J. Phys. Chem.
where 1 is the order of the matrix. BJis a matrix with elements defined as
Egm =
aikajm
Defining S as the matrix which diagonalizes K by the transformation
s-'m = A =
["
1
1997
1983, 87, 1997-2003
with the ijth element written as exp(-Xit jSi;1S8j exp(Xjt 1 Integration of the expression above over time results in the quantity
*.%A,]
The second moment vector can now be written as the second moment in eq 15c can be written in terms of A.
A%) = 2CCD,,S exp(AtJMa@S'Ao(0) a @
We define the fundamental matrices R as
A2(t) = 2JtS exp(-A(t'-
= S exp(At)Ma@S1
t ) ) S ' D Sexp(At)S' dt'AO(0) + exp(KtJA2(0) (We will leave the last term in the above expression in terms of K since it does not involve the diffusion matrix.) The general diffusion matrix can be decomposed into a sum of elementary matrices, E"@
D = CCDa,E"@
so that the second moment is expressed as A2(t) = 2CCD,$@A2(O)
+ exp(Kt)A2(0)
(Al)
a P
By performing the various matrix multiplications we obtain for the klth element of Rap
a P
and the second moment vector can be written as 0 A2(t) = 2CCD,,S exp(htJS'exp(-At)S'E"eS
X
. P
exp(At) dt' SIAo(0)+ exp(Kt)A2(0) The integrand in the expression for A2(t) is the matrix exp(-At )SIE"PSexp(At1
Electron Spin Resonance Studies of Electron Localization In Molten Alkali Metal-Alkali Halide Solutions N. Nlcoloso and W. Freyland' Fachberelch Physlkallsche Chemle, Phlllpps-Unlversitlit,03550 Marburg, West Germany (Recelved: September 27, 1982; In Flnal Form: December 21, 1982)
Electron spin resonance (ESR) has been investigated in different concentrated liquid alkali metal-mixed alkali halide solutions at temperatures up to 700 O C . The ESR data strongly indicate that alkali metals are not dissolved in atomic-likestates in the molten salts. From the g-factor shift of the resonances observed with varying salt matrix, we deduce that localized electron states very similar to that of the F center in the corresponding crystals exist even in nondilute solutions. In agreement with the concentration behavior of the static magnetic susceptibility,the magnitude of the observed spin densities shows, however, that spin-paired states in equilibrium with the paramagnetic F centers are important in concentrated metal-molten salt solutions. At high metal concentrations approaching the metal-nonmetal (M-NM) transition region, a first indication for spin delocalization-possibly via cluster formation-is given by the occurrence of narrow ESR signals with g values close to those of bulk alkali metals.
Introduction Liquid alkali metals form true solutions with their molten salts with a complete miscibility of the two liquids at elevated temperatures.' Thus, with increasing ratio of metal to salt (M-MX) a transition from nonmetallic to (1) M. A, Bredig in -Molten Salt Chemistry", M. Blander, Ed., wiley-Interscience, New York, 1964.
0022-3654/83/2087-1997$01.50/0
metallic states may be continuously studied in a permanent thermal equilibrium state. Concerning the concentration range where this metal-nonmetal (M-NM) transition occurs, the measured concentration dependence of the electrical conductivity1 may be taken as a first clue. The conductivity, for example, of some sodium and potassium solutions is less than IO0 E'cm-' if the metal mole fraction zM lies below about 0.1-0.15. On the basis of the concepts 0 1983 American Chemical Society
1998
The Journal of Physical Chemistry, Vol. 87, No. 11, 1983
developed by Mott2 for the M-NM transitions in condensed matter, solutions with conductivity values below this limit may be considered as nonmetallic in character. This suggests that in comparison with other metal solutions like metal-a"onia3 the M-NM transition in liquid M-MX solutions appears at relatively high metal concentrations probably due to the specific nature of the solvent with strong Coulomb interactions of conduction electrons with the ionic medium. This characteristic together with the phenomenon of M-NM transition is an evident reason for the present interest in the M-MX solutions as a special class of metal solutions. In the current discussion of electron localization in these nonmetallic ionic liquids a variety of different models have been explored so far in the literature; see, e.g., the review by Na~htrieb.