the presence of two distinct water molecules in NH4Al(SO4)2·12H2O. The significant decrease in the frequencies of the stretching modes and the increase in frequencies of the bending modes from the free state values show that water molecules form hydrogen bonds of medium and strong strength [12, 13].
The librational modes of water are characteristic of coordinated water and fall in the 500–900 cm−1 region [14, 15]. This region is complicated by presence of strong absorptions of ν4(SO4) and ν1(Al(H2O)6), and the ν3(Al(H2O)6) is Raman inactive Table 2. The low polarizability of water molecules makes these bands appear weak. Librational modes of water are assigned by comparison with RbAl(SO4)2·12H2O [5], CsAl(SO4)2·12H2O [15], and its partly deuterated analogues. There is no doublet that the bands observed in the 700–900 cm−1 region should be attributed to librations of water molecules, as done in all previous assignments [5–17].Al(H2O)6 Vibrations
The metal cationAl3+ forms an octahedron with surrounding six water molecules. Under Oh symmetry, the ion has six modes of vibration ν1(A1g), ν2(Eg), ν3(F1u), ν4(F1u), ν5(F2g), andν6(F2u). Out of these ν1, ν2, and ν5 are Raman active, ν3 and ν4 IR active, and ν6 inactive in both IR and Raman. Table 2 shows the correlation diagram between the free Al(H2O)6  group vibrations in Oh symmetry and the Al(H2O)6  internal vibrations in Th factor group symmetry through the S6 one in the crystal.
Unambiguous assignments of these modes are difficult as they fall in the region of the anion bending modes, librational modes of water molecules, and external modes. However, a few of these modes are assigned by comparison with the bands observed for theAl(H2O)63+ complex in RbAl(SO4)2·12H2O [5] and in similar compounds in (CH3)2NH2Al(SO4)2·6H2O [13]. The medium bands around 530 cm−1 are due to the ν1 mode of the ion. ν2 modes are observed as very weak bands around 400 cm−1. The triply degenerate symmetric bending mode (ν5) is observed with medium intensity in the Raman spectra, around 330 cm−1, being observed at similar frequencies (517, 416 and 386 cm−1) in the spectrum of potassium alum [18].SO42- Vibration
The four internal modes of a freeSO42- ion with tetrahedral, Td symmetry are at ν1(A1) 981 cm−1, ν2(E) 451 cm−1, ν3(F2) 1104 cm−1, and ν4(F2) 613 cm−1 [19]. Table 2 shows resultant of correlation diagram between the free SO4 group vibrations in Td symmetry and the SO4 internal vibrations in Th factor group symmetry through the C3 one in the crystal. In an ordered structure 15 Raman lines are predicted:(i)
7 stretching modes:2ν1(1Ag, 1Fg); 5ν3(1Ag, 1Eg, 3Fg);(ii)
8 deformation modes:3ν2(1Eg,2Fg); 5ν4(1Ag,1Eg,3Fg).In the ordered lattice, group theory analysis (Table 1) predicts two bands arising from the symmetric stretching mode ν1(Ag and Fg modes). This vibration that involves large changes in polarizability is observed as very intense bands at 990 cm−1 and medium bands at 975 cm−1: in the z(xx)z¯ geometry (Ag and Fg symmetry), in the  z(xy)z¯ geometry (Eg symmetry), and in Z(X′X′)Z¯ geometry (Ag, Eg, and Fg symmetry). The two bands should be attributed to Ag component to two types of sulfate anion, as done in all previous assignments (see [5–17]. The two bands with different intensity are also observed in the single crystal Raman spectrum of potassium alum for x(zz)y