Growth and characterization of AgI polytypes

GROWTH AND CHARACTERIZATION OF Agl POLYTYPES P. R. Prager School of Physics, University of Melbourne, Parkville, Victoria 3052, Australia (Submitted 12May 1983)

1.

INTRODUCTION

Silver iodide is a remarkable substance in many of its properties, apart from its membership of the growing class of compounds which exhibit polytypism. For example, it has a substantial negative coefficient of thermal expansion over the entire temperature range of the stable low-temperature phase (I), while the hightemperature phase has an extraordinarily high ionic conductivity -- o = 1.35 ohm -I cm-I (2,3) -- which places it foremost in the class of superionic conductors (4). Our concern being with the polytypic modifications of Agl, we shall be concentrating our attention mainly on the phases which occur at normal pressure, where such polytypes are to be found in some profusion. However, as will he discussed below, there is some evidence of polytypic transformation at higher pressures, and the complete phase diagram of Agl will therefore be reviewed briefly. Figure 1 sketches the main features of the temperature-pressure phase diagram of silver iodide, based on the work of many investigators from Mallard and le Chatelier (5) in 1883 onwards. At room temperature and normal pressure (within the region labelled II) both a face-centred cubic and a hexagonal modification were originally reported as co-existing (6-8). This situation is characteristic of the circumstances under which binary compounds occur in polytypic modifications. The cubic modification has a sphalerite-type structure (B3) and is denoted as Y-Agl; the hexagonal modification has a wurtzite-type structure (B4) and is denoted as fl-Agl. At 146.5°C and I bar the low-temperature forms undergo a first-order phase transformation to a body-centred cubic structure, u-Agl (region I), with the anomalously high ionic conductivity previously mentioned. The structure of this disordered or 'statistical' phase is an interesting one whose details have undergone significant refinement in recent years. The original model due to Strock (9,10) and Hoshino (ll) was based on limited X-ray powder diffraction data. It envisaged the iodide ions as occupying the 2(a) 000 sites of the space group Im3m, with the two silver ions per unit cell randomly distributed over a total of 42 sites pertaining to this space group: the 6(b) 0~} octahedrally-coordinated sites, the 12(d) ¼0~ tetrahedrally-coordinated sites and the 24(h) 0xx triangularlycoordinated sites (Fig. 2). Vigorous isotroplc harmonic thermal vibration was attributed to both atomic species in this model. Recent studies (|2-15) have been 451

452

P.R.

Prager

300 U O 200

I i00

IIl

[ V I

II 5 PRESSURE

10

i00

kbar

Fig. I.

The pressure-temperature phase diagram of silver iodide. After (27,28).

Fig. 2.

Model of body-centred cubic ~-Agl due to Strock (9,10) and Hoshino (II). The 2(a) sites are represented by large unfilled circles; the 6(b) sites by large filled circles; the 12(d) sites by small filled circles; and the 24(h) sites by small unfilled circles. After (23).

Growth and characterization of Agl polytypes

453

based on more extensive neutron powder diffraction data and single-crystal X-ray diffraction data. The model of a-Agl that has emerged from this work retains the previous iodide framework but confines the distribution of silver ions to just the single set of tetrahedrally-coordinated 12(d) sites and emphasises the anisotropy and anharmonicity of their thermal vibration. The a phase persists to the melting point at 555°C. An interesting 'memory effect' has been reported in connexion with the transition between polycrystalline mixtures of the low-temperature polymorphs, ~+Y, and the high-temperature = phase (7,16). It was observed that the original proportions of B and y were regenerated after a mixture was heated through the 146.5°C transition (but not beyond ~175°C) and then allowed to re-cool. This 'memory effect' was irreversibly erased at temperatures above 170-175°C. Burley (16) attributed the effect to non-cubic ordering of the silver ions in the = structure so that there was preferential occupancy of the different silver sites, 6(b), 12(d) and 24(h), depending on whether a crystallite derived from the face-centred cubic phase or the hexagonal phase. Since Burley's analysis was based on the Strock model of =-Agl, it requires revision in the light of later developments. Phase III is a halite-type structure obtained at around 3 kbar (17-19) when Agl is subjected to pressure at room temperature. A further high-pressure phase (V) was observed at around I00 kbar by Riggleman and Drickamer (20). A CsCl-type structure was originally proposed for this phase by Bassett and Takahashi (21). This finding was later retracted (22), and an unspecified non-cubic system proposed for the structure. Finally, Van Valkenberg (23) and Davis and Adams (24) discovered an intermediate polymorph, phase IV, occupying a narrow stability field between regions II and III. Because of the narrowness of this field and the difficulty in avoiding pressure gradients, structural investigations of this phase by X-ray diffraction techniques have yielded ambiguous results. Thus the crystal system of the phase has been variously identified as hexagonal, tetragonal or orthorhombic (22,24-26). The most recent structural work (26) proposes a large tetragonal unit-cell (Z=32), whereas Moore and Kasper (25) obtained a much smaller tetragonal cell (Z=2) and tentatively proposed a structure formally resembling that of PbO. Another so-called 'memory effect' has been observed in relation to the transition between phases II and IV. Bassett and Takahashi (22), using optical techniques, noted that a mixture of B and ~ phases underwent the transition to the intermediate phase IV at 3 kbar, the 8 component transforming irreversibly and the y component reversibly. Further, they observed that upon repeated cycling through the transition single-crystal domains of phase IV always reappeared in the same places after the first transition, indicating that the y phase had a 'memory' for the intermediate phase. Mellander et a~. (27) emphasised the extreme sluggishness of the initial transition to the intermediate phase and the pronounced hysteresis associated with transformations between this phase and the adjoining phases II and III. Using electrical resistance measurements, they found that samples of ~/y transformed to the intermediate phase more quickly and at a lower pressure on the second of two pressure cycles, indicating a memory of the first transformation, possibly in the form of "some local structures which can act as nuclei in the event of a subsequent transition".

454

P. R. Prager 2.

HIGH-PRESSURE POLYTYPIC TRANSFORMATION

The picture of the phase transformations that take place when silver iodide is subjected to high pressure at normal temperatures is confused. Thus, as we have seen, the early workers (17,]8) overlooked the intermediate phase IV altogether, and subsequent workers have apparently failed to obtain data capable of unambiguous interpretation leading to the definitive structure for the phase. There is a further complication, apparent first from the work of Vedam et aZ. (28), which is of immediate relevance to the consideration of silver iodide polytypism. Vedam et al. performed the first high-pressure studies on large single crystals of silver iodide, previous studies having all used polycrystalline samples. They measured the pressure dependence of the optical absorption of 8-Agl under purely hydrostatic pressure envlroranents, and observed discontinuities in the optical absorption edge at ].14 kbar and 3.4 kbar (Fig. 3). They attributed the shift at 1.14 kbar to the transition from the wurtzite-type phase II to the intermediate phase IV, and the shift at 3.4 kbar -- reported in fact as occurring between 3.2 and 3.6 kbar -- as the transition from the intermediate phase to the halite-type phase III.

1000

t

2000

3000

4000

m

l

0

I

2

i

|

*

,

3

4

5

6

PRESSURE

Fig. 3.

kbar

Pressure dependence of the optical absorption edge for AgI, showing the small discontinuity at l.l kbar. After (28).

These authors observed the persistence of birefringence when their crystals transformed at 1.14 kbar, evidently excluding a wurtzlte-to-sphalerite transition previously suggested by Moore and Kasper (25). The phase following the transition was also observed to be uniaxial, with the principal axis parallel to that of 8-AgI, thereby ruling out orthorhombic symmetry for the new phase. They also argued that it is m o s t unlikely that the slx-fold axis of the 8 phase becomes a four-fold axis at the transition, as would be required for a phase with tetragonal symmetry. Their conclusion was that the transition from the hexagonal wurtzite-

Growth and characterization of Agl polytypes

455

type phase was to another phase with hexagonal symmetry, suggesting a pressureinduced polytypic transition such as that observed in zinc sulphide (29). The work of Vedam et al. places the room-temperature (22°C) boundary between the wurtzite and intermediate phases at 1.14±0.03 kbar, whereas earlier results consistently placed the transition at about 3 kbar. The occurrence of a discontinuity at ~I.I kbar has been confirmed repeatedly in subsequent work on B-Agl single crystals. Fjeldly and Hanson (30) measured elastic constants at 20°C in the pressure range I bar to 2.5 kbar and found discontinuities at about 1.3 kbar. Schock and Hinze (31), operating at pressures up to 2.2 kbar, and Allen and Lazarus (32), operating at pressures up to 2.8 kbar, similarly observed discontinuities in the ionic conductivity in the region of 1 kbar. Hanson et al. (33) conducted Raman scattering studies on single crystals at pressures up to 5 kbar. At room temperature they obtained clear evidence for a transformation at ! kbar; but in addition they observed phase transitions at 3 kbar and 4 kbar. Their work thus establishes that the l.l kbar transition first seen by Vedam et al. is distinct from the transition to the intermediate phase (3 kbar). In view of the relatively large uncertainty in the position of the second transition seen by Vedem et al., namely 3.4±0.2 kbar, it is possible that they failed to observe the intermediate phase, whose stability field is extremely narrow -- 0.6 kbar at 25°C (27). Mellander et al. (27) believed that the failure of Vedam et al. to observe the intermediate phase could be attributed to the sluggishness of the transition, which is most pronounced for finely powdered samples of predominantly the y phase. Against this explanation, however, there is the observation of Davis and Walawender (34) that with sufficiently coarse powders (~50 ~m) of the B phase, the transformation to the intermediate phase is rapid. Despite uncertainty in some of these details the evidence for a distinct 'pre-intermediate' transition at l.l kbar is firm. That the transformation is not from wurtzite-type to sphalerite-type is shown by the persistence of birefringence, the absence of polygonization and the rapidity of the transition (33). Thus the proposal of Vedam et al. (28) that hexagonal silver iodide undergoes a pressure-induced polytypic transformation at I.I khar seems highly plausible. In order to confirm this proposal, X-ray structural studies of single crystals at pressures between I and 3 kbar are needed. None have been reported to date.

3.

STRUCTURE OF THE 'NORMAL' POLYMORPHS

At normal conditions of temperature and pressure two basic modifications of silver iodide have long been recognized: hexagonal S-Agl and low-cubic y-Agl. The relative stabilities of the two forms, and indeed the status of the latter as an authentic phase, are topics for later discussion and are ignored for the present. The two structures are of the wurtzite-type and the sphalerlte-type respectively, and are thus isomorphous with the two basic modifications of zinc sulphide. It should be noted that according to mineralogical usage wurtzite itself is designated ~-ZnS while sphalerite (zinc blende) is designated 8-ZnS (35). In both Agl modifications the silver and iodine atoms are tetrahedrally bonded to four unlike nearest nelghbours. Both structures (Fig. 4) can be pictured as two interpenetrating close-packed arrays of atoms, B-Agl corresponding to hexagonal close-packing ABAB... along [00.I] hex and y-Agl to cubic close-packing ABCABC... along []ll]fcc. In the usual Ramsdell notation for polytypes these structures are designated 2H and 3C. Crystallographic details of the two structures are sunmmrized in Table |.

