NOTES
758
decrease in the collected electron beam current during an exposure. It was found that cutting off the beam for a few minutes when the current had decreased 1-2% remedied the situation. Apparently both KN03 and S a x 0 3 stored a large amount of charge; by cutting off the beam for a few minutes, this static charge could bleed off through the platinum wire in contact with the sample. At low intensities the rate at which the static charge bled off was about equal to or less than the rate a t which charge could build up. This effect, however, was not observed in either Csr\;03or Pb(KO&. CsNO,.-The resuIts on intensity effects are shown graphically in Fig. 2. The G-value for the initial slope was found to be 1.53 f 0.08 for the intensity range 1018-1020e.v./g./sec. This may be compared with the values of 1.44,41.68 f 0.05,8 and 1.72 f 0.lZbobtained by y-radiolysis. In the high dose region there is no basis for comparison with ?-rays from previous work. NaN03.-The results obtained for the decomposition of NaN03 are shown in Fig. 3. The G-value using only the data obtained at a dose rate of IOL8and lox9e.v./g.-l sec.-l was 0.22 f 0.02. This may be compared with the values of 0.16,4 0.25 f 0.02,8 and 0.200 f 0.0042b obtained by y-rays. The results obtained at the highest dose rate (lozoe.v./g.-l sec.-l) do appear to show an intensity effect. However, although these samples mere cooled during irradiation, some unavoidable warming amounting to 8-12' mas observed. Cunningham found about a 50% increase in the G-value of ;?JaSOawhen the temperature was increased from 25 to 60'. The results at the high dose rate accordingly were corrected assuming an average temperature rise of 10'. Pb(N03)2.-The decomposition of lead nitrate (Fig. 4) was studied only in the initial decomposition range. The G-value found for the initial slope was 0.53 f 0.08. This may be compared with the values of 0.48,4 0.44 f 0.048 and 0.432 found by y-ray radiolysis.
VOl. 66
mental error, that there is any appreciable intensity effect. Certainly there is no evidence for reaction (d) above. The agreement between y-ray results and electron beam experiments is as good in most cases as that shown among the different laboratories for the various nitrate decompositions by y-rays. It was not feasible to extend this work to higher dose rates because of the difficulty of dissipating the large amount of heat generated.
THE STRUCTURE OF LANTHASUX FAMILY SILICIDES1 BY A. G. THARP~ Department of Mineral Technology, Unzversity of Caltjornia. Berkeley, Calzfornaa Received August 24, 1961
Perri, Binder, and Post3p4 have described the structures of several rare earth silicides with MSiz ideal lattice types. Their work agreed with, and expanded upon, that previously reported by Brauer and Haag.6 The structures of LaSiz, CeSiz, PrSis, and EuSiz were shown to be tetragonal while structures of NdSiz, SmSiz, GdSiz, DySiz, and YSiz are orthorhombic. Perri, et al., postulated that the tetragonal lattice is characteristic of disilicides of those rare earths with relatively large atomic radii. The orthorhombic structure is a slight distortion of the LaSi2 (tetragonal) type structure. At slightly elevated temperatures, where the effective diameters of the atoms are increased by thermal vibration, the orthorhombic phases transform to the tetragonal structure. Radii of the lanthanum family atoms generally decrease with increased atomic number except that preference for certain electronic configurations causes the radii of some of the atoms to lie off the smooth curve of diameter vs. atomic number. The present work was undertaken to compare the structures of disilicides of the higher atomic number lanthanum family elements, erbium, thulium, ytterbium, and lutetium. If the postulate of Perri, et al., is valid for these elements, YbSiz,. if Discussion such a phase could be prepared, should crystallize The primary step in the decomposition of the in the tetragonal system as do EuSL and disilicides inorganic nitrates has been postulated to be2bss-11 of lower atomic number rare earths, while erbium, thulium, and lutetium disilicides should have the Nos- --e- NOz0 (a) orthorhombic or some other structure. The oxygen fragment produced in (a) reacting
+
as1a,g38
NOzNO$0
+
+ 0 +KOs +XOz-
+
0 2
(b) (c)
and possibly 0+0-402
(d)
It was shown previously5 that a kinetic scheme using reactions (a), (b), and (c) above gave excellent agreement with experiments for the radiolysis of NaN03. It is quite possible that a similar reaction scheme ill show good agreement for some of the other nitrates, particularly Csx'03 and AgNQ3.
