Structure and therm al properties associated with some hydrogen bonds in crystals IV. Isotope effects in some acid phosphates

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Interaction between adsorbed substances. I I 399 R eferen ces Adam, N. K. 1938 The physics and chemistry of surfaces. 2n Adam, N. K., Askew, F. A. and Pankhurst, K. G. A. 1939 Proc. Roy. A, 170, 485.

1 Interaction between adsorbed substances. I I 399 R eferen ces Adam, N. K The physics and chemistry of surfaces. 2n Adam, N. K., Askew, F. A. and Pankhurst, K. G. A Proc. Roy. A, 170, 485. Guastalla, J G.R. Acad. Sci., Paris,189, 241. Langmuir, I J. Amer. Ghem. Soc. 39, Sawai, I Trans. Faraday Soc. 31, 765. Structure and therm al properties associated with some hydrogen bonds in crystals IV. Isotope effects in some acid phosphates By A. R. U bbelohde and I. W oodward ( Communicated by S ir W illiam Bragg, F.R.S. Received 4 A p ril 1941) [Plate 43] The isotope effect has been measured for (NH4)H2P 0 4. Expansion of the crystal lattice takes place on substituting deuterium for hydrogen. The expansion is in the direction of the hydrogen bonds, and is of the same magnitude as in the isomorphous KH2P 0 4. A contraction of the lattice at right angles to the plane containing the hydrogen bonds is considerably larger for (NH4)H2P 0 4 than for KH2P 0 4. From an application of the calculus of errors, the accuracy of the results is estimated to be axl = ± , a 33 = - < ± Further investigations on the monoclinic form of KD2P 0 4 has shown the presence of curious diffuse reflexions in moving-film photographs. Attempts to obtain (NH4)D2P 0 4 or KH2P 0 4 in the monoclinic structure were unsuccessful. In acid phosphates of the general formulae MH2P 0 4 and M2H P 0 4, it is possible to make comparatively small perturbations in the structure of crystals, both by varying the positive ion, and by substituting deuterium for hydrogen. As was described in previous publications, one effect of substituting deuterium for hydrogen in K H 2P 0 4 is that the acid phosphate crystallizes spontaneously from solution in a new form (Ubbelohde and Woodward 1939; Ubbelohde 19396). The tetragonal form of K D 2P 0 4 could

2 400 A. R. Ubbelohde and I. W oodw ard only be obtained by special nucleation, and when compared with the tetragonal form of KH2P 0 4 it showed an expansion of the crystal lattice in the direction of the deuterium bonds. Experiments described in the present paper were carried out to obtain fresh information on the role of hydrogen bonds in determining the structure of acid phosphates. Preliminary information on the structure of the monoclinic form of KD2P 0 4 includes studies of intensities of X-ray reflexions, of pyro-electric properties, and of the curious streaks in moving-film X-ray photographs of single crystals. Further light on the occurrence of the monoclinic form of KD2P 0 4 was also obtained from experiments on the structure and isotope effects of (NH4)H2P 0 4. Attempts to obtain the monoclinic forms of (ND4)D2P 0 4 and of KH2P 0 4 were unsuccessful. The main conclusion from all these experiments is that in the acid phosphates the hydrogen bonds must make a contribution to the lattice structure such that quite different arrangements of atoms can have much the same stability and lattice freeenergy. This may have an important bearing on the thermodynamical properties of the crystals. The isotope effect for (NH4)H2P 0 4 The monoclinic form of (ND4)D2P 0 4. It was shown by Hassel (1925; cf. Wyckoff 1931) that (NH4)H2P 0 4 is isomorphous with KH2P 0 4, and crystallizes in the tetragonal sphenoidal system, space group a b = 7-53 A, c 7-54 A, with four molecules to the unit cell. If (ND4)D2P 0 4 showed a behaviour similar to KD2P 0 4, and could be crystallized in both tetragonal and monoclinic forms, much information about the structure could be obtained by comparing intensities of X-ray reflexions in isomorphous potassium and ammonium salts. To test this possibility, (ND4)D2P 0 4 was prepared by repeated crystallization of (NH4)H2P 0 4 of analytical purity from D20. The final crystallizations were made from 99-6 % D20, so as to leave approximately this proportion of deuterium atoms in the product. In contrast with the behaviour of KD2P 0 4, it was found that in all spontaneous crystallizations of (ND4)D2P 0 4 from supersaturated solutions of varying concentration, only tetragonal crystals were obtained. A further attempt to obtain a monoclinic form of the ammonium salt was made by dropping freshly prepared nuclei of monoclinic KD2P 0 4 into supersaturated solutions of (ND4)D2P 0 4 in 99-6% D20. The crystals obtained could frequently be identified by their external habit, but in doubtful cases the crystal form was identified by taking X-ray rotation photographs. Only

