T H E CRYSTAL STRUCTURE O F CaS04.CO(NH2)2 STERLING B. HENDRICKS Fertilizer and Fixed Nitrogen Division, Bureau of Chemistry and Soils, Washington, D . C . Received June 1 1 , 1938
During the course of studies on salt-urea systems Dr. C. W. Whittaker (1) of this laboratory prepared a well-crystallized material which upon analysis proved to be a urea “coordination” compound of calcium sulfate. Preliminary optical examination showed that the crystals have an unusually high birefringence, approaching that of urea itself. This predicated a sufficiently interesting underlying crystal structure t o warrant a thorough study. Considerable importance, moreover, attaches to this compound as one possibly formed in some fertilizer mixtures. Crystal structure determinations of a number of hydrates and ammoniates have shown the essential validity of Werner’s coordination theory as applied to polar, but uncharged, groups. No attempt, however, has yet been made to find the structure of a coordination compound containing urea, ethylene diamine, or pyridine, etc. This hesitancy has been well based on the knowledge that these large molecules might place insuperable barriers in the way of the analyst and leave him with nothing more than a space group determination for his efforts. The analysis of urea coordination compounds holds some hope when the importance of the inherently high anisotropy of the urea molecule is fully realized. In the case of CaS04.4CO(NH2)2 the optical properties proved to be an unerring guide through the complexities of an unusually complex triclinic crystal. The structure found is perhaps sufficiently accurate to serve as the basis of a future more elaborate analysis. It holds some additional interest in being the first triclinic ionic compound to have yielded its essential crystal structure. CRYSTALLOGRAPHIC AND OPTICAL PROPERTIES
In general the crystals were elongated prisms (0.5 x 0.5 x 1mm.) showing predominant development of the p faces, figure 1, with only the forms a, b, c, p l , and p z present. Two crystals with the z faces developed were measured on the optical goniometer. The results together with the calculated crystallographic constant are given in table 1. A small fraction of the crystals were found to be twinned on (001). One specimen was measured on the universal stage under the microscope. The 1109
1110
STERLING B. HENDRICKS
spherical projection of the twin axis was obtained from the point of intersection of the three great circles connecting in order the projections of the principal directions of the optical ellipsoids of the two crystals. The twin
FIG.1. A TYPICAL CRYSTAL OF CaS01-4CO(NH2)2 TABLE 1 Goniometric measurements
I
L I M I T S OB O B S E R V A T I O N 8
FORM
P
--
100 110 010
a
iio
p2
001 101
z
pi
b C
90"l' 90'2' 90'1' 90"O' 2'9' 41'30'
P P
93'12' 47"3' 00'0' 136"lO' 9'58' 90"39'
9O"O' 90'0' 90'0' 90'0' 2'4' 41"28' p =
to to to to to to
P
90'2' 90'2' 90'2' 9O"O' 2'14' 41'32'
93'12' 47"2' 359'50' 136'7' 9"56' 90'35'
89'45'
p = 90"22'
to to to to to to
92'56' 47'4' O"10'
136"lO' 9'60' 90'43'
X = y =
PACE8 MEASURED
4 4 4 4 2
2
87'53' 86'50'
PO : q o : ro = 0.8796 : 0.8658 : 1 a : b : c = 0.9836 : 1 : 0.8645 Clear signals were obtained only from forms p , and p,. These were accordingly given infinite weight in calculating Y and po'/qB'. The value of LY is particularly sensitive t o p for 001 and therefore is likely to be considerably in error. Forms observed a , (loo), b (OlO), e (OOl), p , (110), p , (ilO), z, (101), ( l i l ) , ( l l l ) , ( i i i ) , ( i l l ) , (ioi). Cleavage absent. The face development indicates:that the crystals are holohedral.
axis was found to be either the b axis or the normal to the b face. A second specimen, giving moderately bright signals from the p faces, was measured on the optical goniometer. The results, which are summarized in table 2,
CRYSTAL STRUCTURE OF
1111
CaSOI.CO(NH2)2
show that the twin axis is the crystallographic b axis and that the composition plane is (001). A number of crystals apparently twinned in other manners were examined on the universal stage and in every instance were shown to be either parallel growths or unrelated crystals closely adhering to one another. The indices of refraction measured under the microscope by the immersion method for Na, light are a t 25°C. : cx = 1.523, fi = 1.583, y = 1.615
The experimental error does not exceed f0.002. negative with 2 V , calculated, 70.0".
