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Nuclear spin relaxation in molten CdCdI2 and ICdI2 mixtures
Volume 78A, number 1
PHYSICS LETTERS
7 July 1980
NUCLEAR SPIN RELAXATION IN MOLTEN Cd-Cd!2 AND I-Cd!2 MIXTURES V.G.I. DESHMUKH’, G.A. STYLES and E.F.W. SEYMOUR Department ofPhysics, University of Warwick, Coventry CV4 7AL, UK Received 4 April 1980 3Cd relaxation data indicates that —1% The ofprevailing added atoms opinion produce is that paramagnetic excess Cd in Cd~ Cdt2 ionsproduces with lifetime diamagnetic —10 ps.Cd~ The ions. concentration “ ofCd’ ions is depressed by excess iodine.
1. Introduction. In an earlier paper [1] a description was given of a study of the nuclear spin—lattice and spin—spin relaxation times, T 1 and T2,3,2O5Tl in molten T1Brfast andrelaxation T1C1 and in Ti-doped For 20 as mdithe observed wasTIBr. interpreted cating the transient existence in the melt of localized paramagnetic centres, perhaps like F-centres in crystals or alternatively simply paramagnetic molecular ions. The present paper describes a similar Investigat3Cd relaxation in molten mixtures of tion of the ‘ Cd1 3Cd nucleus, like 203,205T1, 2 with has Cd and spinwith ~ soI.that Thethe ~ relaxationis not complicated by an electric quadrupole contribution which could mask the magnetic interaction with paramagnetic centres in which we are primarily interested. Unlike the thallium salts, Cd12 will dissolve a considerable quantity of excess metal; the solubility is well established, varying between 2.5 and 4 mol % in the temperature range used in these experiments. It is thus apossible to investigate the effects excess over much wider concentration rangeofthan for metal thallium halides. The solubffity of! is uncertain but no difficulty in dissolving amounts of the order was of 1 experienced mol %. Aconsiderable quantity of experimental data has been accumulated for the molten cadmiumhalides, in both the stoichiometric state and with excess metal, although most of the information is for Cd-CdCI 2 mixtures. The measurements include electrical conductivity, magnetic susceptibility, Ranian spectra, difPresent address: Royal Signals and Radar Establishment, Great Malvern, Worcs. WR14 3PS, UK.
fusion, viscosity, optical absorption and several thermodymanic properties [2,3]. The conclusions drawn thesethat observations are somewhat but itfrom appears the stoichiometric salt isequivocal heavily ionized at all temperatures, and that excess metal dissolves in the salt to form a subhalide, the metal assuming a valence state lower than that normally encountered. The behaviour of the conductivities of CdBr 2, Cd12ofand CdCI2, whichattributed change only slightly on addition metal has been to the formation of the dimer Cd~or the corresponding subhalide Cd 2 Q2 [4] and there is no evidence for formation of the Cd~ion which would produce conduction by electron exchange between Cd~and Cd~,except for a small contribution at temperatures well above the melting point. The magnetic susceptibifity of Cd—CdQ2 shows no detectable paramagnetic contribution on adding metal which seems to confirm the absence of the Cd+ but does not establish the 4~ as ion opposed to other diamagnetic presencesuch of Cd~ species as Cd0. Likewise, cryoscopic and heat of fusion data for metal-doped CdCl 2 suggest the substi2~ions [2]. tution of large cations Cd~ for smaller Cd Thus, there are strong indications that in the cadmium halides and added metal combined with Cd2~atom to form Cd~and there is little evidence of the formation of paramagnetic ions such as Cd~.It should be mentioned, however, that on addition of Ala3 to solid CdCl2 the diamagnetic compound Cd2 (Ala4)2 is formed [51offering clear cut evidence that cadmiuni can exist in the +1 oxidation state. In this paper we show that in order to interpret our 119
Volume 78A, number 1
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7 July 1980
relaxation results it is necessary to assume that paramagnetic centres exist in both stoichiometric Cd!2
0