~ In the approach first suggested by Rice5 electron localization on cations, i.e., atomic-like states, are considered. An alternative model has been proposed by Pitzer6 based on his thermodynamic calculations of the phase diagrams. He suggested that solvated electrons may be formed very similar in nature to the crystalline F center, i.e., an electron trapped at a negative ion vacancy. In a more recent theoretical interpretation of the electronic properties of molten M-MX mixtures, Katz and Rice7have considered another possibility of electron trapping by multisite localized states as a consequence of structural disorder. Besides these models different hypotheses have been raised on the occurrence of spin-paired states with increasing metal concentration. In order to account for the peculiar behavior of the equivalent conductance in molten Na-NaX mixtures, Bronstein and Bredig8 suggested spin pairing in the form of diatomic molecules like Na,, whereas Bettmang in his interpretation of the molar magnetic susceptibility of the dissolved metal in K-KC1 solutions assumed spin pairing via cluster formation. Finally, it should be stated that all descriptions1*12 which treat the electrons or part of the electrons as if they were in extended nearly free electron states have been doubted7 and are not tenable in the light of recent NMR results13 which clearly show that electron localization exists for a few percent of excess metal in the Cs-CsX solutions. Our present experimental and theoretical knowledge may be summarized as follows: In the high-dilution limit the optical absorption data, in particular those of Schmitt and Schindewolf,14 give strong support for the F-center picture. Consistent with this type of electronic bound s t a b are the theoretical calculations by Senatore, Parrinello, and Tosi15 valid in the limit of infinite dilution. For higher (2)N. F. Mott, "Metal-Insulator Transitions", Taylor and Francis, London, 1974. (3)For a recent review on the electronic properties of metal solutions see P. P. Edwards, Phys. Chem. Liq., 10,189(1981),and further references therein. See also J. C. Thompson, "Electronsin Liquid Ammonia", Clarendon Press, Oxford, 1976. (4) N. H. Nachtrieb in "Advances in Chemical Physics", I. Prigogine and S. Rice, Eds., Wiley, New York, 1975. (5) S.A. Rice, Discuss. Faraday SOC.,32, 181 (1961). (6)K.S. Pitzer, J . Am. Chem. SOC.,84, 2025 (1962). (7)I. Katz and S. A. Rice, J . Am. Chem. SOC.,94,4824 (1972). (8)H.R. Bronstein and M. A. Bredig, J. Am. Chem. SOC.,80,2077 (1958). (9)M. Bettman, J. Chem. Phys., 44,3254 (1965). (10)E. G. Wilson, Phys. Rev. Lett., 10,432 (1963). (11)R. H. Arendt and N. H. Nachtrieb, J. Chem. Phys., 53, 3085 (1970). (12)P. J. Durham and D. A. Greenwood, Philos. Mag., 33,427 (1976). (13)S.Sotier and W. W. Warren, Jr., J . Phys. (Orsay,Fr.), 41,C8,40 (1980). See also: W. W. Warren Jr., and S. Sotier, "Proceedings of the Electrochemical Society Meeting, Hollywood, FL, 1980;R. Dupree, D. J. Kirby, W. Freyland, and W. W. Warren, Jr., Phys. Rev. Lett., 45, 130 (1980). (14)W.Schmitt and U. Schindewolf, Ber. Bunsenges. Phys. Chem., 81,584 (1977).
Nicoloso and Freyland
2
3 40 - c
--1 1cm
Flgure 1. ESR cell construction: Pt/PtRh-13% thermocouple (l), Mo tubing (2),A1203 disk (3), Nb screw (4a), Nb ring (4b), Nb cone (4c), Nb screw (5, 6), sapphire capillary (7), liquid sample (8).
metal concentrations and, especially, for conditions approaching the NM-M transition region the existing experimental information is scarce and does not yet allow definite conclusions on the different suggestions sketched above. The thermodynamic datal6 are not inconsistent with the F-center description. A more direct indication has been obtained from ESR measurements4on Na-NaC1 with XM = 0.005 which show that the observed g shift is consistent with the F-center model. The recent NMR studied3 in liquid Cs-CsX systems provided further evidence for the validity of the F-center model and do not support models based on single- or multisite atomic states.13 For more concentrated solutions an indication for possible cluster formation has been reported in a recent neutron diffraction experiment on liquid Rb-RbBr.17 In order to obtain further insight into the nature of the localized-electron states emphasis is given in the present ESR study to the range of high metal concentrations up to the NM-M transition region, i.e., from xM = 0.01 to about 0.1. The main objectives of this work are the following: (i) to study the ESR characteristics of the excess electrons by following systematically the influence of the ionic matrix on the resonance position in a number of different salts; (ii) to obtain approximate information on the magnitude of the spin densities and to compare them with some new results for the static magnetic susceptibility; (iii) to investigate the change in ESR as the concentration of metal is increased toward the M-NM transition region. Due to the considerable experimental difficulties in the (15)G.Senatore, M. Parrinello, and M. P. Tosi, Philos. Mag., [Part] B, 41,595 (1979). (16)H. Yokokawa, 0.J. Kleppa, and N. H. Nachtrieb, J. Chem. Phys., 71,4099 (1979). See also: R. L. McGraw and N. A. Nachtrieb, to be submitted for publication; H. Yokohawa and 0. Kleppa, to be submitted for publication. (17)J. F. Jal, T h k , UniversiG Claude Bernard, Lyon I, France, 1981.
