765
DIFFRACTION PATTERN AND STRUCTURE OF AQUEOUS AMMONIUM HALIDE SOLUTIONS
Diffraction Pattern and Structure of Aqueous Ammonium Halide Solutions’
by A. H. Narten Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 87880 (Receiued August 7, 1969)
The scattering of X-rays from aqueous ammonium chloride, bromide, and iodide solutions ( N H X . -8HzO) has been measured and analy~edat 25’. Radial distribution functions for the three solutions are compared with previously obtained results for ammonium fluoride solutions and for pure water at the same temperature. Intensity and radial distribution functions calculated for the proposed ice-I model for water (Samoilov; Danford and Levy) are in excellent agreement with those derived from the diffraction data. This model describes the influence of C1-, Br-, and I- ions on water structure as deformation and expansion of the hydrogen-bonded network of water molecules, accompanied by an increase in the fraction of molecules in cavity positions.
Introduction For heteratomic liquids such as water the analysis of X-ray scattering data yields intensity and radial distribution functions which contain information about average atomic and molecular configurations. This information cannot be deduced uniquely from the diffraction data. However, assumptions about the average arrangement of molecules with respect to each other may be made, and such a model of liquid structure can be tested against the observations. A considerable amount of evidence2J supports the idea that the hydrogen bonds in liquid water form an extensive three-dimensional network, the detailed features of which are short-lived. Such a structure may arise in a variety of ways from units of nearly tetrahedral symmetry. Most of the proposed models for water are either incompatible with observed X-ray scattering or insufficiently defined for adequate testing. Only the ice-I model proposed by Samoilov6and specified in detail by Danford and Levye has been s h o ~ n ~ to give agreement with both large and small angle X-ray scattering data. This model assumes that the hydrogen-bonded network of water molecules is (on the average, and over short distances from any origin molecule) closely related to a slightly expanded ice-I lattice.* The average structure of this network is very open, with spaces between the groups of molecules in tetrahedral coordination sufficiently large to accommodate additional water molecules. The ice-I model also describes quantitatively the radial distribution in aqueous solutions of nearly tetrahedral molecules9J0 and In particular, the idea that ammonium ions can replace water molecules without much change in the average molecular arrangement13 is strongly supported by X-ray diffraction studies.“ Thus, aqueous ammonium halide solutions may be considered, to a good approximation, as solutions of halide ions in water, and the effect of the ammonium salts on water structure may be regarded as arising primarily from the anions alone. Also, the distribution of electron density in H2O and NH4f is not
sufficiently different for the X-ray method to distinguish between the two species, and this leads to a significant simplification in the interpretation of the diffraction data.
Experimental Section The scattering of monochromatic Mo K a X-rays from aqueous ammonium chloride, bromide, and iodide solutions (NH4X -8H20)has been measured at 25”. Preparation of the solutions, the diff ractometer, the procedure for data collection, the various corrections applied to the raw data, and the final reduction of the data have been discussed in detail e l ~ e w h e r e . ’ ~ ~Both ’~ the raw data and the reduced intensity and radial distribution functions derived from them are available in tabulated form.15 Only a short definition of terms will be given here. Let 47rr2pa8(r) be a distribution function giving the probability that distinct pairs of atoms of type a, P !(1)~ Research
sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation. (2) J. L. Kavanau, “Water and Solute-Water Interactions,” HoldenDay, Inc., San Francisco, Calif., 1964. (3) D . Eisenberg and W. Kaurmann, “The Structure and Properties of Water,” Oxford University Press, New York, N. Y., 1969. (4) A. H. Narten and H. A. Levy, Science, 165, 447 (1969). (5) 0. Y. Samoilov, Zh. Fiz. Chim., 20, 1411 (1946). (6) M. D. Danford and H. A. Levy, J. Amer. Chem. Soc., 84, 3965 (1962). (7) A. H . Narten, M. D . Danford, and H. A. Levy, Discussions Faraday SOC.,43,97 (1967). (8) S. W. Peterson and H. A. Levy, Acta Cryst., 10,70 (1957). (9) A. H. Narten, J . Chem. Phys., 49, 1692 (1968). (10) C. Folrer and A. H. Narten, presented at the Eighth International Congress of Crystallography, Stony Brook, N . Y., Aug 7-24, 1969, and published in the Proceedings. (11) M. D . Danford, “Diffraction Pattern and Structure of Aqueous Ammonium Fluoride Solutions,” ORNL-4244 (1968). (12) A. W. Narten and S. Lindenbaum, J . Chem. Phgs., 51, 1108 (1969). (13) K. Fajans and 0. Johnson, J . Amer. Chem. Soc., 64, 668 (1942). (14) H. A. Levy, M. D. Danford, and A. H. Narten, “Data Collection and Evaluation with an X-Ray Diffractometer Designed for the Study of Liquid Structure,” ORNL-3960 (1966). (15) A. H . Narten, “X-Ray Diffraction Data on Aqueous Ammonium Halide Solutions at 25O,” ORNL-4367 (1969). Volume 74, Number 4
February 19, 1970
766
A. H. NARTEN
are to be found separated by a distance r. The functions pap(r) represent the average distribution of pairs both over time and over the volume of the sample. In these terms, the scattered intensity becomes4
p,! ...._ ,,3(--), and p, Random Distance Distribution ! C )
X-Ray Radial Distribution Functions G(r1
m
i(s)-I(s)/n -
fiz(s) = i=l
m
m
cc
n m
fa(s>fp(s)
a = l j3=1
J0 4+[Pap(r)
- pol
x
sin (sr)/sr dr
(1)
in which a stoichiometric unit containing rn atoms is visualized as representative of the whole sample, which contains n such units. The angular variable s is defined as (4a/h) sin 8, with h the X-ray wavelength and 29
8.53 HO ,
1 -
H,O
-
8
9
",GI
*
NH,
F. X
m
the scattering angle. The term
f$z((s)
is the indepen-
iP1
dent atomic scattering, and the reduced intensity i(s) is the structurally sensitive part of I(s)/n, the measured intensity normalized t o one stoichiometric unit. The bulk number density of stoichiometric units (H20),(NH4+),X,- is denoted by poJ5 and y being mole fractions (x 2y = 1). The atom pair distribution functions p a p ( r ) are not obtainable individually from a single diffraction experiment. It is nevertheless useful to construct a modified radial distribution function (RDF) by Fourier transformation, namely
+
m 7 n
D(r)
3
a=l p=1
+
DaB(r) = 4ar2po (2r/n)
1-
si(s)M(s)sin(sr)ds (2)
0
&tJ..