and Cd—Cd12 solutions. The most natural assumption is that these are Cd~although we do not completely rule out other species such as F-centres. As
10 ~U5)
the2.evidence will beExpetimental seen3Cd this outlined does results not above. necessarily and discussion. conifict Measurewith nuclear spin relaxation have been ments of ~ made on solutions of Cd! 2 containing up to 0.5 mol % excess Cd and 5 mol % excess 1, respectively, at temperatures between 400 and 530°Cusing a pulsed NMR spectrometer. The samples were of Analar punty and were sealed in quartz ampoules after preliminary drying. The relaxation times T1 and T2 obtained at various temperatures are given in table 1 and the results at 400°C are plotted in fig. 1. Measurements of the potentially valuable or Knight 13Cd resonance werechemical inconclusive and shifts of the ‘ are not reported. The 127! resonance was not detected, presumably because of extremely fast quadrupolar relaxation, As can be seen T 1 * T2 and both decrease extremely rapidly with increasing temperature and cadmium content. For I concentrations greater than about 0.5 mol %, T~and T2 are independent of cornposition (possibly indicating a solubility limit) but both exhibit a dramatic decrease between 0.1 mol %I and 0.1 mol % Cd which continues, though more slowly, upT to 0.5 mol % Cd. We have been unable to measure 1 and T2 beyond this composition and conclude that they continue to decrease to values
~
102 10
to’
________________________________ 05
Cd 12 mot 0/0
_________
~—Cd
Fig. 1. Spin—lattice 113Cd (T1) and spin—spin (1’2) relaxation in Cdt times at 7 MHz for 2 solutions at 400°C, shown on a logarithmic scale as a function of composition.
less than 15 M~which is the limit of the apparatus. As T1 and decrease, whether with increasing perature orT2 changing composition, their ratio be-terncomes more nearly unity. Estimates show that except for the 0.5 mol % I and 5 mol % I solutions the relaxation is too fast to be accounted for by generally occurring mechanisms such as nuclear dipolar interaction, anisotropic chemical shift, spin-rotation interaction or scalar interaction with rapidly relaxing iodine nuclei. We therefore propose that as in the case of thallium halides relaxation in the 0.1 mol % I sample and in the stoichiometric and Cd-rich samples must be provided by anudehy13Cd perfine contact interaction between the ‘ us and transient paramagnetic centres produced both thermally and by excess cadmium. We suggest that in
Table 1 Sample
Temperature
T1
T1 IT2
1•js 5%I-Cd12 0,5%I-Cd12 0.1%I-Cd12
Cd12
0.i%Cd-Cd12 0.5%Cd-Cd12
120
405 401 401 450 492 400 455 527 404 443 400 455
05
~.LS
60 150 12 4
000 000 000 300 840 1 000 320 140 140
36 36 <20
3 400 2 200 1 400 640 340 100 100 —
33 17 20 15
18 68 8.6 6.7 2.4 9.6 2.3 —
4.1 2.2 1.8 <1.3
re
C (Cd°)X
Ps
10-6
—
—
56
19 16 8.2 20
7.9 —
12 7.6 6.2 <4
0.074 0.33 0.80 2.6 4.2 6.8 —
20.4 58 54.7 <98
Volume 78A, number i
PHYSICS LETTERS
the stoichiometric material these are created by the thermal dissociation CdI2 Cd’4 + I~,where both 3Cd relaxation will ionsdominated are paramagnetic but thewith ~ the unpairedelecbe by interaction tron on the Cd’4’ ion to which it belongs. (On the other hand the I~ions would be potent sources of relaxation for 127! nuclei.) In the Cd-rich solutions some additional Cd’4 ions may be produced by disruption of Cd0 or Cd~species. Our results could alternatively be explained if some of the Cd0 atoms ionize, each giving rise to a Cd2’4 ion and two Fcentres. The addition of iodine must be expected to depress the number of Cd’4 ions (or F-centres) due to the tendency to form F ions, or possibly I~molecular ions (V centres). The lifetime of the centres may be deduced from the inequality ofT 1 and T2. For a hyperfme contact interaction 1 =2 2S(s + 1) Tel {I +(~s 0.)I)2Te2 } (T1) 5cvA and -+
—
2
1
(T 2)
=
5cvA S(S+1)[re+rel{1 +(WS—c~,3I) Te}]
