The polarizabilities of planar nitrate, carbonate and borate anions in crystal

Lö, B.

doi:10.1016/0022-3697(73)90046-2

Cited by 17 publications

(21 citation statements)

References 8 publications

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“…The ligand polarizabilities increase as follows α H 2 O = 1.442 Å 3 [44] Ͻ α OH -= 2.03 Å 3 [51] Ͻ α CO 3 2-= 3.85 Å 3 . [45] The OH -anions are not particularly polarizable, but they tend to form Ln-O bonds that are shorter [52] than those of water. [53] In order to assess the influence exerted by these anions on the spectroscopic parameters of the lanthanide complexes, some comparisons were necessary.…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, the P solution /P crystal ratio may indicate that the surrounding of the light Ln 3+ ions contains more polarizable components and the overall average allocation of the ligands around the metal cation may be more anisotropic in solution than in the crystals. As far as the polarizability is concerned, it is useful to point out that the experimental values, α, determined for the H 2 O molecule in CaSO 4 ·2H 2 O (gypsum) [44] and for the CO 3 2-anion in CaCO 3 (calcite) [45] transitions may be an indicator of the nephelauxetic effect, which is connected with the metal-ligand distances, the coordination numbers, and the total negative charge accumu- lated around the metal cation.…”

Section: Hypersensitive Transitionsmentioning

confidence: 99%

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Lanthanide Carbonates

2011

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Section: Discussionmentioning

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Section: Hypersensitive Transitionsmentioning

confidence: 99%

Lanthanide Carbonates

2011

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“…The latest and most comprehensive study is that given by Lo (1973).It was on the subjects of calcite and aragonite that Bragg, in his now classical (1924) paper, first succeeded in correlating birefringence with crystal structure, using the pointdipole theory as developed by Lorentz (1909) andEwald (1921). In his approach, however, Bragg considered optical anisotropy to arise from different dipole-dipole coupling along different crystallographic directions, and neglected the possibility of intrinsic anisotropy in the constituent atoms, particularly oxygen.…”

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confidence: 99%

“…The converse was done by Bhagavantum (1942), while Lawless & Devries (1964) took into consideration both sources of anisotropy, but evaluated only nearest-neighbour interactions in their analysis. In his study, Lo (1973) computed, in a manner not subjected to the above criticisms, the cation and anion polarizabilities for all the carbonates and nitrate isostructural with calcite. Lo, in assessing the results of his analysis, considered there to be no established trend between birefringence and cation/anion polarizations or with the cation species.…”

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Structural dependence of the optical birefringence of crystals with calcite and aragonite type structures

Isherwood¹,

James²

1976

Acta Cryst Sect A

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Analysis of the available structural and optical data on calcite and aragonite type materials suggests a relationship between their birefringence, anion size and cation electronegativity.The structural dependence of the birefringence of calcite and the carbonates and nitrates isostructural with calcite, has been the subject of a number of investigations over the past fifty years. The latest and most comprehensive study is that given by Lo (1973).It was on the subjects of calcite and aragonite that Bragg, in his now classical (1924) paper, first succeeded in correlating birefringence with crystal structure, using the pointdipole theory as developed by Lorentz (1909) andEwald (1921). In his approach, however, Bragg considered optical anisotropy to arise from different dipole-dipole coupling along different crystallographic directions, and neglected the possibility of intrinsic anisotropy in the constituent atoms, particularly oxygen. The converse was done by Bhagavantum (1942), while Lawless & Devries (1964) took into consideration both sources of anisotropy, but evaluated only nearest-neighbour interactions in their analysis. In his study, Lo (1973) computed, in a manner not subjected to the above criticisms, the cation and anion polarizabilities for all the carbonates and nitrate isostructural with calcite. Lo, in assessing the results of his analysis, considered there to be no established trend between birefringence and cation/anion polarizations or with the cation species. He summarized his conclusions as 'within the validity of the point-dipole approximation the present investigation indicates that the polarizability of polyatomic anions in crystals is just as dependent on the nature of the constituent atoms as on the crystalline environment in which they are found.' In all the above mentioned studies it is evident that, without exception, the authors assumed that the dimension of the planar anion, CO 2-, NOr, is invariant and independent of the associated cation species. The reason for this assumption is perhaps obvious, namely that in very few cases have any of these structures been determined with adequate precision to evaluate the C-O or N-O bond lengths. However, the field of a dipole decays as a function of the inverse cube of the distance, and this brings in two considerations. Firstly, it is apparent that the induction effect on an oxygen atom by other atoms will be stronger for atoms in the same planar group than for those in neighbouring groups. Secondly, relatively small changes in C-O or N-O bond lengths could have a marked effect on the resultant polarization of the oxygen atoms in the anion and thus the ultimate birefringence of the crystal.

