4436
J . Phys. Chem. 1984, 88, 4436-4438
An Investigation of the Short-Range Order Structure of Amorphous Hydrous Holmium Oxide W. 0. Milligan, D. F. Mullica,* H. 0. Perkins, and C. K. C. Lok Departments of Chemistry and Physics, Baylor University, Waco, Texas 76798 (Received: November 18, 1983; In Final Form: March 2, 1984)
The bulk short-rangeorder (SRO) structure of amorphous hydrous holmium oxide is the subject of this work. A brief discussion of the data collection procedure and data reduction is given. The scattering profile, interference function (Si(S)),and radial distribution function (RDF) curves are shown. A randomized model is discussed for this system and the results of this procedure are presented. Analysis of the RDF discloses the holmium atom to be coordinated to nine oxygens atoms at a mean distance of 2.40 A. The average 0-0 distance is found to be 2.91 and the 0-Ho-0 angle is 74.6'.
Introduction Research in the area of amorphous rare earth gels commenced with the work of Joye and Gamier.' Interest in amorphous material has increased rapidly during the past decade. This interest stems from their potential in technical areas such as semiconductors and catalysts. More recent work includes an investigation by Johansson on a basic nitrate hydrous thorium oxide.2 Much work has been done in the way of probing the structural behavior of the lanthanide compounds by means of single-crystal X-ray analysis. Hydrothermal aging of these gels results in crystalline material of phases that vary with time, temperature, and the concentration of the aging medium. The structures of the lanthanide oxides, trihydroxides, and oxyhydroxides have been well ~haracterized.~ Continuation of this characterization leads to studies on the structural content or S R O of the amorphous forms. The broad-band, diffuse X-ray scattering profiles can be analyzed and transformed into radial distribution functions (RDF) containing this structural information. Coordination numbers and interatomic distances obtained from the RDF often allow the calculation of certain bond angles and may also permit the proposal of an average structural model. Recently a study of the electronic structure of holmium oxide, oxyhydroxide, trihydroxide, and amorphous hydrous oxide by electron spectroscopic methods was r e p ~ r t e d .The ~ results of that study imply that a small amount of 4f covalent bonding exists in these compounds and that electron transfer from the conduction band to the valence band is possible. The catalytic power of the lanthanides may involve the 4f and 5d-6s energy levels. Structural trends observed in other oxyligated lanthanide systems5 prompted the investigation of the SRO structure of hydrous erbium oxide.6 The study using electron spectroscopy for chemical analysis (ESCA)4 coupled to the amorphous study6 warrants a continuation of SRO structural research through the elucidation of the localized structure of amorphous hydrous holmium oxide. Experimental Section Holmium oxide (99.9% purity), which was commercially purchased, was used to prepare amorphous hydrous holmium oxide. A stoichiometric amount of 6.0 N H N 0 3 was used to dissolve Ho,O,. The resultant solution was filtered and cooled P. Joye and C. Gamier, Comp. Rend., 154, 510 (1912). G. Johansson, Acta Chem. Scand., 22, 399 (1968). W. 0. Milligan, G. W. Beall, and D. F. Mullica, "Crystallography in America", Section F, American Crystallographic Association, New 1983, Chapter 9, p 362. W. 0. Milligan, D. F. Mullica, H. 0. Perkins, C . K. C. Lok, and V. Young, J. Phys. Chem., 87, 541 1 (1983). (5) G. W. Beall, W. 0. Milligan, and H. A. Wolcott, J . Inorg. Nucl. Chem., 39, 65 (1977). (6) W. 0. Milligan, D. F. Mullica, H. 0. Perkins, C. K. C. Lok, J. J. McCoy, and H. A. Wolcott, Acra Crystallogr., Sect. A, A40, 264 (1984).
