T H E CRYSTAL STRUCTURE O F POTASSIUM BY E. POSNJAIC
Introduction Among the large number of substances which have at one time or another been X-rayed, the record for potassium is, in a way, a singular one. According to the record no regular diffraction of X-rays, but only a so-called general scattering is obtained a t room temperature by the usual powder method. The first to investigate the crystal structure of the alkali metals was A. W. Hull.’ He reports encountering considerable difficulties in obtaining X-ray diffractions from sodium and lithium and the failure t o obtain any from potassium. The observation that no diffraction was obtained from samples made from freshly melted sodium and lithium and that even samples made from old stock produced a large amount of continuous scattering led him to believe that sodium and lithium were only partly crystalline and that the potassium must be completely amorphous. Later McKeehan2 reinvestigated potassium. He found that if the potassium is cooled to - I~o’, weak reflections as from large crystals are obtained; however, he says that this “crystalline structure does not persist when the temperature is allowed to rise again to about 20O.l’ The conclusion derived from X-ray experiments, that potassium must be amorphous a t room temperature, is very surprising, as the fractured surface of potassium shows brilliant facets and well-defined crystals have been grown even from the molten metal3; and further, of course, because potassium has a definite and sharp melting and freezing point. It is not quite conceivable that an amorphous substance could possess such properties, and R. W. G. Wyckoff4 in discussing this case in his book on “The Structure of Crystals” tries t o explain these conflicting facts by the assumption, not that potassium is an amorphous substance, but that the amplitudes of the thermal vibrations of potassium atoms a t room temperature are so great as to “obliterate the crystalline diffraction maxima.” We do not need, however, to go into the details of this discussion, as it will be shown below that the assumption is unnecessary. The reason for mentioning it is chiefly to call attention to the danger of drawing definite conclusions and of putting too much reliance on a few negative results of X-ray experimentation. The present investigation grew out of experiments on non-crystalline substances, of which potassium was supposed to be one. Contrary to such statements, every sample of potassium that was X-rayed in this investigation Phgs. Rev., 10, 661 ( 1 9 1 7 ) . Proc. S a t . Acad. Sci., 8, 254 (1922). 3C. E Long: J. Chem. S O C ,13, 122 (1860); F. Schroedler: Ann., 20. Pleischl: J. prakt. Chem., 31, 4j (1844). 4 Wyckoff: “The Structure of Crystals,” 372-373 (1924). 2
2
(1836); A .
THE CRYSTAL STRUCTURE OF POThSSIUM
355
showed normal diffraction effects. I n view of this, and for comparison results, a few preparations of sodium and one of lithium were made and X-rayed. These substances also in each case gave definite diffraction effects, which were in good agreement with previous determinations of their crystal structure, and only a short statement concerning these experiments will therefore be given below.
Experimental Part Material and preparation of samples. Metallic potassium from two different sources was used in this work. The stock of one had been in this Laboratory for more than ten or fifteen years and had been originally obtained from the firm of Eimer and Amend. The other was specially obtained for the present experiments from the J. T. Baker Chemical Company (lot S S j2827). Their melting and their freezing points were determined approximately and found to lie close to 6 z 0 , which is very near the accepted value for potassium. Owing to the original interest in potassium as a supposedly non-crystalline substance, Hull’s observation, that the freshly melted or distilled alkali metals appeared to be in an amorphous condition, served to indicate the way of preparing such samples. After some trials, it was found that a thin capillary tube could readily be filled with potassium when the metal was in the molten condition. The following simple procedure was used. X Pyrex tube about 30 cm long and about 2 cm in diameter was sealed off at one end, and a side tube with a good stopcock was sealed on near the open end of the tube. Drawing out a piece of “Jena Cerate Glas” tubing partly into a thin capillary, and inserting the sealed-off end of this tube into a rubber stopper, the length of the capillary was adjusted so that when the rubber stopper with the drawn-out capillary was inserted into the open end of the Pyrex tube, the end of the capillary was about z or 3 mm above the bottom of the Pyrex tube. Pieces of potassium were cut free from crusts and were quickly placed in the tube by taking out the rubber stopper with the capillary projecting into the tube, which was then immediately put back and the whole evacuated by attaching the side tube with the glass stopcock to a pump. After the tube and the capillary inside of it were well evacuated, the pieces of potassium, which were all placed along the side of the tube, were gently heated to cause the metal to melt and to flow to the bottom of the tube. The capillary was then dipping directly into the molten metal. The oxide, which could not be prevented from forming during the cutting of the pieces of potassium and their insertion into the tube, usually stuck to the walls of the tube or floated on the surface of the metal. By suddenly letting a sufficient amount of nitrogen into the tube through the glass stopcock connection, some of the potassium which was about 15 to 20’ above its melting point was forced into the capillary and almost immediately solidified there. After allowing the tube to cool off, the stopcock was opened to relieve the vacuum, and the rubber stopper with the capillary was taken out. A suitable length of the capillary filled with potassium, which was approximately 0.5 mm in