456

P. R. Prager Table I. Crystallographic details of two silver iodide polymorphs

~-~I Space group F43m Lattice constant a = 6.496 A I at (¼,¼,~) + fcc Ag at (0,0,0) + fcc

(47)

~-A~.I Space group P63mc Lattice constants a = 4.592(4) A c = 7.510(4) A I at (I/3,2/3,0), (2/3,1/3,1/2) Ag at (I/3,2/3,u), (2/3,1/3,½+u) Temperature factors Ag: BII = 0.1036(39) I: BII = 0.0619(15)

(36)

with u = 0.6253(15)

B33 = 0.0281(16) 833 = 0.0132(5)

(36)

I

Fig. 4.

Models of the (a) wurtzite and (b) sphalerite structures. After (35).

Growth and characterization of Agl polytypes

457

Because single crystals of B-Agl are available, structural studies of this polymorph have been more detailed than those of Y-Agl, which is available only in microcrystalline (powder) form. Burley's study (36) showed that B-Agl approaches the ideal wurtzite-type structure very closely indeed; thus the value of the positional parameter u = 0.6253 corresponds closely to the ideal value of u = 5/8, and the bond angles and bond lengths indicate almost perfect tetrahedral coordination. The anisotropic temperature factors shown in Table 1 were obtained on the assumption that the thermal vibration is harmonic. They indicate that the ions of the structure are unusually mobile, with RMS radial displacements of 0.28A for silver and 0.22A for iodine. However, re-analysis of Burley's X-ray data and analysis of their neutron data by Cava et aS. (12) showed that the thermal parameters could not be determined uniquely from the diffraction data, but depended on the relative magnitudes of the thermal parameters initially assigned to the two species. This finding was attributed in part to inadequacies in the correction for extinction, and indicates the need for further study in which this inadequacy is rectified, and in which anharmonic thermal vibration is given due consideration. (Cava et al. incorporated third- and fourth-order thermal tensors in their refinement of high cubic ~-Agl, but it is not clear whether these were included in their refinement of the structure of 8-Agl.

4.

4.1.

MICROCRYSTALLINE SILVER IODIDE

Preparation

Microcrystalline or 'powder' samples of silver iodide can be obtained, among other methods, by precipitation from aqueous solution (for example AgNO 3 + KI, AgNO 3 + Nal), by solid-state reaction between silver and iodine, or by quenching from the melt. Rapid precipitation in gelatin yields crystallites whose average diameter is as small as 150A (37), while the maximum size of crystal delivered by precipitation methods is, for silver iodide as for the other silver halides, not more than some tenths of a micron (38). Davis and Petersen (39) and Davis and Johnson (40) have described the preparation of silver iodide aerosols, for use in cloud-seeding projects, in which hlgher-order polytypes were observed. Several methods yielded unusual polytypic powders, the structural discussion of which will be deferred to a later section. Mixtures of 2H (i.e., B-Agl) and the higher-order polytype(s) were obtained from aerosols produced by combustion of solutions of Agl-Nal in acetone, or of Agl in isopropylamine, as well as by sublimation of pure Agl heated to lO00°C. They obtained pure polytypic Agl by heating to 550°C, and then quenching, a solution in acetone of 4 wt% Agl plus 1.23 wt% NH41 (i.e., 2:1 mole ratio). Interestingly, they found that the addition of small amounts of hydriodic acid to the acetone solution, followed by aging for several days, sharpened the diffraction lines and aided complete conversion to the higher polytype. In conjunction with the observed non-stoichiometry of the polytype, this was interpreted as a requirement for excess iodine in order that the phase be stabilized. Unusual polytpism in silver iodide powders was also inferred by Becker and Von Goldammer (41) in the course of their investigations of NMR chemical shifts. They found that nominally 'cubic' powder samples produced by slow precipitation from dilute solutions of AgNO 3 and HI were not truly cubic (i.e., not T-Agl) but either a single polytype of high cubicity or a mixture of such polytypes. No direct structural study of these powders was performed.

P. R. Prager

458 4.2.

Characterization

The characterization of silver iodide powders by the standard Debye-Scherrer X-ray technique is not straightforward. The primary difficulty is to resolve the structural ambiguity which arises because the samples present as mixtures, apparently, of the two room-temperature phases -- low-cublc y-AgI and hexagonal 8-AgI. In addition, several factors may operate to degrade the quality and reproducibility of the diffraction patterns of these powders. 'Preferred orientation' -- the non-random orientational distribution of crystallites within the sample -- makes for poor reproducibility of the diffraction pattern and introduces systematic errors in the observed intensities. In one of the earliest quantitative studies of silver iodide powders, that by ~mlkmeijer and van Hengel (8), preferred orientation was invoked as an explanation of the poor agreement between observed and calculated intensities. Recently, Davis and Johnson (40) similarly invoked this effect to explain systematic discrepancies encountered in their study of polytypic silver iodide aerosols. While preferred orientation effects are not uncommon in powder diffraction in general, the other confounding effects are perhaps less widespread. Singlecrystal studies (42,43) have shown that even at room-temperature hexagonal silver iodide exhibits peculiarly intense thermal diffuse scattering (TDS), which has its origin in unusual low-frequency lattice modes. This intense TDS constitutes part at least of the high background of diffuse intensity observed in powder patterns of ~-Agl (42). Structural disorder in the form of stacking faults will also contribute to the overall diffuse scattering; in addition, such faulting may cause Bragg peaks to be broadened and displaced from their ideal positions (e.g., Warren (44)). The occurrence of random stacking faults is a prominent feature of silver iodide single-crystal diffraction patterns (36,45). Such faulting, in profusion, is highly likely in crystallites that have been subjected to the mechanical stresses of grinding. Additionally, in such a soft and plastic material as silver iodide ('slightly harder than cheese' (46)), strain-broadening of the diffraction lines is also highly probable as a consequence ofmechanical deformation. The 'inferior' quality of silver iodide powder patterns was noted by Lawn (47), for example, who found that in contrast with the copper halides silver iodide yielded diffuse back-reflexion lines and high background intensity. On the basis of powder X-ray diffraction studies, Wilsey (48) originally reported silver iodide as having a face-centred cubic structure of the zincblende type: a finding that was supported by Davey (49). However, Aminoff (50) pointed out that iodyrite,* the naturally occurring mineral form of silver iodide, was conventionally assigned the crystallographic point group C6v within the hexagonal system. He obtained Laue X-ray diffraction patterns from single-crystal sections which displayed Laue symmetry 6/mmm, consistent with the conventional point group assignment based on optical evidence. From his Laue and Debye-Scherrer studies Aminoff concluded that silver iodide was indeed hexagonal and that the structure was probably similar to that of zinc oxide (zincite, isostructural with wurtzite). Wilsey (6) found upon re-investigation that silver iodide powder samples prepared either by precipitation from silver nitrate and potassium iodide solutions or by fusion and quenching gave rise to X-ray diffraction patterns that showed *The mineral has since been renamed 'iodargyrite' following the recommendation of the International Mineralogical Association.

Growth and characterization of Agl polytypes

459

considerable variation. In general the patterns could be indexed only on the assumption that the samples they represented contained mixtures of cubic and hexagonal structures. The proportions varied from one preparation to the next, though not in any obvious systematic manner. In a few exceptional cases including the one reported in Wilsey's original study - only the cubic structure was represented. In all other cases a mixture was indicated, with the hexagonal form predominant. Following Wilsey's work, the variation of the proportions of cubic and hexagonal material in polycrystalline samples produced by different methods and undergoing different treatments has been studied extensively (7,8,37,51-54). Bloch and Mbller (7) found that they could obtain the pure hexagonal form by dissolving Agl in concentrated KI and then re-precipitatingAgl by the addition of water. They claimed to obtain the pure cubic form by grinding or crushing to a powder any coarsely crystalline preparation of Agl. Verwey and Kruyt (51) obtained predominantly cubic material by pulverising Agl that had been fused and quenched, and by precipitation from solutions of KI and AgNO 3 containing excess AgN03, Kolkmeijer and van Hengel (8) reached the general conclusion that excess Ag + favoured the precipitation of cubic Agl, while excess I- favoured the precipitation of hexagonal A81. The same conclusion was reached by Burley (53). Recent work by Byerley and Hirsch (54), who studied dispersions of Agl in gelatin under carefully controlled conditions of ion excess, confirmed this trend for iodine excess to favour the hexagonal form, silver excess the cubic. The poor reproducibility of their results (Fig. 5) was noted by the authors.

I00 t ~o

80

0

60

oo

0

0

40

20

8 °

0 1 2 3 4 5 6 pI

Fig. 5.

Region of iodide excess

o

s 6 5 4 3 2 1 0 Region of pAg silver excess

Effect of ion excess on the structure of microcrystalline AgI according to Byerley and Hirsch (54).

P. R. Prager

460 4.3.

Methods of Determining Hexagonality/Cubicit~

Several methods have been used to estimate the relative amounts of cubic and hexagonal material in silver iodide powders. Schneer and Whiting (55) used a method similar to that described by Averbach and Cohen (56) for the determination of phase proportions of austenite-martenslte. (See also Cullity (57).) This method employs the measured and calculated ratio of the sum of the first four lines found only for the hexagonal structure (}0.0, ]0.], 10.2 and ]0.3) to the sum of the first three lines co~xnon to the hexagonal and cubic structures (00.2/Ill, ]1.0/220 and li.2/31]) - see Fig. 6, which schematically represents the powder patterns of the two s t r u c t u r e s .

Y-AgI

I

E~ H u) z z

[i

. . . . . .

-AgI

I-4

I,., . . . .

5

I

I

i0

20

,...

I, 30

BRAG(; ANGLE THETA

Fig. 6.

I 40 deg

Schematic powder patterns of 7-Agl and 8-Agl for CuK radiation. After (54).

The most common and convenient method (37,52,53) for determining cubicity/ hexagonality uses the relative intensities of the triplet of diffraction lines falling in the range 22° < 2@ < 26 ° for CuK radiation (Fig. 6). In this region the wurtzite-type structure gives rise to three lines (I0.0 at 2@=22.3 ° , 00.2 at 23.6 ° and I0.] at 25.3 ° ) whereas the sphalerite-type structure gives rise to a single line, the I]I reflexion, at the central position of the triplet. Using single-crystal data from Burley (36) for 8-AgI, and assuming that the structure factors for the (00.2) hexagonal and the (Ill) cubic reflexions are equal, Berry (37) constructed the curve reproduced in Fig. 7. The curve shows the calculated X-ray intensity ratio of the central line to the two outer lines of the triplet, as a function of the proportion of cubic material in the mixture. Applying this method, Berry (37) reached the disturbing conclusion that the standard powder diffraction pattern for pure hexagonal silver iodide (58) corresponds in fact to a mixture containing 30% cubic material.