Molten Alkali Metal-Alkali Halide Solutions
ESR experiments associated with the high reactivity of these materials at elevated temperatures, we have tried to keep the measuring temperatures as low as possible by using eutectic salt mixtures with low-lying liquidus temperatures.
The Journal of Physical Chemistry, Vol. 87, No. 11, 1983 1999
Experimental Section General Considerations. In the present ESR study on molten alkali metal-mixed alkali halide solutions the following experimental requirements had to be met. Due to the relatively high liquidus temperatures of the eutectic binary salt mixtures (for the phase diagrams see ref 18) measuring temperatures in the range from 500 to 700 "C have to be achieved. Under these conditions the considerable chemical reactivity of the liquid sample components severely restricts the material choice for the ESR-cell construction. As the vapor pressure above the solutions is not negligible at these temperatures, a vacuum-tight sealing of the sample container is necessary. In addition, several ESR-specific problems have to be taken into account. The sample container must be free of signals in the g-value region under study. For this reason we could not use materials like boron nitride, alumina, or Lucalox which showed a resonance near the free-electrong factor, g,, even if we tried samples of highest available purity. Therefore, we decided on synthetic sapphire for the ESR-cell construction. This choice has several specific advantages. Because of the large g-factor anisotropy of the sapphire resonance-due to transition-metal impurities-a wide signal-free magnetic field range from about 2 to 5 kG for X-band frequencies may be obtained by simply orienting the sapphire. On the other hand, one can use the sapphire signal as an internal calibration standard-like the ruby standard-for the spin density measurements. Another difficulty arises from the relatively high electrical conductivities of the liquid samples studied here. Because of the lossy nature of these liquids and the influence of the skin effect on intensity and line shape, small sample volumes are desirable. As a compromise we have chosen a volume of about 100 mm3 so that the small quantities of the sample components could still be handled. ESR-Cell Construction and Furnace. In Figure 1the ESR cell used in this study is sketched. The liquid sample container consists of a sapphire capillary, closed at one end, with the following dimensions: inside diameter, 3 mm; outside diameter, 4 mm; and total length, about 40 mm. For the vacuum-tight connection of the upper end of this capillary with a niobium closure, different techniques have been tried comprising brazing of the two parts with a glass-forming ceramic cement or with Ni-Ti alloys and diffusion welding. These different sealings turned out to be unsatisfactory since they either were not corrosion resistant against attack by alkali-metal vapor or did not stand temperature cycling. Mechanical sealing as drawn in Figure 1 proved to be successful. With the aid of a niobium screw (6) the edge of the niobium ring (5) is pressed against the spherically polished end of the sapphire (7). Leak testing of this sealing after heating for several hours at 700 "C yielded leak rates of about torr L s-l. After the cell is filled through the opening in the niobium part (5), it can be closed by a niobium cone fitting as shown in Figure 1. This fitting is bored at one end and contains a Pt/PtRh-13% thermocouple which extends to about 1 cm into the sapphire capillary. A second thermocouple is mounted from below and its tip ends near the bottom of the sapphire.
In order to avoid a temperature gradient along the sample, which may cause concentration inhomogeneities in the liquid mixture and, even worse, may lead to disturbing microphonic noise by convection, a precise control of the temperature profile is necessary. This is achieved by two separate heating elements surrounding the cell. One is rigidly mounted in the ESR cavity and consists of Pt wires noninductively wound and stretched on the inside wall of a thin quartz tubing. The sapphire tubing tightly fits into this heating element ensuring good thermal contact. A second small furnace is fixed at the upper end of the cell surrounding the molybdenum capillary (2). This furnace together with the cell is inserted into the cavity from above and fixed via the molybdenum holder (2). For further details of the high-temperature parts see ref 19. Sample Preparation and Measuring Procedure. Polycrystalline alkali halide materials of ultrapure grade (Alpha products, Ventron Corp.) have been dried under highvacuum conditions by heating the salts close to their melting points. In an argon glovebox, weighed amounts of about 100-400 mg were then transferred to the ESR cell. This cleaning and handling procedure proved to be sufficient and has been checked in separate ESR experiments on, e.g., pure Cs salts. No resonances have been observed in these liquid salts, indicating that the concentration of paramagnetic impurities is below the detection limit of the experiment (see below). After the ESR cell is filled with the salt mixtures or the pure Cs salts, small amounts of liquid alkali metal (Alpha-Ventron products, 99.95% purity) are added with the help of a calibrated microliter syringe. Typically, several microliter quantities were taken, depending on the metal concentration. Next, the cell is closed under vacuum (51torr) inside the glovebox and the sample is heated up to the liquid state to accomplish homogeneous mixing. Due to the small amounts of materials handled in this filling procedure, the uncertainty in the metal concentration is relatively large and may amount to about 10% for XM = 0.1, mainly due to slight oxidation of the small metal droplets. A conventional X-band spectrometer (Model BER 418, Bruker Co., Germany) has been used. Its cylindrical cavity (400 X-HT, Bruker Co) operating in the TEoll mode has been modified as described above for the specific hightemperature requirements needed here. After orientation of the sapphire cell in the magnetic field, the sample is heated with the use of two highly stabilized dc power supplies and PID temperature-controlling units. Achievement of the liquidus temperatures is monitored by clear changes in the tuning of the microwave bridge due to the corresponding changes in the Q value on melting. In this way the literature values of the melting points, e.g., of the pure cesium salts, have been reproduced within a few degrees, giving an indication for the temperature error of about f 5 OC. For spectra recording, time-averaging techniques have been employed to improve the signal-tonoise ratio. Typically 20-150 scans of 500-G width and 100-s duration were taken. In order to avoid saturation effects the microwave power level has been kept below 3 mW. Attempts to follow the saturation behavior were not successful mainly because of the long recording times. The upper temperature limit in these experiments of about 700 "C is essentially determined by the maximum possible load of the two miniature heating elements. For the determination of the spin densities of the liquid samples, two calibration procedures have been exploited. First, one of the sapphire signal components-usually
(18) "Phase Diagrams for Ceramists", Vol. 1-3, American Ceramic Society, Columbus, OH.
