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Pauling crystal radius of the hydride ion
Notes
1715
target to the enriched aWl'e, the emission rate of the 495 KeV y-ray was enhanced by a factor of 24.4 '___1.5 in relation to the 326 KeV gammas, while the abundance of lS°Te in relation to XUTe in these target materials differed by a factor of 24-8 -t- 1.4. The gamma-spectra of the two types of sources are shown in Fig. 1. Beta spectra were taken by means of a 1.5 in × 13/16 in. plastic scintillator. The endpoint energy of the short-lived/~-component was found to be 2.7 ± 0.1 MeV. A E-spectrum taken in coincidence with the 495 KeV y-rays showed the same endpoint energy, although the counting statistics were quite low in this case. It is concluded that the observed activity of approximately 4 minute half-life is, in fact, the short-lived 1~7Sn isomer, and that the decay of this isomer is connected with the emission of the 495 KeV ;,-ray. As a weighted mean, 4-1 :t: 0'3 min is given for the half-life. Fig. 2 shows the proposed simple decay scheme, giving a total decay energy of 3'2 :: 0" 1 MeV. Other low-intensity modes of decay are, of course, not excluded. The same figure also includes a slightly simplified decay scheme of the 9.7-min az~Sn.~ The similarity between the two decay structures suggests that the 4'l-min ~JTSn is the low spin isomer. It may also be pointed out, that, if the lowering of the h,,~ level in relation to the ds/2 level, that is taking place between A : : 117 and A = 125, continues at A - 127, the low-spin isomer also is the excited state.
Acknowledgements--This work was supported by the U.S. Atomic Energy Commission under contract AT-(40-1)-1313 and 3235. The author is grateful to Professor P. K. KURODA for his interest and encouragement. Department of Chemistry', Unit,ersity of ArkanscL~, Fa),etterille
P. KAURANEN+*
+*Present address: Department of Physics, University of Helsinki, Helsinki, Finland, c~ S. B. BURSON, J. M. Lr.BLA~C, and D. W. MARrlN, Phys. Rev. 105, 625 (1957).
J. lnorg. Nucl. Chem., 1965, Vol. 27. pp. 1715 to 1717. Pergamon Press Ltd. Printed in Northern Ireland
Pauling crystal radius of the hydride ion (ReceiL'ed 3 March 1965) I~ HiS table of crystal radii PAULINO'~} lists 2'08 /~ as the radius of the hydride ion H -. This magnitude refers to the free ion and is not appropriate to dimensions in crystalline compounds. Comparison of radial distribution functions for Li + and H - ions ~zl with the observed distance in crystalline lithium hydride shows that there is a considerable shortening of the internuclear separation when the oppositely-charged ions interact in the formation of the compound. It seems desirable, therefore, to consider the possibility of deriving a value for the radius of the hydride ion which can be collated with other crystal radii of PAULING. GIBBca' has recently proposed the value r a - ~ 1-40/~ for application with radii due to ZACHARIASEN. 14~ In producing his set of crystal radii of ions PAULI:qG~ took the salts NaF, KCI, RbBr and Csl as standard crystals and in these the cation :anion radius ratio p = r_/r_, was found to be ,-,-0-75 (the equilibrium distance r0 in the B 1 modification of CsI was assessed for use in the calculations). To explain divergences between observed distances and radius sums in other alkali halide crystals, PAULING corrected for a radius ratio effect. By multiplying requisite radius sums by F(p), a function of the radius ratio and of the Born repulsion exponent n, excellent agreement with observed distances was obtained (for full details see Ref. 1). " ' L. PAULING, The Nature of the Chemical Bond (3rd Ed.), Cornell University Press (1960). ~tJ E. HYLLEgAS, Proc. Rydberg Centennial Conf. Lund, Sweden, July 1954 p. 83; H. A. BETHE in GERLAG--SCHEEL'S Handbuch der Physik (2nd Ed.), 24, Part I Verlag Julius Springer, Berlin (1933). ~a~T. R. P. GraB, Progr. Inorg. Chem. 3, 315 (1962). t'~ W. H. ZACHARIASEN,Z. Krist. 80, 137 (1931).