The crystals are optically
TABLE 2 Goniometric measurements on a twinned crystal mounted on (007) The Vscale has been inverted to agree with the previous crystallographic deacription FORM
I
I
I
P
I
rp
FACES
Crystal No. 1
no 010 110 100
Pz b Pl
a
90'2' 90'0' 90"4' 90"4'
to to to to
90'4' 90'4' 90"6' 90'0'
136'9' 359'45' 47"l' 92'40'
to to to to
136"IO' 359'46' 47"7' 92"57'
2 2
315'20 358"53' 46'16' 93'9'
to to to to
315'22' 359"13' 46"19' 93'13'
2 2 2 2
2
2
Crystal No. 2 110 010 110
PI b Pz
100
a
88"55' 87"57' 88"14' 89'40'
to to to to
89"OO' 88'3' 88'16' 90"22'
The measurements on p of the two members of the same form are reduced t o comparable values. Signals, not very clear, were obtained only from forms p .
The orientation of the optical ellipsoid was determined by measurements on the universal stage. The crystals were mounted in an ethylene glycolphthalic anhydride plastic between hemispheres with n, = 1.557. The average results, uncorrected for differences in refractive indices, obtained from a number of crystals are summarized in figure 2. The irregular lines indicate the magnitude of the observational errors. The observed value of 2V is 70", agreeing with the value calculated from the indices of refraction.
X-ray difraction data Rotating crystal and Weissenberg photographs were made with the crystallographic axes as axes of rotation. Copper K radiation was used throughout with a camera radius of 5.01 cm.
1112
STERLING B. HENDRICKS
The lattice dimensions were calculated from the layer line separations. The angles between the axes of the reciprocal lattice and the values of p u , go, and ro were determined from the equatorial zone Weissenberg photographs. The linear elements calculated from these measured quantities are listed in table 3. The values obtained from the x-ray diffraction and optical goniometric data agree very closely save in the case of a, in which instance the goniometric value is suspect.
b '
A
Obfuse Bisecfrix
)( Poles of Facps
0 A cute Bisecfrix FIG.2. STEREOGRAPHIC PROJECTION SHOWING THE OPTICORIENTATION OF CaSO1.4CO(NH& AS DETERMINED ON THE UNIVERSAL STAGE The projection of the c axis is at the center of the figure
Weissenberg photographs were made from four of the layer lines. I n these cases the slit was rotated making sin p = sin p (2) so that the axis of rotation would lie on the reflection sphere, The absence of symmetry around the central image confirmed the triclinic character of the crystals. The intensities of some of the observed reflections are summarized in tables 4 to 9. A most striking characteristic of these data i s that m a n y &pes of planes are either absent or are represented by only a f e w of the possible reflections. The observations can be divided into two classes (cr denotes odd; e, even) :
CRYSTAL STRUCTURE OF
A pprozimately absent
Strzctly absent
boo),
1113
CaSOI.CO(NH&
(OOU)
(OUO)
(ueO), ( e g o )
(OUO)
(Oul), (001)
(Oku), (hOu)
(eul), ( G e l )
(eea), ( m e )
The data from Weissenberg photographs of the third and fourth layer lines are summarized in tables 7 and 8. It can be seen that reflections are TABLE 3 Summary of crystallographic constants WEISSENBERQ
GONIOMETER
X-RAY
OPTICAL
____ ................. y*.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
...................................... ............ ff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................ y................................................. ...................................... qo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ro. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CY*.
a. b.
...........
.............
...........
