Von Dreele, Glaunsinger, Bowman, and Yarnell
2992
different from those used above. However, changes in H positions do not affect the major conclusion that expansion needs to be carried out to higher order than in normal metals. The new neutron data are difficult to accept on a simple chemical basis and raise a question as to the chemical identity of the sample investigated. A c k n o u l e d g m e n t . We wish to thank the National Science Foundation, the Air Force Office of Scientific Research, and the Materials Science Center of Cornell University for their support of this research. We are grateful to Professor Roald Hoffmann and his research group for use of their EHMO programs, to Doctor Edwin Pollock for use of his structure constant program, and to Professor Neil Ashcroft and Doctor Pierre Pfeuty for their encouragement and advice in carrying out this work. We also wish to thank Professor Hans Nowotny of the Institut fur Physikalische Chemie, Universitat Wien, for his kind hospitality to one of us (M.J.S.) during the time this report was prepared.
(3) W. S. Glaunsinger, S. Zolotov. and M. J. Sienko, J. Chem. Phys., 56, 4756 (1972). (4) T. David, P. Damay, and M. J. Sienko, J. Chem. Phys. 62, 1526 (1975). (5) W. Glaunsinger and M. J. Sienko, J. Chem. Phys., 62, 1873, 1883 (1975). (6) F. W. Cagle and H. J. Holland, presented at the 145th National Meeting of the American Chemical Society, New York, Sept 1963. (7) R. Hoffman, J. Chem. Phys., 39, 1397 (1963). ( 8 ) T. L. Loucks, "Augmented Plane Wave Method", W. A. Benjamin, Reading, Mass., 1966. (9) J. C. Slater, Phys. Rev., 81, 385 (1951). (IO) W. A. Harrison, "Pseudopotentials in the Theory of Metals", W. A. Benjamin, Reading, Mass., 1966, p 46. (11) V. Heine and I. Abarenkov, Phi/. Mag., 9, 451 (1964). (12) Reference 10, p 275. (13) J. Korringa, Physica, 13, 392 (1947). (14) W. Kohn and N. Rostoker, Phys. Rev., 94, 11 1 (1954). (15) Therese David, Ph.D. Thesis, Cornell University, 1974. (16) 8. Segall and F. S. Ham, Methods Comput, Pbys., 8, 251 (1968). (17) J. Callaway, "Energy Band Theory", Academic Press, New York, N.Y., 1964, p 9. (18) H. Jones, "The Theory of Brillouin Zones and Electronic States in Crystals", North-Holland Publishing Co., Amsterdam, 1960, p 116. (19) B. Vasvari, A. 0. E. Animalu, and V. Heine, Phys. Rev., 154, 535 (1967).
Discussion References and Notes (1) This research was sponsored by the National Science Foundation under Grant No. GP-17706 and was supported in part by the Air Force Office of Scientific Research and the Materials Science Center at Cornell University. (2) A review of metal-ammonia compounds has been given by N. Mammano in "Metal-Ammonia Solutions", Colloque Weyl II, J. J. Lagowskl and M. J. Sienko, Ed., Butterworths, London, 1970, pp 367-393.
J. THOMPSON. W h a t d o y o u believe w o u l d b e t h e effect o n t h e electrical resistivity o f sphericalizing t h e p o t e n t i a l of Ca(NH&?
M.J. SIENKO. I d o n o t know. Sphericalizing was t h e only way we could handle t h e computation problem. W e did find t h a t t r y i n g various positions o f t h e hydrogen atoms did n o t seem t o make m u c h difference in t h e energy b a n d eigenvalues. However, changing t h e Ca-N distance did.
