Jan., 1952
CRYSTAL STRUC~URE OF HEAVY METAL ORTHOVANADATES
145
CRYSTAL STRUCTURE OF HEAVY METAL ORTHOVANADATES BYW. 0. MILLIGAN AND L. W.VERNON Department of Chemistry, The Rice Inatit&, Houston, Tezas Rscmosd Octobw SO. 1860
The following is a brief summary of the results of this investigation: (1) The orthovanadates of cerium, praseod@um, neodymium, samarium, europium gadolinium, terbium dysprosium, holmium, erbium, thulium, terbium, lutecium, yttrium and scandium possess the &con structure. (2) TAe oxygen parameters for fourteen of these ort ovanadates are z 0.19 f 0.01 and z = 0.35 )r 0.01. For scandium orthovanadate the parameters are z = 0.20 f 0.01 and z = 0.33 f 0.01, (3) The oxygen tetrahedra in scandium orthovanadate are elongated m the direction of the c-sxi~.In the other orthovanadates of this series the oxygen tetrahedra are almost regular.
2
In a previous paper2 from this Laboratory it was reported that the orthovanadata of praaedymium, neodymium, samarium, europium, gadolinium, terbium, dysprosium, erbium, thulium, ytterbium, lutecium and yttrium comprise a tetragonal isomorphous series. The structures of a limited number of orthovanadates have been described in the literature. Broch3 found that yttrium ortho vanadate was tetragonal, possessing a crystal structure closely similar to that of ~ircon.4~Brandt6 found that chromium orthovanadate (CrVO,) was orthorhombic and belonged to space group Di72h Cmcm. Brandt’ has also reported rhodium orthovanadate (RhVOd) to be tetragonal and to possess the rutile structure.’ The results of the previous investigations in this Laboratory and the work of Brandt suggest the desirability of further quantitative studies on the heavy metal orthovanadates.
5
in parentheses in Table IV are the ones obtained from the powder photograph by means of the microphotometer.
Crystal Structure The approach used in determining the structure of the orthovanadates enumerated above is based on the similarity of the powder photographs and t.he structure of yttrium orthovanadate reported by Broch.8 When the X-ray diffraction lines of the orthovanadates of 14 trivalent metals (cerium, praseodymium, neodymium, samarium, europium, gadolinium, terbium, dysprosium, holmium, erbium, thulium, ytterbium, lutecium and yttrium) are indexed in a body-centered tetragonal system, the following reflections are absent: (110), (130), (002), (330), (114), (222)and (150). Theabsence of these reflections suggests the presence of a fourfold screw axis, an u-plane perpendicular to this axis, and a d-plane perpendicular to (110). These symmetry elements Experimental lead t o the following extinctions. Reflections (hkl) k I = 2n; (hkO) only with h Samples of scandium orthovanadate, holmium orthovana- occur only with h date and cerium orthovanadate were prepared by the = 2n and k = 2n; (hhl) only with 1 = 2n and 2h method used in the preparation of the other orthovanadates 1 = 4n. These are the characteristic extincpreviously studied.* The oxide or the oxalate of the trivalent metal was mixed with ammonium metavanadate in tions of space group Dl94h -14/amd. From consideration of the density of these orthoquantities such that equimolar amounts of M201 and VIOS were present. The samples were heated for periods of two vanadates it is found that the unit cell contains hours a t 750-1000”. four molecules of MVOI. Space group Di84h These powder samples were examined by standard X-ray Wraction methods, using CrIGand CuKcrX-radiation. The I4/amd (reference 9) contains two positions with ddraction patterns observed for cerium orthovanadate and four equivalent points and three positions with sixholmium orthovanadate are almost identical with the X- teen equivalent points. radiograms of the other rare earth orthovanadates. The The special positions (a), (b), (j)and (8) (ref. 9) pattern obtained for scandium orthovanadate consists of have additional extinctions. Because of these relatively fewer lines and will be discussed in detail below. The relative intensities were obtained by measuring the additional extinctions the presence of reflections area under the peaks on the X-radiograms, which were pro- (202) and (134) eliminates the possibility of the duced by the Geiger-counter and Brown recorder of the oxygen atoms being in positions (f) or (g). The Norelco X-ray spectrometer. The scanning speed of the spectrometer was one degree (2 0) per minute. The copper oxygen atoms must be in position (h). The atomic radiation was filtered through nickel foil to obtain the cop- positions are: per KOradiation. The X-radiograms of neodymium orthoFour trivalent metal atoms in (a): 000; vanadate, ytterbium orthovapadate and scandium ortho- 1/2; 0 ‘/z 1/4; ‘/a 0 ”4 vanadate are reproduced in Fig. 1. Four vanadium atoms in (b): 0 0 I/Z; 0; Because of the limited angular range of the Norelco spectrometer, the intensities of some of the diffraction lines of 0 l/Z 1/4; ’/P 0 ’/4 scandium orthovanadate were obtained from the q w d e r Sixteen oxygen atoms in (h): (000; 1/2 ‘/z) photograph usin a Moll microphotometer and a hoto- o,x,z; 0, -x,z; x,o, -2; -2,o, -2; 0,’/2 z,1/4 pen” recorder. %he observed intensities which are reported
-
+ +
+
-
-
- 2; 0, ‘/a
(1) Preaented before the Divkion of Physical and Inorganic Chem-
istry at the 118th Meeting of the American Chemical Society, which waa held in Chicago, IU.. September. 1950. (2) Milligan, Watt and Rachford. THIEJ O ~ N A L6S, , 227 (1949). (3) Brooh, 2. phrsik. Chem., 3OB, 345 (1932). (4) Vegard. Phil. Map., 1, 1151 (1926). (5) Vegard, ibid., 4, 511 (1927). (6) Brandt, Arkia Kemi Mineral. Geol., 17A, No. 6 (1943). (7) Brandt. ibid., lTA, No. 15 (1943). (8) Wyckoff, “The Structure of Crystals,” Chemical Catalog Company, (Reinhold Publ. Corp.), New York, N. Y., 1931.