1716
Notes
The alkali hydrides all crystallize with the sodium chloride arrangement, and experimental values for the equilibrium internuclear separation between oppositely-charged ions are given in column 3 of Table 1. Sums of relevant PAULI~G crystal radii and the radius of H - taken as 1.53 A are shown in column 4. If the radius ratio correction is applied, a standard radius for H - can be calculated which should be collatable with corresponding radii of PAULING. It can be seen from column 6 of Table 1 that values for this standard radius are essentially constant in the case of KH, RbH and CsH and approximate to the selected crystal radius 1.53 ,~,. Although, following PAULtN6,c~ the function F(p) TABLE I.--DISTANCES IN
Hydride LiH Nail KH RbH CsH
ALKALI HYDRIDES AND THE RADIUS OF THE HYDRIDE ION
Pauling crystal radius of cation (A)
Observed distance ro (A)
Crystal radius sum (r n- = 1"53) (A)
p
Calculated standard radius of H (A)
0-60 0'95 1"33 1-48 1.69
2.04 2.44 2"85 3'02 3'19
2"13 2"48 2"86 3'01 3.22
0'39 0.62 0'87 0'97 1'10
1"35 1'47 1"53 1"54 1"53
has been used with n = 9, and lower values for n should probably be applied for alkali hydrides, the discrepancy between observed and calculated values of r0 for lithium hydride cannot be explained by the radius-ratio effect. An explanation of the deviations in the case of LiH and N a i l can be obtained from a consideration of ion polarization. ~5~ As a result of polarization, the electronic system of an anion is tightened in the field of a cation and that of a cation is loosened in the field of the anion. The magnitude of these changes depends on the field strength of the polarizing ion and on the polarizability of the other. Polarization of the anion by the cation is usually the more pronounced effect. The hydrideionappears to be very polarizable and its molar refraction [R] ~o in the free gaseous state has been estimated ~6~ to be 37 cm 3 per g. ion. Much lower values are found in crystals, ~7~e.g. [R]D for H - is 5"1 in KH(c) and 4"4. in Nail(c). Since from consideration of ionization potentials and ionic radii the polarizing TABLE 2 . - - T H E STRUCTURES OF CALCIUM HALIDES
Salt CaFa CaCla CaBr~ CaI~
Crystal structure type Fluorite Distorted rutile Distorted rutile Cadmium iodide
Pauling crystal radii r+, A r_, A 0.99 0"99 0.99 0'99
1"36 1'81 1.95 2.16
Observed distance r0, A. 2"36 2.76 ~ , 2.70 t4~ 2.91 c2~,2.88 TM 3-12
Crystal Molar refraction radius sum of free anion (r_ + r_), A, (cm 3 g. ion -1) 2"35 2'80 2"94 3'15
2'5 9-0 12.5 19.0
power of alkali metal ions ~8~ is in the order Li ÷ > Na ÷ > K + > Rb ÷ > Cs ~, the tightening of the electronic system of the hydride ion in the field of cations could primarily account for the discrepancies between observed and calculated interionic distances in LiH(c) and Nail(c). The effect of polarization is also notable in the alkaline earth hydrides CaH~, SrH2 and BAH2. If H - were not easily deformable Call2 might be expected to have the rutile structure and SrH2 and BaHz the fluorite structure. In fact each of the three salts has a packed structure of low symmetry~'~; the metal ions are arranged in nearly perfect hexagonal close packing, the H - ions occupying the (sl K. FAJANS,J. Chem. Phys. 9, 281 (1941). 161K. FAJANS, Chem. Engrg. News 27, 900 (1949); Physical Methods of Organic Chemistry (Edited by A. WEISSBURGER)(3rd Ed.) p. 1169. Interscience, New York (1960). (~) K. FAJANS, Chimia 13, 349 (1959). ts~ D. F. C. MORRIS and L. H. AHRENS,J. lnorg. Nucl. Chem. 3, 263 (1956). c,~ E. Zrt,rrL and A. HARDER,Z. Elektrochem. 41, 33 (1935).
Notes
1717
largest holes. In this structure there are two kinds of non-equivalent H - ions, e.g., the strontium ion in SrH~ has 3Hi at 2.35 A and 4Hzi at 2.71 A as neighbours---cf, the crystal radius sum, 2.66 A. Magnesium hydride MgHs has the ruffle structure ~°~ which is to be expected on geometrical grounds for spherical ions and p = 0.42. However, the observed r0, 1.95 A, is much smaller than the ionic radius sum, 2.18 A, and the shortest H - - H distance is 2'49 A. Although the polarizability of halide ions is less than that of the hydride ion, a similar effect of polarization on observed distances in comparison with radius sums can be noted in the case of calcium halides (Table 2). It follows from the above discussion that a crystal radius of 1.53/~ for H - is collatable with PAULING'Scrystal radii. However, this radius is appropriate only to distances in ionic crystals where polarization is minimal. It can be concluded also that a value r a- ~ 1'53 .~,,rather than the magnitude r~x- = 1.40 A proposed by GIBB,~3~ should be compatible with ionic radii due to ZACHARIASEN.~
Department of Chemistry Brunel College London, W. 3
D . F . C . MORRIS G . L . REED
c~o, F. H. ELLINGER,C. E. HOLLY,B. B. MCINTEER,D. PAVONE,R. M. POTTER,E. STARITZKYand W. H. ZACHARIASEN,jr. Amer. Chem. Soc. 77, 2647 (1955).