(19) N. Nicoloso, Ph.D. Thesis,University of Marburg, Marburg, West Germany, 1982.
2000
1'
The Journal of Physical Chemistry, Vol. 87,No. 11, 1983
Nicoloso and Freyland
TABLE I: g Factors of F-Center Resonances Observed in Liquid Alkali Metal-Eutectic Alkali Halide Mixtures Compared with Corresponding Crystalline Data from the Literature26 liquid MX-M
A
soln
cn c
Flgure 2. ESR spectra of liquid (Na,K)Ci-Rb, x,,, = 0.04 (A) at 700 OC and (B) after cooling below the liquidus temperature; spectrum C shows two of the Na hyperfine lines observed in pure saturated Na vapor at 530 O C (HfB= free-electron resonance field).
shifted to about 2 kG by careful orientation of the cell-is calibrated at room temperature against the intensity standards delivered by the Bruker Co. On heating, it has been found that the intensity of this signal-under otherwise unchanged resonance conditions-closely follows a Curie-law behavior. A second calibration has been performed by measuring the intensities of the ESR resonance of saturated Na vapor up to 530 OC simultaneously with the sapphire resonance. The so-determined spin densities of the vapor phase were than compared with the values expected from the ideal gas law. The agreement between these two evaluations was found to be better than a factor of 5. With this calibration a lower detection limit of about 10l6 spins cm-3 G-l results for the liquid mixed MX-M samples. This limit has been separately checked at elevated temperatures on an additively colored crystalline sample of known F-center concentration (we thank Dr. H. Grundig, I. Physikalisches Institut der Universitat Gottingen, for placing this sample at our disposal) which has been heated into the melt. The accuracy in the g factors reported here is given as Sf0.002. With the large pole gap of 5 cm necessary for the high-temperature setup and the heating wires surrounding the cell, small distortions and inhomogeneities of the field are inevitable. Thus, the relatively large error in g mainly arises from the uncertainty in the absolute value of the magnetic field at the sample position.