3 Isotope effects in acid phosphat the tetragonal form was found. Even the small crystallites adhering firmly to the needle of monoclinic KD2P 0 4 were found to be tetragonal crystals of (ND4)D2P 0 4, on examination with a low-power microscope. Preferred directions of growth of these crystallites, relative to the nucleating crystal, were evident on visual inspection, but could not be established with great precision. The c axis of the growths made an angle of about 20 with the (001) plane of the nucleating crystal. The conclusion from these nucleation experiments is that (ND4)D2P 0 4 shows far less tendency to crystallize in a monoclinic form than KD2P 0 4. The failure to obtain the ammonium crystals in a monoclinic form makes investigations of the structure of the potassium salt much more difficult. The tetragonal form of (ND4)D2P 0 4. Lattice spacings of the deuterium and hydrogen compounds were compared using a multiple exposure X-ray spectrometer (Ubbelohde 1939a). To minimize errors due to absorption, all the crystals used were of similar size and shape. Oscillation and some rotation photographs were taken with crystals mounted for both a and c axes, and unfiltered Cu K radiation from a gas tube was used so as to give /? as well as cc reflexions. In a tetragonal crystal, the axes of the expansion ellipsoid coincide with the crystal axes, and are equal in the direction of the a and b axes. The expansion a' along a plane normally inclined at an angle to the c axis is given by the simple expression a' = A + where an = a22 = A Twelve such equations, each obtained from the mean of several independent measurements of a', were used to calculate the best values of A and B by the method of least squares. The best values were found to be A = ± , = ± , from which an and a33 can at once be calculated. In view of present refinements in the theory of bond lengths in crystals, it is highly desirable to have a reliable estimate of the range of uncertainty attached to any experimental results. For actual bond lengths, such as tha t of hydrogen bonds as determined by Fourier methods, estimates of ranges of uncertainty present a problem not yet completely solved, owing to the fact that no systematic calculus of errors has been devised (Robertson and Woodward 1936; Brill, Hermann and Peters 1939; Robertson 1940). The magnitude of isotope effects can be determined with much greater precision than that of actual bond lengths, both on account of the fact that relative

402 A. R. Ubbelohde and I. Woodward measurements are involved, and because a standard calculus of errors is directly applicable to the results (Whittaker and Robinson 1937).

4 402 A. R. Ubbelohde and I. Woodward measurements are involved, and because a standard calculus of errors is directly applicable to the results (Whittaker and Robinson 1937). To apply this calculus to obtain the probable errors in the values of <x13l and (X33, the original equations are preferably rewritten in the form a' = au [l cos 2 ]/2 + a33[l + cos 2 ]/2. Standard methods when applied to the twelve independent values of a give au = + 0*00269 ± 0*00006, <*33 = - 0*00123 ± 0* A plot of the smoothed curve showing expansion in different directions is given for comparison with the observed values of &' in figure 1, and a polar diagram showing the relation of the expansions to the approximate positions of the hydrogen bonds in the crystal is given in figure 2 (plate 43). e axis minimum F igure 1. Lattice deformation (isotope effect, D for H) for (NH4)H8P 0 4. It will be noted that the isotope effect (D for H) in (NH4)H2P 0 4 is closely similar in direction and magnitude to the effect in tetragonal KH2P 0 4. (An obvious misprint occurs in III, p. 422, but the correct figures are given in the adjoining diagram.) This makes it all the more puzzling that the monoclinic form of the ammonium salt has not yet been obtained. Further points are discussed below. The monoclinic form of KD2P 0 4 In addition to using the tests previously described (Ubbelohde 19396), the chemical identity of the crystals was verified from direct phosphate analyses on a semi-micro scale, using single crystals whose monoclinic structure was previously established by X-ray rotation photographs. An average content of P20 5 found for the monoclinic crystals of KD2P 0 4 was 51*47 % (theory 51*64 %). Together with the molecular weight determination from the X-ray data, this evidence excludes any simple acid salt other

Isotope effects in acid phosphates 403 than KD2P 0 4, and is probably as definite as can be obtained with comparatively small amounts of material.