1715
target to the enriched aWl'e, the emission rate of the 495 KeV y-ray was enhanced by a factor of 24.4 '___1.5 in relation to the 326 KeV gammas, while the abundance of lS°Te in relation to XUTe in these target materials differed by a factor of 24-8 -t- 1.4. The gamma-spectra of the two types of sources are shown in Fig. 1. Beta spectra were taken by means of a 1.5 in × 13/16 in. plastic scintillator. The endpoint energy of the short-lived/~-component was found to be 2.7 ± 0.1 MeV. A E-spectrum taken in coincidence with the 495 KeV y-rays showed the same endpoint energy, although the counting statistics were quite low in this case. It is concluded that the observed activity of approximately 4 minute half-life is, in fact, the short-lived 1~7Sn isomer, and that the decay of this isomer is connected with the emission of the 495 KeV ;,-ray. As a weighted mean, 4-1 :t: 0'3 min is given for the half-life. Fig. 2 shows the proposed simple decay scheme, giving a total decay energy of 3'2 :: 0" 1 MeV. Other low-intensity modes of decay are, of course, not excluded. The same figure also includes a slightly simplified decay scheme of the 9.7-min az~Sn.~ The similarity between the two decay structures suggests that the 4'l-min ~JTSn is the low spin isomer. It may also be pointed out, that, if the lowering of the h,,~ level in relation to the ds/2 level, that is taking place between A : : 117 and A = 125, continues at A - 127, the low-spin isomer also is the excited state.
Acknowledgements--This work was supported by the U.S. Atomic Energy Commission under contract AT-(40-1)-1313 and 3235. The author is grateful to Professor P. K. KURODA for his interest and encouragement. Department of Chemistry', Unit,ersity of ArkanscL~, Fa),etterille
P. KAURANEN+*
+*Present address: Department of Physics, University of Helsinki, Helsinki, Finland, c~ S. B. BURSON, J. M. Lr.BLA~C, and D. W. MARrlN, Phys. Rev. 105, 625 (1957).
J. lnorg. Nucl. Chem., 1965, Vol. 27. pp. 1715 to 1717. Pergamon Press Ltd. Printed in Northern Ireland
Pauling crystal radius of the hydride ion (ReceiL'ed 3 March 1965) I~ HiS table of crystal radii PAULINO'~} lists 2'08 /~ as the radius of the hydride ion H -. This magnitude refers to the free ion and is not appropriate to dimensions in crystalline compounds. Comparison of radial distribution functions for Li + and H - ions ~zl with the observed distance in crystalline lithium hydride shows that there is a considerable shortening of the internuclear separation when the oppositely-charged ions interact in the formation of the compound. It seems desirable, therefore, to consider the possibility of deriving a value for the radius of the hydride ion which can be collated with other crystal radii of PAULING. GIBBca' has recently proposed the value r a - ~ 1-40/~ for application with radii due to ZACHARIASEN. 14~ In producing his set of crystal radii of ions PAULI:qG~ took the salts NaF, KCI, RbBr and Csl as standard crystals and in these the cation :anion radius ratio p = r_/r_, was found to be ,-,-0-75 (the equilibrium distance r0 in the B 1 modification of CsI was assessed for use in the calculations). To explain divergences between observed distances and radius sums in other alkali halide crystals, PAULING corrected for a radius ratio effect. By multiplying requisite radius sums by F(p), a function of the radius ratio and of the Born repulsion exponent n, excellent agreement with observed distances was obtained (for full details see Ref. 1). " ' L. PAULING, The Nature of the Chemical Bond (3rd Ed.), Cornell University Press (1960). ~tJ E. HYLLEgAS, Proc. Rydberg Centennial Conf. Lund, Sweden, July 1954 p. 83; H. A. BETHE in GERLAG--SCHEEL'S Handbuch der Physik (2nd Ed.), 24, Part I Verlag Julius Springer, Berlin (1933). ~a~T. R. P. GraB, Progr. Inorg. Chem. 3, 315 (1962). t'~ W. H. ZACHARIASEN,Z. Krist. 80, 137 (1931).