Results and Discussion (i) Types of Localized Paramagnetic States. In the general discussion of excess electron states in metal solutions: the equilibrium between solvated atomic-like states and solvated electrons is of central importance, i.e. M, + Ma++ e;
(1)
Concerning this problem in molten alkali metal-mixed alkali halide solutions, a first answer is obtained from the following ESR observations presented in Figure 2. Here the ESR spectrum A refers to a liquid equimolar mixture of NaCl and KC1 doped with 4 mol % Rb at 700 OC. Apart from two weak lines, split by 317 f 1 G, a central resonance is observed with a g factor below that of the free electron. When this sample is cooled into the solid state at 650 "C (spectrum B) the central resonance disappears and two sets of hyperfine-split lines show up with A = 317 and 83 G, respectively. In separate experiments on saturated Na vapor taken at comparable temperatures (see, e.g., spectrum C in Figure 2) we have found that the hyperfine splitting (hfs) and line width of the Na atom resonances are identical within experimental error with the main components in spectrum B. Therefore, we attribute these resonances to Na and K atoms, respectively, in the vapor
(Na,K)Cl-Rb, X M = 0.04 (Na,Rb)Cl-Na, XM = 0.04 (Na,Rb)J-Na, XM = 0.025 K( C1,J)-K, XM = 0.045
g factor
1.995
* 0.002
1.988 r 0.002 1.948
I 0.002
1.953
i
0.002
crystal NaCl KC1 NaCl RbCl NaJ RbJ KC1 KJ
g factor
1.9978 1.9958 1.9978 1.9804 1.9494 1.9958 1.9649
I 0.0003 I 0.0001 I 0.0003 I
0.0006
I 0.0006 I 0.0001 I 0.0004
phase above the solid (spectrum B) and the respective liquid phase (spectrum A). The latter assignment is further supported by the fact that in samples where the cell was completely filled with liquid no such lines appeared. The enhanced intensity of the Na lines relative to the K lines in spectrum B may be due to the lower sublimation enthalpy of Na colloids in comparison with K colloids (see, e.g., the article by Seitz20). These results and the fact that we did not observe the hyperfine-split lines of Rb in the liquid or in the saturated vapor phase indicate that the alkali metals are not dissolved in atomic-like states in molten alkali halides. Observations similar to those shown in Figure 2 were made in a number of liquid alkali halides mixtures doped with different alkali metals at concentrations xM 2 0.04.19 In principle, one may envisage the possibility that spectrum A in Figure 2 results from solvated atomic-like species, M,. This would imply an extreme narrowing of the hyperfine splitting into a single line by fast dynamical processes, Le., fast motional or exchange narrowing (see, e.g., ref 21). However, in this case one should expect no strong shift of the resonance position with varying salt matrix. As shown below, the experimental results give the opposite trend. Thus, we arrive at the conclusion that the equilibrium in eq 1 is completely shifted toward the solvated-electron side for the M-MX solutions. The ESR results reported below give rather direct information about the type of solvated-electron states in molten M-MX solutions. It is well-known that in ionic solids excess electrons are stabilized in the form of color centers the major paramagnetic defect being the F center. Its particular ESR characteristics are as follows: 22 (A) The magnitude of the g-factor shift, Ag, is roughly given by23 aga (2) Here X denotes the spin-orbit coupling constant of neighboring cations and anions, which scales with the atomic number, and A E is an excitation energy of the F center which may be deduced from the electronic spectrum. (B) There is inhomogeneous line broadening via the hfs interaction with the nuclei of the salt matrix. Considering the possible variation in Ag of F centers in the liquid state with changing salt matrix, the following aspects are of interest. Neutron diffraction experimentsz4 (20) F. Seitz, Reu. Mod. Phys., 26, 7 (1954). (21) Yu. N. Molin, K. M. Salikhov, and K. I. Zamaraev, "Spin Exchange", Springer-Verlag, West Berlin, 1980, Springer Ser. Chem. Phys. Vol. 8. (22) H. Seidel and H. C. Wolf in 'Physics of Colour Centers", W. B. Fowler, Ed., Academic Press, New York, 1968. (23) A. Carrington and A. D. McLachlan, 'Introduction to Magnetic Resonance", Harper and Row, New York, 1967. (24) J. Derrien and J. Dupuy, J . Phys. (Orsay,Fr.), 36,191 (1975);F. G. Edwards, J. E. Enderby, R. A. Rowe, and D. I. Page, J . Phys. C., 8, 3483 (1975); E. W. Mitchel, P. F. J. Poncet, and R. J. Stewart, Philos. Mag., 34, 721 (1976).
Molten Alkali Metal-Alkali Hallde Solutions
on pure alkali halides have shown that on melting no drastic changes occur in the local structure as far as the number and distance of nearest neighbor ions are concerned. Optical studies on dilute14 and ~ o n c e n t r a t e d ~ ~ M-MX solutions demonstrate that the relative changes in the excitation spectrum (AE)of the F center with varying salt matrix are comparable in the solid and liquid states. Thus, if in concentrated M-MX solutions excess electrons are localized in the form of F-center-like states, a similar trend in Ag in both the liquid and the corresponding solid state is to be expected, i.e., a clear enhancement in Ag with increasing spin-orbit coupling. In Table I the g factors as determined from the center of the ESR resonances observed in several concentrated alkali metal-mixed alkali halide solutions are compared with corresponding crystalliie values taken from the literature.