.............
c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Density (observed).. . . . Density (calculated), . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14.74 14.95 6.47 93'18' 88'36' 89'42' 91"26' 90'22' 86'42' 0.4395 0.4326 1 0.9859 1 0.4327 1.8006 1.820
93"9' 87"53' 89'45' 92'8' 90"22' 86'50' 0.8796 0.8658
1 0.9836 1
0.8645
TABLE 4 Weissenberg photographic data from CaSOd.4CO(NHz)z Equatorial zone, a, axis of rotation. All planes with k odd are strictly absent; the only reflections from planes with 1 odd are listed in table 9
1
Ob2
Ok 4
Ob6
01.2
Oh6
Ok4
~
*
001
V.S.
021 041 061
8.
081 0.10.1
m. m. m.w.
0.12.1 0.14.1 0.16.1
m.s. W.
m.w. W.
V.W.
V.W.
V.S.
V.W.
V.tV.
a. m.s. m.w. m.
W.
? m.s. m.w. m. m.
V.W.
m.w. m.w. m.w.
W.
m. m.w. w.
m.w. w. V.W. a.
m. W.
m. m.w.
m.w. V.W.
w.
m'W*
W.
I
* The following abbreviations are used: v.s., very strong; s., strong; m.s., medium strong; m., medium; m.w., medium weak; w.,weak; v.w., very weak.
1114
STERLING B. HENDRICKS
present only from (uuu),(eea), and ( m e ) . Weissenberg photographs were made from the second layer lines with c and with b as the axes of rotation. Complete indices were not assigned in these cases, since positive and negative values were not differentiated, but it could be seen that planes (u21), TABLE 5 Weissenberg photographic data from CaS04.4CO(NH& Equatorial zone, b, axis of rotation. All planes with h odd are absent; the only reflections from planes with 1 odd are listed in table 9
1
1
A02
201 401 601 801 10.0.1 12.0.1 14.0.1 16.0.1
1
h04
m.6. m. m.w. m.s. m.6.
m. m. m.w. m.
W.
W.
hO6
V.W.
V.W.
S.
m.w. m. mew. a.
m. w.
W.
I
hD4
hO2
a. m. m. m.w. a.
W.
m.w. m.w. m.w.
606 V.W.
W. V.W.
w.
W.
m.
TABLE 6 Weissenberg photographic dala from CaS04.4CO(NH2)2 Equatorial zone, e, axis of rotation. All planes with h or k odd are absent save the few h and IC odd listed in table 9 OkO
hOO h20 h40 h60 h80 h.lO.O h.12.0 h.14.0 h.16.0 hZO hPO h60 hSO h.lTT.0 h.lZ.0
V.S.
m.s.
2kO V.S.
8.
m.
m. m.8. m.8. m. a. m.w,
V.S.
W.
m. a. a.
W.
V.W.
a. m.w.
m.w. w.
W.
El.
4k0
m. m.s. a. m.w. a. a.
I
a. a. m. V.W.
m. V.W.
m.
I V.S.
m.6. m. a. w. m.w.
6kO
.
w mas. m.w. m.w. v.\v. m.w.
8k0
m.s.
10.k.O
12.k.0
14.k.0
V.W.
V.W.
m.w.
a.
W.
m.w.
V.W.
m. m.
W.
W.
a. a. m. m. m.
a. m. maw. m. W.
m.
m. m.8. w.
V.W.
w.
m.w.
(eu2), and (ue2) were strictly absent and (e2u), (uu2) approximately so. Laue photographs were made with the incident beam (W general radiation, 26,000 V peak) parallel and a t slight angles to the b axis. Reflections in the first order (nA = 0.48 to 0.9’6 A.U.) were obtained only from ( m u ) ,
1115
CaSOc. CO(NH2)2
CRYSTAL STRUCTURE OF
(eea) , and (ace), wit,hout particular differentiation in intensities between the three classes. The odd layer lines on the rotating crystal photographs, while present in all cases, are far less prominent than are the even ones. Some strong reflections are present on the odd layer lines however, particularly for values of less than 1.2. Some of these characteristics can perhaps be seen by an inspection of the typical photograph reproduced as figure 3.