356
E. POSNJAK
diameter, was then sealed off a t both ends. This was done by very quick heating and drawing out of the glass, and required for its successful accomplishment a little practice, as overheating caused the metal to react with the glass. This rather detailed description of the preparation of the samples is given on account of the disagreement of the present findings with the former investigations, and because it is thought that the reason for the different findings must lie in the preparation of the sample of potassium. The samples prepared in this way, on exposure t o X-rays by the powder method, were found to give diffraction spots, some only a few while others produced a considerable number of spots. It was quite obvious that this was due to the size and number of crystals present in the sample. T o increase the number and reduce the size of the crystalline particles, heat treatment was resorted to. The samples were heated in water about zoo above the melting point of potassium and then quickly quenched by placing them in a salt solution a t about -18". A picture of a sample treated in this way showed a large increase in the number of diffraction spots. However, it seemed probable that the rate a t which crystals of potassium grew would make it very difficult to obtain by quenching a sufficiently fine-grained preparation and no special attempt in this direction was therefore made. Instead, the well-known method of rotating the sample was used and heattreated preparations were attached to a motor, which rotated them around their axis a t the rate of a revolution per minute during the exposure to X-rays. I n this way satisfactory diffraction pictures were obtained.
The diffraction data f r o m potassium and its crystal structure. The diffraction apparatus used was one made by the General Electric Company' in which the K a radiation of molybdenum is used and in which the distance between sample and photographic film is eight inches. The time of exposure was normal, approximately 250 m.a.h. Sodium chloride was used as usual for the standardization of the spacings. Spacing measurements of the diffraction lines recorded on a photographic film are given in the first column of Table I. The estimated relative intensities of these lines and the squares of the sines of their angles of reflection are given in columns two and three of the table. It is well known that the ratios of the sin20 should give for a cubic crystal values of whole numbers, which are usually small. As will be seen in column four this is the case within the limits of the experimental errors. These whole numbers represent the sum of (h2+k2+Z2) and serve to assign the indices of the planes producing the diffraction lines (columns five and six). I n the last column of Table I, the resulting value of the length of the edge of the unit cube is given for each observed diffraction line. Photographs were obtained from several other preparations and all gave practically identical results. The average values of the length of the edge of the unit cube for each preparation are given in Table 11. ~
W. P. Davey: Gen. Elect. Rev., 25, 565 (rgzz).
THE CRYSTAL STRUCTURE O F POTASSIUM
357
TABLE I Powder photographic data from potassium, Spacing
Estimated intensity
3,770 2.670
IO
2.170
6
I . 889
4
,677 1,537
3
I . 428
2
I
4
I
Ratios of sin20
sin20
0.00886 . O I768 ,02675 ,03530 ,0448 ,0533 , 0 6 1j
2
h?+k2+P
.Oj
2
4.05
4
6.06 8.00
6 8
IO. 15
IO
12.07
I2
‘3.98
I4
Average = 5.329
A
TABLE I1 Average value of a, from different samples. Film number
a0
I35 I45
5,335 5.334 5.329 5,333
170
I75
Average a, = 5.333 i 0.005 A. While not definitely established, it is probable that potassium crystallizes in the cubic system. A careful determination of the density of the alkali metals has been made by T. W.Richards and T. X . Brink‘, giving for potassium a t zoo the value of 0.862. Introducing this value in the usual equation aO3 = m M / p , where uO3is the volume of the cube, m the number of atoms of potassium within the unit, ,If the mass of the potassium atom and p the density of potassium, we find that ni = 2 . 0 2 . This is within experimental error a whole number, as it should be. Accepting, conversely, that two atoms are associated with the unit cell of potassium, the density of potassium calculated by the above formula assumes the value 0.851, which is in good agreement with the direct determination. The only possible cubic arrangement for two like atoms in the unit cell is the body-centered one, with the coordinates: 000;4 4 4. The characteristic structure factor of the body-centered cubic lattice requires that the sum of the indices must be an even number for reflection. As may be seen from Table I this requirement is fulfilled and no other reflections occur. We may further use the semi-empirical formula2
I
0:
(AZ
+ Bz) X
( d / ? ~ ) ?x . ~j
J. Am. Chem. SOC.,29, 1 1 7 (1907). Structure of Crystals,” 201 (1924).
* Wyokoff: “The
358
E . POSNJAK
to calculate for the different planes the intensity of reflection expected for the body-centered arrangement and compare these values, reduced to the same basis, with the estimates of the relative intensity made directly. The results in both cases are always only a rough approximation but a general agreement between the observed and calculated values will be readily seen from Table 111, confirming further the correctness of the body-centered cubic structure .
TABLE I11 Comparison between the observed and calculated intensities from the different reflecting planes of potassium. Indices
lntenaities observed
calculated
I10 (I)
10
IO0 ( 2 )
4
2.2
I12 ( I )
6
5.5
I 1 0 (2)
4 3
'30
(1)
I11 (2)
I
123
2
(I)
10.0
2.0
3.0 0.8 4.1
Experiments with sodzuni and lithium. As mentioned above, a few samples of sodium and one of lithium were made and X-rayed in the same manner as were those of potassium. 30 difficulties were experienced in preparing samples of sodium, but lithium reacted very readily with the glass, probably owing primarily to its higher melting-point. After several attempts a sample of lithium was prepared, which, although it was not so good as those used with the other metals and although it produced considerable general blackening of the film, gave, however, four diffraction lines. I n the former investigation of the structure of lithium by J. M. Bijvoet and A. Karssenl also only four diffraction lines were obtained and in view of the identical results it was not considered worth while to attempt preparing other samples. I n complete agreement with earlier determinations, the length of the side of the unit cube and for lithium 3 . 5 1 1. for sodium was found to be 4.30 Concerning general scatterzng from the alkali metals. Considerable stress has been laid on the general scatteririg obtained from the alkali metals, which was usually ascribed to the amorphous condition of the substance to a smaller or larger extent. The present experiments, while not carried far enough to find the direct cause of such scattering, strongly indicate that such an amorphous portioii in all probability does not exist in the metal. Little if any general scattering was obtained from carefully prepared samples of potassium, and a comparison experiment showed that the amount was approximately the same as that produced by sodium chloride exposed in a similar glass capillary for the same length of time. The observations made seem to indicate that the general scattering is due rather to the formation of films produced by oxidation, moisture or the interaction of the alkali metals with the glass. Some samples of sodium which were probably overheated showed a slight 1
Pror. Roy. .%cad. Sci. Amsterdam, 23, 1365 (1921); Rec. Trav. chim., 42, 859
(1923).
THE CRYSTAL STRUCTURE OF POTASSIUM
359
discoloration and produced more of the general scattering than others, and the sample of lithium, which of course had to be heated considerably higher, produced accordingly a large amount of blackening on the film for approximately the same exposure. McKeehan did not give any experimental data and it is therefore impossible to form a definite opinion in regard to the diffractions obtained by him from a sample of potassium kept a t - I 50' during the exposure. However, the fact that nothing but general scattering was produced when the same sample was exposed a t room temperature would, as a result of the present work, suggest that the weak diffraction obtained a t - 150' may possibly have resulted from the freezing out of some crystals of potassium hydroxide, which disappeared when the exposure was made a t room temperature, owing to the melting of the crystals and formation of a liquid film.
Summary Contrary to former statements, normal diffraction effects are obtained from potassium at room temperature by the powder method. The reason for obtaining only a general scattering and no definite diffraction in former experiments is thought to be the formation of films on the sample of potassium by moisture, by oxidation, or by interaction of the potassium with the glass. The method used for the preparation of samples of potassium is described. The available data indicate that potassium crystallizes in the bodycentered cubic lattice. The length of the edge of the unit cube containing two atoms of potassium is 5 , 3 3 3 + 0 . 0 0 5 b. The calculated density is 0.85 I . The lengths of the edges of the unit cubes of sodium and lithium were redetermined and, in agreepent with earlier determiFations, the value obtained for the former was 4.30 A and for the latter 3 . 5 1 A. Geophysical Laboratory, Carnegie Institution of Washington, Nooember. 192;.