Growth and characterization of Agl polytypes

X e C~ O O + O

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-.4 !

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20

40

60

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Percentage of cubic AgI

X Fig. 7.

Dependence of X-ray intensities on proportions of cubic and hexagonal Agl according to Berry (37).

This finding has been rejected by Natarajan and Rao (59), who cite as contrary evidence (i) the agreement between their powder preparations and the standard patterns ~or cubic and hexagonal material, and (ii) their observation of differences in colour between hexagonal ("bright yellow") and cubic ("orange-red") powders. It appears, however, that Natarajan and Rao are mistaken. Firstly, they fail to meet the point of Berry's claim, which is that there is an inconsistency between the single-crystal structural data and the experimental standard powder pattern-- which is not to say that no experimental preparations match the hexagonal standard pattern. Secondly, with regard to the colour difference: this is justified by Natarajan and Rao by reference to the differences in exciton band positions in the optical absorption spectra of 8-Agl and 7-Agl microcrystals. However, this difference - 417.5 m~ for 8-Agl as against 422.5 m~ for T-Agl (37)would appear too small to underpin the claimed observation of a change from bright Yellow to orange-red. Other authors have not noted so striking a colour difference between cubic and hexagonal preparations: for example, Bloch and M~ller (7) describe both types of preparation as having almost the identical green-yellow appearance. These claims, counterclaims and contradictions point the need for more refined methods of characterizing silver iodide powders. The methods that have been used to date all rely on the peak or integrated intensities of a limited subset of the available reflexiens. With the recent development of powder profile refinement schemes (60) the power of the powder method as a structure-analytical tool has been greatly increased. Application of these schemes to the silver iodide problem would appear to be warranted.

462

P. R. Prager 5.

STABILITY RELATION BETWEEN CUBIC AND HEXAGONAL SILVER IODIDE

The status of the low-cubic y modification of silver iodide, in particular its stability relative to the hexagonal B modification, requires discussion in view of the history of contradictory opinions. As a result of the influential study by Bloch and Moller (7), the Y form was ori~inally believed to be the stable modification between room temperature and 135~C, while the coexistent 8 form (6) was accorded the status of a metastable phase. Between 135°C and the transition to the high-cublc phase at 146°C this relationship was considered to be reversed, with the hexagonal form now the stable phase and the low-cubic form the metastable phase. Figure 8 shows the relevant part of the phase diagram of Agl, after Bloch and ~611er (7).

r r t

B

t l t l ~ I

apour

135 TEMPERATURE

Fig. 8.

°C

Schematic pressure-temperature phase diagram of silver iodide according to Bloch and ~dller (7).

The scheme of Bloch and ~dller was based essentially on the following evidence:

(i) They had apparently succeeded in obtaining 'pure' preparations of both forms - the pure hexagonal form by precipitation of Agl dissolved in concentrated KI solution; the pure cubic form by grinding or crushing to a powder any macrocrystalline Agl. (ii)

Separate samples of cubic and hexagonal material heated at 125~5°C for six weeks were unaltered by the treatment, whereas samples heated for the same period at 135±5°C showed conversion from the cubic to the hexagonal form. This conversion was very much more rapid at higher temperatures - e.g., 'very substantial' conversion within 15 hr at 144°C.

They state that "In complete agreement with [the finding that the cubic (zinc blende) modification alone is stable at normal temperatures below 135°C] is the observation that hexagonal silver iodide is converted to the cubic modification by grinding at normal temperatures. The grinding fulfils the same function as does stirring in a supercooled melt." (Bloch and M~ller (7), p 258. My translation.) They also proposed, in passing, that it should be possible to determine the transition temperature (point a in Fig. S) with greater precision

Growth and characterization of Agl polytypes

463

by establishing the maximum temperature at which grinding was effective in bringing about the transformation from the hexagonal phase to the cubic phase. The stability ordering proposed by Bloch and MSller was generally accepted for the next 25 years or so, despite certain puzzling observations. Thus Verwey and Kruyt (51) accepted Bloch and ~dller's claim that the cubic form is the stable modification, but observed that in some circumstances - vlz, the growth from solution of larger crystals at the expense of smaller crystals as occurs in the process of Ostwald ripening - the metastable modification arose out of the stable one. They justified this with the following statement (Verwey and Kruyt (51) p 144): "This is only possible, thermodynamically, when the difference between the lattice energies of the two modifications is small - smaller, at least, than the surface energy of a mole of the smaller [i.e., the cubic - hence 'stable'] particles." Kolkmeijer and van Hengel (8), accepting the stability of the cubic modification below 135°C, were the first to lay claim to the preparation of this modification directly, by precipitation from solution, rather than by crushing or grinding the pure hexagonal form or a 'mixture'. This claim has not been substantiated (e.g., Lawn (47), and the method of grinding has remained the preferred method for obtaining the cubic form. Manson (61) first cast doubt on the details of the equilibrium regions reported by Bloch and ~Oller. He found that the transformation from the (predominantly) lowcubic form to the hexagonal form took place quite rapidly at 120°C, in conflict with the very slow transformation at 135°C according to Bloch and MSller. However, when his samples were re-investigated after storage at laboratory temperature for one year, Manson found that this transformation had been partially reversed. This implied a stability field for the low-cubic phase, with a transition temperature somewhere between 120 ° and room temperature. The occurrence of the low-cubic modification as a stable phase of Agl was first disputed by Majumdar and Roy (52). They replicated many of the previously reported methods of preparing Agl powders and characterized them by X-ray diffraction* at room temperature (30°C), as prepared, and also after heat treatment at ll0°C and 132°C. As a result of the room temperature investigation they noted: "The first general and surprising result is, therefore, that Agl cannot be synthesized in the pure cubic sphalerite structure in any reproducible manner by methods previously suggested." While they found that a few of their preparations did appear to become more sphaleritic when heated to ll0°C, certainly no consistent pattern of such conversion was evident. Conversely, they found that there was no clear evidence that the sphaleritic material always converted to wurtzite at about 120°C, though in some cases this appeared to be the trend. In addition, Majumdar and Roy studied the effect on their preparations of prolonged heating for periods ranging from two weeks to three months at temperatures between 128°C and 142°C. This was done for the dry material and also in the presence of water and ammonium hydroxide. In most cases good wurtzite structures were formed, whereas in not a single case was a pure sphalerite structure formed. These authors also raised the issue of the significance of grinding or powdering silver iodide samples. They drew attention to the important investigation of zinc sulphide by Smith and Hill (62), in which it was shown that impact comminution of 2H (wurtzite-type) material and 3C (sphalerite-type) material gave rise to qualitatively similar X-ray diffraction patterns; patterns which were, however, distinct from both the original diffraction patterns (Fig. 9). As they noted, of

*Using the I0.0, O0.2/lJl, I0.I triplet. ~

464

P.R.

Prager

Jl •

|

31

,

•

•

•

29

w

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•

27

w

•

w

31

l

29

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27

2{) degrees Fig. 9.

Low-angle diffractograms of zinc sulphide (CuK radiation). Top left is 2H crystalline material; top right, the same after hammering. Bottom left is 3C crystalline material; bottom right, the same after hammering. Smith and Hill (62).

particular importance in the patterns of the comminuted material is the appearance of unresolved spectra on the hlgh-angle side of the first diffraction llne. It was thus clearly established - for zinc sulphide - that the crushing of hexagonal material in this manner did not produce inversion to the cubic phase (as had been previously claimed), but rather produced a randomlsation of the packing, with the introduction of a degree of cubic packing into originally hexagonal material. Similarly, the effect on cubic material of this treatment was seen to be the introduction of a degree of hexagonal packing. The following observations of Smith and Hill are highly germane to our considerations: "The diffraction pattern of the two impacted zinc sulphide specimens [see Fig. 9] resemble (except in breadth of spectra) mixtures of complex polytypes which we have made by prolonged sintering of ZnS in NaCI flux at 850-970°C in evacuated glass tubes. Therefore, we consider the impacted material to contain irregular stacking due to glide twinning, analogous to deformation faulting of hexagonal or cubic close packed metals by cold working." (Smith and Hill (62), p 82.) Majumdar and Roy (52) came to the reasonable conclusion that, in view of the plasticity of silver iodide, intensity measurements using ground or powdered samples were not likely to be reliable; and that (as with zinc sulphide) grinding or powdering was likely to introduce stacking disorder which made the hexagonal material, especially, "look 'more cubic' on cursory examination." In the light of Smith and Hill's study, and presumably on the basis of similar diffractograms, Majumdar and Roy claimed to find "plenty of evidence for several other complex polytypes of Agl." Their final assessment was that there was no evidence for the occurrence of the sphalerite modification as a stable phase of Agl - if it occurred at all - and that therefore the transition y ~ B at ]20 ° or 137°C, as previously reported, was meaningless and should be expunged from the record.

Growth and characterization of Agl polytypes

465

A similar conclusion was reached by Fridrichsons and Mathieson (63) who argued that the absence of adequate proof of a macroscopic ordered phase corresponding to the B3 structure, or of a transition temperature T ~ 8, belied the established viewpoint of the existence of two low-temperature modifications of Agl. They proposed that only the ~ form be recognised as an authentic phase and that the T form be regarded as a disordered or randomized 8 phase. To summarise the present position: While the difference in structure energies between the 8 and y forms of Agl is very small (AU = 149 cal/mole - Burley (53)), 8-Agl is generally recognised as the stable form at atmospheric pressure for all temperatures below the 146°C transition point. (Nonetheless, the belief that the 7 form is stable below 135°C does persist in some quarters (64).) Argument is still possible as to whether an ordered macroscopic 7 phase is obtained at all; but it is well established that as the result of mechanical deformation (in which shearing stresses undoubtedly play an important part (22)), 8-Agl is transformed into a structure in which the original hexagonal close packing is replaced, to a degree, by cubic close packing.

6.

GROWTH OF SILVER IODIDE SINGLE CRYSTALS

It has not been possible to prepare single crystals of low silver iodide by the various techniques of growth from the melt - the standard method for obtaining large silver halide crystals - since upon cooling through the ~ 8 phase transition at 146°C silver iodide undergoes an expansion of 6% in volume (52), which causes fragmentation of the crystals. Because of the very low solubility of silver iodide in water (2.8 x 10-° g/l at 20-25°C (65)), neither is growth of large single crystals from simple aqueous solution feasible. However, silver iodide dissolves readily in concentrated aqueous potassium iodide or hydrogen iodide solutions, forming iodo-complexes; reduction of the iodide concentration causes dissociation of the complexes and growth of silver iodide single crystals. Several different methods based on this process have been employed to produce crystals of maximum dimensions up to I cm. One group of such variants involves the layering of one solution over another so that the required dilution is achieved by diffusion across the interface; a second group of methods involves the use of silica gels; a third proceeds by dilution with water from the vapour phase; a fourth is based on the fact that the solubility of silver iodide in potassium iodide or hydrogen iodide solution decreases with increasing temperature. A brief review of some of these methods has been presented recently by Walliser et el. (38).