where A is the hyperfine coupling constant with a centre of spinS, c is the number of centres per formula unit, v is the number of nuclei affected by a centre at any instant, ws and w1 are the electron and nuclear Larmor frequencies, and re is the time for which the unpaired electron is in contact with a particular nudeus. (Alternatively re might represent the electron relaxation times but our derived values are so short that this is considered unlikely.) As pointed out by Ichikawa and Warren [6], for a very strong hyperfine interaction these equations are only approximately valid, but they are adequate for the semi-quantitative interpretation attempted here. Taking the ratio of these expressions, T1/T2 = 1 + (WS ~~I)2r~l2, which yields the values of Te shown in the table.We have not given values for the 5 mol % I sample since the relaxation may not be dominated by this nism at this concentration. As can be seen, remechadecreases with increasing temperature and with Cd concentration, the former being expected for any lifetime affected by thermal fluctuations. The number of centres can be obtained using an estimate for A. For Cd+ we take the free ion value As~= 2.1 X 1010 rad s~ [7] and p = 1~(For an F-centre a value 10 times smaller would be appropriate as suggested by —
7 July 1980
ENDOR measurements on ionic crystals, with v 10.) The values of c which result are given in the table. For the stoichiometric salt the results indicate that the concentration of centres is about 10~and that they exist for about 10 ps, which is an order of magnitude larger than the time characteristic of rotational or translational ionic motion. In the Cd-rich solutions, although the majority of the excess Cd atoms may produce diamagnetic Cdr as suggested by other experimental evidence, our results show clearly that a fraction produce additional paramagnetic centres. Assuming these are Cd’4 ions, this fraction is 1.5—2% of the excess Cd atoms for 0.1 mol % Cd and 1% for 0.5 mol % Cd at 400°C,and about double these values at 450°C.(These fractions would have to be about ten times larger if the centres were F-centres.) The lifetime of the centres is again ~10 ps but decreases with increasing concentration. We havesomewhat no explanation for such aCd decrease since the surroundings of such isolated centres should not be affected by the concentration of excess cadmium. The temperature dependence of c at all compositions may be approximately described by an energy of formation of 0.5—1.0 eV for the centres, corresponding to the energy penalty required to produce an ion without a closed electronic shell or sub-shell. Similarly the temperature dependence of re suggests a trapping energy ~0.5 eV for the centres corresponding to the energy required to move a centre from the neighbourhood of a particular cadmium ion to another. The presence of Cd+ ions or F centres would clearly lead to a paramagnetic term in the susceptibility. Mowat [8] has found that the addition of 6 mol % Cd does not appreciably alter the mass susceptibility of molten Cd12. His data are consistent with the production of Cdç ions only, with a susceptibility attributed ~Cdr which is moretodiamagnetic than 24’ by antoamount comparable that deduced from Cd Slater rules as found also by Nachtrieb [9] for the the corresponding chloride solution. There is thus no evidence of any paramagnetic contribution in the experimental results. This is not surprising since calculations show that using the numbers of centres deduced above, the paramagnetic contribution would be some 3 orders of magnitude smaller than the experimental error assuming Cd’4’ ion formation (or 2 orders of 121
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PHYSICS LETTERS
magnitude, assuming F-centres). The additional electrical conductivity due to electron exchange can 1~eestimated if we identify the electron hopping frequency Pasç’ i.e. ~1011 s~.Then using 2vR2/6kBT, a = ne~i ne where R2 is the mean square step length and n the
7 July 1980
observed conductivity; there is no such problem with the Cd’4 model since the contribution predicted is so small. We gratefully acknowledge helpful discussions with C.A. Angell, R.M. Cotts and A.T. Rogers, and the support of the U.K. Science Research Council.
