ISOMORPHISM AND ALLOTROPY I N COMPOUNDS
A&O(
747
state of this complex ion is of course not represented by either formula I or formula I1 but is a configuration in which both silver ions are in identical states and in which both oxygen atoms are in identical states. SUMMARY
1. The solubility of silver acetate at 25OC. in aqueous solutions containing various amounts of silver nitrate and silver perchlorate has been determined. 2. The results obtained are interpreted by means of the theory of Debye and Hiickel and by assuming the formation of diacetato-argentate ion and of acetatodisilver ion, 3. The dissociation constants of these complex ions have been determined. 4. It is suggested that the stability of one of these ions is due to resonance. 5. The true activity product for silver acetate has been calculated. REFEREKCES (1) MACDOUGALL, F.H., AID ALLEN,MARTIN:J.'Phys. Chem. 46,730 (1912). (2) MACDOCGALL, F.H.,AND REHNER, JOHN,JR.: J . Am. Chem. SOC. 68,368 (1934).
ISOMORPHIShl AKD ALLOTROPY I S COMPOUKDS OF THE TYPE AZO4 M. A. BREDIG Vanadium Corporation of America, 4.90 Lezington Avenue, New York, New York Received Januaru 7 , 19@
In a number of previous publications, experimental work on the conditions of formation and on some structural relations of calcium phosphates, calcium silicophosphates, and calcium alkali phosphates has been described (5, 7, 8, 13, 14). In the present paper a more detailed interpretation and general discussion of the x-ray data, as obtained in those investigations and published previously (13, 14), is given. It is believed that the results may contribute to the knowledge of the structural relations between various substances with tetrahedral anions, and of the mechanism of crystal transformations in chemical compounds in general. I . POLYMORPHISM OF CALCIUM POTASSIUM PHOSPHATE, a- AND O-CaKPO, Calcium potassium phosphate, CaKPO4, has been shown to exist in two distinctly different crystal modifications' which, on account of the similarity in 1 In the former paper (14) the titles of the x-ray diagram were badly misplaced. Proofs were not submitted to this author. Since the corrections could not be published, they are given below: FIG. 1. Equilibrium diagram of the system potassium sulfate-sodium sulfate. FIG. 2. Equilibrium diagram of the system sodium sulfate-calcium sulfate. FIG.3. a-Potassium rhenanite, containing carbonate.
748
M. A. BREDIG
their x-ray pattern to the principal constituent of “Rhenania-Phosphate”, a German commercial fertilizer, were then designated as “a-and @-potassium rhenanite” (14). Klement and Dihn (19) and Klement and Steckenreiter (20) have reported that the results on the polymorphism of calcium potassium phosphate could not be reproduced. However, the slight but distinct differences in the x-ray diagrams of figures 2 and 4 of the above paper (14),representing a- and @-calciumpotassium phosphate, respectively, as well as the exact determination of the transiion temperature, for the transformation a e @, a t 705°C. f 5 O , through observation of the thermal effect on heating and cooling, are ample evidence for the existence of these two different modifications of calcium potassium orthophosphate (“potassium rhenanite”). Furthermore, a thorough examination of all circumstances also had shown that the appearance in the x-ray pattern of the @-form,of what might seem to be merely x-ray lines additional to those of the a-modification, actually can not be attributed to a mechanical admixture, to a-calcium potassium phosphate. Intable 1 the spacings of both a-and @-calcium potassium phosphates are listed together. Especially a t higher reflection angles, there are cases in which one line of a-calcium potassium phosphate is replaced by two lines of the @-form,both of which have positions different from that of the “corresponding” line of the a-form. In view of these facts, any lack of confirmation that calcium potassium phosphate actually forms these particular two crystal modifications must necessarily be attributed to failure in properly reproducing experimental conditions. In addition, it might be said that, without such polymorphism, calcium potassium phosphate would have represented a strange exception among compounds of the type A2XOI,all of which would be expected to, and actually do, occur in more than one crystal modification. The crystal lattice structure of the high-temperature (or a-) form has now been determined and will be discussed in detail in one of the following paragraphs. The structure of the low-temperature (or @-)form has not yet been determined with the same degree of certainty. In analogy to the majority of the compounds of the type A2X04,and after some futile attempts to interpret the powder x-ray pattern on the assumption of a cubic, hexagonal, or tetragonal structure, it is thought most probable that the lattice of @-calciumpotassium phosphate is orthorhombic, or possibly monoclinic, and pseudohexagonal. A proposal regarding structure is made here, on the assumption that the similarity of the x-ray diagram of the @-formto that of the a-modification suggests a close relationship between both structures. Simply, the hexagonal structure of a-calcium potassium phosphate, as described more fully below, with the Fig. 4 . &Potassium rhenanite, 8-CaKPO,. Fig. 6. Potassium apatite, CasK2(P0,)s. Correspondingly, references in the paper to these figures should read as follows: On page 57 at the end of the paragraph preceding the la&: Fig. 2 and Fig. 4. On page 58 at the end of the paragraph preceding the last: Fig. 6. On page 72 at the beginning of the second paragraph: Fig. 3. On page 76 at the end of the first paragraph: Fig. 3.
ISOMORPHISM h N D ALLOTROPY I N COMPOUNDS
&XO(
749
orthohexagonal unit-cell dimensions uo= 9.67, bo= 5.58, and CO= 7.60 (a:b:c = 4:1:1.36), is thought to be slightly deformed, in j3-calcium potassium phosphate, to form a rhombic, pseudohexagonal cell with u;= 9.74, bi= 5.48, and ci= 7.61 ( u : b : c = 1.775:1:1.39). In agreement with common practice, the crystallographic axes may be exchanged so that the smallest dimension becomes TABLE 1 a- and 6-calcium potassium orthophosphates
8-CaKPOd
a-CaKPOd
1
INDICES OBTEO-
INTENSITY
&Id.
BEXAGOSAL
002 202 310 400 401 402 222 004 422 132
m vst. v.st. V.W.
m st.