6.1.

Layerin$ Methods

Helmholz (66) used concentrated hydrogen iodide solution saturated with silver iodide, overlayered by a thin layer of ethanol. Reduction of the iodide concentration is produced by diffusion of hydrogen iodide into the upper layer, where it reacts with the alcohol. By this method Helmholz obtained hexagonal plates with edges 5 m m i n length, and hexagonal pyramids. Lakatos and Lieser (67) employed a similar method to the above, using methanol instead of ethanol. They obtained hexagonal pyramids up to 4 mm in diameter.

466

P.R.

Prager

In Cochrane's method (68), a saturated aqueous solution of potassium iodide is itself saturated with silver iodide, and the mixture is placed in the lower part of a long-necked bottle. The neck of the bottle is carefully filled with distilled water. Gradual dilution of the AgI-KI solution, by diffusion, leads to the growth of single crystals. A glass rod, the end of which protrudes into the lower solution, increases the yield of crystals. Crystals grown by this method over a period of 6-8 weeks are in the form either of hexagonal prisms up to 2 cm long and 2 mm in diameter, or of hexagonal pyramids up to 3 mm in height and 1.5 mm in diameter. Careful harvesting also yields very fine acicular crystals (firstorder hexagonal prisms) a few hundredths of a millimetre in diameter and several millimetres long. Impurity concentrations are low; in particular the potassium level was reported to be less than 2 ppm (68).

6.2.

Gel Methods

Halberstadt (69) prepared a silica gel from sodium metasilicate, potassium iodide and acetic acid; into this a solution of silver iodide and potassium iodide was allowed to diffuse. Replacement of the solution by water after a week led to the appearance of crystals in the form of hexagonal platelets which grew to about 5 mm diameter. Silicon contamination was low, with an upper limit of less than a few ppm, but considerable concentrations of potassium (up to 6 percent) were detected on some crystal faces. Blank et al. (70) obtained hexagonal platelets approximately 10-12 nnn in diameter from silica gels into which a solution of silver iodide in hydriodic acid was diffused. The purity of the crystals was good, with silicon contamination less than 5 ppm. Suri, Henisch and Faust (71) also studied growth from silica gels into which was diffused silver iodide - potassium iodide complex solutions. They obtained hexagonal pyramids and hexagonal platelets. The pyramids were free of inclusions and cavities, and on spectrographic analysis showed only traces of impurities. The platelets, however, were shown to contain substantial gel inclusions (72).

6.3.

Growth by Dilution from the Vapour Phase

A notably simple method was used by Hills (73) to grow crystals from saturated silver iodide-potassium iodide complex solutions. The solutions were placed in sealed jars or dessicators containing a reservoir of water. Dilution of the solutions with water from the vapour phase was sufficient for crystals to appear within a few days. The harvested crystals were in the form of polyhedra - usually hexagonal pyramids, sometimes hexagonal plates. Analysis by flame emission spectroscopy revealed potassium contamination at the level of almost 300 ppm.

6.4.

Growth by Convective Circulation

Following an observation by Cochrane (74) thatthe solubility of silver iodide in potassium iodide decreases with increasing temperature, Mills et al. (75) devised a method of rapidly growing large single crystals. Their apparatus consists of two vertical chambers connected at top and bottom by two horizontal tubes. One chamber is held at 23°C and contains a solution of potassium iodide saturated with silver iodide, the saturation ensured by the presence of large amounts of undissolved silver iodide. The second chamber is held at about 40°C. The solution circulates through the apparatus by convection, and supersaturation in

Growth and characterization of Agl polytypes

467

the heated chamber results in deposition and growth of silver iodide crystals. A growth period of three weeks produces crystals of a single habit, namely regular hexagonal prisms, which may be up to 6 mm long and 8 mm in diameter. The potassium content of these crystals was determined to be 340 ppm. Because the solubility of silver iodide in hydrogen iodide also decreases with increasing temperature, Walliser et a~. (38) modified the convective circulation method, above, by the substitution of hydrogen iodide for potassium iodide. They obtained transparent hexagonal pyramids, about 5 mm in diameter, after 3-4 weeks of growth. Emission spectroscopy revealed only traces of Mg, Ca, AI, Fe and Cu, the total impurity concentration being less than I ppm.

7.

7.1.

POLYTYPES

Discovery of Polytypism in Silver Iodide

Noting the similarities with earlier findings on zinc sulphide, Majemdar and Roy (52) found evidence of complex polytypism in the powder diffraction patterns of crushed or ground silver iodide. However, no specific polytypic structures were identified by these authors. Earlier, on the basis of his co-operational theory of polytypism, Schneer (76) had predicted polytyplsm in silver iodide, again by analogy with zinc sulphide. More definite evidence for complex polytypism in silver iodide was produced by Davis and Petersen (39). They studied aerosols of Agl prepared by combustion of solutions of Agl-Nal in acetone, of Agl in isopropylemine or of pure sublimed Agl. Indexing of their powder patterns was accomplished on the assumption that a 21-1ayered rhombohedral polytype was present in their samples, intermixed with the normal 2H polytype. Their indexing scheme required £=3n for all peaks (hk£) attributed to the 21-1ayered polytype. This condition is inconsistent with the claim that the pattern represented a rhombohedral polytype, since for a rhombohedral lattice the indices of permitted reflexions (referred to hexagonal axes) are limited by the condition -h+k+£=3n (Verma and Krishna, 1966). Thus their data indicated a 7H polytype rather than a 21R polytype as they had proposed. Subsequently Davis and Johnson (40) investigated this polytype in greater detail and recognised its lower periodicity. They obtained 7H Agl in pure form by heating to 550°C, and then quenching, a solution in acetone of 2:1 mole ratio Agl and NH41. There are three possible 7H polytypes, their layer sequences characterized by the Zhdanov symbols 25, 1213 and Ill4. Reasonable agreement was obtained between observed intensities and those calculated for the 1213 sequence, whereas there was complete incompatibility for the other two sequences. Even for the favoured structure there remained substantial differences between calculated and observed intensities of h0~ reflexions; these were attributed by the authors to preferred orientation of the crystallites. A sunmmry of the results of the analysis by Davis and Johnson (40) is shown in Table 2. Table 2. The Agl 7H polytype of Davis and Johnson (40) Space group P3ml Lattice constants

a = 4.595 A c = 26.291A Zhdanov symbol 12|3 Stacking sequence ABACACB

468

P.R.

Prager

To date, this structure is the only complex Agl polytype identified from powder data. Some of the problems in characterizing Agl powders have been discussed in an earlier section. We draw attention to the much greater background level and peak broadening evident in the diffractometer tracing of the 7H pattern compared with the 2H pattern in Davis and Johnson's paper (40). This strongly indicates an admixture of many polytypes or a high degree of structural disorder in the predominant polytype.

7.2.

Polytypes Identified in Single Crystals

The first report of complex polytypism in silver iodide at the macroscopic level was by Prager (77). Four new polytypes - 4H, 8H, 12H and 16H in the Ramsdell notation - were initially described by this author, and a fifth - also 12H - was later added (78). These remain the only room-temperature complex Agl polytypes unambiguously identified to date, though Brinkmann and Freudenreich (79) (see below) have reported possible structures for a series of hlgh-order polytypes existing at room-temperature or arising from a low-temperature transformation at about -50°C. In addition, Minagawa (80) has reported on the occurrence of complex polytypism in CuxAgl_xl crystals (see below).

7.3.

Growth of polytypic Single Crystals

Of the many methods of growing silver iodide single crystals only Cochrane's (68) method has been reported as giving rise to the higher polytypes. Whereas his method is capable of producing quite large hexagonal pyramids and hexagonal prisms, the latter growing up to several centimetres in length and a few millimetres in diameter, the polytypic crystals investigated by Prager were all in the form of fine, first-order hexagonal-prismatic needles with diameters in the range of approximately 0. I-0.5 mm. Johnson and Schock (81) found that the 4H structure was exhibited by first-order hexagonal prisms grown by Cochrane's method, but that crystals of pyramidal morphology from the same preparation displayed the normal wurtzite-type (2H) structure. They could detect no significant differences in the impurity levels for the two polytypes (i.e., two morphologies). Mashlyatina et al. (82) found both 4H and 2H polytypes in crystals obtained by Cochrane's method, but only the 2H structure in crystals grown by the gel method of Halberstadt (69).

7.4.

Structure of the Polytypes

The layer sequences and other structural details of the five polytypes discovered by Prager (77,78), together with the basic wurtzlte-type structure, are summarized in Table 3. The corresponding X-ray diffraction patterns are shown in Fig. I0; these are all zero-level (hO.£) precession photographs obtained with molybdenum K~ radiation. The structure determination, i.e. the elucidation of the layer sequences, was achieved by direct comparlson of the observed intensities of relfexions along I0.% or 20.£ lines with intensities calculated for all possible layer sequences of the appropriate periodicities. In some cases (Fig. lO d,e) account had to be taken of syntactic coalescence between the higher polytype and 2H or 4H polytypes, so that only reflexions free of contributions from the latter were considered.

Growth and characterization of Agl polytypes (a)

(b)

g

,t. (c)

e

/ (d)

(e)

(f)

Fig. lO.

Zero-level (h0.£) precession photographs of Agl polytypes obtained with Mo K radiation. (a) 2H; (b) 4H; (c) 8H; (d) ]2Ha+2H; (e) 12Hb+4H+2H; (f) 16H. See Table 3 for corresponding Zhdanov symbols and stacking sequences. After (77,78).

469

P. R. Prager

470 Table 3. Polytype number I 2 3 4 5 6

Ramsdell notation 2H 4H 8H 12Ha 12Hb 16H

The Agl polytypes of Prager (77,78)

Zhdanov symbol ii 22 211112 2111121111 1211111121 I1211111111211

Space group P63mc P63mc P3ml P63mc P3ml P3ml

Stacking sequence

Percentage hexagonality

AB ABCB ABCBCBCB ABCBCBCBABAB ABACACACACAB ABABCBCBCBCBCBAB

I00 50 75 83.3 83.3 87.5

The three trigonal polytypes 8H, 12Hb and 16H (space group P3ml) are all of the special type discussed by Ramsdell and Kohn (83) in which the diffraction pattern of the trigonal structure exactly simulates hexagonal symmetry. This is not due to any pseudo-symmetry, but arises in binary close-packed structures of the wurtzite-sphalerite family when the Ramsdel zigzag sequence of the structure is symmetric (i.e., possesses a mirror plane). In these special cases the Zhdanov symbol consists of an odd or even non-symmetrical set of terms followed by the same set reversed (77). The hexagonal polytypes (space group P63mc) are represented by Zhdanov symbols which consist of an odd set of terms repeated (35). Thus in all the reported cases the stacking sequence for the entire unit cell is determined by the sequence for half the unit cell: a circumstance which greatly reduced the labour of trial-and-error structure determination.

