7 '3) and the second summation includes all the atoms lying within a spherical volume o f radius R which is a multiple of the shortest lattice parameter at a given temperature. The 2346 M . 1. V A L I C and D . L L E W E L Y N W I L L I A M S Table 3. Ionic contribution to the EFG tensor as a function of number of atoms considered R N (Qlat t.kv (qiatt .) l 'V (qiatt.)zz A a l t . TJlatt. 3 532 - 0 02147 - 0 00329 0 02476 31-7 -0-734 15 66105 - 0 02087 - 0 00378 002464 3 0 0 -0-694 25 306450 -0-02094 - 0 00374 0 02468 30 0 -0-697 tion are those from Table 4 at 4-2°K. The principal components of q l a t t . are all in the units of IO2'1 c m - 3 . /3 l a u . is the angle in degrees between the Z principal axis of q l a t t . and the C crystallographic axis. 7 j l a t t . is its asymmetry parameter. Table 4. Lattice parameters of gallium T A B C (°K) (A) ( A ) (A) 4-2 4-5156 4-4904 7-6328 78 4-516 4-493 7-636 285-3 4-5195 4-5242 7-6618 Since the convergence of the sums is quite fast (in contrast to the case of indium, etc.), alternative methods for calculating qlatt. have not been considered. In order to see to what extent our ionic model describes the crystal-line field gradient in gallium we compare in Table 5 the experimentally determined para-meters characterizing the E F G at 4-2°K with those calculated assuming an antishielding factor of —9-50 for free + : ! G a ions 17 and Z = 3, from the relation. vQ = e*0(\\ - y « ) Z ( q l a t t . ) „ ( 1 - H a i t . 2 ) l , 2 / 2 A . (13) In particular one should note that the X axis is parallel to the B axis in the ionic model rather than the Y axis in the experimental case which we have indicated by assigning a negative sign to it. The most obvious feature of the experimen-tal results is the very small temperature varia-Table 5. Comparison of ionic cal-culation and experimental results for the EFG tensor E F G vQ (Mc/sec) Piat t . TJlatt. Experiment 11-31 24-3 -0-179 Ionic 2-82 3 0 0 -0-697 tion of both the asymmetry parameter and the orientation of the principal axes. The quad-rupole frequency exhibits the temperature variation shown in Fig. 10 and the results may be combined with the asy'mmetry parameter to give the changes in all E F G components between 285-3° and 4-2°K. We have cal-culated the temperature dependence of qi a l t . using the temperature dependent values of the lattice parameters from Table 4 and assuming the parameters // and v to be the same for all [ M %ec] O 100 200 300 T no Fig . 10. The temperature dependence of the TOGa N Q R frequency. The solid line represents the results of Pomerantz[4J; the experimental points are from the present work. A N U C L E A R M A G N E T I C R E S O N A N C E S T U D Y temperatures. Results for R = 22 are included in the Table 6. All the parameters remain practically constant over the whole tempera-ture range so that thermal expansion alone does not explain the small changes observed. However the explicit temperature dependence of the quadrupolar interaction which arises from the influence of the lattice vibrations is generally the dominant effect[20] and it is possible that this could account for the whole temperature variation. 2 3 4 7 qexp and obtain an alternative solution for qdiff. with an angle /3diff. of 31-6° and 17 = 0'03 and also sensibly temperature independent. However, in view of the close correlation between the angles mentioned above it is likely that our first value is the correct one. In conclusion, our results suggest that the dominant contribution to the gradient is qloc. Watson, Gossard and Yafet[21] estimate that the main contribution to qloc results from the interaction between the ionic and the Table 6. Temperature variation of the ionic contribution to the EFG tensor T ^ U l a t t . (°K) (q , a l , . ) . Y .V (qiatt.)zz (qiatl.)l 'V Aatt. r f l a t t . (Mc/sec) 4-2 - 0 - 0 2 0 9 0 - 0 - 0 0 3 7 3 0 0 2 4 6 3 30-0 - 0 - 6 9 7 2-77 78 - 0 - 0 2 0 8 6 - 0 - 0 0 3 7 7 0-02462 30 0 - 0 - 6 9 4 2-77 285-3 - 0 - 0 2 0 6 3 - 0 - 0 0 4 5 3 0-02516 30-0 - 0 - 6 4 0 2-80 We may now proceed in the spirit of the assumed model and determine the difference tensor qdiff. = (l —^)qioc. = qexP.— (i — y»)Zqiatt. (14) and the results are given in Table 7. It is very interesting to note that the angle /3diff. is al-most equal to the angle /3pair. between the nearest neighbour direction and the C axis which is 15-9 deg. The temperature variation of /3pair is not available in the present literature and it would be of interest to see if its tempera-ture variation is the same as /3diff. Since we can only determine the absolute value of qexp., we can reverse the sign of Table 7. Temperature variation of qdiff. T (°K) (qdlB.) .VA- (q