and x(xy)x orientations at 973 and 989 cm−1 [20]. These last authors assert that the two bands have some Ag symmetry, and there is no indication of a band with Fg symmetry. Although in the studied Raman spectrum of polycrystalline K-alum anly one very strong band is observed below 1000 cm−1 originating from the SO4 symmetry stretching mode ν1(991 cm−1), the weak intensity in the z(xy)z¯ orientation was attributed to spillover of the Ag intensity because the peak positions were identical in both orientations. Intensity ratio of the bands due to the two sites gave a higher value (p1/p2~9.9) than (p1/p2~5) calculated from X-Ray studies [20]. In the Z(X′Y′)Z¯ orientation where only the Eg modes are expected, two very weak bands, with equal intensity, are observed at 986 and 993 cm−1. The presence of two bands for the symmetric stretching mode ν1(Fg) confirms the hypothesis of a disordered structure. The two Fg modes are observed at 985 and 968 cm−1 in the single crystal Raman spectrum of K-Alum [21]. For the symmetric bending mode ν2, three Raman components (1Eg+2Fg) are predicted in all polarization geometries. In the z(xx)z¯ and Z(X′Y′)Z¯ orientations where only the Fg modes are expected, three bands are observed at 440, 460, and at 471 cm−1. Their analogues in RbAl(SO4)2·12H2O and KAl(SO4)2·12H2O  appear at (441, 458 and 480 cm−1) and (441, 458, and 475 cm−1), respectively. Two Eg modes (z(xy)z geometry) are observed at 439 and 460 cm−1. Thus the number of deformation mode ν2 of SO4 shows very clearly the two different orientations of SO42- groupments in this structure.
From group theoretical predictions, five lines(1Ag+1Eg+3Fg) are expected in all orientation for the asymmetric bending mode ν4. In the Z(X′Y′)Z¯ geometry (Eg symmetry) two bands are observed at 614 and 634 cm−1.In the z(xx)z¯ geometry (Ag+Eg symmetry) three bands are observed at 615, 634, and 648 cm−1. The two bands appearing at 615 and 648 cm−1 are assigned to the Ag symmetry. The splitting of the Ag and Eg modes confirms the existence of two types of tetrahedral. In the z(xy)z¯ geometry (Fg symmetry) three bands are observed at 610, 621, and 632 cm−1.
The asymmetric stretching modeν3 is found in the 1000–1160 cm−1 region. Group theory analysis predicts five bands for this mode (1Ag+1Eg+3Fg). In the x(zz)x geometry (Ag+Eg symmetry) as in the x(zy)x geometry (Fg symmetry) and in the Z(X′Y′)Z¯  geometry (Eg symmetry), three (1107, 1131, and 1189 cm−1), four (1034, 1092, 1102, and 1131 cm−1), and two (1134 and 1189 cm−1) bands are obtained, respectively. The bands observed at 1107 and 1131 cm−1, for the first orientation, can be associated to the Ag mode, and those at 1134 and 1189 cm−1 are attributed to the Eg mode. The four peaks observed in the second orientation are attributed to the Fg mode. In the Z(X′X′)Z¯ geometry (Ag+Eg+Fg) symmetry five bands are observed at 1099, 1101, 1131, 1134, and 1191 cm−1. In the polycrystalline spectrum of Raman are observed in the region of the ν3(SO4) modes, in the IR spectra of various alums [21], where 3ν3(SO4) modes predict [19] two intense doublet at ≈1100–1090 cm−1 and two less intense bands at ≈1070–1200 cm−1. These last were assigned to ν3(SO4) modes of the mirror sulfates [22]. Thus the number of ν3(SO4) modes observed in spectra gives evidence that the disorder is indeed in NH4-alum.
