Ammonium Nitrate-Potassium Nitrate Crystal Structures and to Mr. G. Minelli for the help given in the experimental work.
References and Notes (1)(a) M. Lo Jacono, M. Schiavello, and A. Cimino. J. Phys. Chern., 15, 1044 (1971);(b) M. Schiavello, M. Lo Jacono, and A. Cimino, ibid., 75, 1051 (1971). (2)A. Cimino and M. Schiavelio, J. Catal., 20,202 (1971). (3)H. Krischner, K. Torkar, and P. Hornisch, Monatsh. Chem., 99, 1733 (1968). (4) D. S.Maclver, H. H. Tobin, and R. T. Barth, J. Catal., 2, 485 (1963). (5)A. Cimino, M. Lo Jacono, P. Porta, and M. Valigi, 2. Phys. Chem. (Frank-
249 futi'amMain), 51, 301 (1966). (6)J. C. Yates, W. F. Taylor, and J. H. Sinfelt, J. Amer. Chem. Soc., 86, 2996 (1964). (7)H. P. Klug and L. E. Alexander, "X-Ray Diffraction Procedures," Wiley, New York, N.Y., 1954,p 491. (8)S. Greenwald, S. Y. Pickart, and F. H. Grannis, J. Chem. Phys., 22, 1957 (1954). (9)J. B. Goodenough, "Magnetism and the Chemical Bond," Interscience, New York, N.Y., 1963,p 165. (IO)A. J. Leonard, P. N. Semaille. J. J. Fripiat, Proc. Brit. Ceram. Soc., 103 (1969). (11) G.Biasse, Philips Res. Rep. Suppi., 3, 18 (1964). (12)V. Bucciarelli, A. Cimino, and P. Porta, to be submitted for publication. (13) F. C. Romeijn, PhilipsRes. Rep., 8,321 (1953).
Crystal Structures of Three Solid Solution Phases of Ammonium Nitrate and Potassium Nitrate James R. Holden" and Charles W. Dickinson Naval Surface Weapons Center, White Oak, Maryland 209 10 (Received May 13, 1974) Publication costs assisted by the Naval Surface Weapons Center
The crystal structures of ammonium nitrate (AN)-potassium nitrate (KN) solid solutions of eight different compositions in three different polymorphic forms have been determined by X-ray diffraction. The crystal structures of AN-IV and KN-I1 have been refined from X-ray diffraction data. The unit cell of AN-IV is orthorhombic, space group Pmmn containing two formula units. The cell dimensions are a = 5.724, b = 5.455, c = 4.945 8, for AN-IV and a = 5.758, b = 5.456, c = 4.942 8, for a solid solution containing 3.2 at. % potassium ion a t the cation sites. Solid solutions of KN in AN-I11 are orthorhombic, space group Pnma with four formula units per cell. The cell dimensions range from a = 7.694, b = 5.827, c = 7.158 8, for 5.0 at. % potassium to a = 7.635, b = 5.739, c 7.026 8, for 36.6 at. % potassium. The unit cell of KN-I1 is orthorhombic, space group Pnma with four formula units. The cell dimensions are a = 6.436, b = 5.430, c = 9.192 8, for KN-I1 and a = 6.458, b = 5.444, c = 9.211 8, for a solid solution containing 4.8 at. % ammonium ion. The cation coordination "sphere" in the AN-I11 type structures consists of 11 oxygen atoms from 7 nitrate ions. The potassium ions are randomly distributed through the cation sites, and the effective ionic radius appears to be a linear function of the potassium content.