2. 3.800 2.990 2.790 2,425 2.310 2.050
--
'2. 3.800 2.990 2.785 2.410 2.305 2.045 2.045 1.900 1.645 1.645
m
1.900 1.650
600
m
1.610
1.610
314 620
m m
1.570 1.395 1.263
1.573
W
W
V.W.
'
002 022 130 040 041 042 222 004 242 312
{:! 134
m v.st. v.st. V.W.
m st. m W
m V.V.W.
m
m W
It
V.W.
V.W. V.U'.
1.149
V.W.
W
W W
1.119 1.060 1.048
ddcd
INTENSITY
___
m
1.224
W
INDICES OPTEOPEOhlBIC
W
W U'
A.
d.
3.800 2.990 2.790 2.425 2.305 2,055 2.025 1.910 1.655 1.635 1.6201.590 1.570 1.395 1.266 1.2461.235 1.214 1.156 1.134 1.119 1.065 1.048
3.800 2.990 2.790 2.430 2.315 2.050 2.025 1.910 1.645 1.630
{;:ti: 1.575 1.400
Unit-cell dimensions ao
bo.43
bo = 5.58 = 9.67
eo = 7.60 bo:bo.d/a:ca = 0.578:1:0.787
ao = bo = co = a:b:c =
5.48 9.74 7.61 0.563:1:0.782
the a-axis and the largest one the b-axis: namely, U O = 5.48, bo= 9.74, and co= 7.61 ( u : b : c :=0..563: 1:0.782). Table- 1 shows very satisfactory agreement between spacings as measured, and as calculated on this structural basis. For further confirmation, and for a determination of the atomic positions, single crystals would be required, the preparation of which, however, has very slim prospects.
750
M. A. BREDIG
The unit cell of @-calciumpotassium phosphate contains four molecules of CaKPO,. From these x-ray data, a specific gravity of 2.83 is calculated. 11. THE CRYSTAL STRUCTURE OF @-CALCIUM SODIUM PHOSPHATE
Calcium sodium orthophosphate, CaNaPOd, was shown to be not isomorphous at room temperature with either the a- or the @-formof the corresponding potassium compound, but with orthorhoqp '1 &potassium sulfate, Ii&3Oa (13,14). Table 2 demonstrates this isomorphism c@antitatively through a comparison of TABLE 2 Powder z-ray pattern of &calcium sodium orthophosphate and 8-potassium suljate 8-CaNaPOd
U-KSSOI
INDICES
Intensity
011 020 021 002 121 022 130 122 040 220 lo13 1041 132 113 042
dexptl.
d-14.
1.
A.
W
5.52 4.66 3.86 3.43 3.12 2.755 2.675 2.435 2.335 2.275
5.51 4.66 3.85 3.42 3.10 2.760 2.670 2.440 2.330 2.280
m
2.200
V.W.
2.126 2.034 1.928 etc.
W V.W.
m V.W. V.W.
v.st. v.st. V.W. W
st. st.
Intensity
{;:2 2.110 2.035 1.930
dcdod.
A. m V.W.
4.18 3.75
v.st. v.st.
3.01 2.90
m
2.515
m
2.422 2.385
W
st. st.
2.226 2.083 etc.
A. 5.97 5.025 4.17 3.73 3.38 3 .OO 2.90 2.66 2.514 2.500 2.415 2.385 2.290 2.225 2.083
Unit-cell dimensions
a0 bo co a:b:c
* Reference
A. 1. = 6.830 A. = 5.215
= 9.320
= 0.560:1:0.735
an = bo = co = a:b:c =
5.76 A ? 10.05 A: 7.46 A: 0.573:1:0.742
31.
the interplanar distances. The close analogy of the powder x-ray patterns, together with the knowledge of the unit-cell dimensions of potassium sulfate, as determined by other authors (31) from single crystals, also permitted determination, from these powder x-ray diagrams, of the lattice constants of calcium sodium phosphate, of which single crystals are not available. For calcium sodium hosphate, these unit-cell dimensions are ao= 5.215, bo= 9.320,and CO= 6.830 ., corresponding to the ratio a:b:c = 0.560:1:0.735, very similar to that of potassium sulfate, a : b : c = 0.573:1:0.742,with ao= 5.76, bo= 10.05, and co= 7.46 R.
1
ISOMORPHISM AND ALLOTROPY IN COMPOUNDS
A2XOa
751
Xlement and Dihn (19) have found the ratio of the crystallographic axes for calcium sodium phosphate to be a : b : c = 0.516: 1:0.680, quite different’from that of potassium sulfate. A glance a t the close similarity of the x-ray patterns of both substances which these authors, too, claim to have used for determination of the crystallographic axes of calcium sodium phosphate, seems sufficient to show that a deviation of 9 per cent between the two substances is out of the question. Accordingly, the interpretation of the x-ray diagram and the determination of the lattice constants of p-calcium sodium phosphate by Iilement and Dihn is considered incorrect, the error being due to their erroneous choice of indices for the reflecting planes. This is also indicated by the conspicuous disagreement, by approximately 4 per cent, for the reflections “132” and “222” in film 186 of Klement and Dihn, of calculated and measured values of sin?$, which amounts to a t least four times the usual experimental error. I n addition, the occurrence of reflections with the indices 100, 120,030,500, 003,005, and 007, as reported by Klement and Dihn, is in disagreement with the extinction l a w of the space group Di:, determined by Ehrenberg and Hermann (11) for potassium sulfate. Reflections h01, in which 1 is an odd number, and hkO, in which (h+k) is an odd number, are forbidden. I n table 2, only indices which are in agreement with these extinction l a w occur. 3Ieasurements were not extended to smaller d values than those lizted in the table, because the determination of the indices of such interplanar spacings by means of powder patterns must be considered very uncertain. The presence of two different cations in calcium sodium phosphate does not produce an effect on the crystal structure which would distinguish calcium sodium phosphate from potassium sulfate, with only one kind of cation, escept for small differences in the intensities of the x-ray reflections of both substances. With regard to their ionic diameters, calcium and sodium are almost alike, although their charges are different. The presence of two kinds of cations, such as in calcium potassium phosphate, with considerable difference in the size of these cations, produces a t low temperature a different type of crystal lattice, that of p-calcium potassium phosphate, as shown in the preceding section. 111. T H E POLYMORPHISM O F CALCIUM SODIUM PHOSPHATE