In conclusion, X-Ray diffraction studies indicated that the sulphate groups inNH4+ alum is orientationally disordered. The current studies of the polarised Raman spectra give evidence that the disorder is indeed present in the ammonium alum. This is best manifested through the appearance of surplus bands in the spectral regions of vibrations of the sulphate anion.External Modes
10 Ag, 10 Eg, and 21 Fg lines can be expected in the Raman low-frequency range, corresponding to external modes. Experimentally, 11 lines in the z(xx)z geometry (Ag+Eg symmetry), 5 lines in the Z(X′Y′)Z geometry (Eg symmetry), and 10 lines in the x(zy)x geometry (Fg symmetry) indeed exist (Table 3).  Each external mode may be dominated by the contributions from all cations. However, in certain frequency ranges the external modes may be dominated by contribution from one kind of cation (translations) or groups of atoms (rotation). The external modes are assigned by comparison with attribution proposed in RbAl(SO4)2·12H2O and by considering the fact that the translator and libratory modes of NH4+ ion occur at higher wave numbers than those of the SO42- ions. The librations of both NH4+ and SO42- ions are found to be stronger in intensity than the corresponding translational modes. By relative data comparison to the ammonium and rubidium alum, the bands observed in the 53–61 cm−1 region, at 167, 186, and at ~245 cm−1, can be attributed to the  translations and librations of NH4+ ion, since these bands are not observed in the rubidium alum. By similar reasoning we can confirm the attribution of the band observed at 238 cm−1 in rubidium alum to the Rb–O stretching mode [5–18]. Thus, the other bands observed in the 90–150 cm−1 region can be assigned to translational modes and those in the 150–200 cm−1 region to rotational modes of SO42- [5–21].Table 3
Raman band positions and assignments ofNH4Al(SO4)2·12H2O.
z(xx)z¯z(xy)z¯Z(X′Y′)Z¯Z(X′X′)Z¯AssignmentAg+EgFgEgAg+Eg+Fg11m11m—11mLattice modes14w—14w14w16m——16m39w——39w44w47w48w44w—53w—59w61w59m60m61m—73w—73w80w———120w120m——Trans ofSO42-159s153m—159m—186m167m—193s196193mRota ofSO42-—195m—245wbr228w—246wνNH4–O326w329w320w327w440m440w434w440wν2SO42-460m460m459m458m539wbr471w———581sh——615s610s614s614sν4SO42-621s634s632m—902w913w905wν1SO42-915s986s990s990vs990m993m1099m1094wbr1034m1101m1104s1091m1102m1112s1102s1123s1131m1131m1130m1132m1134mν3SO42-−1190m——1191m————1444sν4NH4+1444s1453s—1540sν2H2O—1621sν2NH4+1750s1620m1617mbr1726m1738wbr2210m—2473m2442w—ν1H2O2482w2908m2920m3072m2856m2936m—3132m3103m——3134s—3338m3350m3356mbr3365s—ν3H2O3400wbr3400mbr3376ss: strong; w: weak; m: medium; sh: shoulder; v: very; br: broad.


## 1.2.1. Factor Group Analysis

The ammonium alum,NH4Al(SO4)2·12H2O, belongs to a family of compounds with general formula AM(XO4)2·12H2O (A is a univalent metal such as Na, K, Rb, and Cs; M is a trivalent metal: Al, Ce, In, Fe, Cr, Ir etc.; X is S or Se).According to the crystallographic data [1], the ammonium alum crystallizes in the cubic structure Pa-3 (T6h), Z=4. The site symmetry of sulfate is C3, the trivalent cations occupy S6 sites, and the site symmetry of the two crystallographically distinct types of water molecules is C1. In the model the site symmetry of NH4+ is S6. However, X-ray diffraction studies of ammonium alum by with C3 symmetry. Abdeen et al. [2] indicated the unusual situation of two possible orientations of the sulfate ion, and the  site symmetry of NH4+ is C3. Similar suggestions were deduced from neutron diffraction date by Abdeen et al. [3]. Factor group analysis using standard correlation method [4] has been carried out to determine the symmetries of the vibrations and to predict the IR and Raman active modes.Excluding the acoustic modes, 227 normal modes are predicted.These are distributed as follows:(1)Γoptic=42Ag(R)+42Eg(R)+50Fg(R)+46Au(I)+46Eu(I)+51Fu(IR).