Introduction The crystal structures of potassium nitrate-ammonium nitrate solid solutions of eight different compositions have been determined by single-crystal X-ray diffraction techniques. Our object was to determine which forces control the stability limits of the three solid solution polymorphs with ranges of room temperature stability. The crystal structures of ammonium nitrate (AN) and potassium nitrate (KN), previously determined by neutron diffraction, have also been refined from X-ray data for direct comparison. There are five known polymorphic forms of AN. The two which pertain to this study are AN-IV, stable between -17 and 32.23', and AN-111, stable between 32.23 and 84.10O.I There are three known polymorphs of KN. KN-I1 is stable from below room temperature to about 128' where it transforms to KN-L2 On cooling, KN-I transforms at about 124' to metastable KN-I11 which in turn transforms back to KN-I1 at about 110°.2 At least four different solid solution phases have been re-
ported; KN dissolved in AN-IV (KN-AN-IV), K N dissolved in AN-I11 (KN-AN-111), AN dissolved in KN-I11 (AN-KN-111), and AN dissolved in KN-I1 (AN-KN-11). As increasing amounts of K N are dissolved in solid AN, the IV-I11 transition temperature falls from 32.23' for pure AN to below room temperature and KN-AN-I11 becomes the stable p h a ~ eThe . ~ ~presence ~ of ammonium ion in KNI11 stabilizes this phase to the extent that it can be cooled to room temperature. However, it has been reported that in the presence of water it transforms to a mixture of KNAN-I11 and AN-KN-I1 indicating that it is not thermodynamically stable a t room t e m p e r a t ~ r e Therefore, .~ as the potassium ion content increases, the three room temperature stable solid solution polymorphs are KN-AN-IV, KN-AN-IIIthen AN-KN-11. The crystal structure of AN-IV was reported by both West6 and Hendricks, Posnjak, and Kracek7 in 1932. It has been redetermined more accurately by Choi, Mapes, and Princes by neutron diffraction. The crystal structure of KN-I1 was reported by Edwardsg in 1931 and redetermined The Journal of Physical Chemistry, Vol. 79, No. 3, 1975
James R. Holden and Charles W. Dickinson
250
TABLE I: Preliminary Crystal D a t a Weight % KN in salt mix AN-IV (C, M, and P ) b AN-IV KN-AN -1V AN-I11 (G and W)‘ KN-AN -111-a
KN-AN-111-b KN-AN-111-c KN-AN-111-d KN-AN-111-e KN-AN -111-f
AN-KN -11 KN-I1 (N and LId KN -11 a
0 3
4 10“ 10 20 40’ 30 40
100
Cell dimensions, Crystal size, mm
a
b
C
Crystal volume per formula unit, W3
5.745
5.438
4.942
77.20
0.20 0.19
5. 724(5) 5. 758(2) 7.65
5.455(4) 5.456(3) 5.83
4.945(3) 4.942(2) 7.14
77.20 77.61 79.61
0.40 X 0.28 X 0.19 0.33 X 0.16 X 0.15 0.47 X 0.16 X 0.13 0.34 X 0.18 X 0.12 0.50X0.24X0.20 0.39 X 0.12 X 0.11 0.32 X 0.16 X 0.12
7.694 (4) 7.669(2) 7.660(4) 7.656(1) 7.662(3) 7.635(1) 6.458(5) 6.4309
5.827(3) 5.821 (2) 5.800(4) 5. 777(1) 5. 764(3) 5. 739(1) 5.444(5) 5.4142
7.158(3) 7.120(2) 7. 112(4) 7.083(1) 7.062(3) 7.026(1) 9.211(6) 9.1659
80.22 79.46 78.99 78.32 77.97 76.97 80.96 79.78
0.34 X0.14 XO.09
6.436(1)
5.430(1)
9.192(2)
80.31
0.40 0.41
X X
0.22 0.19
X X
Second crop by evaporation. Reference 8. Reference 11.d Reference 10.
by Nimmo and LucaslO also by neutron diffraction. The crystal structure of AN-I11 was reported by Hendricks, Posnjak and Kracek7 in 1932 and redetermined by Goodwin and Whetstonell in 1947. It has been reported from the results of X-ray powder diffraction that the unit cell dimensions of KN-AN-I11 decrease with increasing K N content, because the ionic radius of potassium, 1.33 A, is smaller than the effective radius of the ammonium ion, 1.48 A.12 The same cause is cited for the increase of the cell dimensions of AN-KN-I11 with increasing AN content.5 Experimental Section Table I lists the preliminary data from the crystals used in this study in order of increasing KN content. Also included for comparison are the cell dimensions used in the most recent reports of the structures of AN-IV,8 AN-III,I1 and KN-ILIO All crystals were grown by slow cooling or subsequent vaporation a t room temperature of saturated water solutions. The weight per cent KN in the dissolved salt mixture is listed followed by the dimensions of the sample crystal. Crystals AN-KN-I1 and KN-AN-111-e were selected from subsequent crops of crystals grown from the same solution. All crystals grew as long thin needles and the specimens used for diffraction measurements were sections broken from longer needles. The needle axes coincide with the a axes of the AN-IV type crystals, the b axes of the AN-I11 type crystals, and the a axes of the KN-I1 type crystals as reported in this paper. All crystals were first aligned and examined with a precession camera then transfered to a Picker FACS-1 computer-controlled automatic diffractometer equipped with a graphite (HOG) monochromator. The unit cell dimensions were obtained from a least-squares fit of the diffraction angles of 12 strong reflections using 0.71069 A as the wavelength of Mo K a radiation. All crystals are orthorhombic. The numbers in parentheses are standard deviations estimated by the leastsquares procedure. The crystal volumes per formula unit are included for comparison of the packing densities in the three polymorphic forms. The periodic absences in the observed X-ray reflections confirm the previously reported space groups for all three The Journal o f Physical Chemistry, Vol. 79, No. 3, 1975