5 Isotope effects in acid phosphates 403 than KD2P 0 4, and is probably as definite as can be obtained with comparatively small amounts of material. The fact that repeated crystallization from pure 99*6 % DaO gave the same salt as crystallization from the original mother liquors is a further argument against any acid salt of composition other than KD2P 0 4. One or two tetragonal crystals were occasionally found amongst the mass of monoclinic crystals of KD2P 0 4 which separate from supersaturated solutions. In order to minimize the effects of slow reversion to the tetragonal form (see below) X-ray studies were usually carried out with crystals separated from solution shortly before exposure. The crystal axes as determined by rotation photographs were found to be (cf. Ubbelohde and Woodward 1939) a = 7-37 ±0-01 A, 6 = ± 0-01 A, c = 7-17 ± 0-01 A; 92. It is estimated that any systematic errors in the above results are unlikely to exceed the order of magnitude of the random errors, which have been calculated according to standard methods, and are as indicated. Moving-film rotation photographs of the zero layer lines for the three axes of monoclinic KD2P 0 4 show that the (0&0) reflexion is halved when k is odd. (On a well-exposed film this was observed up to = 15.) No other halvings are present, so that the space group is C\ P2V A notable feature of the (hko) zone is that the reflexions are very much stronger when h is even. The reflexions are particularly strong and uniform when and are practically absent when h 1. On immersion into liquid air, the crystals develop a strong polarity in the direction of the b axis. A marked cleavage is exhibited parallel to the (001) face, and a less pronounced cleavage parallel to the (100). After immersion in liquid air the (001) cleavage is still more marked. The development of faces in the (M0) and (0 hi)zones is asymmetric, confirming the p the crystal. R eversion op monoclinic to tetragonal crystals When finely powdered, the monoclinic form appears to revert to the tetragonal form of KD2P 0 4 within a few days. For larger crystals, reversion is slower. One specimen, with a, b, c approximately 0-6, 1-0, 2-4 mm., has been investigated with fixed and moving-film rotation photographs during a period of 14 months. Whilst there has been a growth of powder rings, and of splitting into small crystallites, the reflexions characteristic of the original crystal still persist. Certain reflexions, such as the (102), remain undivided and well defined during the change, whereas reflexions such as that corre

404 A. R. Ubbelohde and I. Woodward sponding to (200) show that splitting into crystallites takes place in preferred directions, in this instance with rotation about the 6 axis.

6 404 A. R. Ubbelohde and I. Woodward sponding to (200) show that splitting into crystallites takes place in preferred directions, in this instance with rotation about the 6 axis. The persistence of some small spacing planes is noteworthy, such as (702) and (604). Furthermore, inspection of another monoclinic crystal after 10 months exposure to the atmosphere, on a Hutchinson goniometer, showed that after this interval there was much diffuseness in the reflexion from the (100), but not from the (010) face. These and similar observations show that although a partial rearrangement of the atoms slowly takes place in the monoclinic crystals, the increased stability does not appear to be sufficient to lead to a very radical break up of the original structure. Diffuse reflexions from freshly prepared MONOCLINIC CRYSTALS A remarkable feature of moving-film photographs of crystals of KD2P 0 4, even when freshly separated from solution, is the occurrence of diffuse reflexion streaks, whose intensity is comparable with that of the sharp reflexions (cf. figure 3, plate 43). To verify that these were not due to white radiation from the gas tube used (filtered Cu Koc radiation), a standard crystal of oxalic acid dihydrate was mounted on the second spindle of a two-crystal moving-film spectrometer (Robertson 1934). Although the sharp reflexions from the oxalic acid were much more intense than those from the KD2P 0 4 exposed at the same time, there were practically no streaks connected with them. This showed that the phenomenon was not primarily connected with white radiation from the tube. The streaks in KD2P 0 4 also showed characteristic differences for rotations about the three axes. For c axis rotations, streaks occurred in the sequence of moderately strong sharp reflexions. For example, the approximate centres of large spacing streaks corresponded with the weak or absent (hko) reflexions with h odd. There was no obvious correlation between streaks and Bragg reflexions in rotations about the other axes. Special features illustrated in figure 3 (plate 43) are (1) That streaks are frequently independent of any Bragg reflexions, as at (a). (2) That the extension of streaks with decreasing Bragg angle is very variable; in (6) and (c) the streaks end at approximately 0 = 6, whereas at (d) the streaks persist to the very edge of the film. (3) In certain parts of the film streaks are grouped together in threes, with angular interval of about 7. Further comment on the diffuse reflexions is made below.