% Qualitatively, the g shift in the liquid and crystalline states is found to be of the same magnitude providing strong ESR support for the F-center model in nondilute M-MX solutions. A more quantitative analysis of these data is not possible since, to our knowledge, no g values of mixed crystalline systems with comparable compositions exist. As pointed out above, the crystalline F-center resonances are characterized by a strong inhomogeneous broadening with a total line width AHppranging from 47 G for KC1 to about 700 G for the cesium halides.22 In contrast to this the observed F-center resonances in the liquid salt mixtures are very narrow: the measured line widths are in the range from 5 to 10 G. For the example of the system (Na,K)Cl-Na, XM 6 0.01, Le., at a low metal concentration, the narrow resonance of about 5-G width transforms into a broad, weak line of about 70 G below the liquidus temperature, which may be compared with the width of the FAcenter in solid Na-doped KCLZ2 In general, we could not perform a detailed line shape analysis mainly for two reasons. The signal-to-noise ratio in many cases was not sufficient and, secondly, the resonances had a complex inhomogeneous structure, most probably caused by a g-factor distribution. With respect to this, it is interesting to note that the F-center resonance in KC1-RbC1 mixed crystals2' is characterized by unresolved hyperfine components explainable on the basis of a statistical lattice composition. Such a statistical distribution of nearest neighbor ions should also prevail in the liquid state and should be responsible for the composite structure of the F-center resonances observed here (see, e.g., spectrum A, Figure 2). In some favorable cases, where the signal-to-noise ratio was in the range of 5-10, a deconvolution of the signal could be tried. In these examples it was found that the main component was best fitted by a Gaussian. Finally, it should be stated that we did not find a clear resonance in the solutions with pure cesium halides. This is probably due to the large spinorbit interaction of cesium. When one takes into account fast diffusional or exchange processes, the observed narrowing of the liquid F-center resonances is not surprising. Either process could contribute to the narrowing and a rough estimate for the lower limit of the exchange frequency, toer, may be obtained from the following relation valid in the fast-exchange limit (see, e.g., ref 21): uex = r ( A f Z d 2 / A H p p (3) Here y is the electron gyromagnetic ratio, AHhfais the F-center line width without exchange, and AHpp is the (25) E. Pfeiffer and W. Freyland, to be submitted for publication. (26) D. Schmid, Phys. Status Solidi 18, 653 (1966). (27) J. Arends and A. J. Dekker, Phys. Status Solidi, 5, 265 (1964).
The Journal of Physical Chemistry, Vol. 87, No. 11, 1983 2001
A
E
No-NoC1 F-CENTER
T=llOO°C
I
A
L
0
1
0,05
0,l
0,lS 0.2
XMETA LFlgure 3. Molar magnetic susceptibility, xm(M), of dissolved alkali metal in different M-MX solutions vs. mole fraction of alkali metal, xy: full symbols from thls work,28open symbols for Na-NaCI from ref 11 and for K-KCI from ref 9 extrapolated to 1100 OC. The Fcenter value has been calculated as described In the text. The error bars are ghren for the data of this work.
measured line width in the liquid. With the data given above this yields wer 2 1O'O s-l. Such a high exchange rate suggests a relatively strong F-center aggregation in these liquids. In this context it is worthwhile to note that Schwoerer and W o P observed an exchange narrowing of the F-center resonance in solid KCl after light irradiation from which they deduce an exchange frequency of we, = log s-l. In order to explain this value, these authors in a simple model calculation assume F-center aggregation with an average separation between two defects of about 4-5 interatomic distances.28 (ii) Spin Pairing. The metal concentrations covered in this work, 0.01 < XM < 0.12, correspond to a number density of excess electrons ranging from about 10%to 102l ~m-~ If .all these electrons enter the liquid salt in the form of isolated F centers a high Curie-type spin paramagnetism of independent S = l/z electrons will result. In particular, one would expect a constant paramagnetism per dissolved metal atom if these defects are the only kind of localized electron states. That this expectation is not realized must be inferred from the behavior of the static magnetic susceptibility, plotted in Figure 3. Here the molar susceptibility of the dissolved metal, x,(M), is given as a function of the metal mole fraction, xM, at a constant temperature of 1100 "C, whereby x,(M) has been determined from the difference of the measured molar susceptibility of the solutions and the respective value of the pure salts. In Figure 3 the existing data from the literature9*"are compared with the results from a more recent ~ t u d y of' ~nonmetallic ~~~ Na-NaC1, K-KC1, and Cs-CsCl liquid systems. As can be seen from this plot x,(M) approaches the F-center value at low metal concentrations, whereas it drops continuously with increasing xM and starts to saturate at about XM = 0.1 near the NM-M transition region. The value of the (28) M. Schwoerer and H. C. Wolf, 2.Phys., 175,457 (1963). (29) H. Redslob, N. Nicoloso, and W. Freyland, to be submitted for publication.
2002
Nicoloso and Freyland
The Journal of Physical Chemistry, Vol. 87,No. 11, 1983
Rb x = 0.04 M 700 'C
(N0,K)CI-
(No.K)CI
- Rb,No x
M
=
008
680°C (No,K)CI -NO: x
M
=
012
670'C Hfe
2-L
Flgure 5. Concentration effect on the ESR-resonance in liquid equimolar (Na,K)CI doped wkh different alkali metals in the concentration range 0.04 Ix M I0.12. (Hf, = free-electron resonance field).