structure types. However, for this report, the parameters for AN-I11 and KN-I1 have been converted to refer to “standard settings” listed in the “International Tables for X-ray Crystallography.”l3 Thus, the space group of AN-IV and KN-AN-IV is Pmmn (No. 59); that of AN-111, KNAN-111, AN-KN-11, and KN-I1 is Pnma (No. 62). AN-IV and KN-AN-IV contain two formula units per cell; the others contain four formula units per cell. Refinement of S t r u c t u r e s Reflection intensities were measured by “standard” diffractometer procedures. Data treatment, least-squares structure refinements, and subsequent evaluations were carried out by “standard” calculation methods using a CDC 6400 and the “XRAY System of Crystallographic Programs.”14 Details are given in the microfilm edition of this j0urna1.l~ The starting atomic positions for leastsquares refinement were obtained from previously reported structures of AN-IV, AN-111, and KN-11. Hydrogen atom positions were not well defined by the data. The positions reported from the neutron diffraction determination of AN-IVs were used in the refinement of the structure of KN-AN-IV (see Table 11).The hydrogen positions given in Table I11 for the AN-I11 type structures were estimated from an electron density calculation (Fourier summation) but not entered into the least-squares refinement. Note that the large values of the temperature factors ( U values) produced by the least-squares procedure mean that these atoms make only a small contribution to the calculated structure factors. The potassium content of each solid solution crystal listed in Tables 11-IV was obtained by including a cation site occupancy factor with the other parameters of the leastsquares refinement. Even though the correlation factors were as high as 0.5 between the site occupancy factor and the thermal parameters of the ammonium nitrogen atom in the KN-AN-I11 structures and 0.66 between the site occupancy factor and scale factor in AN-KN-11, good convergence was obtained because all final shift/error ratios were below 0.5.l5
Ammonium Nitrate-Potassium Nitrate Crystal Structures
TABLE 11: Atomic Parameters for AN-IV TvDe Structuresa AN -1V AN-IV (C, M, and P)* This work KN-AN-IV
At.fraction K'
0
0
0.032 (4)
7500 2500 -836(4) 268(11) 441(13) 285(11)
7 500 2500 - 839(5) 22 2 (12) 469(16) 310(13)
7500 2500 -830 (5) 243(13) 488(17) 3 24 (14)
2500 2 500 5067(3) 3 2 5 (10) 312(09) 191(10)
2 500 2500 5074(5) 296(13) 314(13) 247(12)
2500 2500 5080(4) 31 7 0 2 ) 314 (11) 193-(10)
2500 2500 7629 (6) 3 55 (14) 470(18) 199(13)
2500 2500 7639(4) 312(12) 499(14) 220 (10)
2500 2500 7645(3) 316(10) 488(12) 190 (10)
4342(5) 2500 3832(5) 521(15) 742(19) 375(13) 210(10)
4364 (4) 2500 3835(4) 453(11) 824(15) 453(11) 220(10)
4364(3) 2 500 3836(3) 459 (11) 793(15) 421(10) 224(08)
6045(12) 2500 -1898(17) 870(41) 750(38) 1106(48) - 604(41) 7500 lOll(16) 324(16) 784(35) 10 55 (47) 922(43) 461(39) a Fractional translations and temperature factors erence 8.
X
lo4. Ref-
Discussion The bond lengths and angles found for the nitrate ions in potassium nitrate (KN), ammonium nitrate (AN), and their solid solutions are listed in Table V. Note that in the AN-I11 type structures N(2)-0(1) covers a range of 0.014 A, and N(2)-O(2) a range of 0.012 but that there are no trends as the potassium content of the cell increases. Since these ranges are four to six times the standard deviations estimated for individual determinations by the usual leastsquares procedure, one might attach some significance to
a
251
the large differences. However, because the structures differ only in potassium content and there is no apparent correlation between the individual bond distances and the potassium content, it is doubtful that the differences are real. Therefore, these results would indicate that the true limit of error for an individual determination is two to three times that estimated by least squares. However, the differences between the N(2)-0(1) and N(2)-O(2) bond lengths found for the AN-IV type structures range between 30 and 40 times the estimated standard deviations and are certainly significant. Choi, Mapes, and Princes attribute this difference to the fact that O(1) is involved in four strong hydrogen bonds whereas O ( 2 ) is not. This explanation is consistent with the greater symmetry found for the nitrate ion in KN-11. It should be noted that there is also no