1716
Notes
The alkali hydrides all crystallize with the sodium chloride arrangement, and experimental values for the equilibrium internuclear separation between oppositely-charged ions are given in column 3 of Table 1. Sums of relevant PAULI~G crystal radii and the radius of H - taken as 1.53 A are shown in column 4. If the radius ratio correction is applied, a standard radius for H - can be calculated which should be collatable with corresponding radii of PAULING. It can be seen from column 6 of Table 1 that values for this standard radius are essentially constant in the case of KH, RbH and CsH and approximate to the selected crystal radius 1.53 ,~,. Although, following PAULtN6,c~ the function F(p) TABLE I.--DISTANCES IN
Hydride LiH Nail KH RbH CsH
ALKALI HYDRIDES AND THE RADIUS OF THE HYDRIDE ION
Pauling crystal radius of cation (A)
Observed distance ro (A)
Crystal radius sum (r n- = 1"53) (A)
p
Calculated standard radius of H (A)
0-60 0'95 1"33 1-48 1.69
2.04 2.44 2"85 3'02 3'19
2"13 2"48 2"86 3'01 3.22
0'39 0.62 0'87 0'97 1'10
1"35 1'47 1"53 1"54 1"53
has been used with n = 9, and lower values for n should probably be applied for alkali hydrides, the discrepancy between observed and calculated values of r0 for lithium hydride cannot be explained by the radius-ratio effect. An explanation of the deviations in the case of LiH and N a i l can be obtained from a consideration of ion polarization. ~5~ As a result of polarization, the electronic system of an anion is tightened in the field of a cation and that of a cation is loosened in the field of the anion. The magnitude of these changes depends on the field strength of the polarizing ion and on the polarizability of the other. Polarization of the anion by the cation is usually the more pronounced effect. The hydrideionappears to be very polarizable and its molar refraction [R] ~o in the free gaseous state has been estimated ~6~ to be 37 cm 3 per g. ion. Much lower values are found in crystals, ~7~e.g. [R]D for H - is 5"1 in KH(c) and 4"4. in Nail(c). Since from consideration of ionization potentials and ionic radii the polarizing TABLE 2 . - - T H E STRUCTURES OF CALCIUM HALIDES
Salt CaFa CaCla CaBr~ CaI~
Crystal structure type Fluorite Distorted rutile Distorted rutile Cadmium iodide
Pauling crystal radii r+, A r_, A 0.99 0"99 0.99 0'99
1"36 1'81 1.95 2.16
Observed distance r0, A. 2"36 2.76 ~ , 2.70 t4~ 2.91 c2~,2.88 TM 3-12
Crystal Molar refraction radius sum of free anion (r_ + r_), A, (cm 3 g. ion -1) 2"35 2'80 2"94 3'15
2'5 9-0 12.5 19.0
power of alkali metal ions ~8~ is in the order Li ÷ > Na ÷ > K + > Rb ÷ > Cs ~, the tightening of the electronic system of the hydride ion in the field of cations could primarily account for the discrepancies between observed and calculated interionic distances in LiH(c) and Nail(c). The effect of polarization is also notable in the alkaline earth hydrides CaH~, SrH2 and BAH2. If H - were not easily deformable Call2 might be expected to have the rutile structure and SrH2 and BaHz the fluorite structure. In fact each of the three salts has a packed structure of low symmetry~'~; the metal ions are arranged in nearly perfect hexagonal close packing, the H - ions occupying the (sl K. FAJANS,J. Chem. Phys. 9, 281 (1941). 161K. FAJANS, Chem. Engrg. News 27, 900 (1949); Physical Methods of Organic Chemistry (Edited by A. WEISSBURGER)(3rd Ed.) p. 1169. Interscience, New York (1960). (~) K. FAJANS, Chimia 13, 349 (1959). ts~ D. F. C. MORRIS and L. H. AHRENS,J. lnorg. Nucl. Chem. 3, 263 (1956). c,~ E. Zrt,rrL and A. HARDER,Z. Elektrochem. 41, 33 (1935).
Notes
1717
largest holes. In this structure there are two kinds of non-equivalent H - ions, e.g., the strontium ion in SrH~ has 3Hi at 2.35 A and 4Hzi at 2.71 A as neighbours---cf, the crystal radius sum, 2.66 A. Magnesium hydride MgHs has the ruffle structure ~°~ which is to be expected on geometrical grounds for spherical ions and p = 0.42. However, the observed r0, 1.95 A, is much smaller than the ionic radius sum, 2.18 A, and the shortest H - - H distance is 2'49 A. Although the polarizability of halide ions is less than that of the hydride ion, a similar effect of polarization on observed distances in comparison with radius sums can be noted in the case of calcium halides (Table 2). It follows from the above discussion that a crystal radius of 1.53/~ for H - is collatable with PAULING'Scrystal radii. However, this radius is appropriate only to distances in ionic crystals where polarization is minimal. It can be concluded also that a value r a- ~ 1'53 .~,,rather than the magnitude r~x- = 1.40 A proposed by GIBB,~3~ should be compatible with ionic radii due to ZACHARIASEN.~
Department of Chemistry Brunel College London, W. 3
D . F . C . MORRIS G . L . REED
c~o, F. H. ELLINGER,C. E. HOLLY,B. B. MCINTEER,D. PAVONE,R. M. POTTER,E. STARITZKYand W. H. ZACHARIASEN,jr. Amer. Chem. Soc. 77, 2647 (1955).