The Ag,Eg,andFg modes are Raman active, and Fu mode is infrared active.The Au and Eu modes exposed by Suresh et al. [5] as being IR active are really inactive.The contribution of the different groupments (SO4, NH4, and H2O) and the Al3+ ion to the Raman active vibrations are given in Table 2.Our polarized measurements were conducted on the (001) and (111) faces of the single crystal (Figure1).Photograph showing (a) face (001) and (b) face (111) things ofNH4Al(SO4)2·12H2O.
(a)(b)Analysis of the tensor components shows that, on (001) face, the Fg modes were obtained in the z(xy)z¯ geometry, the z(xx)z¯ geometry gives both the Ag and the Eg modes. Eg mode can be observed when the crystal is oriented as in (111) face and incident and scattered beams are perpendicular -Z(X′Y′)Z¯, and in polarizations parallel -Z(X′X′)Z¯ geometry the Ag, Eg, and Fg modes can be observed.The polarized Raman spectra recorded for these different geometries are shown in Figure2, and the frequencies of the observed bands and their vibrational assignments are given in Tables 1 and 2 (the spectra were collected from 5 to 4000 cm−1).Table 1
Active modes ofNH4Al(SO4)2·12H2O.
External modesInternal modesLSO4,TSO4,TAl,,LH2O,TH2O,LNH4,TNH4SO4NH4H2OActivityν1ν2ν3ν4ν1ν2ν3ν4ν1ν2ν3RamanAg110331110111011222(αxx+αyy+αzz)Eg110331101110111222(2αzz‒αxx-αyy,αxx‒αyy)Fg330993312331233222(αxy,αyz,αxz)Table 2
Correlation table of theAl(H2O)63+ octahedral.
FreeAl(H2O)63+ Oh symmetrySite groups S6 symmetryFactor groups Th6Figure 2
Raman spectra ofNH4Al(SO4)2·12H2O. The geometries and the corresponding mode symmetries are given in each diagram.


## 1.2.2. Results and Discussions

NH4+ Vibrations
The internal modes of vibration of freeNH4+ ion with Td symmetry have average frequencies at 3033, 1685, 3134, and 1397 cm−1 for ν1(A1), ν2(E), ν3(F2), and ν4(F2) modes, respectively, [6].
The stretching vibrationsNH4+ ion and the water molecule were observed in the 2900 to 3500 cm−1. It was possible to separate the absorption bands observed in the Raman  spectra of  NH4Al(SO4)2·12H2O by comparison with the RbAl(SO4)2·12H2O sample. The differences observed between the two spectra are most likely due to the  NH4+ vibrations. Indeed, the bands observed in the second at 1444 cm−1 in theZ(XX)Z¯ polarisation and at 1453 in the Z(X′Y′)Z¯   polarisation, and not observed in RbAl(SO4)2·12H2O, are most likely assignable to the asymmetric bending (ν4) mode of NH4+. By similar reasoning we can deduce that the band observed in NH4Al(SO4)2·12H2O at 2442/2482 and at 2210/2473 cm−1 in the -z(xx)z¯ and -Z(X′X′)Z¯ polarisation, respectively, corresponds to the combinations of bending modes ν2 with the internal rotation mode ν6. Appearance of these bands indicates that the NH4+ ion does not rotate freely in the crystalline lattice, thus the ammonium ions form hydrogen bonds in the crystals [7–10]. The bands observed in the z(xx)z polarisation at 3134 cm−1 can be assigned to the asymmetric stretching ν3(Ag) vibrations.H2O Vibration
The vibrational frequencies of a free water molecule are at 3756 (ν3), 3652 (ν1), and 1595 cm−1(ν2) [11]. By comparison  with RbAl(SO4)2·12D2O, and (CH3)2NH2Al(SO4)2·6H2O, it was possible to identify the vibrational frequencies of water molecule in NH4Al(SO4)2·12H2O.