significant difference in the bond lengths found in the nitrate ions of the AN-I11 type structures. None of the solid solution crystals reported in this paper produced any X-ray reflections not accounted for by the reported unit cell or any detectable intensities at the positions of space group extinctions. Therefore, there is no evidence for a nonrandom distribution of potassium ions at the ammonium sites of the AN-IV or AN-I11 type structures or for a nonrandom distribution of ammonium ions at the potassium sites in AN-KN-11. Figures 1-3 show the arrangement of the ions and the coordination of the cations in the three structure types covered in this paper: AN-IV, AN-111, and KN-11. The cation positions, shown as the major component, actually contain a random distribution of ammonium and potassium ions such that the probability of finding a potassium ion at one particular site is equal to the atomic fraction of potassium in the crystal. The positions of the surrounding atoms are probably slightly different when a site is occupied by a potassium ion than when it is occupied by an ammonium ion so the nitrate ion positions found by the diffraction procedure would also be a weighted average of their positions throughout the crystal. The projection directions of Figures 1-3 were chosen such that the ions lie on mirror planes parallel to the paper at 1/* or 3/4 of the cell translation interval perpendicular to the paper. The oxygen and hydrogen atom positions listed in Tables 11-IV are identified in the figures. In all cases O(1) lies on the mirror plane with N(2) while O(2) and its symmetrically related mate (the third oxygen atom of the nitrate ion) lie above and below the mirror plane. In KNAN-IV, the ions also lie on mirror planes perpendicular to the b axis. The interionic distances labeled A through F refer to the corresponding columns in Table VI; G through J refer to Table VIL The determining factor in most ionic crystal structures is the cation coordination. In the AN-IV type structures, (Figure l), each cation is surrounded by 12 oxygen atoms from 8 nitrate ions (4 on the same mirror plane, 2 above, and 2 below). Four of the 12 oxygen atoms form hydrogen bonds with the four hydrogen atoms of the ammonium ion. These bonds, shown as B and C in Figure 1,have H-0 distances of 2.050(7) and 2.161(7) 8, and N-H-0 angles of 154.4(8) and 172.6(9)' in AN-IV as reported by Choi, Mapes, and Prince.s Using the hydrogen positions from their neutron diffraction determination, our corresponding distances would be 2.042 and 2.164 h; for AN-IV and 2.054 and 2.162 A for KN-AN-IV. The closest approach to the center of the cation, A, is not a hydrogen bond. The other The Journal of Physical Chemistry, Vol. 79, No. 3, 1975
James R. Holden and Charles W. Dickinson
252
TABLE 111: Atomic Parameters for AN-I11 Type Structures= KN-AN-I11 AN-I11 (G and W)b
At. fraction K'
a
b
0.050(3)
0.093(3)
- 200
- 106 (3)
7500 3169(3) 396(11) 296(10) 356(11) - 19 (8)
-ll0(3) 7 500 3 168(4) 366(14) 291(13) 3 57 (13) -24(10)
- 114(4)
7500 3200
1450 2 500 1400
1550(2) 2 500 1257(2) 302(8) 288(8) 319(9) -22(6)
1550(3) 2 500 1268 (3) 289 (10) 306(11) 318(10) -50)
8 50 2 500 3000
598(3) 2 500 2663(3) 614(12) 428 (9) 413(10) 193(8)
1750 600 600
20 11(2) 640 (2) 534(2) 492(8) 351(7) 539 (8) 77(5) 49(5) -93(5)
0
-
0.120(4)
7500 3 168 (4) 382(15) 314(14) 3 57 (15) - 11(1)
d
e
-
f
0.250(5)
0.333(4)
0.366 (4)
- 118 (5) 7 500
-113(2)
- 125(2)
3 167(5) 266 (21) 320(20) 373(21) 403)
7500 3166(2) 357(9) 272(9) 342(9) - 5(5)
7500 3162(2) 356(9) 265(8) 3 54 (8) -26)
15 54 (3) 2 500 1264(3) 285 (10) 300(10) 323 (10) -11(7)
1557(3) 2 500 1268(3) 264 (11) 332(12) 306 (11) - 29 (8)
1557(2) 2 500 1280(3) 270 (9) 320(10) 300(9) - 34 (7)
1555(3) 2 500 1293(3) 269(9) 306(9) 314(9) -15(7)
600 (3) 2 500 2678(3) 609 (14) 437(12) 404(11) 184(10)
598(3) 2 500 2679 (3) 609 (14) 432(12) 387(11) 179(10)
60 2 (4) 2 500 2694(4) 585 (15) 399(13) 370(12) 153(11)
603 (3) 2 500 2 71 7 (3) 543(12) 393(10) 363(10) 136(9)
602(3) 2500 2717(3) 560(13) 381(11) 374(10) 141(9)
2012(2) 638(3) 537(2) 489 (9) 380 (9) 526 (9) 67(6) 430) -99(6)
20 1 5(2) 640 (3) 540(2) 49 5 (9) 379(9) 532 (10) 79 (6) 43 ( 7 ) - 111( 7 )
2022(2)
643 (3) 543(2) 487(10) 384(11) 515(11) 60 (7) 49 (8) -115(7)
2023(2) 632(3) 545(2) 471(8) 385(9) 516(9) 59 (6) 51(6) - 130 (6)
2019(2) 618(3) 551(2) 468(8) 374(9) 539(9) 73(6) 51(6) -128(7)
7500 4024 1769 (348)
-1125 7500 4027 963 (203)
.1130 7 500 4028 2945(830)
-1135 7 500 4031 685 l(4324)
981 7500 3910 1217(212)
980 7 500 3913 1397(301)
9 78 7 500 3913 867 (186)
9 74 7 500 3916 2002(646)
- 1118
a
C
- 144
- 148
- 151
8887 2372 1751(198)
8889 2366 1754(222)
8894 2365 168 5 (2 56)
Fractional translations and temperature factors
X
- 1145
4032 7359(4574)
7500 4033 4517 (2169)
969 7 500 3916 1712 (49 1)
9 70 7500 3916 1 2 18 (3 56)
- 161
- 163
8902 2357 2227(4 57)
8909 23 50 2784 (662)
lo4. Reference 11.