(1) (2) (3) North York, (4)
0022-3654/84/2088-4436$01 S O / O
to 273 K. An excess of aqueous ammonia, at 273 K, was added in order to precipitate the hydrous gel. This precipitant was washed thoroughly with distilled ice water by refrigerated centrifugation until all the nitrates were removed. The gel was quickly air dried, and then the resultant powder was ground finely and desiccated in a current of dry nitrogen. Samples of this batch were used for all physical measurements. A Perkin-Elmer 521 grating IR spectrophotometer was employed to obtain an IR absorption spectrum of the dried gel over the range of 4000-250 cm-I. The absorption spectrum closely matches the erbium analogue. An 0-H stretch associated with hydrogen bonding was observed in the 3400-3700-cm-' region. A broad band centered at 1525 cm-' can be attributed to the deformation mode of water. Metal-oxygen deformations are seen at 650 cm-' and Ho-OH stretching at 370 cm-'. A thermal gravimetric analysis on the hydrous oxide was performed using a Perkin-Elmer TGS-1 thermobalance. The analysis was run at 2.5 O C m i d while purging with dry nitrogen. The weight loss corresponds to a loss of 4.10 (10) water molecules per formula unit of Ho20,. This corresponds to the basic formula Ho(OH),-O.5H20. A density (4.85 g ~ m - of ~ )the loose powder was acquired with a Quantachrome (Model S.py- 1) stereopycnometer. The dry hydrous holmium oxide powder was pressed, in a drybox under a positive nitrogen pressure, into a 2 X 4 cm sample cell until a smooth mirrorlike surface was obtained. X-ray fluorescence analysis on the sample, which was used to collect X-ray diffraction data, verified the presence of holmium. The sample was mounted on a modified horizontal Siemens-K805 diffractometer. Radiation from the Mo X-ray tube was monochromized with a NaCl crystal. Thus the Mo K&!line was used for the diffraction experiment. Data were collected in the range of 2 5 28 5 155 in a 20 step-scan mode with a 3300 SP Kevex-ray Si(Li) detector. The step sizes employed were 0.2' for 28 < 75O and 1.0' for 28 > 75'. A Digital PDP 11/03 computer controlled the stepping motor and collected the scattered intensities. A total of 40 000 counts per step 28 was collected resulting in a relative standard deviation of 0.5%. The counting chain employed is described elsewhereS6Systematic checks on the primary beam's intensity were made throughout the data collection procedure. No corrections for drift were required. Analysis A profile of the SRO structure of amorphous materials is obtained through the production of a RDF which is transformed from an interference function, S i ( S ) . The scattered intensities were corrected for polarization effects according to Azaroff.' An absorption correction was applied according to the method of Levy, Agron, and Danford.* The 20 values were transformed to S values where S is defined as (47r sin 8/A) in units of A-'. The diffracted (7) L. V. Azaroff, Acta Crystallogr., 8, 701 (1955). (8) H. A. Levy, P. A. Agron, and M. D. Danford, J . Appl. Phys., 30,2012 (1959).
0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 19, 1984 4431
SRO in Amorphous Hydrous Holmium Oxide
I
I
I 0
2
4
8 SI$\
6
10
12
14
r(A1
16
Figure 1. The corrected and normalized scattering curve for holmium
hydrous oxide. Note the oscillation about the independent scattering curve. The abscissa is arbitrarily scaled (electron units).
Figure 3. rC(r), the Fourier transform of the interference function (atoms units). The smooth dotted curve at low r is related to the bulk
density. I
r(.N
Figure 4. RDF for holmium hydrous oxide and the average density
curves (atoms A-' units).
Figure 2. The interference function, Si(S), as calculated from eq 2 (abscissa units are A-').
rC(r) = 4 w 2 [ p ( r )- pa] = [ 2 r / r ] D R ( r )
(3)
(la)
DR(r) = JsmSi(S) exp(-aS2) sin ( S r ) d S
(4)
(1b)
The term exp(-aS*) is an artificial temperature factor where a has a value of 0.0005 A2. A curve of rG(r) values vs. radii ( r ) is presented in Figure 3. The R D F in it's final form is given as
intensity, after polarization and absorption corrections, can be expressed as ID(S)
= I(S) + IB(S)
and the background intensity, I,, is defined as IB
= Icoh(S)
+ Icp(S) + I m ( S )
The calculated values of Si@) are plotted against S in Figure 2. A Fourier transform of the function Si(S) results in a reduced function, rG(r), and is in a form similar to that presented by Warren:13
ID@) is the diffracted intensity, Z(S) is the interference scattering, IWh(S) is the coherent atomic scattering, Zcp(S) is the Compton scattering, and I,,,@) represents the multiple scattering contribution. The independent coherent scattering curve for the unit of composition ( H O O ~ , ~ Hwas , ) calculated from the analytical scattering factors, A, with appropriate anomalous dispersion c o r r e c t i o n ~ . ~ JThe ~ data were normalized to the independent scattering curve by a high angle method. The Compton contribution" was calculated and the percent multiple scattering determined.12 The maximum value for double scattering was 2.44% at S = 14.0. Both Compton and double scattering contributions were subtracted. The final corrected scattering curve, IC,is shown in Figure 1. The interference function, SI'(S),is given by the relation
(9) "International Tables for X-ray Crystallography", Vol. 4, Kynoch Press, Birmingham, 1974. (10) D. T. Cromer and S . Liberman, J . Chem. Phys., 53, 1891 (1970). (11) D. T. Cromer, J . Chem. Phys., 50, 4857 (1969). (12) B. E. Warren and R. L. Mozzi, Acta Crystallogr., 21, 459 (1966).
where
+ [2r/~]DR(r)
47rr2p(r) = 4nr2pa
(5)
where p(r) is a density function and pa is the average atomic density either determined experimentally or derived from the shape of the rG(r) curve at small r values. The radial distribution function of hydrous holmium oxide, oscillating about an average density curve, is given in Figure 4. Often a pair function, W ( r ) , relating the localized densities to the bulk density is used in favor of the RDF.
W(r) = p ( r ) / p a = 1 + D R ( r ) / 2 r 2 r p ,
(6)
Results and Discussion As seen in Figures 1 and 2, the corrected experimental scattering curve and its calculated interference function, Si(S),oscillate smoothly about the independent scattering curve and zero, respectively. This is evidence to the fact that the high angle nor(13) B. E. Warren, "X-Ray Diffraction", Addison-Wesley, Reading, MA, 1969.