From group theoretical predictions, 18 lines (6Ag+6Fg+6Eg) are expected in all orientation (Table 1).
In thez(xx)z¯ orientation six bands are observed at 1620, 1726, 2856, 3103, 3356, and 3400 and are close to those (1678, 1735, 2900, 3085, 3360, and 3412 cm−1) reported by Abdeen et al. [3], RbAl(SO4)2·12H2O  for RbAl(SO4)2·12H2O. In the z(xy)z¯  geometrics (Fg symmetry) five bands are observed at  1617, 1738, 2936, 3365, and 3376 cm−1. Their analogues in RbAl(SO4)2·12H2O appear at 1605, 1632, 2985, 3120, 3330, and 3380 cm−1. In the  Z(X′Y′)Z¯ geometry (Eg symmetry) only three bands (from six predicted) are observed at 2908, 3072, and 3338 cm−1. The bands observed in each orientation at ~1700 cm−1 can be assigned to the HOH bending vibration ν2(H2O). The bands observed in the 2800–3500 cm−1 region are assigned to the symmetric and asymmetric stretching modes of water molecules. The observed bands in the stretching and bending regions show the presence of two distinct water molecules in NH4Al(SO4)2·12H2O. The significant decrease in the frequencies of the stretching modes and the increase in frequencies of the bending modes from the free state values show that water molecules form hydrogen bonds of medium and strong strength [12, 13].
The librational modes of water are characteristic of coordinated water and fall in the 500–900 cm−1 region [14, 15]. This region is complicated by presence of strong absorptions of ν4(SO4) and ν1(Al(H2O)6), and the ν3(Al(H2O)6) is Raman inactive Table 2. The low polarizability of water molecules makes these bands appear weak. Librational modes of water are assigned by comparison with RbAl(SO4)2·12H2O [5], CsAl(SO4)2·12H2O [15], and its partly deuterated analogues. There is no doublet that the bands observed in the 700–900 cm−1 region should be attributed to librations of water molecules, as done in all previous assignments [5–17].Al(H2O)6 Vibrations
The metal cationAl3+ forms an octahedron with surrounding six water molecules. Under Oh symmetry, the ion has six modes of vibration ν1(A1g), ν2(Eg), ν3(F1u), ν4(F1u), ν5(F2g), andν6(F2u). Out of these ν1, ν2, and ν5 are Raman active, ν3 and ν4 IR active, and ν6 inactive in both IR and Raman. Table 2 shows the correlation diagram between the free Al(H2O)6  group vibrations in Oh symmetry and the Al(H2O)6  internal vibrations in Th factor group symmetry through the S6 one in the crystal.
Unambiguous assignments of these modes are difficult as they fall in the region of the anion bending modes, librational modes of water molecules, and external modes. However, a few of these modes are assigned by comparison with the bands observed for theAl(H2O)63+ complex in RbAl(SO4)2·12H2O [5] and in similar compounds in (CH3)2NH2Al(SO4)2·6H2O [13]. The medium bands around 530 cm−1 are due to the ν1 mode of the ion. ν2 modes are observed as very weak bands around 400 cm−1. The triply degenerate symmetric bending mode (ν5) is observed with medium intensity in the Raman spectra, around 330 cm−1, being observed at similar frequencies (517, 416 and 386 cm−1) in the spectrum of potassium alum [18].SO42- Vibration