approaches D (the distance from the central cation to the O(2) atom labeled D), and E make a broad range of coordination distances, 0.36 A. The 0-0 distance shown as G is the only short interanion contact in any of the structure types. In the AN-I11 type structures, each cation is surrounded by 11 oxygen atoms from 7 nitrate ions (3 on the same mirThe Journaiof Physical Chemistry, Voi. 79, No. 3, 1975
-156 8899 2361 2357(487)
- 1139 7 500
ror plane, 2 above, and 2 below). The hydrogen positions shown in Figure 2 were estimated from electron density calculation^.^^ If correct, these positions would indicate no strong hydrogen bonding. The only possibility would be a pair of bifurcated bonds accompanying the distances designated as E. The H-0 distances would be 2.22 A in KNAN-111-a and the N-H-0 angles would be 150'. The dis-
Ammonium Nitrate-Potassium Nitrate Crystal Structures
253
s
TABLE IV: Atomic Parameters for KN-I1 Type Structuresa __
___
KN -11
d ,’c
~
I
(E)b (NandL)‘ This work AN-KN-I1 ___..___.-._._______-_-__.I__.._.._.___.
-4t. fraction K’
_ l _ l _
1.000
1.000
1.000
0.952(6)
2500 2500 4160
2568(2) 2500 4166(1) 378(8) 275(7) 261(4) 15(6)
2551(1) 2500 4164(1) 311(5) 238(4) 248(4) 11(2)
2553(8) 2500 4164(1) 336(4) 255(4) 261(4) 14(1)
4 152(1) 2500 7548(1) 233(4) 275(3) 303(4) 3(3)
4156(3) 2500 7551(3) 192(9) 250(11) 297(11)
4155(3) 2500 7548(2) 208(8) 271(9) 315(9) 14(6)
4107(2) 2500 8902( 1) 522(6) 408(6) 282(4) -72(3)
4098(4) 2500 8907(3) 500(15) 407(14) 272(11) -- 80(09)
4109(3) 2500 8908(2) 529(12) 437(13) 288(9) -87(8)
4151(1) 4492(1) 6866( 1) 495(4) 258(4) 415(4) -48(2) 48(3) 480)
4129(3) 4501(3) 6864(2) 493(10) 268(9) 392(9) ..-3 8 ( 7 ) 520) 640)
4133(2) 4493(3) 6865(2) 541(9) 290(7) 417(8) --4 5 (6) 54(6) 65(5)
4170 2 500 7500
16(8)
C
\
’ 4
/
314
1 114
314
c!b
4
-2
L
Figure 1. Cation coordination in AN-IV type structures,
a
4170 2500 8830
4170 4440 6860
a Fractional translations and temperature factors erence 9. Reference 10.
X
lo4
* Ref-
tances between the center of the cation and the 11 oxygen atoms which make up its coordination “sphere” (A through F in Figure 2) cover a narrower range than in AN-IV, 0.23
!
m
dji”’0
Flgure 2. Cation coordination in AN-Ill type structures. a T----
_ _ I -
o--oo 114
I
I,
0 314
A.
In the KN-I1 type structures, each cation is surrounded by 9 oxygen atoms from 6 nitrate ions (2 on the same mirror plane, 2 above, and 2 below). The distance range in the coordination “sphere” is quite narrow, 0.09 A. (See Figure 3.) The monovalent cations which can partially replace ammonium ion in AN to form solid solutions are those with ionic radii close to the effective ionic radius of ammonium ion.12 Thus, using the values listed by Pauling,I6 potassium (1.33 A), tellurium (1.44 A), rubidium (1.48 A), and cesium (1.69 A) will replace ammonium (1.48 A), but sodium (0.95 A) will not. As might be expected, the way in which a dissolved ion changes the polymorphic transition temperatures of AN depends upon its ionic radius relative to that of ammonium.12 Figure 4 shows the change in crystal volume per formula unit a t room temperature as the potassium content increases. The size of the rectangle around each
Flgure 3. Cation coordination in KN-II type structures.