A Neutron Qiffraction Study of Hexaammine-d3-calcium(0)at 75 K1 R. B. Von DreeIe,* W. S. Glaunslnger Department of Chemistry, Arizona State University, Tempe, Arizona, 8528 1
A. L. Bowman, and J. L. Yarnell Los Alamos Scientific Laboratory, Los Alamos, New Mexico, 87544 (Received July 28, 1975)
The structure of Ca(ND& was determined by powder neutron diffraction a t 75 K. The atomic parameters were refined by least- squares fitting of the diffraction profile. Ca(ND3)S crystallizes in the space group Imam with a = 9.0137(4) 8, and Z = 2. The standard profile residual was 0.109 for eight parameters and a profile range 10' 5 28 5 50° for X = 1.27963 A. Ca(ND& has highly distorted ND3 molecules arranged in an exact octahedron around the Ca atoms with fourfold rotational disorder for each ND3. The Ca-N distance is 2.69 A. One N-D bond is normal, 0.94 A, while the other two are extremely long, 1.39 A. There is no hydrogen bonding in the structure and virtually all nonbonded contacts are greater than van der Waals distances..
Introduction Previous investigations of' the alkaline earth and lanthanide metal--liquid ammonia systems showed that a hexammine metal [M(W&)L;, M = Ca, Sr, Ba, Eu, and Yb] compound was formed and that it had unusual metallic properties similar to those of Li(NH3)4.2-5X ray powder diffraction of these compounds indicated t,hat The Journal of Physical Chefnistry* Vu/. 79, No. 26, 1975
they have a body-centered cubic structure which is maintained down to at least 77 K. However, because of the high scattering power of the metal atoms, these studies could not establish in detail the structural arrangement of the ammonia molecules. It is clear that this detailed structural information for these compounds is required before their properties can be understood, therefore we have performed a neutron powder diffraction analysis of one of the hexam-
Neutron Diffraction Study of Hexaammine-d3-calcium(O)
2993
9320
EC03
I
I1
403cl
~l
r l l 7;cc
" Flgure 2. View down the Ca-N bond (z axis) showing the disposition of the dlsordered NOS molecules for model a and model b. The lines marked m denote the positions of the mirror planes for the space group lm3m.
Figure 1. Neutron powder diffraction pattern for Ca(ND& taken at 75 K.
mines, Ca(ND3)6, to establish the structure and thermal motion of the ammonia molecules at 75 K.
Experimental Section Sample Preparation. Deuterated ammonia was prepared by allowing sodium cyanide to react with deuterated water a t 140°C for 1 hr in a 75-ml stainless steel bomb capable of withstanding 300 atm.8 The ND3 thus prepared was dried and purified by repeated distillation onto sodium metal. A Ca(ND3)c sample for neutron diffraction was prepared by distilling a stoichiometric quantity of ND3 onto freshly cut calcium metal placed in a specially cleanedg 2 X 4 cm cylindrical quartz ampule. The ampule was sealed off and allowed to warm to room temperature to ensure complete reaction. This sample showed no visible signs of decomposition during the preparation and subsequent neutron data collection. Neutron Data Collection. Neutron powder diffraction data (Figure 1) were collected a t 75 K on a modified tripleaxis diffractometer a t the Omega West Reactor, Los Alamos Scientific Laboratory. A mean neutron wavelength of 1.27963(8) A was obtained by reflection from the (220) planes of a Cu monochromator at a 20, of 60°.The flux a t the sample was -lo5 n cm-2 sec-l. The wavelength was calculated from the diffraction pattern of a NbO standard; these diffraction peaks were accurately Gaussian in shape. The sample was cooled by conduction in the tail of a liquid nitrogen Dewar. (Liquid nitrogen boils at 75 K under ambient pressure a t Los Alamos, New Mexico.) The data were collected over the range 10.0 I 20 I 70.0' in steps of 0.10020. The counting time a t each step was determined by the time required for an incident beam monitor count of lOOK obtained with a fission counter. Absorption and extinction effects proved to be negligible and no corrections were necessary. Since the peaks were completely resolved, background corrections were made at points bracketing each peak with a linear interpolation across the base of each peak. The observed background can be entirely ascribed to scatter from the quartz sample tube. Structure Analysis and Refinement. Since both the observed neutron diffraction pattern (Figure 1)and the x-ray results indicate a body centered structure with two Ca(ND& molecules per only the space groups I m 3 , I m 3 m , 123, and I43m are compatible with this result. The
