Ralph 0. Moyer Trinty College Hartford, Connecticut 06106
I I I
Synthesis and Structure of Magnesium Oxide or Calcium Oxide An integrated inorganic-physical experiment
T h e applications of X-ray crystallography are extensive and range from metallurgical t o biochemical molecular studies. One has onlv to read the current literature to he convinced t h a t X-ray crystallography and structure determination are topics of continuing interest. The objectives of this laboratory experiment were (1)t o demonstrate t h a t hinarv oxides can be D r e ~ a r e dhv thermal decomposition of ox; compounds s u i h as oxalates and (2) to introduce elementary X-ray crystallography and its application t o the determination of structure. Two recent lahoratory texts give good discussions of X-ray powder diffraction technique^.^.^ Our integrated lahoratory is a one semester program with two 3-hr lahoratory sessions per week. O n the average the sequence of experiments reported here requires four 3-hr sessions. For the most part, students enroll in physical chemistry and inorganic chemistry lecture course s concurrently with the integrated lahoratory. T h e inteerated conceDt of svnthesis. followed bv characterization. conveys to the studknt a sense of continuity and commun: icates the methodolom -- of the practicing- chemist. Furthermore, characterization of "one's own compound" gives students a vested interest in their experimental d a t a and reduces the task of d a t a acquisition t o a personal level.
Presented at the 165th Annual Meeting of the American Chemical Society, Dallas, Texas, April 1973; see Abstract No. CHED
067.
Jolly, W. L., "The Synthesis and Characterization of Inorganic Compounds,'' Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1970, p. 411. Hofacker, U. A,, "Chemical Experimentation, An Integrated Course in Inorganic, Analytical, and Physical Chemistry," W. H. Freeman and Ca., San Francisco, 1972, p. 107. Skooe. -. D. A,. and West. D. M.. "Fundamentals of Analvtieal Chemistry," 2nd Ed., ~ o l ~t i n e h a r t ,and Winston, I n e . , - ~ e w York, 1969, pp. 355-357,
612 / Journal of ChemicalEducation
Trial structures: a, rock salt: b, zinc blende.
Experimental T h e following sequence is recommended: (1) synthesis of magnesium or calcium oxide, (2) elemental determination for magnesium or calcium, (3) apparent density determination, (4) X-ray powder diffraction analysis, and (5) structure determination. Synthesis of MgO or CaO
Magnesium nitrate, Mg(N0sh .6H20,6.2 mmole, was dissolved in 150 ml of deionized water; and 6.2 mmale of (NHI~CZOI.H20 was dissolved in 150 ml of deionized water. Both solutions were heated to 8WC, whereupon the oxalate solution was added to the solution of Mg2+ with vigorous stirring. The mixture was cooled to room temperature, preferably overnight, filtered an a medium porosity glass filter, and dried at 110°C overnight. The dried oaalate was transferred to a 50-ml porcelain crucible and heated with a Fisher burner for approximately 2 hr; after which, the covered crucible was placed in a muffle furnace and heated to 8CQeC, preferably overnight. The magnesium oxide was cooled to roam temperature. A similar procedure uar followed for the preparation oi calcium oxide. The reagents were 5 8 mtnole of C ~ I U O ~IHIO. ) ~ . and 5.8 mmole 01 ~. \ t l., .r K ~ . The decumvoait~ontrmueratum for - ~.OH90. the calcium oxalate was $ 5 0 " ~ .Both the magnesium oxide and calcium oxide were sealed in 3-dram opticlear vials with parafilm (American Can Co.) and paraffin wax. The chemical equations representing the two step synthesis are below
Table 1. X-Ray Indexing Data; Magnesium Oxide sin' 8
0.1003 0.1381 0.2746 0.3759 0.4098 0.5439 0.6434
where M = Mg or Ca. Elemental Analysis Calcium was analyzed by direct eomplexometric titration with EDTA and magnesium by the cdmparable indirect te~hnique.~ Apparent Density Determination The liquid buoyancy principle was used to measure the apparent density of the binary oxide. Some of the binary oxide sample, in the form of fine powder, was compressed at approximately 5,MlO psi into a cylindrical pellet approximately % in. high and 'I4 in. in diameter. The pellet was placed in a Nichrome wire basket and submerged in approximately 30 ml of carbon tetrach!oride. Entrapped air in the pellet was removed by applying a partial vacuum to the submerged pellet in a vacuum desiccator. The temperature of the carbon tetrachloride was measured; and the apparent density of the pellet was calculated according to the following equation Paw =
A A-B
(density of CCI,)
111 200 220 311 222 400
331 420
0.6782
422 511
08101 0.9080
RRR
Table 2. Unit Cell Formula: Magnesium Oxide Number of "Molecules"
Theroetical Density, g/ce
1 2 3
0.917
d
R fifi'l.