point represents two estimated standard deviations on either side as calculated from cell dimensions listed in Table I and the atomic fractions listed in Tables 11-IV. Among the AN-111 type structures, the formula volume definitely The Journal of Physical Chemistry, Vol. 79,
No. 3, 1975
James R. Holden and Charles W. Dickinson
254
TABLE V: Nitrate Ion Bond Lengths and Angles
AN-IV (C, M, and Pp AN-IV This work
1.266(4) 1.268(3) 1.268(3) 1.245(3) 1.240(3) 1.245(3) 1.247 (4) 1.251(3) 1.237(3) 1.254(3) 1.241(2) 1.247(4)
KN-AN -1V
KN-AN-111-a KN-AN -111-b KN-AN -111-c KN-AN -111-d KN-AN -111-e KN-AN -111-f AN-KN -11 KN-II (N and L ) b KN-I1 This work a Reference 8. * Reference 10.
1.222(3) 1.230(3) 1.237(2) 1.252(2)
1.254(2) 1.247(2) 1.242(2) 1.247(2) 1.251(2) 1.254(2) 1.246(1) 1.257(2)
120.0(3) 119.9(1) 119.8(1) 120.1(1) 120.2(1) 120.1(1) 120.2(1) 120.3(1) 120.3(1 ) 120.1(1) 120.1(1) 120.1(1)
120.0(3) 120.3(2) 120.4(2) 119.8(2) 119.6(2) 119.9(2) 119.6(2) 119.4(2) 119.4(2) 119.8(2) 119.9(2) 119.7(2)
TABLE VI: Coordination Distances to Listed Cation (A) B
C
D
E
F
2
2
2.935(4) 2.926 (3) 2.929(3) 1 3.007 (3) 2.982(4) 2.977(4) 2.955(5) 2.930(2) 2.918(3) 1 2.847(3) 2.828(2) 2.843 (3)
2.971(3) 2.959(3) 2.976(1) 2 2.986(2) 2.982( 1 ) 2.971(2) 2.960(1) 2.953(1) 2,939(1) 2 2.856(2) 2.845(4) 2.848(2)
2 3.147(3) 3.153(2) 3.149(2) 2 3.022(2) 3.009(3) 3.000(3) 2.987(3) 2.978(2) 2.962(2) 2 2.890(2) 2.885(3) 2.879(2)
2 3.200(4) 3.187(3) 3.195(2) 2 3.092 ( 2 ) 3.082(3) 3.077(3) 3.072(4) 3.064 (2) 3.04 l ( 2 ) 2 2.900(2) 2.884 (3) 2.893(2)
4 3.272 (3) 3.282 (3) 3.286(3) 2 3.116(3) 3.109(3) 3.105(3) 3.099(4) 3.103(2) 3.100(2) 2 2.935(3) 2.925 (1) 2.925(1)
2 3.217(3) 3.203 (3) 3.200(3) 3.191(4) 3.185(2) 3.172(2)
A
No. to each cation AN-IV (C, M, and P)a AN-IV KN-AN -1V
No, to each cation KN-AN-111-a KN-AN -111-b KN-AN -111-c KN-AN-111-d KN-AN-111-e KN-AN -111-f No. to each cation AN-KN-I1 KN-I1 (N and L)* KN-I1 For AN-IV type structures A O(2) at x, y , z and 114 -x, y , z B O(1) at x, j~, -1 1 z and 1 + x, y , -1 + z C O ( 1 ) at 1 - x , -y, 1 - 2 and 1 -x, 1 -y, 1 - 2 D O(2) at x, y , -1 + z and 1'4 -x, y , -1 + z E O(2) at 1 - x, - y , - 2 ; 1 - x, 1 - y , - z ll/z- x , - y , -2, and 1'4 -x, 1 - y , - z For AN-I11 type structures A O(1) at -x, 1 - y ! 1 - 2 B O(1) at x, y : z and x, 1 + y , z c O(Z) at -V2 + x, 1 + y , '/2 - 2 ; -'h + x, '/z - y , '/* - z D O(2) at x, 1 + y , z and x, /'2 - y , z E o(2)at '4 -x, '/z + y , V2 + z ; '/2 - x, - y , '/z + z F o(2)at --x, 1 - y , - 2 ; -x, -V2 + y , - Z For KN-I1 type structures A o(1)at -i/2 + x , y , 1V2 - z B O(Z) at 1 - x , 1 - y , 1 - 2 ; 1 - x , '4 - y , 1 - 2 c O(Z) at '4 - x, -'A + y , -'/z + z ; '/2 - X, - Y , - 7 2 + z D o ( 2 ) at x, y, z ; x, '4 - y , z E o(1)at 'h - x, -14 + y , --'A + z ; 'h - x, z/' + Y, -'/z + z a
Reference 8. * Reference 10.