two noncentrosymmetric space groups I23 and 143m were rejected because they required a disorder of the ammonia molecules which leads to a set of positions very nearly the same as those for the centrosymmetric space groups I m 3 and I m 3 m , respectively, and hence would be indistinguishable from them. A plausable model in the space group I m 3 was subsequently shown to give a poorer refinement than the same model in I m 3 m and that space group was also rejected. Two models (Figure 2 ) for the orientation of a disordered ammonia molecule in the space group I m 3 m were developed and refined. In both models the Ca atoms are in fixed positions at the origin and body center of the cell surrounded by an exact octahedron of nitrogen atoms. The nitrogen atoms are in the 12 e special positions (0, 0, Z) with one variable coordinate. One deuterium atom occupies for 25% of the time the special position 48j (0, Y , Z) for the first model (Figure 2a) and 48k (X, X , 2 ) for the second model (Figure 2b). In both models the two other deuteriums are accommodated in a general position with 50% occupancy placed such that the threefold symmetry of the ammonia molecule is maintained. Thus both models have a fourfold rotational disorder of the ammonia molecules with the ND3 in the second model rotated 45' from the first. These models were refined by a least-squares fitting of the diffraction profile, the details of which are described elsewhere.l0J1 The computer program used in this analysis enabled the use of some simple constraints which allowed the testing of models of varying complexity. (A modified version of a Fortran program written by H. M. Rietveld was used in this analysis.) Since the diffraction pattern shows no identifiable peaks above 20 = 50' only the data in the range 10' I 2 0 550' wab used in the analysis. Initially the position of the idealized ND3 molecule was refined for the two models (three parameters). The ND3 molecule was oriented with its threefold axis coincident with the Ca-N bond. Both models gave identical results with a diffraction profile residualll R p = 0.248, a weighted profile residualll Rpw = 0.272, and a Ca-N distance of 2.45 8, for the first model and Rp = 0.249, Rpw = 0.272, and a Ca-N distance of 2.46 8, for the second model. The two models had virtually identical overall temperature factors a t 7.5 and 7.3 A2, respectively. A much better refinement for both models resulted when two additional parameters, which in effect describe the N-D bond distance and the Ca-N-D bond angle, were allowed to vary; the threefold symmetry of the ND3 molecules was still maintained. For the first model an N-D distance of 1.18A, a Ca-N distance of 2.78 A, and a Ca-N-D angle of 83.8' was obtained with Rp = 0.155 and Rpw = 0.147. The second model gave exThe Journal of Physical Chemistry, Vol. 79, No. 26. 1975
2994
Von Dreele, Glaunsinger, Bowman, and Varnell
CRLC I U M [ 0 1 H E X R M M I NE
1
[:I: (r:
c
I
'\\
6000
I
15
20 TWO-THETA
25
30
35
DEG.
40
45
50
Flgure 3. Observed and calculated neutron powder diffraction profile from least-squares refinement of Ca(ND&. The points are the observed intensities corrected for background and the solid line is the calculated diffraction Drofile. A difference curve is also shown.
TABLE I: Atomic Positions for Hexaammine-d,-calcium( O)a Atom
X
Y
z
Ca N
0 0 0 0.130 ( 2 )
0 0 0.100 (4) -0.082 (2)
0
0.298 ( 2 ) 0.328 (6) 0.286 (2) UValue in parentheses is the estimated standard deviation in the last significant figure. D1 D2
actly the same results with a N-D bond length of 1.16 A, a Ca-N bond of 2.77 8, and a Ca-N-D angle of 84.1° for the residuals Rp = 0.159 and Rpw = 0.147. The temperature factors remained unchanged for this refinement and was 7.4 Az for both models. A further significant improvement was obtained for the first model when the positions of each deuterium atom were allowed to refine independently (eight parameters) to give the residuals Rp = 0.109 and Rpw = 0.098. This breaks the threefold symmetry of the ND3 molecules. The attempt to refine the second model in the same way failed because the two deuterium atoms in the general position moved toward the special position 48j occupied in the first model whereupon the least-squares diverged. Because of this result, it seems clear that the first model more properly represents the distribution of deutrium atoms in the structure and it will be discussed below. Three other structural models were also refined. A model based on the first positional model with individual temperature factors for the atoms showed no change in the residuals despite large changes in the temperature factors from the average value. Clearly, there is not enough diffraction data to be able to refine individual temperature factors. Another model which was a composite of both positional models was also refined. In this model the angular relationship of the deuterium atoms to each other was fixed while effectively allowing the N-D distance and the Ca-N-D angle for each to vary. This refinement did not significantly reduce the residuals from those obtained from the best refinement of the first positional model. This result suggests that the first positional model better represents the true structure rather than a completely disordered model or one in which there is unhindered free rotation of the ammonia molecules about the Ca-N bond. A third model in which half of the possible positions in the first positional model The Journal of Physical Chemistry, Vol. 79, No. 26, 1975
Flgure 4. A
perspective representation of the structure of Ca(ND&.