Besides the crystal phase described in the preceding section, another one was found in the experiments on calcium sodium phosphate (13), which produced an x-ray pattern entirely analogous to that of a-calcium potassium phosphate. It therefore might simply have been described as a corresponding second modification of calcium sodium phosphate. However, this phase was obtained only if more than one molecule of carbon dioxidw.two_molecules of phosphorus pentoxide wasts-present in ttie preparation. Since it never occurred in purZ-calcium sodium phosphate, and since, in addition, products with less than one molecule of carbon dioxide per two molecules of phosphorus pentoxide most frequently were mechanical mixtures of rhombic calcium sodium phosphate with this carbonatecontaining “sodium rhenanite”, it could not be considered justifiable to designate it as a modification of calcium sodium phosphate; it was therefore described as a
752
M. A. BREDIQ
quaternary compound, CarNae(PO&COa, and was called “sodium carbonate rhenanite” (13). With further investigation, however, a transition point a t 705OC. was found in calcium potassium phosphate ;thus a-calcium potassium phosphate, isomorphous with ‘ ‘ C ~ ~ N ~ O ( P O ~ )w&s ~ Cshown O ~ ” , to be a truly stable phase only above that temperature (14). Below this transition point, a-calcium potassium phosphate could be stabilized by the addition of carbonate, with formation of a solid solution of the approximate composition Ca4Ke(P04)4COs. The suspicion was strengthened that the so-called quaternary compound Ca4Nas(P04)&03, too, was nothing but a solid solution of sodium carbonate in a high-temperature form of calcium sodium phosphate which differed from calcium potassium phosphate only in its speed of transformation, in the pure state, into the low-temperature phase. That is, without the presence of carbonate, this hypothetical form of calcium sodium phosphate, analogous in structure to a-calcium potassium phosphate, could never be preserved by quenching even from 1200°C. This complete analogy, with respect to the existence of a high-temperature modification, limited only by the difference in the ease of transformation in rapid cooling, actually could be demonstrated thereafter by x-ray photographs of calcium sodium phosphate, taken directly a t elevated temperatures, as well as by the thermal effect in cooling and heating. Such x-ray photographs clearly prove the presence, in pure calcium sodium phosphate above 70O0C., of a phase entirely analogous to “Ca4Nas(PO4)4COa” and to a-calcium potassium phosphate. The transition point is 680°C. It was previously observed a t roughly 700°C. in preparations of calcium sodium phosphate which contained silicate (13). The occurrence of this high-temperature form (a) of calcium sodium phosphate apparently has been confirmed by Schleede and coworkers (29, 30). Also, Klement and Steckenreiter (20)claim to have obtained it even at room temperature by quenching calcium sodium phosphate from the molten state. A determination of the transition point was not reported by these authors. Ouvrard (27) has mentioned several crystallized phases of calcium sodium phosphate, but since he attributed different chemical compositions to them, he cannot well be considered the first observer of the polymorphism of calcium sodium phosphate, &s stated by Klement and coworkers. These latter authors were not able to reproduce the stabilization of the a-form of calcium sodium phosphate by sodium carbonate, by preparing the solid solution of the composition Ca4N%(PO&CO3. Their failure, though difficult to understand, might be attributable to overheating of their reaction product, which might cause decomposition of this “sodium carbonate rhenanite” in accordance with the following equation (13): Ca4Sae(PO4)&08 = 3CaNaPO4
+ NasPO4 + CaO + COz
The suggestion has been made in a recent U. S. patent (No. 2,221,356), dealing with the direct manufacture of sodium phosphate from rock phosphates and alkali oxide (carbonate), that carbon dioxide be excluded or driven off completely
ISOMORPHISM AND ALLOTROPY I N COMPOUNDS
AzXOa
753
from the reaction product. This suggestion is believed to be a t least partly connected with the formation of that water-insoluble sodium carbonate rhenanite which contains, in one single solid phase, calcium, alkali metal, phosphorus pentoxide, and carbon dioxide, which prevents part of the phosphorus pentoxide from being converted into water-soluble sodium phosphate. The above equation represents an equilibrium depending on temperature, carbon dioxide pressure, and concentration of the components. IV. THE NEW GROUP OF ISOMORPHOUS HIGH-TEMPERATURE MODIFICATIONS O F COMPOUNDS O F THE TYPE
AzXO4
A . a-CaNaPO4 and a-CaKP04 The lattice constants of a-calcium sodium phosphate and a-calcium potassium phosphate were derived from powder x-ray patterns by means of the Hull-Davey curves. Table 3 contains the interplanar distances as measured and as calculated for an hexagonal lattice. The agreement is considered very satisfactory. The elementary cell contains two molecules of CaSaP04 (or CaKP04).
