1168
J. Phys. Chem. 1980, 84, 1168-1171
Electrical Resistivity of Ca(NH,),,
Sr(NH3)8,and Ba(NH,),
M. J. Mobley, W. S. Glaunslnger,+ Depa~mentof Chemistty, Arizona State Universiw, Tempe, Arizona 8528 1
and J. C. Thompson'' Department of physics, Universw of Texas at Austin, Austin, Texas 78712 (Received Ju& 17, 1979) Pubiicatkm costs assisted by the National Science Foundation
Measurements have been made on polycrystalline samples over the 4-330 K range by using an electrodeless technique. These compounds are metallic in behavior with residual resistivities of 5, 22, and 28 p.Q cm for Ca(NH3)s,Sr(NH3)6,and Ba(NH&, respectively. The calcium compound exhibits a sharp increase and inflection in its resistivity at 37 K. A less pronounced inflection is observed in Ba(NH3)6at 42 K. Slight inflections are suggested in Sr(NH3)6at 23 and 69 K. These inflections have been attributed to phase transitions. Melting and a subsequent increase in conductivityis observed in Ca(NH,), at about 265 K. The temperature dependence for the resistivities correlate well with the CESR line width data available on Ca(NH& and Sr(NH3)@The data suggest these solids have low Debye temperatures and that ammonia diffusion contributes significantly to electron scattering above 100 K. Magnetoresistance was observed for Ca(hTH& at 4.2 K. The field dependence of the resistivity followed a 1.3 power law indicative of an uncompensated metal. No magnetoresistance was observable for the Sr and Ba compounds.
Introduction The continuing interest in solutions of alkali metals and alkaline earth metals in ammonia, which have demonstrated unusual metallic properties, has stimulated an interest in the solid metal-ammonia compounds. Of the six such compounds known to exist (Li(NH3)4and M(NH3I6where M = Ca, Sr, Ba, Yb, and Eu), the alkaline earth compounds are a unique set being formed from elements in the same periodic group. The large increase in ionic radius and atomic weight in going from calcium to barium should have a considerable affect on the respective compounds. Thus, a study of the comparative properties of the alkaline earth hexaammines should provide a good basis for understanding these compounds. We report here the results of electrical conductivity measurements on the solid hexaamniines Ca(NH&, ST("^)^, and Ba(NH3)6. This is the first report of such data on S T ( N H ~and ) ~ Ba-
spective lattice constants of 9.12, 9.57, and 9.97 A determined from X-ray powder diffraction studies.6 The actual electron densities are probably much lower due to Brillouin-zone-contact effects.
Experimental Section Samples were prepared by first cutting the alkaline earth metals into rods approximately 6 cm long X 0.3 cm diameter in an argon atmosphere. Surface tarnish was removed by shaving the rods until they were the proper weight to produce a 7-cm long hexaammine sample when reacted in a 0.67-cm i d . quartz ampole. A stoichiometric volume of NH, was distilled onto the rods inside the quartz ampoles. By controlling the distillation, the alkaline earth metals were allowed to react slowly from the bottom up in an attempt to ensure complete reaction and uniform filling of the ampole. The sample tubes were sealed under vacuum at a length of -11 cm and set in a dry ice-ethanol ("31., bath for approximately 6 h to complete the reaction. Our investigation of the conductivity of these comA similar sample preparation was employed to investipounds was prompted by a previous report' on the congate elastic and inelastic neutron scattering, continuous ductivity of Ca(NH3)6,which indicated unusual behavior, and by reports of unusual structures,2molecular m ~ t i o n , ~ ~wave ~ NMR, ESR, Raman scattering the magnetic susceptibility, and thermal properties of these materials.6 and magnetic properties5 of these compounds. There is These data are consistent with single phase samples; any also theoretical interest in these compounds. As lowsecond phase must be below 1%. electron-density metals they provide model systems for Because of the inevitable problem of sample decompoinvestigating the electronic behavior of metals in the lowsition at the electrode and poor sample-electrode contact, electron-density regime. The low-electron-densityderives an electrodeless technique was used for determination of from expansion of the metal cation by octahedral coorconductivities. The basis for such a technique and been dination of six ammonia molecules to form a molecular ion described by Zimmerman6 and others."'l Such a techwhich occupies about eight times the volume of the metal nique has been used to determine the conductivity of ancation. An upper limit to the conduction electron density other metal-ammonia compound, Li(NH3),.12 The techcan be calculated by assuming the molecular ion is twice nique is essentially that of observing the eddy current ionized, M(NH&$+, freeing two electrons per molecule to losses which change the Q of a coil when a cylindrical the conduction band. The free-electron densities ( X conductor is introduced into its core. The quantity which ~ m - are ~ ) calculated to be 0.52,0.46, and 0.40 for Ca("3)6, was actually measured was the change in resistance of the Sr(NH3)6,and Ba(NH&, respectively. These calculations coil, AI?, which has been given by MacLachla~i'~ assume the body-centered cubic structure and the re+ Supported by U.S. National Science Foundation, DMR 7509215A02. 4 Supported by U.S. National Science Foundation, DMR 76-84338, and by the R. A. Welch Foundation.
0022-3654/80/2084-1 l68$0l .OO/O
where x2 = wpu2u, M(x),O,(x), and doh) are spherical Bessel @ 1980 Amerlcan Chemical Society
Electrical Resistivity of M(NH,),
The Journal of Physical Chemistry, Vol. 84, No. 10, 1980
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functions, w is the frequency, a is the sample radius, b is the coil radius, fi is the permeability, and Lo is the inductance of the empty coil. It i s convenient to work in a region whew all but the first term of the expansion of eq 1may be neglected (where r is small). This is easily done by working at low frequencies for samples with low conductivities. Equation 1 thus becomes
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Temperature dependence of the resistivity of Sr(NH3)8.