TABLE 7 Il'eisseiiberg photographic data f r o m CaS04,4CO(NH?), Fourth layer line, a, axis of rotation. All planes with k odd are strictly absent; the only reflertion from planes with 1 odd are listed in table 9
-I
401 421 441 46 1
I
I
4ki
ins. \I' ~
4h4
I
.
S.
\v .
4.8.1
m.w.
4.10.1 4.12.1
a.
m.\v.
I 1
111.
m.\v. n1.w. :I. :I.
1
TABLE 8 Weissenberg photographic data Jrom CaS04-4CO(NHp)2 Third layer line, a, axis of rotation. All planes with IC even are strictly absent 310 a. 330 V . W . 350 w. 370 V . V . W . 390 13'. 3.11.0 a. 3.13.0 a. 3.15.0 w.
I I
1
1 ~
310 a. 350 \v. 370v.w. 390 a. 372 W. 332 m s . 352 a. 392 a. 392 a. 3.11.2 \v.
311 V . W . 331 V . W . 351 V.W. 371 V . W . 391 m.w. 332 13'. 35%m.w. 372 a.
311 V.S. 331 a. 351 m.
387 a. 351 a. 377 W .
1
311 s. 33T a. 351 w. 37T a.
3gi W. 3.11.1 a. 312 \v. 332 m.
'
!
373 W . 333 V.\V. 353 \I'. 374 11,.
333 \v.
1
315 w.
Although unambiguous index assignments can only be made for Weissenberg and Laue photographs it can nevertheless be seen that none of the reflections of greater than medium intensity on the odd layer lines with a and b as axes of rotation had close to the same values of 5 as reflections on the two adjacent layer lines. Since the values of the angles, a,p, and y are very close t o 90" it follows that the planes giving reflections on the odd layer lines in general have different values of 11 and I, or of k and I than those
1116
STEHLIXG R. HENDRICKS
present, on the even layer lines. This then would be compat,ible with the presence chiefly of planes ( m e ) and (OW), as borne out by the Weissenberg photographs of the layer lines. The subduing of the odd layer lines with c a,sthe axis of rotation can be explained in the same manner. The density calculated on tho basis of the unit of structure containing four CaSOn.4CO(NH,), is 1.820. This value agrees with that determined by the centrifugal suspension method, 1.8006. The 1 per cent discrepancy arises chiefly from errors in the values of the fundamental lattice constants. Thespacegroup iseither P1, o r p i . The face development. and the character of the signals indicate that the crystals belong to t,he holohedral
FIG.3. ROTATINU CLWSTAL P~zo~ot:n~~ws Copper K radiation; n axis of rotation
division of the triclinic system. The derived structure, akhough isomorphous with Pi, does not depend upon the assumption of holohedry. THE STRUCTURAL AND OPTICAL PROPERTIES OF CALCIUM SULFATE AND UREA
The crystal structure of anhydrite, CaSOa (3), is known with sufficient accuracy to show t,hat eight oxygen ions of sulfate groups are in the first coordination sphere around each calcium ion. In gypsum (4), as described a t the present time, each calcium ion is surrounded by four oxygen ions of sulfate groups and two water molecules of closest approach. In
CRYSTAL STRUCTURE OF
CaSO4.CO(NH&
1117
calcium oxide and in the various silicates containing calcium the coordination number for oxygen ions has been found to be six, seven, or eight. The most trustworthy value for the Ca++ to 0-- distance for a coordination number of 6 is 2.40 A.U., as found for calcium oxide. For coordinations of 4 to 8 this value would be expected to be between 2.25 and 2.55 (5). The values observed in the various calcium silicates are close to 2.40, usually between 2.35 and 2.55. The sulfur to oxygen distance has not yet been determined in a sulfate. It is quite safe to assume, however, that it is the same as the phosphorus to oxygen distance in KH2P04 (6), namely, 1.56 A.U., and that the oxygen ions are at the corners of regular tetrahedrons surrounding the sulfur ions. The described structure of gypsum is of questionable accuracy since the calcium-oxygen distances are as small as 2.1 A.U. and since the first coordination sphere around calcium contains but six oxygen atoms, of which only four are ions. The structure is perhaps sufficiently accurate to indicate
FIG.4. THE INTERATOMIC DISTANCES IN A UREA MOLECULE The centers of all the atoms are in the same plane. The directions of maximum, mean, and minimum polarizations are shown.