Ubbelohde & Woodward Proc. Roy. Soc.,, volume 179, plate 43 maximum expansion + 0 0027 F igure 2.

7 Ubbelohde & Woodward Proc. Roy. Soc.,, volume 179, plate 43 maximum expansion F igure 2. Isotope effect (D for H) in relation to hydrogen bond directions, which are within 2 or 3 of a axis. (Faciny p. 404)

Isotope effects in acid phosphates405 D iscussion The main conclusions from the experiments are as follows: (1) In (NH4)H2P 0 4 the replacement of H by D leads to an expansion of the crystal, at

8 Isotope effects in acid phosphates405 D iscussion The main conclusions from the experiments are as follows: (1) In (NH4)H2P 0 4 the replacement of H by D leads to an expansion of the crystal, at right angles to the c axis. Assuming that the hydrogen bonds lie nearly parallel to the (001) plane, as in the isomorphous KH2P 0 4, this implies that the hydrogen bonds expand on substituting deuterium. Within the experimental error, the expansion is the same as in KH2P 0 4, though the contraction at right angles is some three times as large in the ammonium salts. By applying the calculus of errors, a comparatively high accuracy can be attained in the measurement of isotope effects. (2) No definitive attempt can yet be made at calculating the detailed structure of monoclinic KD2P 0 4. This is partly due to lack of isomorphous salts, and partly to the streaks or diffuse reflexions which are a prominent feature in moving-film X-ray photographs of this salt. The high absorption coefficient (p = 147 per cm. for A = 1*54) imposed a further limitation on estimates of the absolute intensities of reflexion from single crystals. It may be noted that after assuming a model of the phosphate group, there are still 32 parameters to be adjusted in proposing a trial structure. Tentative conclusions can, however, be drawn about the positions of the potassium atoms, since these are the dominating factors governing the intensity of the large spacing planes. The strength and uniformity of the (OfcO) series, when k is even, suggests that the potassium atoms lie near to planes parallel to (010), and a distance \b apart. Inspection of the axial series, and the (hko) projection, suggests that the projections of the potassium atoms are displaced from the corners of rectangles, with edges fa, fc. The distance between adjacent potassium atoms is of the order 3*7 A. (3) A comparison of (NH4)H2P 0 4 with KH2P 0 4 suggests that the ammonium ion may have only a tetrahedral symmetry at the temperature investigated. This suggestion is of some interest in view of possible rotational transitions in the phosphates (cf. Annual Reports 1940). Thermal investigations are being carried out on these crystals, but in the meantime a brief summary may be given of the structural evidence. From a detailed study of the structure of KH2P 0 4 (West 1930), it was concluded that the phosphate ion probably exhibited a slight distortion from tetrahedral symmetry. Each potassium atom was found to be surrounded by eight oxygen atoms, four at a distance of 2*79 A and four at a distance of 2*81 A. The shortest distance between oxygen atoms on neighbouring phosphate groups (i.e. the length of the hydrogen bond) was found

406 A. R. Ubbelohde and I. Woodward to be 2-54 A. An alternative structure, with phosphate groups showing complete tetrahedral symmetry, was not in such good agreement with the experimental results.