I
1
1
10~1~ Flgure 4. ESR spectra obtained in liquid (Na,Rb)CI-Na, xM = 0.04, at different temperatures. The reciprocal temperature dependence of the intensity of the main signal is plotted below (H, = free-electron resonance field).
F center given in Figure 3 contains the diamagnetic contribution of the s ground state which has been calculated with the orbital radius given in ref 15. As the recent NMR studiesI3 of the dynamics in different M-MX solutions have shown that delocalized, nearly free electron states do not contribute to the behavior in this concentration range, the concentration dependence of xm(M)clearly indicates that spin-paired localized states play an important role. In the present ESR study, further support of this view is given by the observed spin densities. A first estimate of the number of liquid F centers is obtained relative to the simultaneously measured internal sapphire standards by comparing the intensities of the respective signals. If one takes, for example, the sample of Figure 2, this comparison yields an upper limit of 5 x lo1*spins ~ m - ~In. order to get the absolute number of spins, this value has to be corrected for the skin effect. For v = 9.5 GHz and a conductivity of a = 7 Q-l cm-l-a typical value' of M-MX solutions with X M = 0.04-the skin depth is determined as 0.2 mm in comparison with the liquid sample radius of
1.5 mm. Thus, we obtain for this sample an upper limit of the absolute concentration of F centers of 2 X 1019~ m - ~ , which is about 10% of the total number density of doped metal atoms. Both the behavior of the static magnetic susceptibility and the magnitude of the ESR spin densities suggest that in concentrated M-MX solutions an equilibrium between F-center-likedefects and electrons localized in diamagnetic species has to be considered. Consistent with this description is the temperature dependence of the F-center resonance observed in liquid (Na,Rb)Cl-Na, xM = 0.04, which is presented in Figure 4. Besides a weak signal at the free-electron resonance position (see section iii) the F-center signal with g = 1.988 f 0.002 is shown which exhibits a clear increase with temperature from 550 to 630 "C. (For experimental reasons the signal has been recorded in a mixed dispersion-absorption mode30 leading to the distorted line shapes shown in Figure 4.) As given in the insert of Figure 4 the temperature dependence of the intensity of the F-center signal determined in two separate experiments follows an Arrhenius plot with an activation energy of AE = 0.5 f 0.15 eV. With our present knowledge of the M-MX systems, different interpretations of AE may be discussed. If exchange interaction is the dominating factor for spin pairing, an equilibrium between F centers and F aggregates similar to the solid state is an obvious and probable consequence. Then species like the F2 centers (see, e.g., ref 31 and 32) should be of special relevance. In this context it is interesting to note that for some metal solutions the observed spin pairing of solvated electrons has been associated with a closely analogous diamagnetic impurity, the b i p o l a r ~ n ~ , ~ ~ involving two separate cavities each containing an electron associated with a cation. On the other hand, in the general discussion of M-NM transitions in monovalent metal systems like expanded fluid alkali metals34or some metal s01utions,3~,~ one has to allow for such diamagnetic species like dimers, M2, or metal anions, M-. In this case the observed value of AE might just be correlated with the corresponding dissociation or ionization energies which are (30) C. P. Poole, 'Electron Spin Resonance",Wiley-Interscience,New York, 1967. (31) W. B. Fowler in 'Physics of Colour Centers",W. B. Fowler, Ed., Academic Press, New York, 1968. (32) C. Z. van Doorn, Philips Res. Rep. Suppl., No. 4 (1962). (33) N. F. Mott, J. Phys. Chem., 84, 1199 (1980). (34) W. Freyland, Comments Solid State Phys., 10, 1 (1981). (35) J. L. Dye, Angew. Chem., Int. E d . Engl., 18, 587 (1979). (36) P. P. Edwards and M. J. Sienko, Acc. Chem. Res., 15,87 (1982).