2
3
4
-0 2
3
4
5
6
7
--ri%)Figure 1. X-Ray distribution functions for aqueous ammonium halide solutions. Resolution of near-neighbor interactions between halide and water (W) based on ice I model of Figure 3.
G(r) D ( ~ ) / 4 d p o (3) which approaches unity for large values of r . The function G(r) should not be confused with the atom pair correlation function g(r) to which it would be equal only if f a ( s ) f p ( s ) M ( s )= 1, for all a,p.
curves for pure water" and for two ammonium fluoride solutions" studied previously. The curves for the ammonium fluoride solutions are very similar t o the R D F of pure water, and the significance of small differences has been discussed elsewhere.l1 Throughout the following discussion, the term water (W) will be used to describe interactions involving the oxygen atoms of water molecules and/or the nitrogen atoms of ammonium ions (indistinguishoablein this treatment). The maximum at 2.85 A in the R D F of pure water (Figure 1) corresponds to -4.4 interactions between oxygen atoms.7 A corresponding water-water interaction is visible as a shoulder in the chloride and bromide solutions, and RS a partially resolved maximum at 2.91 in the ammonium iodiie solution. The halide-water interaction occurs $t 3.2 A for the chloride, 3.3 for the bromide, and 3.6 A for the iodide solution. A distinct shoulder on the short-distance side of the water-water peak in the NHJ solution (less pronounced in the NH4Brsolution, and not resolved in NH&I) must be ascribed to interactions between hydrogen atoms and
Results Observed Difraction Pattern. Radial distribution functions for the three ammonium halide solutions studied here are shown in Figure 1, together with the
(16) J. Waser and V. Sohomaker, Rev. Mod. Phys.,25, 671 (1953). (17) A. H. Narten, M. D. Danford, and H. A. Levy, "X-Ray Diffraction Data on Liquid Water in the Temperature Range 4-2OO0C," ORNL-3997 (1966).
with M ( s )
=
La:,
fa(s)
for s
smax,the maximum
values of s accessible in scattering experiments, and M ( s ) = 0 otherwise. Introduction of this modification function into (2) makes the product f a ( s ) f s ( s ) M ( s ) nearly independent of s and, thus, removes from the resulting R D F the average breadth of the distribution of electron density in the atoms. The relationship between component X-ray pair distribution functions Dap(r) and 4nr2pas(r)is one of convolution.l8 A convenient way to present radial distribution functions for liquids of different density po is to introduce a normalized R D F
The Journal of Physical Chemistry
DIFFRACTION PATTERN AND STRUCTURE OF AQUEOUS AMMONIUM HALIDESOLUTIONS halide ions. Since these interactions contribute to the R D F in proportion to the product f&of the X-ray form factors of hydrogen and halide, that is proportional to 54 : 36 : 18: 10 from iodide to fluoride, one would not expect their resolution for the chloride and fluoride solutions. In the iodide solution, this shoulder is most pronounced and occurs around 2.6 8;since this distance is very nearly equal to the difference between W . .I(3.6 d) and the intramolecular W-H (-1 d) distance, the conclusion is that some water molecules (ammonium ions) have average orientations such that one W-H. .I- angle is close to 180". Although there is no reasonable doubt about the preceiing interpret+ tion of the R D F features below-4 A, quantitative resolution of these peaks and shoulders is quite uncertain without additional assumptions. Proposed Model. I n water and in the ammonium fluoride solutions, each water molecule (or ion) has an average of -4.4 first neighbors, indicating predominantly tetrahedral coordination. Further evidence for tetrahedral coordination comes from the sequence of positions of maxima and minima in the R D F (Figure 1): there is a high concentration of neighbors centered around an average distance rl = r0(8/3)"', with ro the first neighbor water-water peak, for all curves in Figure 1. Furthermore, the broad minima and maxima around 5.5 A and 7 A roughly coincide with distances of low and high atom pair concentrations expected for a slightly expanded ice-I lattice. It has already been mentioned that the proposed ice-I models*bdescribes the radial distribution in water' and the ammonium fluoride solutions" quantitatively. Intensity and radial distribution functions calculated for this model are also in excellent agreement with the X-ray data for
767