1.835
2.752
(1)
where A is the pellet weight in air and B is the pellet weight in carbon tetrachloride. X-Ray Diffraction Analysis A small quantity of powdered binary oxide sample was loaded into a capillary tube, 0.5 mm a d . and 0.01 mm wall thickness (General Rand Corporation, Edison, New Jersey). The sample was exposed to nickel-filtered Cu K, radiation for -30 min using a General Electric XRD 6 instrument. Diffraction lines, recorded on Kodak Medical X-ray film NS 54T, were measured to 0.01 cm using a General Electric Fluoroline illuminated reader. The Straumanis method was used to calculatethe Bragg angle, tl ; and the intensity of each diffraction line on the photographic film was qualitatively noted. Discussion The sequence of events leading to the structure assignment of the binary oxide was (1) indexing the X-ray powder pattern, (2) calculating the unit cell dimension, (3) determining the number of "molecules" of binary oxide, and (4) assigning a structure to the respective oxide by trial and error. The search for the correct crystal system, i.e., indexing the pattern, was confined to cubic symmetry and the three Bravais lattices, i.e., primitive, body centered, and face centered systems. The interplanar spacing, d, was calculated from the Bragg equation
where X is the averaee waveleneth of the comer . . K a radiation and 0 is the experimentally determined Hragg angle. For cubic lattices. the following relationshir, between the interplanar spacing and the ill& indices, h k 1, holds
where a is the unit cell length. A relationship between sin20 and the sum of the Miller indices is the r e d t of combining eqns. (2) and (3)
The sum of h2 + kZ + l2 is always an integer with XZ/4a2a constant. The crystal system of the alkaline earth oxide was obtained by noting certain systematic absences of N or hkl. For example, the primitive cell will have no sys-
tematic absences; and all planes will reflect. In the case of the body centered cell, reflections are systematically ab1, where n is a n integer, i.e., sent when h + k + 1 = 2n when N is odd. Face centered cells display reflections where h, k, and 1 are all even or all odd, i.e., never mixed. Several integers such as N = 7, 15, 23, and 28 are not possible. Indexing data lifted from a student's report for magnesium oxide are found in Table 1. Clearly, according to the sequence of N values in Table 1, the X-ray powder diffraction indexing data for magnesium oxide are consistent with face centered cubic symmetry. All the diffraction lines on the photographic film should be assigned. Students observed lines in addition to the ones reported in Table 1, usually of weak intensity and occurring near the stronger reflections. These lines were caused by the presence of copper KO radiation which was not filtered entirely by the nickel foil. T o be certain however, the following equation, based on the Bragg Law, was invoked
+
In order to assign KO radiation as responsible for the origin of the "extra" line, the sinZO for the line multiplied by the constant (XKa)Z/(XK[3)2 must equal the sin20 value for the corresponding ru reflection. The next step leading to structure determination was the calculation of the unit cell leneth. " , a.. mine e m . (5). Because the error in sinZ@decreases as 0 app&ches 906, the value of the unit cell narameter a t the hiehest anele 0 " was selected. The next step was to determine the number of "molecules" of the binary oxide in each cell. Our approach was to calculate first the unit cell volume and then the theoretical density assuming one to six "molecules" per unit cell. The experimental density was then compared with the theoretical values to determine which theoretical value came closest to the experimental. Again, data in Table 2 were lifted from a student's report. The experimental apparent density determined by the liquid