7.5.

Hexa~onality and Birefrin~ence

Table 3 includes the percentage hexagonality = of the listed polytypes. quantity is derived from the relation (86)

This

2k = ~n/lO0 where 2k is the number of elements in the Zhdanov symbol and n is the number of layers in the unit cell. ~ is defined as the percentage of close-packed planes which are in a hexagonal nearest-neighbour environment (84). For the 2H structure ~=I00, for the 3C structure affiO. Several important physical properties have been shown to be linearly related to ~ - e.g. the band gap in silicon carbide (85) and absorption edge and birefringence in zinc sulphide (84). Brafman ~t al. (86) have shown that, once the constant of proportionality between birefringence (A~) and percentage hexagonality has been established experimentally, the above relation provides invaluable information for the structure determination of higher-order polytypes. Thus, they have solved a large number of zinc sulphide polytype structures by using measured ~irefringence values to restrict the possible Zhdanov symbols to those with a predetermined number of elements, 2k. In the case of silver iodide the structures of the relatively low-order polytypes discovered to date have been solved without recourse to this type of information. Measurements of the birefringence of the 2H and 4H polytypes have been reported by Prager (77); they confirm the linear dependence of A~ on ~ and establish the constant of proportionality: see Table 4.

471

Growth and characterization of Agl polytypes Table 4. Measured birefringences A~ at wavelength = 589 nm for two Agl polytypes of known percentage hexagonality

7.6.

Polytype

a

103A~

2H 4H

I00 50

17.8 8.9

The 4H Polytype

The most common of the higher polytypes in silver iodide is undoubtedly the 4H (22) polytype - Fig. II. The layer sequence, ABCB, is the only one possible for the four-layered polytype. The 4H structure was found by the author to be the most common structure in freshly harvested acicular crystals grown by Cochrane's method; indeed, almost all the needles studied were found to have this structure initially, and the stable 2H form was virtually absent. The high frequency of occurrence of the 4H polytype may well be a correlate of the morphology - recalling the restriction to acicular crystals. As noted earlier, Johnson and Schock (81) observed the 4H structure in first-order hexagonal prisms but found that pyramidal crystals had the normal 2H structure. f

4H-Agl C •

Ag

Ol

Fig. II.

Structural model of the 4H polytype.

After (96).

Johnson and Schock (81) carried out a complete three dimensional analysis of the 4H polytype using diffractometrlcally acquired data. Their results are s1,-marized in Table 5. The parameters in the Table are based on full-matrix least-squares refinement, including anomalous dispersion and anisotropic temperature factors. Atoms of the same species were constrained to move together by varying only the z-parameter of iodine and allowing only one set of thermal parameters for each species. Relaxation of these constraints, which were not imposed by the spacegroup, led to no significant improvement in the least-squares fit.

P. R. Prager

472

Table 5. Structural parameters of the Agl 4H polytype, after Johnson and Schock (81) Atom

Wyckoff No.

x

y

z

Ag(1) Ag(2) I(I) 1(2)

2(a) 2(b) 2(a) 2(b)

0 I/3 0 I/3

0 2/3 0 2/3

I/4 0 0.4384(4) z-I/4

Lattice parameters

a = 4.5979(40),

BII 6.6(2)A 2 6.6(2) 4.2(I) 4.2(I)

B33 6.3(a)A 2 6.3(2) 3.6(2) 3.6(I)

c = 15.029(7) A

The temperature factor is expressed as: exp

{-¼ [(hma .2 + k2b ~2 + he a~b ~) BII + £2c'2 B33] }

For comparison with Table I, note that 8i:J = ~ Bi:ai3 .aj Apart from the gross change in stacking sequence, the only significant difference between the 2H and 4H structures is the somewhat greater deviation from perfect tetrahedral coordination observed in the 4H polytype. Thus, in the 4H polytype the Ag-I bond parallel to the c-axis is slightly longer than the three (equivalent) oblique Ag-I bonds: 2.832 A versus 2.811 A, respectively. These are to be compared with the corresponding bond distances, 2.813 A and 2.814 A, in the 2H polytype, where almost perfect tetrahedral coordination obtains (36).

7.7.

Other High-Order Polytypes

Brinkmann and Freudenreich (79) used a novel nuclear magnetic resonance (NMR) method to investigate polytypism and polytype transformations in silver iodide. An account of the theory according to these authors is given below. 7.7.1. Quadrupole splitting of the NMR signal in silver iodide. The NMR signal of the iodine nucleus, 1271, suffers quadrupole splitting into five components - the central line plus four satellites - as a result of the interaction between the nuclear electric quadrupole moment and an inhomogeneous crystal field. In Agl the crystal field at the site of the iodine nucleus was found to be always axially symmetric. The resonance shift H-H o of the central line with respect to the unshifted line H o (obtained for vanishingly small quadrupole interaction) is given by 9~ C 2 H-Ho 400 ~ sin2~ (l-9c°s2e) where: ~ is the radiation frequency, Y is the known gyromagnetic ratio of 1271, 8 is the angle between the applied magnetic field and the electric field gradient tensor (FGT) at the iodine site, and C = eQVzz/h is the quadrupole coupling constant. It describes the strength of the coupling between the nuclear quadrupole moment eQ and the component Vzz of the FGT along the symmetry axis. Measurement of the resonance shift determines the coupling constant and thus, if the quadrupole moment is known, the FGT.

Growth and characterization of Agl polytypes

473

Brinkmann and Freudenreich found that, in addition to the known silver iodide 1271 NMR signal with coupling constant C = 7.91Ml{z (87), soma of their crystals yielded additional resonances with smaller coupling constants ranging from 2-5 Mllz. For a given crystal, the intensities of the signals were in the ratios of small integers. 7.7.2. Polytype identification. The field gradient tensor at a particular site is determined by the distribution of surrounding charges; it varies with the inverse cube of the distance and reflects the site syuxnetry. Since all FGT's in silver iodide were found to be axially symmetric, with the symmetry axis parallel to the c-axis, Brinkmann and Freudenreich reasoned that the different coupling constants represented FGT's corresponding to atomic arrangements that differed only along the direction of the c-axis; in other words, that the different signals arose from different polytypic stacking sequences. In Y-Agl the cubic point symmetry of the iodine site entails a null FGT, while in 8-Agl the FGT has a non-zero value corresponding to C = 8 MHz. Intermediate polytypes would be expected to be responsible for intermediate values. Because of the inverse cube law only near neighbours are significant in determining the FGT, and Brinkmann and Freudenreich proposed a schema relating the observed quadrupole coupling constants to the different configurations about a given iodine layer, restricting their considerations to the two nearest layers above and below. This is shown schematically in Fig. 12, where the configurations are represented by partial Ramsdell layer-sequences about an iodine layer at the centre. The relative intensities of the signals (i.e. central lines) are in the ratios of the frequencies with which the configurations occur within the structure. In a 4H polytype there are just two configurations, type II and type IV, and they occur with equal frequency; hence, according to this scheme, a 4H crystal should give rise to two central signals of equal intensity. Brinkmann and Freudenreich observed such signals in several of their crystals and therefore identified them as 4H polytypes. The coupling constants for the two signals were 3 MHz and 5MBz (Fig. 12). Similarly, type I, III and V configurations will be present in any polytype which includes ...]1311... sequences in its Zhadanov symbol, and consequently there will be three central signals. This was the case for several other crystals investigated by Brinkmann and Freudenreich, and they associated the 2 Mllz and 4.5 MHz quadrupole coupling constants with the type I and type III configurations respectively. (The type V configuration corresponds to the wurtzite type sequence ...lllll... with C = 8 MHz.) The results of Brinkmann and Freudenreich's investigations are sun~arized in Table 6. Two of the structures were identified after the samples had transformed following thermal treatment, as discussed in a later section. The authors determined ratios of intensities with an uncertainty of about 3%. The results quoted in Table 6 indicate that the samples investigated were single polytypes rather than mixtures of polytypes, since if the latter were the case no such simple intensity ratios would be expected. 7.7.3. Ambiguity of the pol7t~pe identification. Unfortunately, the structural information provided by the NMR technique on the environment of iodine nuclei in silver iodide is too limited to determine uniquely the layer sequences or indeed the periodicities of unknown polytypes. The structures provided by Brinlunann and Freudenreich must therefore be regarded only as possible structures which require confirmation by conventional diffraction techniques.

P. R. Prager

474

Table 6. S1-,msry of results of NMR investigation of Agl polytypes, after Brinkmann and Freudenreich (79)

Sample number I 4a*

Quadrupole coupling constants eQVzz/h (MHz)

Ratio of intensities of signals

Ramsdell symbol

Zhdanov symbol

7.87 8.01

-

-

I:0:0

2H

II

2 3 4

-

5.00 5.07 5.02

3.12 3.17 3.07

0:I:I

4H

22

5 6

8.04 8.08

4.50 4.43

2.02 2.07

1:1:1

12H

11311311

3a'

7.98

4.55

2.11

4:1:1

24H

(11)43113(11)4

7

7.96

4.50

2.06

8:1:1

40H

(11)83113(11)8

8

7.98

4.46

2.00

18:1:1

80H

____(11)183113(11)18

*Sample number 4 after heating to 100°C #Sample number 3 after cooling to 150°C Note that a series of misprints in the published Table (79) has been corrected, using information kindly provided by Brinkmann (88). The ambiguity in the structure determination by the NMR technique arises because no one-to-one correspondence exists between a particular set of signals and a single structure. Thus, while it is true that only one 12H polytype (1131111311, as shown in Table 6) could be responsible for the set of three signals in the ratios I:1:I*, such a set would also be obtained from, for example, the 24H polytype 1113113113113111. Hence in this particular case independent confirmation of the periodicity would be required before the proposed structure could be accepted. The problem is compounded for higher-order polytypes, when it is easy to see that different sequences of the same order would give rise to identical sets of signals. For example, the 40H polytypes (11)83113(11) 8 (11)713(11)231 (11) 7 (11)73(11)33(11) 7 , for which configurations of type I, III and V occur with similar frequencies, would all produce 2 MHz, 4.5 MHz and 8 MHz signals with their intensities in the ratios 1:I:8.

*Provided we accept the assignment of signals-to-configurations as proposed by Brinkmann and Freudenreich. Brinkmann (88) has stated that theoretical calculation of the coupling constants has not been possible; .indeed Sholl (89) has shown that even for 2H Agl the experimentally obtained coupling constants cannot be correctly calculated. However, the proposed assignment could be confirmed by a diffraction study of the same samples as used in the NMR study.