number of carriers per unit volume, we find the additional conductivity at 400°Cfor 0.5 mol % Cd to be about 1 X l0~ ~ cm~.This is to be compared with the experimental result of Grantham [4] of 40 X 10~cz—1 cm1, so that, as concluded by Grantham, this increase in a is likely to be mainly ionic rather than electronic. If we had used our F.
References
centre model we would have predicted an additional conductivity of ~‘10 X i04 ~21 cm~, which is about 25% of that observed. However, we estimate an activation energy for electron conductivity of 1 1.5 eV (formation plus motion) which contrasts with the observed value of 0.2 eV. The F-centre model would therefore appear to be inconsistent with the
(Plenum, 1979). [4J L.F. Grantham, J. Chem. Phys. 44(1966)1509. [5] J.D. Corbett, Burkhard Chem. Soc. 83WJ. (1961) 76. and L.F. Druding, J. Am. [6] K. Ichikawa and W,W. Warren, Phys. Rev. B20 (1979) 900. [71 E.G. Jones, Proc. Phys. Soc. 45 (1933) 625. [81 R.D. Mowat, Internal Report, University of Warwick (1979). [9] N.H. Nachtrieb, J. Phys. Chem. 66 (1962) 1163.
122
[1] V.G.I. Deshmukh, E.F.W. Seymour and G.A. Styles, ~ Letters 74A (1979) 432. [2] M.A. Bredig, Molten (Interscience,in: NY, 1964).salt chemistry, ed. M. Blander [3] W,W. Warren, in: Advances in molten salt chemistry, Vol. 4, eds. J. Braunstein, G. Mamantov and G.P. Smith
PHYSICS LETTERS
7 July 1980
NUCLEAR SPIN RELAXATION IN MOLTEN Cd-Cd!2 AND I-Cd!2 MIXTURES V.G.I. DESHMUKH’, G.A. STYLES and E.F.W. SEYMOUR Department ofPhysics, University of Warwick, Coventry CV4 7AL, UK Received 4 April 1980 3Cd relaxation data indicates that —1% The ofprevailing added atoms opinion produce is that paramagnetic excess Cd in Cd~ Cdt2 ionsproduces with lifetime diamagnetic —10 ps.Cd~ The ions. concentration “ ofCd’ ions is depressed by excess iodine.
1. Introduction. In an earlier paper [1] a description was given of a study of the nuclear spin—lattice and spin—spin relaxation times, T 1 and T2,3,2O5Tl in molten T1Brfast andrelaxation T1C1 and in Ti-doped For 20 as mdithe observed wasTIBr. interpreted cating the transient existence in the melt of localized paramagnetic centres, perhaps like F-centres in crystals or alternatively simply paramagnetic molecular ions. The present paper describes a similar Investigat3Cd relaxation in molten mixtures of tion of the ‘ Cd1 3Cd nucleus, like 203,205T1, 2 with has Cd and spinwith ~ soI.that Thethe ~ relaxationis not complicated by an electric quadrupole contribution which could mask the magnetic interaction with paramagnetic centres in which we are primarily interested. Unlike the thallium salts, Cd12 will dissolve a considerable quantity of excess metal; the solubility is well established, varying between 2.5 and 4 mol % in the temperature range used in these experiments. It is thus apossible to investigate the effects excess over much wider concentration rangeofthan for metal thallium halides. The solubffity of! is uncertain but no difficulty in dissolving amounts of the order was of 1 experienced mol %. Aconsiderable quantity of experimental data has been accumulated for the molten cadmiumhalides, in both the stoichiometric state and with excess metal, although most of the information is for Cd-CdCI 2 mixtures. The measurements include electrical conductivity, magnetic susceptibility, Ranian spectra, difPresent address: Royal Signals and Radar Establishment, Great Malvern, Worcs. WR14 3PS, UK.