One dlsordered NDs molecule is shown with four adjacent ND3 molecules each in one of their possible orientations. A number of intera-
tomic distances and angles are also shown.
was occupied according to the space group I m 3 was refined and gave higher residuals than the best refinement in I m 3 m . Because of the restrictions imposed by the space group I m 3 , it requires a high correlation of possible disorder positions for neighboring ammonia molecules. There are no restrictions for the space group I m 3 m ; this result is consistent with the fact that nearly all the nearest neighbor contacts between ammonia molecules are greater than the van der Waals distance regardless of their orientation,
Results and Discussion The observed and calculated neutron powder diffraction profile intensities from the best refinement of the first positional model for Ca(ND3)b are shown in Figure 3. A difference curve is also shown. The atomic coordinates obtained in this refinement are given in Table I along with the estimated standard deviations given by the least-squares analysis. Drawings showing the relative positions of the ammonia molecules about the calcium atom are shown in Figure 4. Pertinant bond lengths and angles are shown on this drawing. The lattice parameter obtained in this analysis is a0 = 9.0137(4) 8 at 75 K. The most striking feature of the structure of Ca(ND3)e is the considerable distortion of the ammonia molecule. The principal distortion is an elongation of two of the N-D bonds to 1.39 A; the third N-D bond, 0.94 8, is essentially normal as compared to N-D bonds of 1.00 A found12 in solid ND3. In addition, these ammonia molecules are much flatter with D-N-D angles of 122 and 115' as compared to solid ND3 where the D-N-D angles are 110'. This makes the D-D distances in each molecule much longer, 2.05 and 2.35 8, than in normal ND3, 1.65 8. These results are entirely consistent with the very narrow proton NMR linewidths observed13 for Ca(NH3)e and Ba(NH3)e. The reduction in dipolar coupling by the long N-D bonds and long D-D distances along with the indicated thermal motion provides a complete explanation of the line widths. These effects will be discussed in more detail in the accompanying paper.13 Although the ammonia molecules are coordinated to the calcium via the nitrogen, the pseudotrigonal axis of each ammonia is not coincident with the Ca-N bond but makes
Neutron Diffraction Study of Hexaammine-d3-calcium(O) an angle of 13' with it. As a result the Ca-N-D bond angles are quite different. The angle for the normal N-D bond is 106' which is close to the ideal tetrahedral angle of 109.5' but the two long N-D bonds are very nearly at right angles, 86', to the Ca-N bond. The Ca-N distance is 2.69 A which is greater than the sum of the Ca metallic radius14 of 1.736 A and the N tetrahedral covalent radius15 of 0.70 A. It is also longer than the Ca-NH2R coordinate bonds, 2.59 A, found16 in the eight-coordinate compound, Ca(NH2NHC00)2.H20. The high degree of thermal motion, Bo, = 7.7(6) A2, as is evident in the rapid fall-off of intensity in the neutron diffraction pattern is consistent with the disorder required by the space group Irn3m. A consideration of the possible intermolecular D-D contacts show that a pair of adjacent ND3 molecules are in contact, 1.98 A, for only one of the positions allowed for each as compared to the van der Waals contact distance. This one restriction in the relative positions of the ND3 molecules would prevent completely free rotation about the Ca-N bond hence the deuterium atoms are found in fixed but disordered positions. However, it does appear from the narrow proton NMR line observed a t this temperature13 that the ammonia molecules are undergoing hindered rotation or tunneling which is also consistent with these results. The intramolecular contacts between Ca(ND3)6 groups are all much greater than the van der Waals distances regardless of the orientation of any of the ND3 molecules. There appears to be no hydrogen bonding in this structure, the closest nonbonded N- - -D distance is 3.08 A. References and Notes (1)Work supported in part by the United States Energy Research and De-
velopment Administration (ERDA).