B. The high-temperature modi3cations of sodium and potassium sulfates
(a-)
The isomorphism of the low4emperature forms of calcium sodium phosphate and potassium sulfate also suggested isomorphism of the high-temperature modifications. The structure of the high-temperature form of potassium sulfate has not been known, except for a brief discussion by Goldschmidt (15), who attributed to it an hexagonal structure analogous to that of phenacite, BeZSiOd. X-ray patterns of potassium sulfate above its transition point a t 590°C. do not confirm this view, but show ths', a-potassium sulfate is isomorphous with a-calcium sodium phosphate (table 3). Accordingly, calcium sodium phosphate and potassium sulfate are polyisomorphous compounds, with transition points at 680' and 59OoC., respectively. At no temperature are they isomorphous with phenacite, the lattice of which is of a more complicated nature, with nine times as many A s 0 4 molecules in the smallest hexagonal unit cell. Further comparison with known structural data of the literature also revealed that for the high-temperature modification of sodium sulfate, ?;a,sOa(I), a powder x-ray pattern had been obtained by Kracek and Icsanda (21), which in table 3 is demonstrated to be entirely analogous to those of a-potassium sulfate, a-calcium sodium phosphate, and a-calcium potassium phosphate. Recently, Ramsdell (28) has obtained the lattice constants of the hexagonal form of sodium sulfate, NdOd(I), or a-sodium sulfate, a. = 5.385, co = 7.270, and has found that it can be stabilized at room temperature through formation of a solid solution with sodium carbonate. This is in complete analogy to the conditions described for the system CaNaP04-NazCOs in the preceding section. The isomorphism of a-sodium sulfate(1) and a-potassium sulfate had also been indicated by microscopic observations and by the thermal equilibrium (meltingpoint) diagram (22), showing an uninterrupted series of solid solutions. The only substance known heretofore, having the particular structure which was now found in the high-temperature modifications of the alkali sulfates and
M. A. BREDIQ
Y I
-
I
ISOMORPHISM AKD ALLOTROPY IN COMPOUSDS
A2XO4
755
calcium alkali phosphates, has been glaserite, KarSa(S04)~. While Gossner (16), who determined the structure in detail, considered glaserite as a definite binary compound, van't Hoff and Barschall (37) pointed to the existence of a series of solid solutions, including the composition Ii3Na(S04)2. Table 3 demonstrates the isomorphism of glaserite with the high-temperature modifications of the alkali sulfates. Glaserite therefore will have to be considered simply a solid solution, in the high-temperature form, of both potassium sulfate and sodium sulfate. Figure 1 illustrates, somewhat schematically, the equilibrium relationships. The four individual compounds a-NazS04(I),a-KzSOd, a-CaXaPO4, and a-CaKPOcrepresent the first members of a new group of isomorphous compounds of the type A2XO4. Among other substances of this molecular composition, more will be found to belong to this new group. For instance, rubidium sulfate,
I
.
100
.
.
, . . . . I 100
50
%so,
NnZS0+
N*+X4
Cas&
MXERRCEM FIG.2
MOLE R R E N T FIG.1
FIG.1. Equilibrium diagram of the system potassium sulfate-sodiurn sulfate FIG.2. Equilibrium diagram of the system sodium sulfate-calcium sulfate
cesium sulfate, potassium selenate, and potassium chromate, as well as silver sulfate and silver selenate, known to be isomorphous with the low-temperature (@-) forms of potassium and sodium sulfate, respectively (23), are very likely to assume, above their transition points, the hexagonal structure of glaserite. Many other substancea of the type A2X0,,such as chromates, vanadates, molyhdates, tungstates, etc., can be expected to join, in their high-temperature modifications, the new structural group. The atomic positions in the new isomorphous group, as determined by Gossner for glaserite, are as follows:
A, cations: (OOO); (004); &(# 4 u ) X, central atoms of tetrahedrons (P, S, Si, etc.): &(+
0,oxygen atoms:
5
j=($ w ) ;
*(P,
P, 9 ; 21% zi,
5 v)
4;P, ZP, d
756
M. A. BREDIG
For glaserite, Gossner determined the parameters u = 0.875, t~ = 0.27, w = 0.46, p = 0.20, q = 0.20. They can be expected to vary slightly in the other substances of the group, in accordance with the dimensions of the substituting ions. The space group is D$. It is interesting to note that a lattice of such a structure can take up relatively large amounts of carbonate ions, BS is demonstrated by the formation of the solid solutions CaNaP04-NazC03, CaKP04-K2COs, and NazS04-NazCOI mentioned above. Sodium sulfate and sodium carbonate have been known to form an uninterrupted series of solid solutions in equilibrium with the molten phase (22). The only way in which carbonate ions may enter the sulfate or phosphate lattice is by simple replacement of XOa anions, so that not all oxygen places of the AzX04lattice are occupied in such mixed crystals. The change of the x-ray pattern, accompanying the entrance of carbonate, is of a very minor nature (cf. figures 2 and 3 of reference 14).
C.Some other alkaline-earth alkali phosphates Isomorphism of one of two reported forms of each of the compounds strontium sodium phosphate and barium sodium phosphate, possibly the low-temperature forms, with the high-temperature form of calcium sodium phosphate has been demonstrated qualitatively (20). By using the reported reflection angles of the schematic diagrams, approximate value of the lattice constants can be obtained:
..I
SrKaP04... . . . . . . . . . . . . . . . . . . . . . . . . BaNaP04........ . . . . , . . . . . . . . . . . .
5.48
5.64
I
7.36 7.35
I
1.34
1.30
I,
3.55 4.17
It does not seem certain that these modifications of strontium sodium phosphate and barium sodium phosphate, isomorphous with a-calcium sodium phosphate or sodium sulfate(I), are the phases truly stable at room temperature, since they were obtained by quenching from a rather high temperature, 700°C. Rather, it is quite likely that another, third, modification exists below the range of these hexagonal forms. In addition, the same reasons which prevented Klement and coworkers from observing the particular x-ray interferences of the low-temperature (6-) form of calcium potassium phosphate may be responsible for a possible failure to recognize corresponding details in the x-ray patterns of strontium sodium phosphate and barium sodium phosphate. Possibly, the original x-ray patterns of these substances may actually have shown complete analogy, not with the hexagonal a-form, but with the orthorhombic p-form of calcium potassium phosphate. These relations therefore require clarification. D. &XO4 structures in calcium silicophosphates Comparison of powder x-ray patterns of calcium alkali-metal phosphates with that of a seemingly complicated calcium silicophosphate, prepared by Troemel and Korber (35), of the composition Ca8(PO&(Si04)z.s,had indicated isomorphism of these substances (13). The same mixed cdcium phosphate silicate, with