fusion, viscosity, optical absorption and several thermodymanic properties [2,3]. The conclusions drawn thesethat observations are somewhat but itfrom appears the stoichiometric salt isequivocal heavily ionized at all temperatures, and that excess metal dissolves in the salt to form a subhalide, the metal assuming a valence state lower than that normally encountered. The behaviour of the conductivities of CdBr 2, Cd12ofand CdCI2, whichattributed change only slightly on addition metal has been to the formation of the dimer Cd~or the corresponding subhalide Cd 2 Q2 [4] and there is no evidence for formation of the Cd~ion which would produce conduction by electron exchange between Cd~and Cd~,except for a small contribution at temperatures well above the melting point. The magnetic susceptibifity of Cd—CdQ2 shows no detectable paramagnetic contribution on adding metal which seems to confirm the absence of the Cd+ but does not establish the 4~ as ion opposed to other diamagnetic presencesuch of Cd~ species as Cd0. Likewise, cryoscopic and heat of fusion data for metal-doped CdCl 2 suggest the substi2~ions [2]. tution of large cations Cd~ for smaller Cd Thus, there are strong indications that in the cadmium halides and added metal combined with Cd2~atom to form Cd~and there is little evidence of the formation of paramagnetic ions such as Cd~.It should be mentioned, however, that on addition of Ala3 to solid CdCl2 the diamagnetic compound Cd2 (Ala4)2 is formed [51offering clear cut evidence that cadmiuni can exist in the +1 oxidation state. In this paper we show that in order to interpret our 119
Volume 78A, number 1
PHYSICS LETTERS
7 July 1980
relaxation results it is necessary to assume that paramagnetic centres exist in both stoichiometric Cd!2
0
and Cd—Cd12 solutions. The most natural assumption is that these are Cd~although we do not completely rule out other species such as F-centres. As
10 ~U5)
the2.evidence will beExpetimental seen3Cd this outlined does results not above. necessarily and discussion. conifict Measurewith nuclear spin relaxation have been ments of ~ made on solutions of Cd! 2 containing up to 0.5 mol % excess Cd and 5 mol % excess 1, respectively, at temperatures between 400 and 530°Cusing a pulsed NMR spectrometer. The samples were of Analar punty and were sealed in quartz ampoules after preliminary drying. The relaxation times T1 and T2 obtained at various temperatures are given in table 1 and the results at 400°C are plotted in fig. 1. Measurements of the potentially valuable or Knight 13Cd resonance werechemical inconclusive and shifts of the ‘ are not reported. The 127! resonance was not detected, presumably because of extremely fast quadrupolar relaxation, As can be seen T 1 * T2 and both decrease extremely rapidly with increasing temperature and cadmium content. For I concentrations greater than about 0.5 mol %, T~and T2 are independent of cornposition (possibly indicating a solubility limit) but both exhibit a dramatic decrease between 0.1 mol %I and 0.1 mol % Cd which continues, though more slowly, upT to 0.5 mol % Cd. We have been unable to measure 1 and T2 beyond this composition and conclude that they continue to decrease to values
~
102 10
to’
________________________________ 05
Cd 12 mot 0/0
_________
~—Cd
Fig. 1. Spin—lattice 113Cd (T1) and spin—spin (1’2) relaxation in Cdt times at 7 MHz for 2 solutions at 400°C, shown on a logarithmic scale as a function of composition.