9 406 A. R. Ubbelohde and I. Woodward to be 2-54 A. An alternative structure, with phosphate groups showing complete tetrahedral symmetry, was not in such good agreement with the experimental results. In this structure, the K O distances were 2*82 A, and the length of the hydrogen bond 2-48 A. When either of these phosphate groups is inserted into the lattice of (NH4)H2P 0 4, placing the phosphorus and nitrogen atoms at positions corresponding with phosphorus and potassium atoms in KH2P 0 4, the following results are calculated: H bond distorted phosphate ion 2-57 A tetrahedral phosphate ion 2-53 A distance (NH4) O 4 O atoms at 3-06 A 4 O atoms at 2-91 A 4 O atoms at 3-13 A 4 O atoms at 2-89 A Unlike the potassium ion, which is surrounded by eight oxygen atoms at practically equal distances, it will be seen that the ammonium ion appears to behave like a sphere deformed by tetrahedral bulges. Some uncertainty attaches to calculations of the greatest and least radii of this deformed sphere, but the difference of radii is estimated to lie between 0* 15 and 0*24 A. The only way to avoid the conclusion that the ammonium ion behaves in this way is to equalize the (NH4) O distances, and this would involve a phosphate ion even more distorted than in West s model, and also an elongation of the hydrogen bond. From the close agreement in the magnitude of the isotope effect in the potassium and ammonium salts any great difference in the length of the hydrogen bond is unlikely. The fact that the ammonium salt shows a markedly bigger contraction (cf. figure 2) at right angles to the directions of the hydrogen bonds, on replacing H by D, than was observed for tetragonal KH2P 0 4, is probably associated with the longer c axis and more open packing in this direction in the ammonium salt. This might lead to a larger Poisson contraction accompanying the expansion of the hydrogen bonds. In view of the precision with which isotope effects can be measured, a knowledge of the coefficients of elasticity of the phosphate crystals in various directions would be of value, and might lead to a direct estimate of the strength of the hydrogen bond. Finally, attention may be drawn to the unsolved problem of the origin of the diffuse streaks in moving-film photographs of monoclinic KD2P 0 4. The possibility has not yet been completely eliminated that these are similar in origin to the diffuse spots observed for a variety of crystals when these are set up to give Laue reflexions (Preston 1939; W. H. Bragg 1940; Lonsdale, Knaggs and Smith 1940). With Cu K radiation, the fogging of the

Isotope effects in acid phosphat film was too extensive, on account of the high absorption of the crystals, to establish diffuse spots in Laue photographs of monoclinic K D 2P 0 4, but they were

10 Isotope effects in acid phosphat film was too extensive, on account of the high absorption of the crystals, to establish diffuse spots in Laue photographs of monoclinic K D 2P 0 4, but they were readily obtained using molybdenum radiation from the 5 kw tube. No complete correlation has yet been established between these diffuse spots and the streaks obtained in moving-film photographs, though the results emphasize the value of moving-film technique, in characterizing diffuse reflexions more completely than is possible from stationary photographs. An alternative possibility which is receiving attention is that the KD2P 0 4 crystals contain lattice imperfections which are essential for the stability of the monoclinic structure. If the single crystals were merely strained owing to their rapid separation from solution, and exhibited various types o f slip, it would be difficult to explain why KH2P 0 4 does not show streaks in moving-film photographs in corresponding intensity, or alternatively, why KD2P 0 4 does not at once separate in the tetragonal unstrained form. Further discussion of the curious behaviour of KD2P 0 4 must await fresh experimental information. Thanks are due to the Managers of the Royal Institution for the facilities provided, and to Mr H. Smith for his collaboration in some of the experiments. R eferences Ann. Rep. Chem. Soc. 1940, p Bragg, W. H Nature, Lond., 146, 509. Brill, Hermann and Peters 1939 p Hassel 1925 Z. Elektrochem. 31, 523. Lonsdale, Knaggs and Smith 1940 Nature, Lond., 146, 332. Preston 1939 Proc. Roy. Soc. A, 172, 116. Robertson 1934 Phil. Mag. 18, 729. Robertson 1940 Trans. Faraday Soc. 36, 913. Robertson and Woodward 1936 J. Chem. Soc. p Ubbelohde 1939 a J. Sci. Inatrum. 16, 155. Ubbelohde Proc. Roy. Soc. A, 173, 417. Ubbelohde and Woodward 1939 Nature, Lond., 144, 632. West 1930 Z. Kri8tallogr. 174, 306. Whittaker and Robinson 1937 Calculus of observations. Blackie. WyckofF 1931 Structure of crystals. Chemical Catalog Company.

SOLID STATE 18. Reciprocal Space

SOLID STATE 18. Reciprocal Space SOLID STATE 8 Reciprocal Space Wave vectors and the concept of K-space can simplify the explanation of several properties of the solid state. They will be introduced to provide more information on diffraction