buoyancy technique, was 3.47 g/cc; and hence consistent with four "molecules" per unit cell. Assignment of atomic sites in a structure is a trial and error process in which the information derived from intensities of the diffraction lines on the photographic film is essential. In order to propose trial structures, the formula of the compound, the number of formula units, and the crystal symmetry must be known. In order to convey the message of trial and error, two structures, consistent with the above observations were proposed, i.e., the rock salt Volume 52, Number 9, September 1975 / 613
and zinc hlende structures. Illustrations of the trial structures are shown in the figure. Both structures are consistent with (1) the ratio cif alkaline earth binary oxide stoichiometry of one cation to one anion, (2) four formula units of the oxide per unit cell, and (3) face centered cubic symmetry. Each ion in the proposed structures should translate 0 % 5, 5 0 'h, 'h % 0 and end up a t a site occupied hy a like ion. Fractionnl coordinates for the four oxidc ions in hoth structures are located at 0 00, 'n h 0, % 0 5, 0 % %. In the case of the rock salt structure the four alkaline earth ions fill all the octahedral holes and hence, are located a t 'h 'h 'h, 0 0 3, 0 'h 0, lh 0 0. For the zinc hlende structure, one half of the tetrahedral holes are filled by the four alkaline earth ions located a t Y, ?/a Y4, %'I4 Y4. % #3/4, 3/4 ?43/4. To determine which of the two trial structures was correct for the alkaline earth binary oxide, the diffracted intensities were calculated using the following equation
where IF1 represents the absolute value of the structure factor, p is the multiplicity, and the quantity within the brackets is the Lorentz-polarization factor. The structure factor, F, for an hkl reflection in terms of the atomic positions uuw for N ions was calculated using the following equation
where f is the individual atomic scattering factor. Altematively, the trigonometric form of eqn. (8) may be invoked
Table 3. X-Ray Intensity Data; Magnesium Oxide 7 -
hkl
----Calculated-Zinc Blende
111 200 220 311 222
10
400
6
5
45 26
2
331 420 422
12 22
511
17
3
Relative Intensity---------Rock Salt
O h m d
11
weak
53
vy strong atmng wk medium
100
8 16 7
4 24 27 4
medium medium
weak med strong med strong vy weak
vy
ASTM
10 100 52 4 12 6 2
17 15 3
222
worthwhile to point out that there are several repetitive calculations; and students wrote computer programs for these calculations. The results of a student's structure analysis for magnesium oxide is submitted in Table 3. The Miller indices for ten reflections are listed in column 1. The next two columns list the normalized intensities calculated for each structure. The fourth column is a record of the observed intensities from the student's film. Clearly, it can be seen that the observed qualitative intensities agree more closely with normalized intensity values for the rock salt structure. Hence, the student concluded that the rock salt structure was probably the correct structure for magnesium oxide. Data in the fifth column were lifted from the ASTM reference card for magnesium oxide." Acknowledgment It is a pleasure to acknowledge my colleague, Prof. Henry A. DePhillips, Jr. for his suggestions and assistance. This work was part of a curriculum development program supported by a NSF-COSIP Grant NO. GY8397.
'
Convenient sources of atomic scattering factors, multiplicities, and Lorentz-polarization values are found in B. D. Cullity's text "Elements of X-Ray Diffraction."' It is
Cullity, B. D., "Elements of X-Ray Diffraction," AddimnWesley Publishing Co., Reading, Mass., 1959, pp. 474-479. 5Smith. J. V.. (Editor) "X-Rav Powder Data File." Inoreanic Sets 1-5, '~mericanSO& for ?;&ing Materials, ~hiladelphia, Pa., 1960, p . 581.
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