less than 15 M~which is the limit of the apparatus. As T1 and decrease, whether with increasing perature orT2 changing composition, their ratio be-terncomes more nearly unity. Estimates show that except for the 0.5 mol % I and 5 mol % I solutions the relaxation is too fast to be accounted for by generally occurring mechanisms such as nuclear dipolar interaction, anisotropic chemical shift, spin-rotation interaction or scalar interaction with rapidly relaxing iodine nuclei. We therefore propose that as in the case of thallium halides relaxation in the 0.1 mol % I sample and in the stoichiometric and Cd-rich samples must be provided by anudehy13Cd perfine contact interaction between the ‘ us and transient paramagnetic centres produced both thermally and by excess cadmium. We suggest that in
Table 1 Sample
Temperature
T1
T1 IT2
1•js 5%I-Cd12 0,5%I-Cd12 0.1%I-Cd12
Cd12
0.i%Cd-Cd12 0.5%Cd-Cd12
120
405 401 401 450 492 400 455 527 404 443 400 455
05
~.LS
60 150 12 4
000 000 000 300 840 1 000 320 140 140
36 36 <20
3 400 2 200 1 400 640 340 100 100 —
33 17 20 15
18 68 8.6 6.7 2.4 9.6 2.3 —
4.1 2.2 1.8 <1.3
re
C (Cd°)X
Ps
10-6
—
—
56
19 16 8.2 20
7.9 —
12 7.6 6.2 <4
0.074 0.33 0.80 2.6 4.2 6.8 —
20.4 58 54.7 <98
Volume 78A, number i
PHYSICS LETTERS
the stoichiometric material these are created by the thermal dissociation CdI2 Cd’4 + I~,where both 3Cd relaxation will ionsdominated are paramagnetic but thewith ~ the unpairedelecbe by interaction tron on the Cd’4’ ion to which it belongs. (On the other hand the I~ions would be potent sources of relaxation for 127! nuclei.) In the Cd-rich solutions some additional Cd’4 ions may be produced by disruption of Cd0 or Cd~species. Our results could alternatively be explained if some of the Cd0 atoms ionize, each giving rise to a Cd2’4 ion and two Fcentres. The addition of iodine must be expected to depress the number of Cd’4 ions (or F-centres) due to the tendency to form F ions, or possibly I~molecular ions (V centres). The lifetime of the centres may be deduced from the inequality ofT 1 and T2. For a hyperfme contact interaction 1 =2 2S(s + 1) Tel {I +(~s 0.)I)2Te2 } (T1) 5cvA and -+
—
2
1
(T 2)
=
5cvA S(S+1)[re+rel{1 +(WS—c~,3I) Te}]
where A is the hyperfine coupling constant with a centre of spinS, c is the number of centres per formula unit, v is the number of nuclei affected by a centre at any instant, ws and w1 are the electron and nuclear Larmor frequencies, and re is the time for which the unpaired electron is in contact with a particular nudeus. (Alternatively re might represent the electron relaxation times but our derived values are so short that this is considered unlikely.) As pointed out by Ichikawa and Warren [6], for a very strong hyperfine interaction these equations are only approximately valid, but they are adequate for the semi-quantitative interpretation attempted here. Taking the ratio of these expressions, T1/T2 = 1 + (WS ~~I)2r~l2, which yields the values of Te shown in the table.We have not given values for the 5 mol % I sample since the relaxation may not be dominated by this nism at this concentration. As can be seen, remechadecreases with increasing temperature and with Cd concentration, the former being expected for any lifetime affected by thermal fluctuations. The number of centres can be obtained using an estimate for A. For Cd+ we take the free ion value As~= 2.1 X 1010 rad s~ [7] and p = 1~(For an F-centre a value 10 times smaller would be appropriate as suggested by —
7 July 1980