Considering the range of intensities used in these studies it does not appear, within experi(10) P. Dolgan and T. IT, Davis. J Chem. Phys , 27, 333 (1957). (11) L. K. NnrayLnswainv, Trans Faraday Soc., 31, 1411 (1935).
Experimental Preparation of Samples .-Disilicides of thulium and ytterbium vrrere prepared by direct syntheses from the elements. Disilicides of erbium and lutetium were synthesized by reducing the sesquioxides of the rare earths with an excess of silicon. The rare earth oxides, rare earth metals, and the silicon were 99.9+% pure. The reactions between thulium and silicon and between ytterbium and silicon were carried out in tungsten crucibles under a slight positive pressure of helium or argon or in vacuo. Vacuum preparation wa2 somewhat undesirable since considerable quantities of thulium or ytterbium would vaporize from the reaction chamber. The argon or helium was dried by passing it through a 30411. column of phos(1) This work was supported by the Office of Naval Research. ( 2 ) Department of Chemistry, Long Beach State College, Long Beach, California. (3) J. A. Perri, I. Binder, and B. Post, J . Phys. Chem., 63, 616 (1959).
B. Post, ibid., 63, 2073 (1959). ( 5 ) G. Brauer and €1. Heap, 2.anorg. allgem. Chem., 267, 198 (1952)
(4) J. A. Perri, I. Binder, and
phoric anhydride and magnesium perchlorate. No evidence of oxidation of either the samples or containers could be observed. A few preparations were carried out in tantalum, molybdenum, and graphite containers to determine whether or not the phases formed were influenced by reaction with the container. No container reaction could be observed visually or by X-ray anaIyses. ErzO8 and LuzOa were heated with silicon in tungsten, molybdenum, tantalum, and graphite previously impregnated with silicon. These preparations were usually carried out in vacuo. A reaction temperature of about 1200" was used for synthesis from the elements. Temperatures of 1300 t o 1500O were used for svnthesis by reduction of an oxide. The samples prepared by reduction of the oxide with silicon were made by raising the temperature very slowly until rapid evolution of gases was obtained as was evident by the quantity of material condensing on the walIs of the vacuum system. B temperature of 1350' gave good results. The preparations were heated a t maximum temperature for 0.5 to 4 hr. Thulium disilicide and ytterbium silicide were prepared with a sufficiently large excess of silicon to obtain free silicon
TABLE I CRYSTALLOGRAPHIC DATAFOR TmSia Cu KOIRadiation (K, = 1.5418 A.) hk
759
NOTES
April, 1962
sin* &bed
sin'
&iod
Imbeda
in the preparation. Thulium disilicide also was prepared with enough excess thulium to yield a lower thulium silicide.