- x , I / 4 - 2;
q1/2,1/4
2
+
+ +
2;
-x,1/*,1/4
+
Calculation of Intensities.-The relative intensities were calculated by means of the equation
‘’
1
+
C O E ~28
sin3 cos e X pF’
where each term has the meaning given in ref. 9. (9) “Internationale Tabellen sur Bestimmung von Kriitabtrukturen,” Gebrilder Borntraeger, Berlin, 1935.
W. 0. MILLIGAN AND L. W. VXRNON
146
Vol. 56
6 5
Id
4 3 2 1
6 5 4 3
d
E
2
1 6 I'
5 4
d
2 m
3 2 1
14
26
20
32
38
44
50
56
62
68
74
80
20.
Fig. 1.-Geiger counter X-radiograms of neodymium orthovanadate, ytterbium orthovanadate and scandium orthovanadate.
After substituting the atomic positions given above and simplifying, the following structure factor is obtained for reflections with h k 1 = 2n:
abnormal. The values of the parameters are probably close to '/4 and s / ~ . The final values of the parameters were determined by the method of trial and error. The values Fhkl = 2[1 4-exp a i ( k Z/2)1 [ f ~ fv exp 7r ill of the parameters were varied untjl a good general f 4f0 { [exp (2n ilz) cos 2nkx + exp ( - 2 ~ilz) cos 2r h]+ exp xi(k + 1/2) agreement between the calculated intensities and [exp (2n zlz) cos 2r hz + exp ( -217 i l z ) the experimentally determined intensities was obcos 27r kzl 1 tained. From examination of this structure factor it is The X-ray diffraction lines on the powder photoseen that for reflections with k 1/2 = 2n 1the graph of scandium orthovanadate can be indexed in oxygen atoms alone contribute to the diffraction. the body-centered tetragonal system. The unit It will also be noted that when 1 is odd the phase of cell dimensions of all of the orthovanadates studied the waves diffracted by the trivalent metal atoms are given in Table I in absolute angstrom units. differs by 180 degrees from the phase of the X-rays Calculation of the density using the unit cell in Tadiffracted by the vanadium atoms. Reflections ble I and four molecules of ScVOa per unit cell gives with k 1/2 = 2n 1should be very weak; lines TABLE. I with 1 odd should be weak and lines with 1 even UNITCELLDIMENSIONS should be strong. Compound a,A. 0 , A. c/a Only values of x between zero and a half need be SCVOI 6.78 6.12 0.90 considered since for an oxygen atom a t (0x2)there LUVO4 7.01 6.19 .88 is an equivalent atom at (OZz). Values of z between Y bVO4 7.04 6.23 .89 zero and a half are the only ones that need be conTmV04 7.00 6.20 .89 sidered since larger values would give the same reErVOd" 7.07 6.25 .88 sults with the a and b axes interchanged. HOVOi 7.06 6.25 .89 The reflection (220) is relatively weak although E YVOl 7.10 6.27 .88 is even. From consideration of the structure facDyVOi 7.10 6.27 .88 tor it is seen that this means that cos 4nx must have TbVOi 7.15 6.31 .88 a large negative value. The structure factor for the 7.19 6.33 .88 GdVOi (220) plane does have a large negative value when 7.20 6.35 .88 EUV04 x = Although the (202) reflection is caused by 7.24 6.36 .88 the oxygen atoms only, it is relatively strong. This SmVOl 7.33 6.43 .88 NdVOi fact means that sin 4n z(1 - cos 4nx) must be a 7.30 6.42 .88 large number. The function above does have large PrVO4 values when x = 1/4 and z = 1/8 or 3/g. If z is equal 7.34 6.47 .88 CeVOd to ' / 8 , the interatomic distances in the crystal are a 25% yttrium.
+
+
+
+
+ +
+
+
I .