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Temperature ( K )
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The conductivity of a sample is determined from the slope of a plot of AR vs. w2. AR is actually determined by taking the difference in resistance of two identical coils, one containing the sample and one used as a reference, both at the same temperature. The coils were 2745 turns of no. 40 copper wire applied in four layers. The dimensions were 4.45 cm long X 0.90 cm i.d. with an empty inductance of 13.2 mH. The coils were mounted, reference above sample, on a frame consistiing of two 3-mm diameter thin-walled stainless steel tubes. These were centered in a 20 cm long X 2 cm i.d. copper jacket which completely enclosed the coils and assured uniform temperature. This assembly was suspended in a Janis liquid He gas flow cryostat (Model DT) with t b e temperature regulated by a PAR Model 152 temperature controller. Sample temperature was monitored with a copper-constantan thermocouple which was calibrated at liquid He and liquid N2temperatures. Coil resistances were measured with a Wheatstone bridge by balancing t b a bridge with decade resistors. The circuit was driven by a Wavetek Model 114 oscillator in the range from 0 to 10 kHz. Bridge imbalance was measured with a PAR lock-in amplifier (Model 121). As the bridge was balanced, the circuit had to be tuned using decade capacitors in series with the coils. Tuning was achieved by minimizing the first haromonic I S observed in the imbalance signal on a Tectronix 502A oscilloscope. High temperature (265-330 K) measurements were made on the conductivities of Ca("3)6 and Ba(NH3)& This was doine by first recording the temperature dependence of the resistance of an empty coil in a circulated oil bath over this temperature range. The temperature dependence of the resistance of the coil plus sample is then determined by warming these in the oil bath. The difference in resistance between the coil plus sample and the empty coil at each temperature is then used to calculate the resistivity. These measurements were done at a single frequency, 10 kHz. The tail section of the Janis cryostat was centered between the pole faces of a Yarian V7200 electromagnet
20 10
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50
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200
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Temperature ( K )
Flgure 3.
Temperature dependence of the resistivity of Ba(NH3)B.
which was used to determine the transverse magnetoresistance from 0 to 10 kG. Results and Discussion The observed temperature dependences for the electrical resistivities of Ca("3)6, Sr(NH3)6,and Ba(NH3I6 are presented in Figures 1-3. The error bars in these plots are precision estimates for the experimental method, The accuracy of determined resistivities is approximately &20%. The accuracy is limited because of possible voids in the sample affecting the fill factor. Each of the figures (1-3) presents data obtained for one of a pair of samples of each compound which were examined. While there was some difference between the measured resistivities of the two samples of each compound, the general features of their temperature dependence are identical. The differences are to be expected because of the observed dependence of the resistivity on the thermal history of the sample as well as the possibility of differences in sample geometry and composition. This was demonstrated by monitoring the resistivity at 77 K of a Sr("3)6 sample against the time it had been setting in a dry ice-ethanol bath since initial reaction. The sample showed a 14% variation in the interval of from 2 to 11 h in the bath with a resistivity minimum occurring at about 6 h. The residual resistivities extrapolated from temperature dependence plots were determined to be 5,22, and 28 f i f l cm for Ca(NH&, Sr(NH3)6,and Ba(NHJ6, respectively. The most prominent features of the temperature dopendence curves are the inflections. This is particularly so in the case of Ca(NH3)6(Figure 1) where there appears to
1170
Mobley, Glaunsinger, and Thompson
The Journal of Physical Chemistry, Vol. 84, No. 10, 7980
be clear evidence of a phase transition at 37 K. This sharp inflection in the resistivity has been reported previously by McDonald and Thompson.14 X-ray powder diffraction studies of these compounds indicate they have a bodycentered cubic structure at least down to 77 K.15 The most likely explanation for the sharp transition in the resistivity of Ca(NH3)6is the existence of a structural phase other than bccub below 37 K. There are no structural data yet available on this compound below 77 K to confirm this transition. Neutron diffractions studies on Ca(ND& by Von Dreele et a1.2 have indicated no transitions from a bccub structure down to 6 K from this deuterated hexaammine. However, there is some evidence from the temperature dependence of NMR spin lattice relaxation times that the bccub phases of Ca(NH& and Ca(ND3)6may have slightly different structures.16 Structural differences between the protonated and deuterated forms of metal-ammonia compounds are quite probable as exemplified by lithium tetraammine which is reported to have a hcpub to fccub phase transition at 82 K for Li(NH&,17 whereas Ii(ND3)6has been indexed as bccub from 30 K to the melting point.l* Deuteration of the calcium compound changes the molecular weight by more than 10% which can have a considerable effect on the structure. The distorted ammonia geometry proposed from neutron diffraction studies of Ca(ND3)6suggests the possibility of more subtle type of structural transition, going from a distorted to a more normal ammonia geometry. It is difficult, however, to see how such a transition would account for the dramatic inflection in the Ca(NH& resistivity. In the high temperature region, 265-330 K, where the resistivity of Ca(NH3)6was determined by continuously monitoring the change in coil resistance as the sample was heated in an oil bath, the resistivity was observed to actually decrease as indicated in Figure 1. This decrease is similar to that observed in Li(NH& above the melting point at 89.6 K.12 This indicates a melting point for the Ca("3)6 compound between 240 K, the highest temperature at which a static resistivity measurement was made, and 265 K. To confirm this melting, an ingot of Ca("3)6 was cut under liquid Nz and sealed in a quartz ampole. The sample was placed in an oil bath 268 K where it was observed to melt before reaching equilibrium with the bath. This is t