Results Crystallographic Data.-All preparations were examined by powder X-ray diffraction techniques. A 114.59 mm. Debye-Scherrer powder camera was used. Examination of the X-ray diffraction data showed that the four disilicides, ErSiz, TmSi2, YbSi2, and LuSi2, crystallize in the hexagonal system. These data were compared with that for other hexagonal disilicides and found to be similar to those for p-USi2 and P-ThSi,. Accordingly, these phases were assigned the space group C6/ mmm. The atom positions are one metal atom in (0, 0, 0) and two silicon atoms in i (1/3, 2/3, l/2). Thulium disilicide gave diffraction patterns of especially good quality. Three of these were measured and indexed. Intensities of the diffraction lines were estimated visually. Approximate theoretical intensities were calculated by utilizing the formula 1
+ COS^ 2e
F Z P sin2 e cos B where F is the structure factor, p is the multiplicity cos2 20/sin2 0 cos 0 is the trigonofactor, and 1 (r
rcalad
001 100 101 002 110 102 111 200 201 112 003 202 103 210 211 113 300 212+ 30 1 203 004 104 302 220 22 1 213
0.0358 0.0359 m+ 18 .0557 .0558 S 50 ,0917 .0915 vvs 100 ,1434 ma .I437 11 .1674 .1675 S27 ,1992 .1994 mb 16 .2033 ,2033 10 m .2229 .2232 m6 ,2591 .2591 8 20 ,3108 .3109 S 19 absent .3227 ... 1 .3668 .3667 m6 ,3785 .3778 m 11 .3903 .3907 wb 5 .4264 .4265 S 18 .4904 ,4902 W 2 .so22 ,5023 W 5 ,5333 .5332 m7 abcent 2 .5373 *.. ,6451 .5451 W 7 absent .5728 0 ... ,6286 .6306 w3 .6449 .6447 Wb 8 .6690 .6686 w4 .7050 .7044 2 W .7123 .7122 m13 310 .7250 ,7243 w 3 114 .7405 ,7399 W 8 311 ,7609 ,7601 14 TVb 204 ,7960 ,7957 w4 222 ,8123 ,8118 m 10 303 ,8241 ,8237 w 3 3 12 ,81879 ,8675 m 10 400 ,8916 ,8915 w -3 005 absent ,8950 1 ... 40 1 ,9270 ,9273 m12 105 .9509 ,9507 wb 15 214 ,9628 ,9628 mb 19 19 223 ,9904 . 9908 m a vvs = very very strong, = strong, = medium, = weak. This reflection and subsequent Ones are for copper ICa, radiation (Kal = 1.5405 A,). 1-
+
metrical polarization correction factor. The calculated intensities are in good agreement with the observed intensities. These crystallographic data for TmSin are given in Table I. The diffraction data and intensities for ErSi2, YbSi,, and LuSi2 are in excellent agreement with that for TmSiz. The YbSi2 phase gives a diffraction pattern with rather poor back reflections. This indicates poorly formed crystals, but since no splitting of the diffraction lines can be obsersed, the hexagonal structure is correct. The unit cell dimensions and X-ray densities for ErSiz, TmSiz, YbSiz, and LuSiz are given in Table 11. TABLE I1 CELLPARAMETERS AND THEORETICAL DENSITIES Cornpound
ErSi,
TmSi2 YbSi:! LuSip
ao,
3 3 3 3
A. 786 768
77 745
co,
A.
4 089 4 071 4.10 4 046
Theoretica density, gJcm.8
7 31 7.48 7 54 7 81
Discussion Perri and co-workers3 showed by detailed intensity measurements and calculations that the composition of the gadolinium silicide with the MSiZ type ideal lattice is about GdSil.l. The hexagonal phases reported in this work appear to have very close to the ideal composition. An excellent X-ray pattern for TmSiz was obtained from a sample prepared by combining silicon with thulium in a gramatom ratio of 3: 1. This diffraction pattern showed a very faint silicon pattern, and a very weak diffraction line for the strongest reflection of Tniz03. This sample was studied with the Geiger counter diffractometer. Intensities for these diffraction lines which have an amreciable silicon contribution were measured by deikrmining the area under the diffraction curve. Theoretical intensities were talculated assuming a random absence of siljfon atcms
NOTES
760 I
I
I
I
-
3 0 0)
z
5452 50 -
I 58
i 60
I
64 66 68 70 Atomic number. Fig. 1.-Molecular volume of lanthanum metal disilicidm us. atomic number of the metal.