(2)(a) E. W. Lemaster and J. C. Thompson, J. Solid State Chem., 4, 163 (1972);(b) M. D. Rosenthal and B. W. Maxfield, ibid., 7, 109 (1973). (3) W S. Glaunsinger, S. Zolotov, and M. J. Sienko, J. Chem. Phys., 56, 4756 (1972). (4)T. David, W. S. Glaunsinger, S.Zolotov, and M. J. Sienko, "Electrons in Fluids", Colloque Weyl 111, J. Jortner and N. R. Kestner, Ed., SpringerVerlag, New York, N.Y., 1973,pp 323-339.
2995
(5) W. S. Glaunsinger and M. J. Sienko, J. Chem. Phys., 62, 1873 (1975). (6) N. Mammano and M. J. Sienko, J. Solid State Chem., 1, 534 (1970). (7)F. W. Cagle and H. J. Holland, presented at the 145th National Meeting of the American Chemical Society,New York, N.Y., Sept 1963. (8) U. Schindewolf, "Metal-Ammonia Solutions", Colloque Weyl 11, J. J. Lagowskl and M. J. Sienko, Ed., Butterworths, London, 1970,pp 495-496. (9)S. Naiditch and J. E. Wreede, J. Vac. Sci. Techno/.,5, 54 (1968). (IO)H. M. Rietveld, Acta Crystallogr., 22, 151 (1967). (11)H. M. Rietveld, J. Appl. Cryst., 2, 65 (1969). (12)J. W. Reed and P. M. Harris, J. Chem. Phys., 35, 1730 (1961). (13)R. F. Marzke and W. S . Glaunsinger, J. Phys. Chem., this Issue. (14)L. Pauling, "The Nature of the Chemical Bond", Cornell University Press, Ithaca, N.Y., 1960,p 403. (15)L. Pauling, ref 14,Chapter 7. (16)A. Braibanti, A. M. M.Lanfredi, M. A. Pellinghelll, and A. Tiripicchio, Acta Crystallogr., Sect. B, 27, 2261 (1971).
Discussion M. J. SIENKO. What would be the effect on the neutron diffraction results of a rotation or an oscillation of the ammonia group about an axis that is not the Ca-N axis? Could that account for the apparent two N-D bond lengths? R. VON DREELE. Any oscillation or rotation of a normal ammonia molecule about an axis that passes through or near the nitrogen, Le., near the center of mass, will not result in longer apparent N-D distances. If anything the N-D distances in this situation would appear to be shorter than they actually are. In any case, for the degree of thermal motion indicated in this structure such corrections would be of the order of 0.01 8, or less. W. GLAUNSINGER.Experimental evidence in favor of the structure of the ammonia molecule in Ca(NH3)6 derived from our neutron diffraction study is provided by the observed low-temperature proton NMR line width in Ca("3)6. Making the reasonable assumption that the intramolecular contribution to the proton line width is dominant and that the hydrogen'atoms in an ammonia molecule tunnel rapidly a t low temperatures, for the observed Gaussian line shapes the calculated line width is about 6 G for the conventional NH3 molecule and about 2 G for the NHs geometry found by neutron diffraction. The experimental line width of is in very good agreement with our about 2 G at 50 K in Ca("3)6 proposed neutron-diffraction structure. I would like to point out that further evidence for the unusual ammonia-molecule geometry found in our neutron diffractior: study could be obtained by investigating the N-H stretching region for the ammonia molecules in Ca(NH&.
The Journal of Physical Chemistry, Vol. 79, No. 26, 19?5