I
CRYSTAL Srwrciww OF HEAVYMETALORTHOVANADATES
Jan., 1852
147
a value of 3.54g./cc. The density of scandium orthovanadate was determined experimentally by the pycnometer method and a value of 3.6 g./cc. was obtained, TABLE11
atoms and in some cases the intensity will be too weak to be observed. The intensities of the diffraction lines of scandium orthovanadate were calculated by the method outlined above. The results are given in Table IV,
RELATIVE INTENSITIES OF NdV04 AND YbVOl
TABLEIV X-RAYDIFFRACTION DATAOF ScV04
hkl
101 200 211 112 220 202
301 103 231 132 400 123 411 240 004 303 402 332 204 233 242 341 501 224 143 134 251 152 a
NdVO4 Calcd. Obsd.
Calcd.
YbVO4
0.6 0.4 1.4
2.9 10.0 1.5 7.6 2.4 0.6 2.0 1.1 2.0 6.1 2.4 0.7 0.6 1.2
0.31 .2
o.g
0.31 .2
0.7
-02 1.5
a
.02 1.6
a
3.2 10.0 1.4 7.9 2.1 0.5 1.4 0.8
1.3 5.8
1.7
1.7
"l] 0.1 .02
1.4
.08
0.5
05]
a
'."]1.4 0.3 .Ol
V.W.
.I
V.W.
1.5
1.6
4.6 10.0 2.1 8.3 2.3 0.4 1.5 0.9 1.6 6.0 1.6
Obsd.
0.8
0.5 2.0
3.2 10.0 1.7 7.8 2.7 0.5 2.1 1.2 1.9 6.8 2.2 0.9 0.5 1.9
2.0
0.2 le2] .02
1.7
*6] .1
0.8
1'2] 0.4 .Ol .2 1.6
a
1.5 V.W. V.W.
1.7
Not observed.
TABLE 111 L)ISTANCIS IN NdVOa, YbVOI, YVo4, scVo4, INTERATOMIC
A.
v-0 (O-OL
(0-0). M-0 M-0 a
NdVO4
YbVOi
Yvo4'
ScVOi
1.69 2.78 2.76 2.36 2.65
1.63 2.68 2.66 2.27 2.56
1.64 2.70 2.67 2.30 2.73
1.74 2.70 2.92 2.07 2.38
Reported by Broch.6
Indexing the reflections of scandium orthovanadate in the above manner gives a large number of extinctions (see Table IV). Examination of the absent reflections reveals that scandium orthovanadate has the same systematic extinctions as the other orthovanadates enumerated above. In addition to these systematic extinctions, scandium orthovanadate has a pseudo-extinction; many reflections with I odd are missing. If scandium orthovanadate has the same structure as the other orthovanadates enumerated above, the pseudo-extinction can be explained. When 1 is odd the wave diffracted by the scandium ion is 180' out of phase with the wave diffracted by the vanadium ion. Since the scattering powers of V+5 and Scfaare approximately the same, X-ray diffraction by planes with odd I is caused almost entirely by the oxygen
hkl
101 200 211 112 220 202 301 103 231 132 400 123 411 004 240 303 402 332 204 233 242 341 501 224 143 134 251 152 440
105 125 404 343 800 161 352 260 116 136 712 624 336
Interplanar spacings A. Calcd. Obsh.
4.50 3.38 2.71 2.57 2.39 2.27 2.12 1.950 1,793 1.755 1.693 1.695 1.588 1.525 1.513 1.514 1.485 1.415 1.390 1.382 1.360 1.322 1.322 1.285 1.280 1.243 1.231 1.220 1.200 1.201 1.130 1.133 1.128 1.128 1.097 1.086 1.075 0.997 .921 .915 876 .857 I
Not observed.
a
3.38 2.71 2.58 2.89 2.27 2.12 1.950 a
1.760 1.690 a a
1.530 1.510 a a
1.420 1.395 1.380 a
a a
1.290 a a
1 .230 1.220 1.200 a a
1.135 a
1.127
Relative intensity Crtlcd. Obsd.
0.00 10.0 1.4 6.2 0.7 1.3 0.5 .3 .04 5.9 2.1 0.2 .04 .3 1 .o
a
10.0
1.4 6.1
1.1 1.8 0.9 0.6 a
6.2 2.5 a
0.5 1.1
0.01
0.03 1.9 1.0 0.3 .1 .05 .04 .9 .03 .1
.2 .9 .4
Q
2.1 1.2 0.3 0
a a
1.0 a 4
0.2 .9 .4
.07 .Ol .5 .Ol .5
a
.01
1.086 1.075 0I998 .921 ,013 .878 .854
.9 .4 .6
.7 1.0
1.0 0.3
* From microphotometer.
Discussion The calculated and experimental intensities of the X-ray diffraction lines of neodymium orthovanadate and ytterbium orthovanadate are given in Table I1 for the parameters 2 = 0.19 and z 0.35. It will be noted that there is good general agreement between the calculated intensities and the intensities measured by means of the Geiger counter. Since the intensities of most of the interference maxima are not very sensitive t o changes in the values of the parameters, it is difficult to estimate the accuracy of the parameters. However, =I