ISOMORPHISM AND ALLOTROPY I N COMPOUNDS
AzXOa
757
a slightly different composition, C~.I(PO~)Z(S~O&, has also been identified by means of x-ray diffraction patterns by Nagelschmidt (26) in basic open-hearth furnace slags. According to the data listed in table 3, Ca7(P04)z(Si04)2appears to possess the simple hexagonal crystal lattice of a compound of the type A2X04, isomorphous with the a-modifications of the alkali sulfates. One of the x-ray reflections listed by Nagelschmidt (d = 1.862) could not be interpreted with the hexagonal lattice constants. However, it seem to be permissible to ascribe this very weak line to an impurity. I t was the only line which appeared with different, and somewhat higher, intensity in a second sample, prepared by Troemel, which apparently had not undergone the process of purification applied by Nagelschmidt to his own sample. The agreement between the values of the specific gravity, as measured directly by Nagelschmidt and as calculated from the lattice constants, is very good. Kagelschmidt observed that the substance was optically biaxial, which would be contradictory to hexagonal symmetry. The very small angle between the optical axes permits the explanation that a slight deformation of the hexagonal crystal, possibly due to severe temperature conditions, produced this optical effect. In Ca7(P04)2(SiO&, one-eighth of the cation positions of the hexagonal AzXO4 structure are not occupied. Substances, particularly solid solutions, with unoccupied cation positions are not unusual. I t has been pointed out previously (13, 14) that such a deviation from the ideal composition of the structural type is not surprising in view of the high temperatures a t which such substances are prepared. Ca5(P04)2Si04, which in the form of silicocarnotite is another well-known constituent of open-hearth furnace slags (7, 26), is reported to occur in a second high-temperature form which was described as having an x-ray pattern quite analogous to that of a-calcium sodium phosphate (20). From the published data on the x-ray diffraction lines, the hexagonal lattice constants of this form are obtained as approximately ao = 5.21, cn = 6.90, and c / a = 1.32. The average mas3 content of the simple hexagonal unit cell of Cas(P04)n(Si04), corresponding to 2Na2SO4or 2CaNaP04,is Ca3.33(P04)~ 33(Si04)o6 7 , and that of Ca?(P04)z(SiO& is CaB5(P04)(Si04). In Ca6(P04)z(Si04),even as much as one-sixth of the cation positions of the AzXO4 lattice are vacant. A number of preparations, composed of calcium and alkali-metal cations and of sulfate, phosphate, and silicate anions, were found to be isomorphous with a-calcium sodium phosphate, although the cation positions of the a-calcium sodium phosphate space lattice were not completely occupied (20). Kot “mixed compound”, but “mixed crystal” or “solid solution”, seems the proper name for such substances that are crystallized in the form of a simple compound of the type AZX04 and contain a certain quanbity of components deviating from AzXO4 in molecular composition. For instance, a substance such as “Na&aS,O d , designated by Klement and Steckenreiter (20) in accordance with earlier work by Muller (25) as a “binary compound”, is nothing but a solid solution, or a mixed crystal, of a certain amount of calcium sulfate in a-sodium sulfate(1).
758
M. A. BREDIQ
It has already been emphasized by Grahmann (17) that it is not permissible to draw any conclusion from the occurrence of a maximum in the solidification curve of solid solutions as to the existence of a particular binary compound. This author pointed to the fact that a maximum analogous to that in the system NasS04-CaSOl appears in the solidification curves of a number of similar systems, such as K2S04-SrS04 (at 5 mole per cent strontium sulfate), in Na2S04-PbS04 and KtSO4-CdSO4 (at 7 mole per cent lead sulfate and cadmium sulfate, respectively) and in K2S04-BaS04 (at 10 mole per cent barium sulfate), that is, a t compositions to which no simple binary molecular formula can be ascribed. Also, in the system Na2S04-CaS04, the maximum does not actually occur a t the exact composition 20 mole per cent, but rather at 22.5 mole per cent, according to the original data of Muller. Therefore, a substance such as ‘“a*CaSs020” represents just one of a limited series of isomorphous compositions (Ca,Na)2(S04),starting with pure sodium sulfate and having the crystal structure of a-sodium sulfate with numerous unoccupied cation positions. Only the detection of x-ray reflections, in addition to those of a-sodium sulfate and corresponding to a “superstructure” and to an organized, instead of a statistical, distribution of the calcium ions, would invalidate this view. A modified equilibrium diagram of the system NazSO~-CaS04, construed according to the experimental data of Muller with the confirmation of the new x-ray data, but without the assumption of the binary compound L~NagCaS5020”, is drawn in figure 2. With the observation, by Muller, of the eutectoid point a t 178’C., the new a-sodium sulfate phase boundary line (dotted), connecting the eutectoid with the eutectic line and marking the solubility of calcium sulfate in a-sodium sulfate, seems in most satisfactory agreement. Decomposition of the more concentrated solid solutions is too slow a t temperatures not far above the eutectoid temperature, owing to the lack of diffusion a t such low temperatures, to permit, in continuous cooling as in the thermal analysis runs, complete precipitation of calcium sulfate and transformation of the a-solid solution into the low-temperature forms of sodium sulfate. This explains the failure of Muller to obtain the actual phase boundary line for the a-solid solution and the transformation, in mixtures with more than 10 mole per cent calcium sulfate. Similarly, substances such as “Ca5(P04)zSi04”or “ C ~ ~ ( P O ~ ) Z ( S ~are O ~not )Z” considered binary compounds of Ca2Si04with CaB(PO4)2,but just members of a continuous series of solid solutions of calcium phosphate in calcium orthosilicate, of the composition Ca2_~(P04).(Si04)1-,,in which z has been found (30) to range 2
from about 0.20 to 0.67, and which are isomorphous with a simple hexagonal compound A&04, such as a-potassium sulfate. The occurrence, in ‘kalcium silicophosphates”, of a crystal structure analogous to that of &potassium sulfate has also been briefly reported (30),with z being less than 0.20. Besides these two crystal structures, isomorphous with a- and @-potassium sulfates, respectively, and besides that of silicocarnotite, a fourth structure was found in “calcium silicophosphates” by Bredig, Franck, and Fuldner (7). This phase sometimes occurs in calcined rock phosphate, in addition to or in