Molten Alkali Metal-Alkali Halide Solutions
of the order of 0.5 eV. By analogy with the solid M-MX systems another possible interpretation of the observed AE value is given by the reaction enthalpy of the equilibrium between F centers and colloids which in the solid typically lies between 0.4 and 0.6 eV.20937 (iii) Concentrated Solutions. Upon increase of the metal concentration toward the NM-M transition region, a clear concentration effect is manifested in the ESR spectra. In Figure 5 the spectra of different (Na,K)Cl-M solutions up to xM = 0.12 are compared. Apart from the F-center resonance which approximately remains at the same position and increases slightly in line width, a separate peak is found for the sample with the highest concentration. After subtraction of the F-center signal this resonance is described by g = g, and a linewidth of about 5 f 1 G. Although the g value is suitable, this resonance cannot arise from bulk Na or K metal for the following reason. Extrapolating the measured line width of liquid sodium38 to 700 "C, one obtains a AHpp= 40 G which is incompatible with the width of the above signal. For bulk potassium metal an even wider line must be expected.38 A striking similarity exists, however, between the above resonance and the ESR observations in a number of systems characterized by clustering phenomena. These comprise alkali polymers in concentrated metal-rare gas mixtures,39small metal particles in systems like quenched alkali metal-hexamethylphosphoramide,40irradiated-annealed sodium azide,41neutron-irradiated lithium fluoride,42and F aggregates or colloids in highly doped alkali halidesa3' The close analogy in the ESR properties leads us to suggest that spin-delocalized states via cluster formation may occur in liquid M-MX solutions near the NM-M transition region. The behavior of the static magnetic susceptibility x,(M) (see Figure 3) which near xM = 0.1 reaches values directly comparable in magnitude to the Pauli spin susceptibility of the corresponding liquid alkali metals at these temperature^,^.^^ is consistent with this model. As expected for the Pauli behavior no strong temperature dependence of xmis found in this range. Concerning the size of the clusters, a rough estimate may be given. As stated above the narrow signal cannot be explained by a relaxation mechanism of the Elliott typeu (37) A. E. Hughes and S. C. Jain, Adu. Phys., 28, 717 (1979). (38) R. A. B. Devine and R. Dupree, Philos. Mag., 21,787 (1970);22, 657 (1970). (39) J. P. Bore1 and J. L. Millet, J. Phys. Colloq. (Orsay, Fr.) C2, supplement au no. 7, 38, C2-115 (1977); J. P. Goldborough and T. R. Koehler, Phys. Reu. A , 133, 135 (1964). (40) R. Catterall and P. P. Edwards, J. Phys. Chem., 79,3010 (1975); S. C. Guy and P. P. Edwards, Chem. Phys. Lett., 86,150 (1982). See also P. P. Edwards, J. Phys. Chem., 84, 1215 (1980). (41) D. A. Gordon, Phys. Reo. E,13,3738 (1976); M. Smithard,Solid State Commun., 14, 407 (1974). See also several papers in J. Phys. (Orsay,Fr.) C2, Cod. Int. sur les Petites Particules et Amas Inorganique, Lyon, France, 1976. (42) C. Taupin, J.Phys. Chem. Solids, 28,41(1967); D. E. Kaplan and P. J. Bray, Phys. Rev., 129, 1919 (1963). (43) W. Freyland, Phys. Reu. E, 20, 5104 (1979). (44) R. J. Elliott, Phys. Reu., 96, 266 (1954).
The Journal of Physical Chemistry, Vol. 87, No. 11, 1983 2003
which is certainly valid as long as the particle diameter is larger than the electron mean free path, A, in bulk metals. For the alkali metals A is of the order of 20-30 A around 1000 K giving an uppermost limit of about 30 A for the diameter of the clusters. In small particles the relaxation mechanism will be inhibited once the mean energy level spacing is comparable with kT,37which gives an estimate of the cluster size of about 20-30 atoms for these systems.
Summary and Conclusions The ESR results of this work provide no indications for the occurrence of bound atomic-like states. On the other hand, the data give strong support for the F-center model which is particularly demonstrated by the characteristic g-factor shift observed with varying the salt matrix. In the concentration range studied here spin pairing plays an important role. This may be derived from the magnitude of the F-center spin densities and is consistent with the concentration behavior of the static magnetic susceptibility. Concerning the type of different possible diamagnetic species, no conclusions can be drawn on the basis of the magnetic properties alone. Here further investigations of, e.g., the optical properties are necessary and are in preparation.26 The observed narrowing of the liquid Fcenter resonances may be taken as an indication that exchange interaction is a dominating factor in the process of spin pairing. This should proceed with increasing metal concentrations toward the NM-M transition region leading to the formation of larger aggregates or clusters. A first ESR indication for clustering phenomena is derived from the observation of a separate resonance which shows a striking similarity with the ESR characteristics of small metal particles. The main conclusion from the magnetic properties reported here is that concentrated nonmetallic M-MX solutions are determined by an equilibrium between F-center analogous states and spin-paired species or higher aggregations. With increasing metal concentrations a continuous transformation from localized Curie-type states to spin-delocalized states should be considered before the onset of metallic transport characteristics. In this respect a close similarity may be noted with the magnetic properties of other M-NM systems like the highly doped semiconductor~.~~
Acknowledgment. We thank Dr. G. Schonherr for his assistance during part of the experimental work. We are grateful to Dr. R. Dupree for a critical reading of the manuscript. Financial support of this work by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie is gratefully acknowledged. Registry No. NaC1, 7647-14-5; KCl, 7447-40-7; RbC1, 779111-9; Rb, 7440-17-7; Na, 7440-23-5. (45) D. F. Holcomb in "The Metal-Nonmetal Transition in Disordered Systems", L. F. Friedman and D. P. Tunstall, Eds., SUSSP Publications, Edinburgh, 1978.