The four internal modes of a freeSO42- ion with tetrahedral, Td symmetry are at ν1(A1) 981 cm−1, ν2(E) 451 cm−1, ν3(F2) 1104 cm−1, and ν4(F2) 613 cm−1 [19]. Table 2 shows resultant of correlation diagram between the free SO4 group vibrations in Td symmetry and the SO4 internal vibrations in Th factor group symmetry through the C3 one in the crystal. In an ordered structure 15 Raman lines are predicted:(i)
7 stretching modes:2ν1(1Ag, 1Fg); 5ν3(1Ag, 1Eg, 3Fg);(ii)
8 deformation modes:3ν2(1Eg,2Fg); 5ν4(1Ag,1Eg,3Fg).In the ordered lattice, group theory analysis (Table 1) predicts two bands arising from the symmetric stretching mode ν1(Ag and Fg modes). This vibration that involves large changes in polarizability is observed as very intense bands at 990 cm−1 and medium bands at 975 cm−1: in the z(xx)z¯ geometry (Ag and Fg symmetry), in the  z(xy)z¯ geometry (Eg symmetry), and in Z(X′X′)Z¯ geometry (Ag, Eg, and Fg symmetry). The two bands should be attributed to Ag component to two types of sulfate anion, as done in all previous assignments (see [5–17]. The two bands with different intensity are also observed in the single crystal Raman spectrum of potassium alum for x(zz)y and x(xy)x orientations at 973 and 989 cm−1 [20]. These last authors assert that the two bands have some Ag symmetry, and there is no indication of a band with Fg symmetry. Although in the studied Raman spectrum of polycrystalline K-alum anly one very strong band is observed below 1000 cm−1 originating from the SO4 symmetry stretching mode ν1(991 cm−1), the weak intensity in the z(xy)z¯ orientation was attributed to spillover of the Ag intensity because the peak positions were identical in both orientations. Intensity ratio of the bands due to the two sites gave a higher value (p1/p2~9.9) than (p1/p2~5) calculated from X-Ray studies [20]. In the Z(X′Y′)Z¯ orientation where only the Eg modes are expected, two very weak bands, with equal intensity, are observed at 986 and 993 cm−1. The presence of two bands for the symmetric stretching mode ν1(Fg) confirms the hypothesis of a disordered structure. The two Fg modes are observed at 985 and 968 cm−1 in the single crystal Raman spectrum of K-Alum [21]. For the symmetric bending mode ν2, three Raman components (1Eg+2Fg) are predicted in all polarization geometries. In the z(xx)z¯ and Z(X′Y′)Z¯ orientations where only the Fg modes are expected, three bands are observed at 440, 460, and at 471 cm−1. Their analogues in RbAl(SO4)2·12H2O and KAl(SO4)2·12H2O  appear at (441, 458 and 480 cm−1) and (441, 458, and 475 cm−1), respectively. Two Eg modes (z(xy)z geometry) are observed at 439 and 460 cm−1. Thus the number of deformation mode ν2 of SO4 shows very clearly the two different orientations of SO42- groupments in this structure.
From group theoretical predictions, five lines(1Ag+1Eg+3Fg) are expected in all orientation for the asymmetric bending mode ν4. In the Z(X′Y′)Z¯ geometry (Eg symmetry) two bands are observed at 614 and 634 cm−1.In the z(xx)z¯ geometry (Ag+Eg symmetry) three bands are observed at 615, 634, and 648 cm−1. The two bands appearing at 615 and 648 cm−1 are assigned to the Ag symmetry. The splitting of the Ag and Eg modes confirms the existence of two types of tetrahedral. In the z(xy)z¯ geometry (Fg symmetry) three bands are observed at 610, 621, and 632 cm−1.