4438
The Journal of Physical Chemistry, Vol. 88, No. 19, 1984
Milligan et al.
TABLE I: Coordination Numbers (CN), Bond Distances (A), and Angles (deg) type CN M-0 M-0 0-0 HoOOH 7 2.25 (6) 2.39 (5) 3.01 (8) 9 9
Ho(OH)3
AHHO'
2.444 (3)
2.874 (5) 2.91
2.416 (3) 2.40
M-M
0-M-0
ref
3.79 3.91 1 3.78
81.1 (20) 72.5 (1) 74.6
14 5
b
Amorphous hydrous holmium oxide. *This work.
PEAK
1 2.40 2 2.81 3 3.78
i uo.o 0.0
uo-no
--IXPlRlMENr
** G A U S S I A N 00
PI1
DllliRlNCE
I
2
4
6
8
10
12
14
i6
I
sli\-'I
Figure 6. The calculated interference function, Si(S),obtained from the randomized model (arbitrary scaling).
oo
18
2 2
26
?
. 2
0-
34
3.8
42
I
Figure 5. Resolution of the 0-0 peak from the RDF is obtained by subtracting the RDF from the Gaussian fitted M - O and M-M peaks. The abscissa is arbitrarily scaled. malization was successful. The reduced function, rG(r), is presented in Figure 3. The bulk density, pa, can be determined from this curve at small values of r. This is shown by the smooth dotted curve at 0 < r < 1.8 in Figure 3. This smooth curve was used in this region, low r, in calculating the RDF, Figure 4, so as to minimize distracting and meaningless features in this region. The peak positions observed in Figure 4, the RDF curve, are indicative of interatomic distances while peak areas are related to coordination numbers. The position of the first peak maximum in Figure 4 is found at 2.40 8, and represents the average Ho-O bond distance. The shoulder on the high r side of this maximum (see Figure 5 , a blownup section of Figure 4 in the final form of RDF as 47r?p(r)) can be resolved by fitting the surrounding peaks to Gaussian forms. This shoulder resolved to a very symmetrical peak with it's center at 2.91 A. This peak is designated as an 0-0 interaction. From the Hc-0 and 0-0 distances, one can calculate an average 0-Ho-O angle of 74.6'. The third observed peak at 3.78 A is assigned to the Ho-Ho interatomic distance. These interatomic distances are reasonable and can be compared to known crystalline materials, see Table I. The holmium atom is found to have nine [9.08 (lo)] oxygen atoms radially located at an average distance of 2.40 A. The number in parentheses represents an error estimated from the standard deviations in the Gaussian least-squares fit mentioned previously. It is possible to calculate an interference function, M(S),or a RDF of model systems from set arrangements of atoms and then alter the arrangement until it agrees with the form obtained experimentally. The calculations involving the interference function are largely based on modifications of Debye'sI5 scattering equation which involves only the magnitude of the interatomic distances, not the angular part.I6 Calculations of this type can (14) A. N. Christensen, Acta Chem. Scund., 19, 1391 (1965). (15) P. Debye, Ann. Phys., 46, 809 (1915).
be made either on a microcrystalline model of known structure which is thought to be similar or on some more randomly packed particle.17 If a microcrystalline model is used, the resultant Si(S) curve rapidly becomes crystallike in it's appearance with the peaks becoming sharper and more numerous as the crystal size increases. The interference function curve displayed in Figure 6 was arrived at in a different fashion. A particle was constructed that contained all the average distances observed in the experimental RDF. A D3* symmetry about the Ho atom was assumed. Next, this particle was replicated along the three axes in order to enlarge the unit. The periodicity was then destroyed by applying a function which displaced all atoms in the crystal by some boundary limited random amount. A Gaussian random number generator was employed to displace each atom a limited maximum distance of 0.40 A, within a sphere of enclosure. The periodicity was removed but the average distances were still maintained. After observing Figure 6, it is obvious that the resultant curve is similar to the experimentally determined curve. The information obtained from this randomized model and from the RDF concerns only averages. A recent paper by Milligan et aL4 brought forth comments on the resemblance of the 01,photoelectron spectra between HoOOH and the amorphous hydrous holmium oxide. The similarity is drawn from the appearance of two different O,, photoelectron signals obtained from both materials. Crystalline HoOOH is known to have two types of oxygen environments, an 0 atom and an OH group. This similarity, observed in the electron spectroscopy for chemical analysis (ESCA) study, implies the existence of two different oxygen environments in the amorphous material. The RDF obtained in this study presents only one average Ho-O distance but the peak is very broad. This broadening may be the result of two average distances that merge to form one peak or it may be the convolution of both M-0 and M-OH peaks. Acknowledgment. The authors thank The Robert A. Welch Foundation for the financial support of this work (Grant No. AA-668) and Baylor University. We also thank E. L. Sappenfield for his helpful comments related to the preparation of this manuscript. Registry No. HO(OH)~.O.~H~O, 9 1424-89-4. (16) G. S.Cargill, J . Appl. Phys., 41, 12 (1970). (17) C. H. Bennet, J . Appl. Phys., 43, 2727 (1972).