Growth and characterization of Agl polytypes

oo.Ooo.O oo

I 0 MHz

0

2.0 MHz

0

475

oo

II 3.0 MHz

0

oO. oO. Oo llI 4.5 MHz

Fig. 12.

7.8.

IV 5.0 MHz

V 8.0 MHz

Relationship between iodine configurations and resonance shift of the central llne of the NMR signal. The solid circle represents the central, reference iodine layer, and the open circles represent the two nearest iodine layers above and below. The first and last configurations correspond to purely cubic stacking and purely hexagonal stacking, respectively.

Polytypes in the Copper Iodide - Silver Iodide System

Minagawa (80) recently investigated the Cul-Agl quasi-binary system, using crystals grown from concentrated aqueous KI solution by Cochrane's method (68). Cul and Agl powders were dissolved in the solution in the molar ratio X : I-X. In the resultant crystals, composition CuxAgl-xl , the actual molar ratios x : l-x were determined by atomic absorption spectroscopy. It was found that nominal copper concentrations were markedly higher than actual concentrations as a result of the precipitation of Cul out of solution. Pure (x= 0) silver iodide crystals, which grew in the form of hexagonal prisms, were found by Minagawa to possess the 2H structure exclusively, contrary to the experience of others (64,77,79,81). No birefringence studies were carried out (90), so the possible existence of small polytypic domains is not excluded. On the other hand it is not inconceivable that some contamination is essential to the growth of polytypic Agl crystals and that Minagawa's procedures alone excluded the necessary contamination. It has been found (91) that the incidence of polytypism in Pbl 2 crystals grown from silica gel could be appreciably increased by the introduction of minor amounts of impurity (~300 ppm Agl); and that the percentage of higher polytypes in Cdl 2 crystals grown by evaporation from aqueous solution

476

P.R.

Prager

showed a seasonal variation which correlated with the relative dust content of the air (92). Opposed to this line of argument is the previously noted fact that Johnson and Schock (81) were unable to detect any significant differences in the impurity levels (a few ppm of Ca, Cu/Si, Fe/Mg) of 2H and 4H Agl crystals obtained from the same preparation by Cochrane's method. Minagawa (80) did observe long-period polytypes in crystals grown from solutions with the lowest nominal copper concentration (X = 0.05). The crystals grew in the form of hexagonal pyramids and hexagonal prisms; the actual copper concentrations were very low but indeterminate: x < 0.025. The long-period polytypes 6H, 8H, 10H, 12H, 18H and 24H were observed, in addition to the heavily faulted 2H structure. Unfortunately the layer sequences of the higher polytypes were not determined. Among the crystals grown from solutions with nominal copper concentrations of 5-15%, the majority were found by Minagawa to possess the 4H structure. Actual copper concentrations were in the range 0.025 < x < 0.092. The hexagonal-pyramidal habit was most c o ~ o n but some hexagonal-prismatic 4H crystals were also obtained. Solutions with nominal copper concentrations in the range 25-50% and actual concentrations in the range 0.15 < x < 0.28 yielded tetrahedral crystals possessing the 3C sphalerite-type structure. The same preparations also yielded tabular hexagonal-prismatic crystals formed from heavily faulted twins of the 3C structure. The sphalerite-type structure for pure Cul (93), was confirmed in this work. Minagawa obtained a linear dependence of reduced lattice parameters against copper concentration, thus confirming that the CuxAgl-xl crystals grown by Cochrane's method obey Vegard's law and form a series of substitutional solid solutions in which the copper ions substitute for silver ions (94,95). The stabilization of the cubic structure by substitutional copper ions represents a reversal of the situation reported by Burley (53). He showed that under conditions of crystal growth which favoured the incorporation of excess cations into interstitial positions in the Agl network copper ions should (in conformity with simple crystalchemical arguments) enter tetrahedral sites and stabilize the hexagonal structure.

8.

8. l.

DEFECT STRUCTURE

Stacking Faults and Disorder-Diffuse Scattering

Single-crystal diffraction patterns of silver iodide polytypes frequently exhibit diffuse scattering characteristic of disorder in the stacking sequence of basal planes (36,45). For instance, Burley (36) found that only three out of a total of 62 crystals he examined were sufficiently free of stacking disorder for the purpose of carrying out a structure determination. The scattering due to disorder takes the form of ~ontinuous diffuse rods along certain reciprocal lattice rows parallel to the c -axis - specifically, rows HK.L with H-K = 1,2 mod 3. Rows with H-K = 0 mod 3 are unaffected by variations in the stacking sequence: they show neither the diffuse rods due to random disorder nor, in higher polytypes, the extra Bragg reflexions arising from ordered variations in the stacking sequence. Other possible diffraction effects of stacking faults, dependent on the type of fault, are the broadening of Bregg peaks and shifts in the Bragg peak positions.

Growth and characterization of Agl polytypes

477

Figure 13 is a precession photograph illustrating the disorder diffuse scattering along the 10.L and 20.L rows in a silver iodide "mixed" polytypic crystal, i.e. one in which several polytypes are in syntactic coalescence. The predominant polytype is the 4H, although the 8H (211112) polytype is also clearly evident and the 2H cannot be excluded. An interesting feature is the fading or disappearance of the scattered intensity along the rows in the region 10.2-10.4 (indexed according to the 4H polytype). This is due to the modulation of the scattered intensity by the function F*F = f2Ag + fl2 + 2fAgflC°S(2~L~/4)

(~ = 0.75)

where F is the structure factor for a double layer of Ag-I atoms separated by a fraction ~ of the repeat distance in the c direction. Since fAg s fl, the intensity periodically fades to essentially zero (96).

Fig. 13.

Zero-level (HO.L) precession photographs of 4H+8H+2H Agl crystal showing moderate disorder diffuse scattering - streaking - along IO.L and 20.L reciprocal lattice rows. MoK radiation.

Diffraction effects due to stacking faults in 2H or hexagonal close-packed (hcp) crystals and 4H or double hexagonal close-packed (dhcp) crystals have been considered by many authors, including Wilson (97); Jagodzinskl (98); Gevers (99); Christian (I00); Lele, Anantharaman and Johnson (I01); Lele, Prasad and Anantharamal (102) and Prasad and Lele (103). The latter discussed the diffraction effects of nine different types of stacking faults in the dhcp structures; faults which had been identified by Lele, Prasad and Rama Rao (104,105) and typified by the virtual processes leading to their formation. The three relevant operations are glide, removal of close-packed layers and insertion of close-packed layers. The processes are not necessarily unique. Table 7 lists each fault together with the process of fault fomation, the fault vector and the structure resulting from the successive insertion of the fault. (Resultant structures are specified in the configurational notation - e.g.~ the dhcp structure is represented by ...ch... to show the alternation of cubic and hexagonal layers.)

P. R. Prager

478

Table 7. Faults in the dhcp structure, after Prasad and Lele (I03)

Fault

Intrinsic-c Intrinsic-h Intrinsic-2c Intrinsic-2h Intrinsic-3c Intrinsic-3h Intrinsic-oh Extrinsic-4c Extrinsic-cch F = I14[00011

Process of formation

Insertion of Removal of I Insertion of Removal of 2 Removal of I Insertion of Glide Double glide Insertion of

1 layer + Glide layer + Glide 2 layers + Glide layers layer I layer + Glide

I layer

Fault vector

Resultant structure

+F i S -F ± S +2F ± S -2F -F +F± S iS iS +F

c h c h h c ch ch ccch

S = II3[IT001

Prager (96) investigated the intrinsic-2h fault in detail, this being the only fault of the nine whose ordered (i.e., periodic) insertion into the dhcp structure according to an appropriate rule would produce the intermediate polytypes of Table 3 - or any other polytypes whose Zhdanov symbol consists solely of l's and 2's. This found application in a study by Prager (78) of a disordered Agl crystal which included 12H, 4H and 2H polytypes in syntactic coalescence (see Fig. 10e). Figure ]4 shows the observed disorder-diffuse intensity from this mixed crystal, together with the diffuse intensity I d calculated from a model in which intrinsic2h faults are randomly distributed through a 4H parent structure. According to the theory, id = IFI2

u(l-u) ~2+(l-2~)cos2~h3/2

where ~ is the random fault probability and h 3 is a continuous variable corresponding to the L index. The best fit was obtained for ~ = 0.85. Now, for values of ~ greater than 0.5 the structure is more appropriately described as a faulted 2H structure, since ~ = l corresponds to the fully ordered 2H structure (resultant structure 'h' in Table 7). Thus, the value ~ = 0.85 represents a ! slightly faulted 2H parent structure with fault probability ~ = l-u = 0.15. Almost as good a match between observed and calculated intensity of diffuse scattering was obtained using Wilson's (97) model for growth stacking faults in the hcp structure. The best value for the fault probability with this model was again found to be ~' = 0.15. The forced conclusion was that the 4H regions of the crystal were probably well-ordered and that the disorder was associated with faulting of the 2H regions. There must be reservations about such conclusions drawn from the study of structurally inhomogeneous (i.e., mixed) crystals. Certainly, disorder of varying degree has been observed in 4H crystals that are structurally homogeneous as evidenced by their uniformity of birefringence. Further study of such uniform crystals is required in order to obtain a satisfactory model for the faulting that is so common in Agl polytypes.

Growth and characterization of Agl polytypes

Fig. 14.

8.2.

479

Observed (circles) and calculated (continuous line) disorder-diffuse scattering along IO.L reciprocal lattice row in an AgI crystal containing 2H, 4H and 12H polytypes. Range from L = 0-19, indexed according to 12H. After (78).

Arc in~

The phenomenon of arcing is a second manifestation of defect structure important in polytypic crystals. The term is used in the context of slngle-crystal oscillation, rotation or Laue photography to describe the extension of diffraction spots into small arcs composed of two or more maxima connected by a strip of diffuse intensity (I06). Sometimes more complicated figures (triangles, hexagons, etc.) are obtained on Laue photographs; these are termed 'rings'. Agrawal and Trlgunayat (I07,108) have reported detailed studies on solution-grown cadmium iodide polytypic single-crystals in which arcing is a very common occurrence. They have provided a most satisfactory explanation of the phenomenon in terms of the formation of tilt boundaries (that is to say, low-angle grain boundaries) as a consequence of the vertical allgmnent of edge dislocations of the same sign. Such a boundary divides the crystal into two blocks tilted relative to one another about an axis lying inside the contact plane of the boundary parallel to the Burgers vectors of the aligned dislocatlons. The dislocations involved are unit dislocatlons wlth Burgers vectors a/3(2110) or Shockley partlals with Burgers vectors a/3(1010). The perfect dislocations arise from slip within the planes of closest pa~king, the basal planes {0001}, and in the directions of closest packing, <2110), these being the most likely slip Elanes and slip directions, respectively, The partial dlalocations a/3(1010) also lie in the basal plane. They are either independently created, since the structure of Cdl 2 favours slip in the direction of (10To) as well as in the direction of closest packing, or else they are formed by the dissociation of the perfect dislocation according to the:reactlon a/3(1120) = a/3(lO[O) +

a/3(OlTO).