62
in the lattice and a composition of TmSil.?S. These calculated intensities were not in as good agreement with the observed intensities as were the calculated intensities for the composition TmSiz. Two films of preparations with a silicon to thulium ratio greater than two were measured. Both films show a weak silicon diffraction pattern. The cell parameters for these phases of TmSiZ were calculated and the agreement with those for the phase known to be near the composition TmSiz was excellent. No variation in intensities could be observed. It therefore was concluded that the composition of the thulium silicon phase was very close to TmSiz. X-Ray patterns for samples prepared by varying the silicon to metal ratio showed only the hexagonal MSiz phase and that of a lower silicide for thulium and ytterbium when the gram-atom ratio was about 1.75. Apparently the structures of these phases are not changed by varying the silicon composition as are those of thorium and uranium with the MSiz type ideal lattice. Previous ~ ~ shows that a-ThSiz has about the ideal composition while p-ThSiz is silicon deficient. The lower atomic number lanthanum family MSiz phases that are isostructural with a-ThSiz and a-USi28 apparently do not show the p-MSi2structure modification. That YbSin crystallizes in the same crystal system as the other three disilicides reported in this paper is not consistent with the previously reported3.4 structures for rare earth disilicides if the ytterbium atom is assumed to have the same relatively large size as found in the metal and if the ratio of atom sizes is the important factor in determining the system in which a phase should crystallize. That the cell parameters for YbSi, are (6) G. Brauer and A. Mitius, 2. anorg. zb. alZgem. Chem., 249, 325 (1942). (7)E.L.Jacobson, R. D.Freeman, A. G . Tharp, and A. W. Seamy, J . A m . Chem. So?., 7 8 , 4850 (1956). (8) W.13. Zachaiiasen, Acta Crust., 2,94 (1949).
Vol. 66
only slightly larger than those of TmSi2 and LuSiz suggests that the silicon-silicon contacts determine the crystal volume or that the average number of bonding electrons of ytterbium atoms in YbSi:, is more nearly the same as for atoms of adjacent lanthanide elements in their disilicides. The graph of molecular volume of lanthanum family disilicide phases v8. atom number of the metal atoms shown in Fig. 1 demonstrates the variation of cell sizes and consequently of metal atom sizes found in these disilicide phases. The trend in cell dimensions correlates rather closely with the variation in atom sizes for the pure lanthanum family elements. There is, however, somewhat less variation in cell sizes between the hexagonal phases than in the tetragonal and orthorhombic phases. The hexagonal disilicide phases of erbium, thulium, lutetium, and especially of ytterbium, might be expected to transform at high temperatures to tetragonal or orthorhombic forms isostructural with the disilicides of the lighter lanthanide elements. No evidence of such high temperature transformations could be obtained. Since considerable rearrangement of atoms would be required for the structural transformation to occur, it might be expected that very rapid cooling would quench any high temperature phase. Only the hexagonal phase was observed when samples were cooled at rates of over 500' per min.
A MODIFIED DIFFUSION TIME-LAG BY IRVING FATT Miller Institute for Basic Research i n Science and Department of Mznsral Technology, Universitg of Cali fornaa, Berkeleg Received December 86, 1961
The time-lag measurement described by Barrer, FrischJ2and Goodknight and Fatt often is used to measure diffusion coefficients, or if the coefficient is known, to obtain information on pore structure parameters of porous media. Barrerl derives the time-lag equation for a linear porous body in which there are no dead-end pores (cul-desacs). Goodknight and Fatt3 have extended this derivation to include porous media in which there is dead-end pore volume. The initial and boundary conditions from which r k ~ his time-lag ~ ~ equation require that Barrer derives the porous plug be initially at a uniform concentration below that which will be imposed at the upstream end at time zero. The outflow end is maintained at the initial concentration and the cumulative amount of material diffusing out of this end is measured as a function of time. It often is more convenient to have initially in the porous plug a uniform concentration equal to that which will be maintained at the upstream end, and at time zero to lower the concentration a t the outflow end. The cumulative amount of material diffusing out of this end is measured as a function of time. This system will be shown below to have a time-lag similar to that of Barrer, differing only by sign and a numerical coefficient. Both time-lags (1) R. M. Barrer, J . Phys. Chem., 67, 35 (1953). (2) H.L. Frisoh, ibid., 63, 1249 (1959). (3) R. C.Goodknight and I. Fatt, ibid., 65, 1709 (1961).
