ISOTOPE-EFFECT IN RESISTIVITY OF SCANDIUM HYDRIDE

Abstract The temperature dependent resistivities of ScH 2 and ScD 2 differ by an Einstein term with θ E = 1600 K and θ E /√2, respectively.

Heat capacity measurements [1,2] have shown that the phonon spectra of YH 2 and ZrH 2 contain high frequency Einstein modes due to the presence of H in these compounds. Substitution of D for H resuited in a decrease in the Einstein temperature by V~-, with corresponding changes in the temperature dependence of the heat capacity. We suspected that electron scattering from these Einstein modes would also be evident in the electrical resistivities of transition metal hydrides. We chose to work with the isoelectronic, iso-structural pair ScH 2 and SoD 2, since they are easily prepared [3] and there are no competing higher hydrides of Sc [3,4].
Solid pieces of Sc (99.9%) were reacted with hydrogen (UHP) or deuterium (99.5%) at a pressure of one atm at 600°C for several hours. The temperature was then lowered to room temperature over a period of 12 hours. Gravimetric analysis of representative samples of the hydride indicated a stoichiometry of the final products given by SCH1.98±0.02. X-ray analysis of Sell 2 showed a face-centered-cubic lattice with lattice parameter 4.783 -+ 0.001 A, in excellent agreement with previous determinations [3,4]. Apart from two very weak extra lines in the X-ray patterns which indicate the presence of a few percent of Sc203 in the samples, all diffraction lines were due to ScH 2.
The resistivities of our samples of ScH 2 and SoD 2 showed very small resistance minima near 4 K which were probably due to trace magnetic impurities in the Sc. No superconductivity was observed above 2 K for  The data lie on a straight line for temperatures below 100 K, since in this temperature range the temperature dependent resistivities are identical: RScH2 = A + BRScD2 (15 K~T~ 100 K). Above 100 K, however, RScH2 = A +BRScD2 + A(T), where A(7) is a function of temperature to be discussed below.
In order to analyze the temperature dependent deviation A(7), we assume that the only difference in the temperature dependent resistivities of ScH 2 and ScD 2 is due to conduction electron scattering by Einstein modes whose Einstein temperatures are 0 E and 0E/V~-in the respective compounds [1,2]. Howarth and Sondheimer showed [6] that to lowest order, the resistance due to scattering by an Einstein mode is proportional to E(0 E, 7)[M, where M is the mass of the atoms responsible for the Einstein mode, and

E(O E, 7) is a function given by E(O E, 7) = (T sinh 2 X
(0E/27))-1. Therefore, if our model is correct, we have In fig. 1, we have plotted A(7) verstls D(0 E, 7) for 0 E = 1400 K, 1600K, and 180OK. Comparing eq. (1) with the data in fig. 2 yields 0 E = 1600 + 100 K. The constant of proportionality in eq. (1) can also be determined from the slope of the plot for 0 E = 1600 K, thereby completely specifying the Einstein mode scattering versus temperature (in our arbitrary units). Our value of 0 E is in good agreement with the Einstein temperatures of 1700K [1] and 1500K [2] found from heat capacity measurements for the similar compounds ZrH 2 and YH 2, respectively. The relative scattering cross section of acoustic to optical modes can be obtained from the high temperature limit (T~O R, T~OF_ .) where the atoms in the compound scatter independently. Using the asymptotic forms of the Bloch-GrOneisen and Einstein terms, we have in our arbitrary units the following high temperature limit (normalized to the same atomic vibration amplitude T/M02): RSeH2 = RBloch.Griineisen + REinstein T T = 42.6 e 6.7 --MScH2 02 MH 02'E The first term represents the acoustic mode scattering in which we suppose the hydrogen atoms to follow rigidly the Sc motion, and the second term the Einstein contribution from both hydrogen atoms. A more specific model would be required to further compare the relative Sc and H scattering cross sections. We note, however, that the ratio of the two coefficients (6.4) is in rough agreement with the simple estimate obtained by assuming +3 and + 1 charges on the Sc and H, respectively, and additivity of cross sections of Sc and H in the acoustic mode scattering; i.e., (9+2)/2 = 5.5.