This process results in the formation of an extended dislocation in which the two partials, having repelled each other and separated out, are connected by a strip of faulted crystal, i.e., a region of stacking fault. The details of the figures - arcs and rings - observed in the diffraction photographs depend on whether slip has occurred in one direction only or in two or more equivalent directions simultaneously. Sllp in only one direction produces a single tilt boundary that divides the crystal into two regions. Under suitable

480

P.R.

Prager

conditions of observation, e.g., an oscillation or rotation photograph with the rotation axis perpendicular to the tilt axis, this will produce a splitting of a Bragg peak into a pair of spots lying along an arc parallel to the rotation axis. The spots are symmetrically displaced from the central position and correspond to the two mutually tilted blocks. The continuous strip connecting the maxima arises from the continuously distorted region between the two blocks. Simultaneous slip in more than one direction leads to the formation of multiple, mutually tilted blocks or regions, and correspondingly complex diffraction figures, especially on Laue photographs. The formation of arcs results from the regular arrangement of dislocations in the vertical plane, i.e., the plane containing the c-axis; and the dissociation of perfect dislocations produces stacking-faulted regions. The irregular arrangement of stacking faults normal to the c-axis produces the streaking discussed above, whereas the regular or ordered arrangement of stacking faults normal to the c-axis in crystals with layer and close-packed structures gives rise to the polytypic variants of some basic structure. Thus, there is a close relationship between the phenomena of streaking and arcing and the occurrence of polytypism. This relationship has been discussed by Trigunayat and his co-workers (]06,109-I]]) who have examined the frequencies with which arcing, streaking and polytypism are observed in the isomorphous compounds cadmium iodide, lead iodide and cadmium bromide.

8.3.

Arcin~ in Silver Iodide

The arcing phenomenon described above, or one closely related to it, is occasionally observed in silver iodide (45). In general, the Agl studies have relied on zero-level precession photographs which map the a*-c* reciprocal lattice net. Arcing is here manifested as a tangential extension of the diffraction spots into the segments of an arc, with several maxima in the intensity distribution (Fig. 15). A detailed analysis in the manner of Agrawal and Trigunayat (107,108) has not been performed. Examination of several cases in which a-axis transmission Laue photographs are available of specimens for which arcing was observed on a*-c* precession photographs shows that arcs with multiple maxima on the latter correspond to complex rings on the former (Fig. 16).

Fig. 15.

Zero-level (HO.L) precession photograph showing the arcing effect in a copper-doped Agl 4H crystal.

Growth and characterization of Agl polytypes

Fig. 16.

481

Transmission Laue photograph, beam parallel to a-axis, showing formation of complex rings for a copper-doped Agl 4H crystal. The effect is apparent only for the strongest reflexions. Same crystal as in Fig. 15.

In the absence of more detailed analyses it is not possible to confirm that the same processes underly the arcing phenomenon in Agl as in Cdl 2 and the other layer compounds. In Cdl~ as we have seen, arcing is the consequence of the vertical alignment into graln boundaries of glissile dislocations of the same sign - either during the growth phase (107,108) or upon heat treatment (106,111). The changes in arcing observed upon heat treatment of Agl are discussed below; they do not parallel those described for Cdl2, and so it appears that the underlying processes must be different. One other observation makes the inference of similar processes in Agl and Cdl 2 during the growth phase probelmatic. Thus, it was noted that whenever a crystal was accidentally strained, e.g., in the process of cleaving a small section from a long needle, the subsequent diffraction photographs invariably showed strong arcing. The arcing observed in precession photographs from crystals which were thought to have been thus damaged was not apparently different from that observed in crystals in which no damage was suspected.

9.

TRANSFORMATION OF POLYTYPES

Transformations occurring atnormal pressure are discussed below. A probable transformation betweem hexagonal polytypes at room temperature and a pressure of 1.1 kbar was canvassed in an earlier section.

9.1.

Transformation at Room Temperature

The majority of Agl crystals grown by Cochrane's method and displaying the common hexagonal-prismatic growth habit possess the 4H structure initially. When viewed under the polarizing microscope normal to the optic axis (i.e., the c-axls, which is parallel to the long axis of the needles) these crystals usually exhibit uniform birefringence (AB = 8.9 x 10-3 (77)). This optical homogeneity does not, however, guarantee the absence of any stacking disorder, and X-ray diffraction photographs

482

P . R . Prager

generally show the previously described diffuse scattering distributions characteristic of stacking disorder. (By contrast, in the case of ZnS needles it has been shown by Mardix and Steinberger (112) that uniformly birefringent regions of the crystal are perfectly ordered, and stacking disorder is confined to regions between bands of uniform birefringence.) Variability in the intensity of the disorder-diffuse scattering from crystal to crystal indicates a substantial variability in the degree of disorder superposed on the 4H structure, but the range of fault probabilities has not been determined. Crystals which have been stored at room temperature (25 ± 5 °C) for months and years generally appear banded or striated under the polarizing microscope. The bands, whose widths range from a few microns to a few milllmetres, are perpendicular to the c-axis. Each band represents a region of uniform birefringence and hence, because of the proportionality between birefringence and hexagonality, a region of constant hexagonality. Regions with different hexagonalities are presumed to have distinct polytypic structures. The polytypes identified to date in these needles lie in the range from 50% hmxagonality (4H) to |00 percent hexagonality (2H): see Sections 7.4 and 7.5. The following previously unpublished observations illustrate the transmission of crystals with the 4H structure at growth. A pair of very fine needles, each about I mm x 0. I r~n, was harvested from KI solution after three weeks growth. Optical examination between crossed polarizers at three months from the beginning of the growth period showed the needles to be clear and completely uniform in their birefringence (Fig. 17). At seven months the needles were seen to have developed a few fine, isolated striae - i.e., narrow regions of contrasting birefringence. At ten months one of them (crystal A) showed a few bands of different birefringence; the other (crystal B), many more such bands. X-ray diffraction study of a fragment of crystal A confirmed that the structure was basically 4H with superposed stacking disorder. Considerable arcing was apparent in the diffraction photograph, the cleaving having been poorly carried out. Finally, examination of photomicrographs taken 24 months after initiation of growth showed that, in crystal A, the original birefringence persisted over more than 90 percent of the needle, with a few uninterrupted bands of up to I00 um in breadth. Very fine regions characterized by two other birefringences were distributed along the needle.

Fig. 17.

Photomicrograph of a pair of Agl hexagonalprismatic Agl needles, crystals A and B, three months after initiation of growth. Dimensions ~I x 0. l x 0. I mm. Uniform 4H structure.

Growth and characterization of Agl polytypes

483

There were about 50 bands in all (Fig. ]8). Crystal B, by contrast, contained no extensive uniform regions whatsoever, but was composed of some 200-300 very fine striae of the order of 5 ~m in breadth. At least five distinct birefringencies were noted (Fig. 19). The difference brought about by aging in two initially similar crystals is quite striking. These observations illustrate the transformation from the 4H structure to complex arrangements of several polytypes, mostly unidentified, in syntactic coalescence. Because of the narrowness of the regions of presumed uniform structure, identification of all the polytypes in these crystals would be extremely difficult. Optical and X-ray studies such as these serve to establish that the higher-order polytypes in AgI are not formed during growth of the crystals but emerge from the 4H structure in the aging period immediately following growth. It seems reasonable to suppose that they may be formed by the screw dislocation-controlled expansion of stacking faults, which is the well established mechanism for the development of ZnS polytypes out of the basic 2H structure during the cooling-down period after growth from the vapour phase (112,113). Direct evidence for such a mechanism is lacking at present. Indirect evidence to support a screw dislocation mechanism is the apparent restriction of AgI polytyplsm to acicular crystals, which may be taken to indicate growth about a single, axial, screw dislocation in accordance with Frank's theory (II4).

i!~ ¸/

Fig. 18.

Agl crystal A after two years, showing development of polytypic regions.

Fig. 19.

Agl crystal B after two years, showing development of polytypic regions.

484

P.R.

9.2.

Prager

Transformation at Elevated Temperatures

Transformation of the metastable 4H and higher polytypes towards the stable 2H structure takes place rapidly at quite moderate temperatures, well below the temperature of the polymorphic transition at ]47°C. As Table 8 shows, the detailed course of the transformation is variable from crystal to crystal, depending perhaps on the defect structure including degree of disorder, as well as the polytypic composition. The following points are based on Table 8 and similar observations: Table 8.

Effect of heat treatment on Agl needles

Crystal number

Initial structure

Temperature (°C)

1

4H

80

20

2H + small amount of 4H + possible trace of 3C

I00

60

Increase in proportion of 2H

95±10

90

2H + small amount of 4H + possible trace of 3C

2

4H

3

4H

4

4H

Time (min)

Result

75

I0

No change in birefringence

I00

I0

2H + v slight streaking

130

25

Increase in birefringence indicates 2H structure Many fine black striae

95±25

5

6*

4H + 8H (211112)

2H + 12H

80

No change Striae mostly disappeared 2H structure confirmed

I15

225

70 90

60 60

No change

95

105

No change

125~5

50

12~±5

250

I00

I0

Increase in 8H; decrease in 4H

2H with fairly strong wings + trace of 4H No further change 2H + 12H ( 2 1 1 1 1 2 1 1 1 1 )

*Two optically similar fragments from the same needle - one heated, one not heated.

9.2.1. Relative stabilities of polytypes. Higher-order polytypes, or regions of higher-order polytypic structure in syntactic coalescence with regions of the 4H or 2H structure, appear to be more stable than the 4H structure itself, as seen for example in crystals 5 and 6.