ISOMORFEISM AND ALLOTROPY IN COMPOUNDS -42x04
759
place of the structure of a-tricalcium phosphate, which also can dissolve certain amounts of calcium silicate in solid solution. Its composition is approximately Ca4PzSiOll but could not be fully ascertained thus far because of the erratic occurrence of this structure, which also caused it to be designated as “compound X” ( 7 ) . “X” is not isomorphous with any known A2XO4 structure, although its composition may be represented as a combination of Ca?SiOa with CazP207, aa well as of Cas(PO4)2 with CaSiOs. Besides having this structure “X”, and also that of a-tricalcium phosphate, the combination Ca4PzSiOll w&s reported to occur in a third form (30), isomorphous with a-calcium sodium phosphate (glaserite structure). In this form, it is considered as a solid solution of Ca2P20Tin Ca2Si04. V. INTERMEDIARY COMPOUNDS, SOLID SOLUTIONS, AND POLYMORPHISM
The observation that substances which had previously been described as definite compounds, as, for instance, NasCa(S04)s,Ca4Piaa(P04)pCOa,or &Sa(SO&, actually are solid solutions of calcium sulfate in a-sodium sulfate, of sodium carbonate in a-calcium sodium phosphate, and of sodium sulfate in apotassium sulfate deserves a brief general discussion. The number of chemical “compounds” described in the literature and listed in the handbooks of inorganic chemistry can probably be reduced by hundreds of items, of sometimes very conspicuous composition, when the true nature of these alleged “intermediary phases” as being solid solutions is revealed by the discovery that their crystal structure is identical with one of various crystal modifications of one of their components. In the case of the calcium silicophosphates, the component calcium orthosilicate, Ca2Si04,is of the molecular type AzXO4 for which at least two of the occurring crystal structures (those of a- and @-potassiumsulfates) are characteristic. Of the three crystal modifications of calcium orthosilicate, the lowand medium-temperature forms, @- and y-, are comparatively well known and are not isomorphous with any of the four crystal forms of calcium silicophosphates mentioned above. However, according to Hansen (18), the third modification of calcium orthosilicate actually is not known, because it is stable only above the transition point a t 1420°C. and cannot be preserved below that temperature by quenching. The evidence to the contrary, as presented by various authors from thermal, optical, and x-ray measurements, to prove that the a-modification had been obtained, is not convincing. All the observed differences between the so-called monoclinic, high-temperature a-form and the orthorhombic, medium-temperature @-modificationare very slight (3, 4, 10, 12, 32, 31) (e.g., x-ray patterns and specific gravity, 3.27 and 3.28). They do not exceed the differences which might be expected if the @-formactually was present in both cases, but was produced in different ways: that is, in one case, by holding it, before quenching, in its own temperature range of stability, between 700” and 140O0C., and, in the other case, by rapid transformation from the a-form by rapid cooling from above 1420°C. Thus, the characteristic formation of fine twin lamellae in the alleged a-calcium orthosilicate samples, produced by
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quenching from temperatures above 142OoC., together with the close similarity of the optical and x-ray data, may well be taken as an indication that transformation into the ,%form had occurred, and that therefore the a-modification actually has never been observed thus far. Furthermore, it is not very plausible that in a substance such as calcium orthosilicate, a monoclinic form should be stable at higher temperatures than an orthorhombic form, while transformation, above 142OoC.,into a crystal modification of higher symmetry, such as the hexagonal structure of a-sodium sulfate, would be quite,understandable. However, even if the existence above 1420’C. of the monoclinic form, as assumed by several authors, were admitted, the existence of a fourth modification, of the simple hexagonal structure, is still conceivable in the wide temperature range below the melting point a t 2200°C. X-ray photographs of calcium orthosilicate a t such high temperatures might be applied to clarify these relatiom. The occurrence, in “calcium silicophosphates”, of various crystal forms si believed to be due to the instability, at lower temperatures, of the hexagonal high-temperature (a) structure of the calcium orthosilicate solid solutions. At very high temperatures substances such as Ca6(P04)2(Si04),in the silicocarnotite form as well as in the glaserite structure, such &s Ca,(P04)2(SiO&, which is which is isomorphous with glaserite, and such rn (Ca2Si04,1/12Ca3(P04)2), isomorphous a t room temperature with ,%potassium sulfate, and the like, are believed to take on the truly hexagonal structure of the high-temperature (CY-) form of the alkali sulfates, but to be transformed, in cooling, into the various structures of solid solutions in calcium orthosilicate, adjusted to the amount and nature of foreign additions and to the thermal conditions. In Ca?(PO4)2(SiO& and in the “high-temperature form” of Cas(P04)2(Si04),the hexagonal structure appears to be preserved, In the silicocarnotite form of the latter, transformation apparently has occurred from the hexagonal high-temperature form of the calcium orthosilicate solid solution. It is yet to be determined whether this means the formation of a definite compound, such as CazSiOd.Cas(P0J2, from a solid solution,-which, in principle, is quite possible,--or whether Cas(POa)z(Si04),in the form of silicocarnotite, must be considered just another form of a solid solution of calcium phosphate in calcium orthosilicate. This may be done by investigating more thoroughly the equilibrium conditions, or, by means of x-ray diffraction, the distribution (order or disorder), in the crystal lattice, of the orthophosphate and orthosilicate anions or of the unoccupied calcium positions. No interpretation other than the assumption of a solid solution of a small amount of calcium orthophosphate in calcium orthosilicate seems having the structure of a simple compound possible for (Ca&3i0~,l/12Ca~(P04)~), ASXO, such as &potassium sulfate.* The trimorphism of preparations of the approximate composition CarP8iOll
* W. G . Taylor (33) recently described a substance KzO.23Ca0.12SiO~aa an intermediate compound in the system CanSiO,-CaKzSiO,. His x-ray data, however, seem to show quite clearly irromorphism with D-K2SO,, that is, with a simple compound of the type A2X0,: K10.23Ca0~12SiOz,therefore, will have t o be considered, quite analogously t o (Ca,SiO,, 1/12Cal(PO,)2), aa a solid solution (CanSi04,1/11CaKnSiO,) which at high temperatures is very likely to aasume glsserite structure.