ENDOR measurements on ionic crystals, with v 10.) The values of c which result are given in the table. For the stoichiometric salt the results indicate that the concentration of centres is about 10~and that they exist for about 10 ps, which is an order of magnitude larger than the time characteristic of rotational or translational ionic motion. In the Cd-rich solutions, although the majority of the excess Cd atoms may produce diamagnetic Cdr as suggested by other experimental evidence, our results show clearly that a fraction produce additional paramagnetic centres. Assuming these are Cd’4 ions, this fraction is 1.5—2% of the excess Cd atoms for 0.1 mol % Cd and 1% for 0.5 mol % Cd at 400°C,and about double these values at 450°C.(These fractions would have to be about ten times larger if the centres were F-centres.) The lifetime of the centres is again ~10 ps but decreases with increasing concentration. We havesomewhat no explanation for such aCd decrease since the surroundings of such isolated centres should not be affected by the concentration of excess cadmium. The temperature dependence of c at all compositions may be approximately described by an energy of formation of 0.5—1.0 eV for the centres, corresponding to the energy penalty required to produce an ion without a closed electronic shell or sub-shell. Similarly the temperature dependence of re suggests a trapping energy ~0.5 eV for the centres corresponding to the energy required to move a centre from the neighbourhood of a particular cadmium ion to another. The presence of Cd+ ions or F centres would clearly lead to a paramagnetic term in the susceptibility. Mowat [8] has found that the addition of 6 mol % Cd does not appreciably alter the mass susceptibility of molten Cd12. His data are consistent with the production of Cdç ions only, with a susceptibility attributed ~Cdr which is moretodiamagnetic than 24’ by antoamount comparable that deduced from Cd Slater rules as found also by Nachtrieb [9] for the the corresponding chloride solution. There is thus no evidence of any paramagnetic contribution in the experimental results. This is not surprising since calculations show that using the numbers of centres deduced above, the paramagnetic contribution would be some 3 orders of magnitude smaller than the experimental error assuming Cd’4’ ion formation (or 2 orders of 121
Volume 7 8A, number 1
PHYSICS LETTERS
magnitude, assuming F-centres). The additional electrical conductivity due to electron exchange can 1~eestimated if we identify the electron hopping frequency Pasç’ i.e. ~1011 s~.Then using 2vR2/6kBT, a = ne~i ne where R2 is the mean square step length and n the
7 July 1980
observed conductivity; there is no such problem with the Cd’4 model since the contribution predicted is so small. We gratefully acknowledge helpful discussions with C.A. Angell, R.M. Cotts and A.T. Rogers, and the support of the U.K. Science Research Council.
number of carriers per unit volume, we find the additional conductivity at 400°Cfor 0.5 mol % Cd to be about 1 X l0~ ~ cm~.This is to be compared with the experimental result of Grantham [4] of 40 X 10~cz—1 cm1, so that, as concluded by Grantham, this increase in a is likely to be mainly ionic rather than electronic. If we had used our F.
References
centre model we would have predicted an additional conductivity of ~‘10 X i04 ~21 cm~, which is about 25% of that observed. However, we estimate an activation energy for electron conductivity of 1 1.5 eV (formation plus motion) which contrasts with the observed value of 0.2 eV. The F-centre model would therefore appear to be inconsistent with the
(Plenum, 1979). [4J L.F. Grantham, J. Chem. Phys. 44(1966)1509. [5] J.D. Corbett, Burkhard Chem. Soc. 83WJ. (1961) 76. and L.F. Druding, J. Am. [6] K. Ichikawa and W,W. Warren, Phys. Rev. B20 (1979) 900. [71 E.G. Jones, Proc. Phys. Soc. 45 (1933) 625. [81 R.D. Mowat, Internal Report, University of Warwick (1979). [9] N.H. Nachtrieb, J. Phys. Chem. 66 (1962) 1163.
122
[1] V.G.I. Deshmukh, E.F.W. Seymour and G.A. Styles, ~ Letters 74A (1979) 432. [2] M.A. Bredig, Molten (Interscience,in: NY, 1964).salt chemistry, ed. M. Blander [3] W,W. Warren, in: Advances in molten salt chemistry, Vol. 4, eds. J. Braunstein, G. Mamantov and G.P. Smith