Growth and characterization of Agl polytypes

485

9.2.2. Emergence of intermediate polytypes. Crystal 5 shows that the transformation from 4H to 2H may proceed via intermediate polytypes, especially where, as in this instance, a macroscopic 'seed' of the higher polytype is present. (The X-ray diffraction finding that the crystal was originally composed of two polytypes, identified as 4H and 8H, was confirmed by optical examination of the crystal between crossed polarizers, which showed it to be made up of just three regions, with the central region having a birefringence greater than that of the two identical outer regions.) This emergence of higher-order polytypes was also seen in the studies on aging at room temperature. 9.2.3. Cubic packing. The appearance in crystal 4 of black striae - narrow bands which are optically isotropic - implies the formation of limited regions within which the cubic stacking sequence ...ABC... prevails. Whether or not these regions are well-ordered would be interesting, but difficult to establish. The disappearance of the striae with further low-temperature annealing shows that the cubic structure, if it is indeed formed, is metastable. It should be noted that diffraction photographs of other crystals (e.g., crystals 2 and 5) showed faint reflexions which indicated the formation during heat-treatment of traces of the cubic phase. 9.2.4. Random stackin~ disorder. Transformation towards the 2H structure appears to be accompanied by a reduction (or at least by no increase) in random stacking disorder, as judged by the intensity of streaking. Thus, as is the case in Cdl2, the effect of heating is not to promote the formation of fresh stacking faults but rather to bring about the redistribution or elimination of existing faults. This can be contrasted with the effect of heating on several other polytypic compounds, e.g., Pbl2, SiC and ZnS, where heating generally leads to increased disorder as polytypic transformations are approached (106,111). 9.2.5. Arcin~ and win~s. In no case has heating produced an observable increase in arcing in Agl. This is in direct contrast to the observations in Cdl 2 where heating - particularly the first heating run in a series of runs - frequently produces arcing or intensifies existing arcing. The increase in arcing is attributed to the thermally-induced migration of previously immobilized edge dislocations to existing low-angle boundaries (106,111). In the case of Agl the corresponding effect of heating is sometimes to prdouce 'wings', Fig. 20. These wings resemble the arcs of Section 8.2 in that the diffraction spots are similarly extended; however, they differ in that there is a single central maximum in the intensity distribution, as opposed to the multiplicity of maxima found along the arcs. Wings have been observed in the diffraction patterns obtained both from Agl crystals that originally displayed arcing (crystal l, for example) and from those that did not (e.g., crystal 2). In the former case the effect of the heat treatment was to eliminate the arcing. (As implied in their respective definitions, arcs and wings are mutually exclusive: it is not possible to have just one maximum at the same time as having two or more maxima.) In the simple arcing phenomenon, the bimodally distributed blocks are responsible for the two displaced maxima, while the strip of intensity connecting these spots is deemed to arise from the continuously distorted region between the blocks i.e., the tilt boundary itself (lOg). In the case of the wing phenomenon, since there is just a single maximum, a bimodal or multimodal distribution of blocks is precluded and it must be assumed that distorted regions separate blocks with the same mean orientation. Obviously, therefore, a somewhat different account is required to explain the formation of wings as opposed to arcs, though we cannot at present provide it.

486

P.R.

Fig. 20.

9.3.

Prager

Zero-level precession photograph (Mo K radiation) showing the formation of 'wings' after heat treatment causing transformation from 4H+SH+2H to 2H. The diffraction pattern from this crystal before heat treatment is shown in Fig. ]3.

Transformation at Low Temperatures

As part of their previously mentioned NMR study of A~I, Brinkmann and Freudenreich (79) investigated the temperature-dependence of the 1271 quadrupole coupling constants. Starting with samples identified as having the 4H structure initially, they confirmed the irreversible transformation to the 2H structure at 100°C which had been reported by Prager (45,77). In addition, however, they found that upon cooling a 4H crystal there was a further transformation at about -50°C as evidenced by the appearance of a third NMR signal with a large coupling constant (C = 7.97 MHz) and small changes in the coupling constants of the original two signals (see Table 6). On the basis of the observed intensity ratios 4:1:! of these signals they proposed that the 4H polytype had undergone transformation to a 24H polytype with Zhdanov symbol (11)43113(11) 4 . We have shown that the determination of periodicity and stacking sequence by this NMR technique is ambiguous in general; therefore the proposed structure for the transformed polytype cannot be regarded as definitive. These considerations do not, however, compromise the evidence presented by Brinkmann and Freudenreich for the actual occurrence of a lowtemperature transformation in 4H Agl. Further optical and X-ray or neutron diffraction studies of this transformation are needed.

9.4.

Transformation in the Copper Iodide - Silver Iodide System

9.4.1. Room temperature transformation. The 4H polytype was found by Minagawa (80) to be the most conlnon polytype in the low-to-moderate range of copper concentrations, between 3 and 9 mol.% (Section 7.8). The 3% crystal were unaltered after aging at room temperature for two years. This increased stability of the 4H copper doped Agl crystals grown by Cochrane some six years earlier. X-ray diffraction revealed the 4H structure only, and the structural homogeneity was confirmed by optical examination between crossed polarizers which showed the hexagonal needles to be uniformly biregringent. Their appearance was

Growth and characterization of Agl polytypes

487

thus similar to that of freshly harvested needles of undoped Agl. Minagawa's findings for the 6 and 9% copper crystals were most interesting. They showed that the original 4H polytype transformed over a period of months to heavily faulted twins of the 3C structure, passing through an intermediate stage in which 4H and 3C-twin polytypes coexisted in syntactic coalescence, as alternating microdomains distributed perpendicular to the c-axis. The crystals with the higher copper content (x = 0.09) transformed more rapidly, the 4H polytype having disappeared after 6-|2 months; those with the lower copper content (x = 0.06) took two years to transform completely. Crystals which possessed the 3C structure originally (copper concentrations in the range 0.]5 < x < 0.23), were found to be structurally unaltered after aging at room temperature over the two year period. 9.4.2. High temperature transformation. Structural changes under heating were also studied by Minagawa. Groups of 4H crystal with x ~0.03, 0.06 and 0.09 were heated at 130°C for ]0-60 min and quenched to room temperature. All crystals were found to have transformed to mixtures of the 4H structure and twins of the 3C structure. Further heat treatment at the same temperature for I-4 weeks resulted in complete conversion to twins of the 3C structure, the speed with which this occurred increasing with increase in the copper content. No reversion from the twinned 3C structure to the 4H structure was observed within a further 6 months in crystals with x = 0.03. 9.4.3. Cul - Agl phase diagram. Results of the Cu Ag. I system accordlng to M1nagawa are summarlzed in the schematlc p~ase dlagram, Fig. 2], which shows that the structures 2H, faulted 2H (+ higher-order polytypes), 4H and 3C occur with increasing copper concentration. Small concentrations of copper tend to stabilize the 4H structure, but higher concentrations result in increasingly rapid conversion to twins of the 3C structure at room temperature. The observed stabilization of the cubic form is in accordance with the existence of the rare mineral miersite, (Ag,Cu)l, which possesses the sphalerite-type structure and was formerly found at Broken Mill, Australia (95,1]5). •

•

'

•

°

X

- X

•

However, details of the diagram in the region x ~ 0 are questionable. As shown previously, the 4H polytype certainly belongs to this region, as do the higherorder polytypes, many of which derive from the 4H polytype. In addition, the transformation from the 4H to the 2H structure for crystals with x ~0 is well established (45,77,79).

130 °C 1

3C

RT ~ 2H

FAULTED 2H 4H

4H-~TWINSOF 3C

i

o

3c

3c

w

;

AgI

9

ioo cuI

I00 x

F i g . 21.

Schematic phase diagram o f t h e CuxAgl_xI system a c c o r d i n g to Minagawa (80).

488

P. R. Prager lO.

CONCLUDING REMARKS

The investigation of the silver iodide structural system has been in progress now for over one hundred years~ and a complex phase diagram has gradually emerged. Polytypic variants have been reported at three positions on the diagram: the room temperature and low temperature variants at normal pressure, and the variants on either side of the polytypic transformation reported to occur at room temperature and l.l kbar. The results of earlier investigations on powder samples were sometimes contradictory and inconclusive because of the irreproducibility of samples prepared by different methods - or altered by different mechanical treatment (crystalline silver iodide being an unusually soft and plastic material). Recent single-crystal studies have established a potentially rich field of polytypic variants in silver iodide, though only modest numbers of actual polytypes have been identified and studied in detail. A family of polytypes intermediate between the 4H (22) polytype and the stable 2H wurtzite-type structure undoubtedly exists, in which only 2's and l's appear in the Zhdanov symbol. There is also some evidence for another family, also derived from the 4H polytype, in which 3's and l's dominate the Zhdanov symbol. Why these families of polytypes in Agl are apparently restricted to crystals grown by a single method from the range of methods available remains a mystery. As in the more thoroughly studied systems - ZnS, SiC and the layer compounds such as Cdl2 and Pbl2 - stacking faults and their distribution under the control of screw dislocations are thought to be important to an understanding of the genesis of polytypes. However, only very indirect evidence for the involvement of screw dislocations in Agl polytypism is available at present. Further study of the defect structure of Agl single crystals is needed to elucidate the mechanism of development, over a period of months, of the higher-order polytypes as they emerge out of the metastable 4H parent structure.

Acknowledgements - The original work on silver iodide was performed at the University of New England. I am grateful to Professor Neville Fletcher for the opportunity of working there, and to the members of his group, particularly Dr Grahame Harvey and Dr David Mills, for their co-operation. I am indebted to Dr Zwi Barnea of the University of Melbourne for commenting on the manuscript, and to Mr Russell Creek for assistance with the photography.

REFERENCES

I. 2. 3. 4. 5.

G. G. Harvey and N. H. Fletcher, J. Phys. C 13, 2969 (1980). C. Tubandt and E. Lorenz, Z. Phys. Chem. Sto-~hiom. Verwandschaftsl. 87, 513, 543 (1914). A. Kvist and A. M. Josefson, Z. Naturforsch. A 23, 625 (1968). G. Luther and H. Roemer, Phys. Stat. Solid. B IO-6, 511 (1981). E. Mallard and H. Le Chatelier, C. R. Hebd. Seances Acad. Sci. 97, I02

(]883). 6. 7. 8. 9. I0. II. 12.

R. B. Wilsey, Phil. Mag. 46, 487 (1923). R. Bloch and H. M~611er, Z. Phys. Chem., Abt. A 152, 245 (1931). N. H. Kolkmeijer and J. W. A. van Hengel, Z. Kr~allogr., Kristallgeom., Kristallphys., Kristallchem. 88, 317 (1934). L . W . Strock, Z. Phys. Chem., Abt. B 25, 441 (1934). L. W. Strock, Z. Phys. Chem., Abt. B 31 , 132 (1936). S. Hoshino, J. Phys. Soc. Jap. 12, 315 (1957). R. J. Cava, F. Reidinger and B. J. Wuensch, Solid State Commun. 24, 411 (1977).

Growth and characterization of Agl polytypes 13. 14. ]5. ]6. 17. 18. 19. 20. 2]. 22. 23. 24. 25. 26. 27. 28.

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THE AUTHOR

P. R. PRAGER

Peter Prager graduated from the University of Melbourne in 1965 with a BSc, and completed his PhD in physics there in 1971 after having spent a short period at the Polytechnic Institute of New York. He subsequently worked at the University of New England and Monash University, before returning to the University of Melbourne where he is currently a visiting research fellow. In 1977 he forsook physics temporarily to complete a degree in psychology at Monash University, and for a time he tutored there in that discipline. His research interests are in accurate X-ray structure analysis and crystalphysics - as well as polytypism and silver iodide. His interest in silver iodide arose serendipitously at the University of New England when the crystal he borrowed for the purpose of aligning a precession camera gave rise to the wrong diffraction pattern.