ISOMORPHISM AND ALLOTROPY I N COMPOUNDS
A&Oi
761
can be interpreted by the existence of a stabilized hexagonal Ca2SiOd-Ca2PzOr solid solution in one case, of a solid solution of CaSi03in a - C a ~ ( P 0 4in ) ~another, and, in the case of “X”, either as a modified form of a solid solution of CaSiOa in Cas(PO& or as a compound Ca3(P04)t.CaSiOa or CazSiO4.Ca~PzOr. Because a t least two of the structures occurring in “calcium silicophosphates” have been found to be structures of simple compounds of the type AzX04, and because calcium orthosilicate is the only component which corresponds to this formula, the term “calcium phosphatosilicate” (24) for these substances appears preferable to the designation “calcium silicophosphates”. VI. THE MECHANISM OF STABILIZATION OF UNSTABLE MODIFICATIONS
The high-temperature forms of some compounds of the type AzX04, such as sodium sulfate, potassium sulfate, calcium sodium phosphate, and calcium orthosilicate, cannot or can only with difficulty be preserved at room temperature by quenching. They can, however, be stabilized, preferably by the addition of compounds such as carbonates, alkaline-earth sulfates, tricalcium orthophosphate or dicalcium pyrophosphate, which deviate from AzX04 either in the composition of the anion XOaor in the number of the cations. An addition tends to stabilize an unstable form if it is insoluble in the stable modification of the compound, or if it is soluble only in an amount much smaller than that dissolved in the originally unstable structure. Low solubility in the low-temperature form can be expected, ( a ) if the added substance has a molecular composition different from the compound to which it is added, particularly with respect to the number of atoms in the molecule, and ( b ) if the added substance, though analogous in molecular composition, is not isomorphous with the low-temperature form of the compound to which it is added. The stabilization of a-sodium sulfate or a-calcium sodium phosphate by sodium carbonate, of a-calcium potassium phosphate by potassium carbonate, of an hexagonal form of calcium orthosilicate by calcium orthophosphate or calcium pyrophosphate, and of a-sodium sulfate by calcium sulfate are specific examples for the former case, while the latter is represented by glaserite, (K,Xa)2S04,and by the stabilization of the hexagonal lattice in solid solutions of CazSi04-CaXaP04. Two variations must be distinguished in the mechanism of stabilization: (1) The high-temperature form of the pure compound may be made truly stable, thermodynamically, relative to a heterogeneous mixture of the low-temperature forms of the components of the solid solution. Glaserite, approximately KsNa(S04)~,probably is such a stable mixed crystal (37). ( 2 ) The stabilization may consist only in a very considerable reduction in the speed of the transformation, so that in rapid cooling it can be stopped completely. This sluggishness of a two-component system is explained by the need for diffusion-too slow in solids a t low temperatures-to permit precipitation of the added component which is insoluble in the low-temperature phase of the main constituent of the solid solution. It is not possible to preserve the high-temperature a-forms of pure sodium
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sulfate or potassium sulfate a t room temperature even with the fastest rate of quenching, from the molten state. It is however possible, though difficult, t o preserve the a-form of calcium sodium phosphate. It is not difficult to obtain a-calcium potassium phosphate. For an explanation of these differences in the behavior of isomorphous modifications of chemical compounds, it seems quite possible to assume that, owing to the method of preparation a t high temperatures, both the latter substances actually differed sufficiently from the ideal composition A a O 4 to be considered as not truly pure compounds. In the case of the two calcium alkali phosphates, precipitation from solid solution of a certain amount, hourever small, of impurities, such as calcium orthophosphate, calcium pyrophosphate, sodium orthophosphate, and potassium orthophosphate, might be required for transformation into the low-temperature 0-forms, but does not take place during the short time period of quenching. One additional influence, among others, is the position of the transition point which determines the relative and absolute temperature range in which diffusion has to take place. In the alkali sulfates these transition points lie about 500°C. below the melting points, while this distance in calcium sodium phosphate and calcium potassium phosphate amounts to more than 700OC. A similar precipitation mechanism has, for instance, been assumed as an explanation of the stabilization of a-tricalcium phosphate by small amounts of calcium oxide or calcium silicate (8). Instead of stabilization of the high-temperature form or of formation of the stable low-temperature form, there may occur at times the formation of another crystal modification from the high-temperature solid solution on cooling, owing to the presence of foreign substances. This new crystal form may not occur in either component of the solid solution in its pure state. In the solid solution, it may be either truly thermodynamically stable, or it may only be metastable compared with a more stable form of the solid solution or with a mixture of the low-temperature forms of the components. Silicocarnotite, Cas(PO&3i04, may be such a case (or it may also be a definite binary compound), and Ca~SiOa,l/l2 Cas(P04)z may be another one, representing a crystal form of the type AzX04, unknown in pure calcium orthosilicate. Possibly the phase “X”, of the approximate composition Ca4(P04)2Si03, also belongs to this class, unless it represents a definite ternary compound in the system CaO-P206SiOZ. The stabilization of unstable crystal structures by foreign substances has more recently been studied by Buerger and Bloom (1, 2,9). For instance, senarmontite, the high-temperature form of antimony trioxide, has been found to occur a t room temperature, stabilized by small amounts of impurities. The stability of the aragonite form of calcium carbonate has also been found to be due to the presence of impurities. Many more examples are listed in the work of Buerger and Bloom. Among metallic systems in which these phenomena have been studied more extensively, the austenitic 18-8 stainless steel has recently been shown by Uhlig (36) to be stabilized, by little more than 0.10per cent of nitrogen, against thermal transformation into a-ferrite though not against transformation by cold work. A more detailed study of the mechanism of stabilization of and precipitation
ISOMORPHISM .4KD ALLOTROPY IN COMPOUKDS
AzXOi
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from solid solutions, in crystal transformations of chemical compounds, can be expected to yield further interesting results in all those various fields, of pure chemistry as well as of technology, in which the properties of crystallized solids are of importance, as in ceramics, where transformation phenomena have found due attention, or in pigments, catalysis, and others. As an example, one commercially important property of the phosphates, discussed in this and previous papers, will be briefly mentioned. The high-temperature forms of Cas(P04)n(a-tricalcium phosphate), of a-calcium sodium phosphate, and of Ca5(P04)2Si04 (glaserite structure) are more readily soluble in ammonium citrate solution and, therefore, appear to be better suited as fertilizers than the corresponding low-temperature modifications, (3-Ca8(P04)z (8), @-calcium sodium phosphate, and silicocarnotite (29). While we may expect a metastable crystal modification to be more soluble than the stable form, that behavior might also be attributed to the presence of small amounts of apatite, which may be precipitated from the solid solution during transformation into the low-temperature phase and which may inhibit dissolution of portions of the low-temperature phases. VII. SUMMARY
1. In the temperature range below their melting points, alkali sulfates constitute with alkali alkaline-earth phosphates a new group of isomorphous compounds &X04 of a simple hexagonal structure (glaserite type) which is expected to include many more compounds of the AzXO4 type, particularly a t elevated temperatures. Below their transition points, in accordance with the increased influence, a t lower temperatures, of the properties of the individual ions, the majority of the members of the group have individual crystal structures, mostly of orthorhombic symmetry. 2. The crystal structure of the low-temperature ((3-) form of calcium sodium phosphate is identical with that of orthorhombic P-potassium sulfate, and its lattice constants were derived from the powder x-ray pattern on the basis of this complete analogy. h preliminary structure proposal is made for p-calcium potassium phosphate. 3. The occurrence of solid solutions of calcium phosphate in calcium orthosilicate (CazSi04),which are isomorphous with glaserite, leads to the assumption that calcium orthosilicate itself may belong, above its upper transition point a t 142OoC., to the structural group of hexagonal high-temperature forms of the glaserite type. Other crystal forms of these solid solutions of calcium phosphates in calcium orthosilicate have other structures, such as that of (3-potassium sulfate. 4. Besides true thermodynamic stabilization, slowness of diffusion and, therefore, of separation of one solid phase into two or more solid phases is considered as a controlling factor for the stabilizing effect of foreign additions in many crystal transformation phenomena occurring in chemical compounds.