decreases as the proportion of cation positions occupied by the smaller potassium ions increases. As expected, ammonium ions appear to increase the formula volume in KN-11; however, contrary to expectation, potassium ions appear to increase the formula volume in AN-IV. Also, note that the The Journal of Physical Chemistry, Val. 79, No. 3, 1975
relative size of the formula volumes in the three structure types is the reverse of what would be predicted based solely on the volume of the cations present. That is, AN-IV structures with the most ammonium ions have smaller formula volumes than AN-I11 structures with more potassium ions,
255
Ammonium Nitrate-Potassium Nitrate Crystal Structures
TABLE VII: Anion-Anion Distances Less T h a n 3.3 A G
I
J
2 (3.310) 3.291(3) 3.286(3) 3.267(3) 3.249(3) 3.235(3)
2 3.274(2) 3.265(5) 3.266(4) 3.275(5) 3.275(4) 3.257(4)
H
No. to each nitrate 4 2 AN-IV (C, M, and P)" 3.049(4) 3.243 AN-IV 3.049(4) 3.244(4) KN-AN -1V 3.050(3) 3.242(3) No. to each nitrate 2 2 KN-AN-111-a 3.209(3) 3.233(3) KN-AN-111-b 3.196(4) 3.219(3) KN-AN-111-C 3.187(4) 3.209(3) KN-AN-111-d 3.184(4) 3.198(3) KN-AN-111-e 3.180(3) 3.192(3) KN-AN -111-f 3.168(3) 3.183(3) No. to each nitrate 2 2 AN-KN-I1 3.230(3) 3.274(3) KN-I1 (N and L)b 3.217 3.257 KN-I1 3 . 2 19(3) 3.257(3) For AN-IV type structures G o ( 2 ) to O(2) at 1 - x, - y , 1 - z , and at .1 - x, 1 - Y , 1 - z H o(1)to O(2) at x, y , 1 + z , and at 'h - x, Y, 1 + 2 For AN-I11 type structures G o(1)to ~ ( 2 at) -'h + x, Y , /'2 - z H O(1) to O(2) at -'h + x, '4-y, '4- z and at -'A + x, y, '12 - z -x, /'2 + y , /'z + z and at 'Iz- x , -Y, 'A + 2 I o(1)to O(2) at J O(2) to O(2) at -x, - Y , - 2 For KN-I1 type structures G ~ ( 2to) ~ ( 2 at) -'h 4 x, y, 1 '4 - z and at 'Iz+ x, Y, 1'/2 - z H o(2)to 0(2) at x, 1V2 -Y, z a Reference 8. Reference 10.
n
2.8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
ATOiMlC FRACTION K'
Figure 5. Shortest cation-oxygen distances vs. fraction of cation sites occupied by potassium ion.
crystals which grew either during or after cooling of a solution of a 30/70 wt 96 mixture of K N and AN heated to about which in turn have smaller volumes than KN-I1 with nearly all potassium ions. The volumes of the first five AN-I11 type solid solutions form a logical trend with increasing potassium content; that is, decreasing at a decreasing rate (see Table I and Figure 4). However, the last point, KN-AN-111-f, does not follow this trend. A possible explanation is that this composition is not thermodynamically stable a t room temperature, but that this crystal formed at a higher temperature and then supercooled. The evidence to support this postulate is that crystals AN-KN-I1 and KN-AN-111-e were selected from successive crops produced by evaporation of the same solution at room temperature. Therefore, the composition of KN-AN-111-e might be expected to be near the limit of solubility of K N in AN-I11 at room temperature. On the other hand, KN-AN-111-f was selected from a batch of
80°.
If these structures are controlled primarily by electrostatic forces, the oxygen atoms should form coordination spheres around the cations such that the cation-oxygen distances are equal to the sum of the effective ionic radii. The observed range of cation-oxygen distances would be explained by the fact that the oxygen atoms are parts of rather bulky nitrate ions and not separate spherical ions. In this case, the shortest distances should be the best measure of the contact distance, The circles in Figure 5 are a plot of the average of the three shortest cation-oxygen distances (columns A and B in Table VI) in the AN-I11 and KN-I1 type structures us. the atomic fraction potassium ion at the cation sites. Excluding KN-AN-111-f for the reasons cited above, a least-squares fit of these points to a straight line gives the following: The Journal of Physical Chemistry, Voi. 79, No. 3, 1975
256
D = 2.996 - 0.1501F where D is the interionic distance and F is the atomic fraction potassium. This line is shown in Figure 5 . This relation gives 2.846 8, as the interionic contact distance between a potassium ion and a nitrate oxygen atom ( F = 1.000). Using the value given by PaulingI6 for the ionic radius of potassium, 1.331 8,, one obtains 1.515 8, for the effective ionic radius of a nitrate oxygen atom. The extrapolated value for the ionic contact distance between an ammonium ion and a nitrate oxygen atom is 2.996 8, (F = 0.000). Subtracting 1.515 8, gives 1.481 8, as the effective ionic radius of the ammonium ion, which is exactly the value given by Pauling.16 In view of the accuracy of the distances and atomic compositions used to make this correlation, the