that the water molecules are near the calcium ions, the distances as given being 2.40 A.U. Consideration of a number of ammoniates and hydrates suggests that such polar groups approach to within about 2.80 A.U. of calcium ions, the limits of this value being very wide Inspection of the crystal structure of urea shows that the oxygen ends of the molecules are near the NH2 groups of other molecules. The closest intermolecular distances of approach are: 0 to NH2, 3.15 A.U. The properties of urea indicate that its molecules are polar, the NH2 groups being positive with respect to the oxygen atoms. I n general the birefringence of sulfates RzS04,RS04,or Rz(S04)3is low, since a regular tetrahedral grouping of isotropic resonators, such as afforded by a 504 group, is isotropic. The indices of refraction of anhydrite, CaSOr, are CY = 1.571, p = 1.576, y = 1.614, with the density, p equal to 2.93. In gypsum a = 1.520, = 1.523, and y = 1.530 with p = 2.32. The
1118
STERLING B. HENDRICKS
birefringence of calcium sulfate formed by dehydrating gypsum a t low temperatures is less than 0.015. Urea crystallizes in the tetragonal system with a = p = 1.484, y = 1.602, and p = 1.335. The direction of maximum polarization is parallel to the twofold axes of the molecules. a and p are perpendicular to the plane of half the urea molecules and parallel to the planes of the other half. The optical properties of a lattice formed by the translation repetition of
C
0axis
FIG.5 . POSSIBLE ARRANGEMENTS OF THE Ca++ IONSAND SOa GROUPS ALONG THE e AXIS OF CaSOd.4CO(NH2)2 Rotations about the c axis are not determined. The calcium-oxygen distances are (a) 2.43 A.U., (b) 2.64 A.U., and (c) 2.68 A.U.
urea molecules can not satisfactorily be calculated a t the present time. It is sufficient however to indicate, as permitted by elementary considerations, that a’,p’, and y’ would have the directions shown in figure 4,with p’ somewhat smaller than y’ and a’very small compared tc! p’ or 7’.
The crystal structure of CaS04.4CO(NH2)2 The explanation of the many types of absent reflections affords the starting point for the structure determination. The lattice must approach
CRYSTAL STRUCTURE OF
1119
CaS04.CO(NH2)2
very closely to being a face-centered one, particularly in the a and b directions. Each atom must have approximate translations of 000; 046; $0;; $30. The calcium atoms can be placed in these positions without loss in generality. The regular tetrahedral sulfate groups having sulfur to oxygen distances equal t o 1.56 A.U. are to be placed within this lattice of calcium ions, in a manner such that the Ca++ t o 0-- distances are about 2.40 A.U. Fortunately, there are but three ways in which this can be accomplished. These are shown in figure 5 The arrangement shown in figure 5a gives interatomic distances in better agreement with expectation than do the other two. TABLE 9 Weissenberg photographic data from CaS01.4CO(NH2)2 Reflections observed from (eeu) and ( o n e )
(021) w. (041) m. (081) m.w. (0.16.1) m. (003) V . W . (063) m . n . (0.16.3) m.
(021) m.s. (031) m. ( 0 . 1 2 , l )V.W. (0.13.1) w. ( 0 , l G . l ) w. (0.18.1) w.
(0.10.3)v . w (0.12.3)m.
(20T) UT. (40T) m.s. (601) V . W .
(330)
(201) V.W. (401) m.w. (10.0.1)
V.W.