the ammonium chloride, bromide, and iodide solutions (Figures 1 and 2). This model describes the average short-range order in liquid water in terms of a slightly expanded ice-1like network of hydrogen-bonded water molecules, each network molecule being tetrahedrally surrounded by four others. Three of these network neighbors occur at an average distance PI,and the fourth at an average distance Pz (in the solid P1 ~ 1P! 2 ) . The structure of this network is very open, with spaces between the groups of molecules in tetrahedral coordination sufficiently large to accommodate additional water molecules a t a distance Pa from the nearest network molecule (these cavities are not occupied in solid ice-I). In pure water,' about half the cavities are occupied by "interstitial" molecules which interact with the network by less directional but by no means negligible forces. The complexity of the first coordination shell is explained by the model in terms of the distinctly different average environments of network and cavity molecules. However, both of these "species" exist in environments which are distorted from the average, and these distortions are implied by sizeable root-mean-square (rms) variations in interatomic distance. The parameters of the ice-I model for the ammonium fluoride solutions1' are very similar to those of pure water a t the same temperature, and Danford" concluded that the nearly tetrahedral NH4+ and F- ions A
08 04
NH G I . 853 H
00 -04
-0.8 0.8 0.4
-
2 0.0 2-04
-0.8
U 04 0.0 -0 4
+ 4 + OBSERVED - CALCULATED
-0.8 -1.2
'
1
'
~
"
"
"
'
~
'
1
'
'
'
'
'
I
,
'
1
'
1
'
1
,
I
Figure 2. Reduced intensity functions for aqueous ammonium halide solutions. Calculated curves for i c e 4 model of Figure 3.
Figure 3. Average arrangement of water molecules and ammonium ions around a halide ion (ice-I model). Each halide ion has six neighbors at a distance Pa, point symmetry DSh. Each water molecule (ammonium ion) has three water (ammonium) neighbors a t a distance PI,of which only two are shown, and one neighbor at a distance P2 (Table I). The six water molecules (ammonium ions) are oriented such that one hydrogen atom points toward the halide ion. Large instantaneous distortions from this average configuration occur in the solutions. Volume 74, Number 4 February 19, 1970
768
A. H. NARTEN
0
8 0
-ti t-
8
m
9 0
-ti 0)
r 0
can replace a water molecule in either a network or cavity 'position. The same assumption was therefore made for the ammonium ions in the chloride, bromide, and iodide solutions. I n contrast, the large and spherically symmetric chloride, bromide, and iodide ions were assumed to occupy cavity position only. Some relevant parameters of the model for water and the ammonium halide solutions are summarized in Table I. While the PI distance between network molecules (Figure 3) remains nearly constant, the P2 distance increases drastically from water and the ammonium fluoride solutions to the chloride, bromide, and iodide solutions. The rms variation in the P2 interaction shows a corresponding increase, indicating that there is a wide distribution of instantaneous P2 distances about the mean value. This may be taken as an indication that the hydrogen-bonded network is severely distorted from the average, so that the cavities occupied by chloride, bromide, and iodide ions are much larger than those containing a water molecule. While in water and in the ammonium fluoride solutions only about half of the cavities are occupied, this fraction increases with the size of the halide ion until all cavities are occupied by water molecules or ions in the case of the iodide solution (Table I). At the same time, the interactions between cavity water molecules and the network, as well as between cavity water molecules and the chloride, bromide, or iodide ions, become so diffuse that they give rise to uniform distributions of average distances.
Conclusions 01
8 $1
3
0
01
8
$1
? 0
The Journal of Physical Chemistrld
The effect of chloride, bromide, and iodide ions on the structure of liquid water at 25", insofar as it can be deduced from the RDF directly, thus seems to be twofold : the average distance betweoen near-neighbor wate? molecules increases from 2.85 A in pure water to 2.91 A in NHJ, indicating weaker hydrogen bonding in the solutions. At the same time, the average number of nearest (water-water) neighbors decreases significantly, and this may be taken as an indication that not only the average strength but also the average number of hydrogen bonds per water molecule is smaller in the chloride, bromide, and iodide solutions than in pure water and in the ammonium fluoride solutions. I n terms of the ice-I model, the influence of halide ions on water structure can be summarized as follows. In order to accommodate the relatively large chloride, bromide, and iodide ions, the hydrogen-bonded network of water molecules expands anisotropically; in this way, each water molecule in the network retains three nearest water neighbors within hydrogen-bond distance, while the bond corresponding to the P2 distance is broken (Figure 3). At the same time, the fraction of water molecules in cavity positions increases significantly from chloride to iodide; i.e., the degree to randomness of the system increases.