precision of this agreement is fortuitous. However, it indicates that the unit cell dimensions and atomic positions of the AN-I11 type solid solution structures can be explained by assuming that the ammonium-potassium cation behaves as a single entity whose effective radius is a linear function of the potassium content. An indication that 1.515 A is a reasonable value for the ionic radius of the oxygen atom is the fact that twice this value, 3.030 A, is slightly smaller than the shortest distance between oxygen atoms in any of the structures, 3.050 8, (see Table VII). The X points in Figure 5 mark the shortest distances between cation centers and oxygen atoms in the AN-IV type structures (A and B in Table VII). These distances are shorter than would be predicted by the relation given above which correlates the distances found in the AN-I11 and KN-I1 type structures. However, distance B involves hydrogen bondings and, if the hydrogen atom positions are stabilized by hydrogen bonding, A is a contact distance between an oxygen atom and the ammonium nitrogen atom instead of the ammonium ion acting as a unit. Because the atomic positions in the AN-111 type solid solutions do not change significantly with potassium content, the positions listed for KN-AN-111-a at room temperature (22 f 2') are probably a better approximation of the values for AN-I11 above the transition temperature (32.23') than those reported in 194711 based on less accurate X-ray data. The positional parameters found for KN-I1 at 100' are not grossly different from those found a t 25'.1° In any case, the transition at 32.23'l appears to be from a polymorph (ANIV) in which hydrogen bonding is an important factor to one in which it is not (AN-111). The extra stabilization energy provided by hydrogen bond formation in AN-IV must be partially offset by the greater electrostatic repulsion due to shorter distances between oxygen atoms carrying partial
The Journaiof Physical Chemistry, Voi. 79, No. 3, 1975
James R . Holden and Charles W. Dickinson negative charges (those designated G in Table VII). When the hydrogen bond energy is sufficiently lowered due to increased thermal motion of the hydrogen atoms, AN-I11 becomes the lower energy (stable) form. As potassium replaces ammonium ion in a KN-AN-IV solid solution, the hydrogen bonding energy is "diluted" and the temperature at which KN-AN-111 becomes the lower energy form is lowered. At an atomic fraction of between 0.032 and 0,050 (if crystals KN-AN-IV and KN-AN-I11 -a from this study were both thermodynamically stable), KN -AN-I11 becomes the stable polymorph at room temperature.
Acknowledgment. The authors gratefully acknowledge financial support from the Army Materiel Command, Picatinny Arsenal, Dover, N.J. and the Naval Ordnance Systems Command, Washington, D.C. S u p p l e m e n t a r y Material Available. A listing of structure factor amplitudes will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supplementary material from this paper only or microfiche (105 X 148 mm, 24X reduction, negatives) containing all of the supplementary material for the papers in this issue may be obtained from the Journals Department, American Chemical Society, 1155 16th St., N.W., Washington, D. C. 20036. Remit check or money order for $8.00 for photocopy or $2.00 for microfiche, referring to code number JPC-75-249. References and Notes (1) T. Seiyama and N. Yamazoe, J. CrystalGrowtb, 2, 255 (1968). (2) F. Jona and G. Shirane, "Ferroelectric Crystals," Pergamon Press, Oxford, 1962. (3) J. Whetstone, Can. J. Res., 266, 499 (1948). (4) E. Janecke, H. Hamacher, and E. Rahlfs, Z.Anorg. Ally. Cbem., 206, 357 (1932). (5) R. V. Coates and J. M. Crewe, Nature (London), 190, 1190 (1961). (6) C. D. West, J. Arner. Cbem. Soc., 54, 2256 (1932). (7) S. B. Hendricks. E. Posnjak, and F. C. Kracek, J. Amer. Cbem. Soc., 54, 2766 (1932). (8) C. S. Choi, J. E. Mapes, and E. Prince, Acta Grystallogr., Sect. 8, 28, 1357 (1972). (9) D.A. Edwards, Z.Krisistallogr. Kristallgeorn., 80, 154 (1931). (10) J. K. Nimmo and B. W. Lucas, J. Pbys. C: Solid State Pbys., 6, 201 (1973). (1 1) T. H. Goodwin and J. Whetstone, J. Cbern. Soc., 1455 (1947). (12) J. Morand, Ann. Cbern. (Paris), 10, 1018 (1955). (13) "International Tables for X-ray Crystallography," Vol. iil, Kynoch Press, Birmingham, England, 1962. (14) J. M. Stewart, G. J. Kruger, H. L. Ammon, C. Dickinson, and S. R . Hall, Technical Report No. TR-192, Computer Science Center of the University of Maryland, 1972. (15) See paragraph at end of text regarding supplementary material. (16) L. Pauling, "Nature of the Chemical Bond," 3rd ed, Cornell University Press, Ithaca, N.Y. 1960.