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“…This is the reason why Lawless & Devries (1964) had to exclude MgCO 3 when they determined the least-squares oxygen polarizability ellipsoid in fitting the refractive indices of carbonate minerals. In his study, Lo (1973) …”

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Point-dipole theory and optical birefringence of calcite-type carbonates

Pohl¹,

Ram²

1979

Acta Cryst Sect A

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A critical survey of the literature has revealed that recent structure determinations and optical data are available for only three calcite-type carbonates: calcite, rhodochrosite and magnesite. For these structures, the limitations of the pointdipole approximation are discussed.The point-dipole model was introduced by Bragg (1924) to explain quantitatively the birefringence of calcite and aragonite with respect to the crystal structures. In this approach optical anisotropy arises from differences in dipole-dipole coupling along different crystallographic directions. This source of anisotropy is connected with the Lorentz-factor tensor. In addition, however, optical anisotropy may arise from an intrinsic anisotropy in the constituent ions. In this case electronic polarizability tensors should be considered.In order to investigate the relation between atomic arrangement and double refraction, the crystals of carbonates have been used repeatedly. The latest studies are those given by Isherwood &James (1976) andPohl (1978). In his paper Pohl (1978) has developed a method to determine the electronic polarizabilities of ions from structural and optical data by a least-squares fit. The method is based on Bragg's (1924) model of point dipoles and on an exact calculation of Lorentz-factor tensors. This model satisfactorily accounts for the double refraction of aragonite-type carbonates. In the present paper we discuss the application of the method to calcite-type carbonates.Structural parameters of only three calcite-type carbonates have been determined: calcite (Chessin, Hamilton & Post, 1965), rhodochrosite (Brown & Forsyth, 1967) and magnesite (Oh, Morikawa, Iwai & Aoki, 1973). Optical constants are given by Winchell & Winchell (1964). Application of Pohl's (1978) method yields the electronic polariz- Bragg's (1924) ideas, the birefringence arises from the oxygens within the isolated COl-groups: the stronger the birefringence the stronger the influence of the O z-ions on each other. Strengthening of the oxygen interaction can take place in two ways. Firstly, the distance between the carbon and oxygen can be diminished. Secondly, the polarizability of the oxygen ion can be increased. Since the C-O distance is fixed according to the structure determination, only an increased polarizability of the 0 2-ion remains. However, this results in an increased mean refractivity which in return is compensated by a smaller polarizability of the cation, thus explaining the above results.To overcome the shortcomings encountered with the Bragg model of point dipoles, two improvements may be considered. Firstly, the point dipoles can be positioned outside the atomic centers, because the outer electrons responsible for the optical effects may have a center of gravity distinct from that determined by X-rays. Secondly, an intrinsic anisotropy can be allocated to the polarizability of the ions. Both of these improvements involve the introcluction of at least one extra parameter. Thus the number of adjustable parameters will exce...

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The polarizabilities of planar nitrate, carbonate and borate anions in crystal

Cited by 17 publications

References 8 publications

Lanthanide Carbonates

Lanthanide Carbonates

Structural dependence of the optical birefringence of crystals with calcite and aragonite type structures

Point-dipole theory and optical birefringence of calcite-type carbonates

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