The author is indebted to Dr. Albert R. Frank, t o the late Dr. S. Caro, and t o Dr. H. H. Franck for having been granted the opportunity to begin this
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invastigation in their research laboratory, and for their helpful interest in its progress during its earlier stages. REFERENCES BLOOM, M. C.: Am. Mineral. 24, 281 (1939). BLOOM, M. C., AND BUERGER, M. J.: Z. Krist. 96, 365 (1937). BOWEN,N . L., SCHAIRER, J. F., AND POSNJAK, E.: Am. J. Science 26, 273 (1933). BRANDENBERGER, E . : Schweia. Arch. angew. Wiss. Tech. 3, 239 (1937). BREDIG,M. A , : Z. physiol. Chem. 216, 239 (1933). BREDIG,M. A.: J.Am. Chem. Qoc.63,2533(1941). BREDIG,M. A., F R . ~ N C K , H . H., AND F~JLDXER, H.: Z. Elektrochem. 38, 158 (1932). BREDIG,M.A , , FRANCK, H . H., AND F ~ ~ L D NHE. :RZ., Elektrochem. 39, 959 (1933). BUERGER, M. J.: Proc. Natl. Acad. Sci. U. 5. 22, 685 (1936). DAY,A. L., ALLEN,E. T., SHEPHERD, E. S., WHITE,W. P., AND WRIGHT,F. E.: J. Am. Chem. SOC. 28, 1089 (1906); Am. J. Sci. [4] 22, 265 (1906). EHRENBERO, W., AND HERMANN, C.: Z. Krist. 70, 163 (1929). FERGUSON, J. B., AND MERWIN,H. E . : Am. J. Sci. [4] 48, 85 (1919). FRANCK, H . H., BREDIG,M. A., AND FRAXK, R.: Z. anorg. allgem. Chem. 230, 1 (1936). FRANCK, H. H., BREDIG,M. A,, AND KANERT,E.: Z. anorg. allgem. Chem. 237, 49 (1938).
GOLDSCHMIDT, V. AX. : Geochem. Verteilungsgesetze VII, 107 (1926). GOSSNER,B.: Neues Jahrb. Mineral. Geol. B67A, 89 (1928); Strukturbericht, 19131928, p. 378; Z. Krist. 39, 155 (1904). GRAHMANN, W.: Z. anorg. Chem. 81, 266 (1913). HANSEN,W. C.: J. Am. Ceram. SOC.11, 68 (1928). KLEMENT, R., AND DIHX, P.: Z. anorg. Chem. 240, 40 (1938). KLEMENT, R., AND QTECKENREITER, F.: Z. anorg. Chem. 246, 236 (1940). KRACEK, F. C., AND KSANDA, C. J.: J. Phys. Chem. 34, 1741 (1930). LANDOLT-B~RNSTEIN: Physikalisch-chemische Tabellen, Vol. I, p. 605. J. Springer, Berlin (1923). LANDOLT-B~RNSTEIN: Physikalisch-chemische Tabellen, 5th edition, Suppl. 1'01. 111. J. Springer, Berlin (1935). MELLOR,J. W.: T r e a t i v on Inorganic and Theoretical Chemistry, Vol. VI, p. 364. Longmans, Green and Company, London (1925). MULLER.H.: Neues Jahrb. Mineral. Geol... S U_ D .DVol. ~ . 30, 1 (1914). i 2 6 j NAGELSCHMIDT, G.: J. Chem. SOC.1937, 865. (27)OUVRARD, L.: Compt. rend. 106, 1600 (1888). (28) RIMSDELL, L. s.: Am. Mineral. 24, 109 (1939). (29) SCE:LEEDE, A.: Angew. Chem. 63, 65 (1940). (30) SCHLEEDE, A,, MEPPEN,B., AND RATTAY,K . H.: Angew. Chem. 60, 613, 909 (1937). (31) Strukturbericht, Vol. 11; Z. Krist., 420 ff. (1936). (32) SUNDIVS, N.: Z. anorg. Chem. 213, 343 (1934). (33) TAYLOR, W. C.: J. Research Natl. Bur. Standards 27, 311 (1941). (34) TILLEY,C. E.: Mineralog. Mag. 22, 77 (1929). (35) TROEMEL, G., AND K ~ R B E R A.:, Arch. Eisenhtittenw. 7, 7 (1933). (36) UHLIG,H. H.: Trans. Am. SOC.Metals, Preprint, 1941. J. H., AND BARSCHALL, H.: Z. physik. Chem. 56, 212 (1906). (37) VIK'T HOFF,