( 1 2 . 0 , l )m.w. (14.0.1)V . W .
(003) V.W. (203) w. (603) m. (12.0.3)w. (12.0.3) w.
V.W.
(T50) w. (150) w. (350) V . W .
(550)
V.W.
(750)
V.W.
(970) V.W. (390) V.W. (590) V.W. (9.11.0)\v.
(0.14.5) w FOURTH LAYER L I N E A X I S OF ROTATION
a.
(401)m.s. (421) m.s. (44T) w. '(46T) w. (441) m.s.
(401) m. (431) w. ( 4 , l i I l ) V.W. (4.12.1) 147.
The arrangement of figure 5b will be used as the basis for later drawings, but none of the possibilities must really be considered as excluded. I n none of the cases do considerations of distances alone fix the group in its rotation around the c axis. In no instance can b0t.h the symmetry of the point group P y and the complete translations of a face-centered lattice be maintained. The arrangements 5b and 5c will, however, preserve the face centering in the a and b directions, and that of the sulfur atoms in the c direction. They appear somewhat more reasonable for this reason, as well as on account of the arrangements they give oxygen ions around the calcium ions. In any case the calcium ions are equidistant from four oxygen
1120
STERLING B. HENDRICKS
ions of closest approach. Strong electrostatic forces are effective in holding the lattice together in the c direction only. It is somewhat instructive to consider the twinning in crystals of gypsum, anhydrite, and CaS01.4CO(NH2)2. I n general the composition plane of a twinned crystal is one across which the electrostatic binding forces are great and in which the atoms are brought into approximate juxtaposition by rotation about the twin axis. I n gypsum and anhydrite the composition plane and twin plane are the same and contain only sulfate groups or calcium ions, (101) of anhydrite and (100) of gypsum, or sulfate groups
tc*6.47A
FIG.6.
ARRANQEMENT OF THE
eaff
AND
sod-- IONS
IN THE U N I T OF STRUCTURE OF
CaSOa.BCO(NHa)z
and calcium ions, (012) of anhydrite. These are all planes across which the binding forces are relatively great, The twinned crystals of CaS04. 4CO(NH2)2 thus might be expected, as observed, to have (001) as the composition plane. The birefringence of CaSO4.4CO(NH&, which is almost as great as that of urea, is t o be explained by the arrangement of the urea molecules in its structure. These molecules, moreover, must be placed with their oxygen ends near positive charges, calcium ions, and their NH2 groups near negative ions, the oxygen atoms of the sulfate groups. The lack of prominent cleavage allowed by the calcium sulfate framework is prevented by the urea arrangement. The interatomic distances mentioned in the last section
CRYSTAL STRUCTURE OF
CaSO4.CO(NH&
1121
must be satisfied approximately as must also the fundamental face-centered translations. Since the direction of O( does not differ greatly from that of c the planes of urea molecules can not deviate widely from being perpendicular to e. This would also require the obtuse bisectrix and the optic normal to be in (001) with the polarizations along them not greatly different. A manner, and apparently the only one, of satisfying these manifold requirements is that shown in figures 6 and 7. The undetermined factors
FIG.7. A PROJECTION OF ONE HALFTHE UNITOF STRUCTURE ON (OO1)o The distances of various atoms above and below the plane are shown. The projection on (001)i is obtained by translating the origin of this figure to z = $, y = 0 . The unit of structure can be formed by the combination of the two projections.
in this approximate structure are (1) the exact positions of the sulfate groups and their rotations around the c axis, and (2) the details involved in fixing the positions of the urea molecules, chiefly translations. The structure is complete enough to show qualitative agreement between observed and calculated intensities of reflection for simple planes. The various types of absences are accounted for, but of course not in a unique manner. The observed intensities and calculated structure factors for low order reflections from the phacoids are: T H E J O U R N A L O F PHTBICAL CHEMISTRY, VOL. X X X V I I , N O ,
9
1122
STERLING B. HEKDRICKS
+ FS f 2.9F0 SO