The asymmetric stretching modeν3 is found in the 1000–1160 cm−1 region. Group theory analysis predicts five bands for this mode (1Ag+1Eg+3Fg). In the x(zz)x geometry (Ag+Eg symmetry) as in the x(zy)x geometry (Fg symmetry) and in the Z(X′Y′)Z¯  geometry (Eg symmetry), three (1107, 1131, and 1189 cm−1), four (1034, 1092, 1102, and 1131 cm−1), and two (1134 and 1189 cm−1) bands are obtained, respectively. The bands observed at 1107 and 1131 cm−1, for the first orientation, can be associated to the Ag mode, and those at 1134 and 1189 cm−1 are attributed to the Eg mode. The four peaks observed in the second orientation are attributed to the Fg mode. In the Z(X′X′)Z¯ geometry (Ag+Eg+Fg) symmetry five bands are observed at 1099, 1101, 1131, 1134, and 1191 cm−1. In the polycrystalline spectrum of Raman are observed in the region of the ν3(SO4) modes, in the IR spectra of various alums [21], where 3ν3(SO4) modes predict [19] two intense doublet at ≈1100–1090 cm−1 and two less intense bands at ≈1070–1200 cm−1. These last were assigned to ν3(SO4) modes of the mirror sulfates [22]. Thus the number of ν3(SO4) modes observed in spectra gives evidence that the disorder is indeed in NH4-alum.
In conclusion, X-Ray diffraction studies indicated that the sulphate groups inNH4+ alum is orientationally disordered. The current studies of the polarised Raman spectra give evidence that the disorder is indeed present in the ammonium alum. This is best manifested through the appearance of surplus bands in the spectral regions of vibrations of the sulphate anion.External Modes
10 Ag, 10 Eg, and 21 Fg lines can be expected in the Raman low-frequency range, corresponding to external modes. Experimentally, 11 lines in the z(xx)z geometry (Ag+Eg symmetry), 5 lines in the Z(X′Y′)Z geometry (Eg symmetry), and 10 lines in the x(zy)x geometry (Fg symmetry) indeed exist (Table 3).  Each external mode may be dominated by the contributions from all cations. However, in certain frequency ranges the external modes may be dominated by contribution from one kind of cation (translations) or groups of atoms (rotation). The external modes are assigned by comparison with attribution proposed in RbAl(SO4)2·12H2O and by considering the fact that the translator and libratory modes of NH4+ ion occur at higher wave numbers than those of the SO42- ions. The librations of both NH4+ and SO42- ions are found to be stronger in intensity than the corresponding translational modes. By relative data comparison to the ammonium and rubidium alum, the bands observed in the 53–61 cm−1 region, at 167, 186, and at ~245 cm−1, can be attributed to the  translations and librations of NH4+ ion, since these bands are not observed in the rubidium alum. By similar reasoning we can confirm the attribution of the band observed at 238 cm−1 in rubidium alum to the Rb–O stretching mode [5–18]. Thus, the other bands observed in the 90–150 cm−1 region can be assigned to translational modes and those in the 150–200 cm−1 region to rotational modes of SO42- [5–21].Table 3
Raman band positions and assignments ofNH4Al(SO4)2·12H2O.
z(xx)z¯z(xy)z¯Z(X′Y′)Z¯Z(X′X′)Z¯AssignmentAg+EgFgEgAg+Eg+Fg11m11m—11mLattice modes14w—14w14w16m——16m39w——39w44w47w48w44w—53w—59w61w59m60m61m—73w—73w80w———120w120m——Trans ofSO42-159s153m—159m—186m167m—193s196193mRota ofSO42-—195m—245wbr228w—246wνNH4–O326w329w320w327w440m440w434w440wν2SO42-460m460m459m458m539wbr471w———581sh——615s610s614s614sν4SO42-621s634s632m—902w913w905wν1SO42-915s986s990s990vs990m993m1099m1094wbr1034m1101m1104s1091m1102m1112s1102s1123s1131m1131m1130m1132m1134mν3SO42-−1190m——1191m————1444sν4NH4+1444s1453s—1540sν2H2O—1621sν2NH4+1750s1620m1617mbr1726m1738wbr2210m—2473m2442w—ν1H2O2482w2908m2920m3072m2856m2936m—3132m3103m——3134s—3338m3350m3356mbr3365s—ν3H2O3400wbr3400mbr3376ss: strong; w: weak; m: medium; sh: shoulder; v: very; br: broad.



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*Source: 128401-2011-05-19.xml*