ORIENTATIONAL EFFECTS IN THE POLYMORPHIC TRANSFORMATIONS OF SULPHUR BY C. BRISKE AKD N. H. HARTSHORNE Dept. of Inorganic and Structural Chemistry, The University, Leeds, 2 Received 31st January, 1957 When films of y-sulphur are inoculated with cc-sulphur, or mechanically by scratching, certain relative orientations of the two forms are preferred, and there is a pronounced tendency to preserve these orientations as growth of the a-phase proceeds. The implica- tions of these results as regards the mechanism of the transformation process are discussed. Earlier work on the transformation of /3-(monoclinic) to a-(rhombic) sulphur 1 9 2 has shown that the activation energy (as deduced from the temperature coefficient at temperatures far below the transition point) is equal to the internal latent heat of sublimation of the /3-form, or nearly so, suggesting that the process is analogous to that of crystal growth from a vapour phase. This is consistent with the ob- servation that when an a-crystal advances across the boundary between two differently orientated /3-crystals, it does so without apparent change of orientation (ref.(l), fig. 9), indicating that the transition layer between the two forms is com- pletely disordered. The observed rate of advance of the interface is, however, at least lo3 times greater than that calculated on this basis at temperatures between - 15" (the lowest temperature at which the rate has been measured) and 20°, though the discrepancy decreases with rise of temperature, and near to the transi- tion point (95.5"), there is agreement between the observed and calculated rates to within a power of ten.2 Similar considerations apply to the monotropic transformation of ?-(mono- clinic) to a-sulphur at low temperatures.Between - 15" and 20" the rate of advance of the interface is of the same order as that for p- to cc-sulphur,3 and measurements of the temperature coefficient so far made correspond to an activa- tion energy of between 20 and 26 kcal/mole, within which range the internal latent heat of sublimation of y-sulphur almost certainly lies. (The values for a- and @-sulphur are 23.2 and 22.6 kcal/mole respectively, and that for y-sulphur cannot be very different.) Furthermore, there is no apparent change of orientation when an a-crystal crosses the boundary between two differently orientated y- crystals.Assuming that the vapour pressure of y-sulphur is not more than about twice that of p-sulphur, the discrepancy between the observed and calculated rates is again of the order of 103. The calculated rates just referred to are those given by the product of the supersaturation x and the vacuum rate of evaporation of a-sulphur calculated from the Langmuir expression m = ap/(2nMRT)*, where rn is the rate in moles cm-2 sec-1, a is the condensation coefficient (taken here as unity), p is the vapour pressure, and the other symbols have their usual significance, This product is multiplied by Nd3 (N is the Avogadro number, and d the mean lattice spacing) to give the linear rate of advance of the interface? Now Bradley4 has shown that the rates given by the Langmuir expression agree with those actually observed for a-sulphur over the range 15" to 32.5", if the condensation coefficient is taken as 0-7, i.e. -unity, and making the reasonable assumption that this agreement holds over a wider range of temperature, it seems clear that the above method of calculation must give the maximum rate of advance of the interface for a mechan- 196FIG. 1.-Typical spherulite of y-sulphur FIG.2.-Film shown in fig. 1 after between crossed polars (vibration direc- transformation to a-sulphur between tions of polars parallel to edges of crossed polars (vibration directions of [To face page 197 figure). polars parallel to edges of figure).C . BRISKE A N D N . H . HARTSHORNE 197 ism consisting simply of the evaporation of molecules from one form and their condensation on the other.The large discrepancy between the observed and calculated rates therefore suggests that some secondary mechanism associated with an activation energy lower than the heat of sublimation is involved in the transformation, i.e. a displacive process, and, if so, the possibility arises that the orientation of the unstable phase will have some influence on that of the stable phase. The results reported in this paper show that such an effect does in fact exist in the transformation of y- to a-sulphur in thin films, though it is not per- ceptible in the crossing of a single crystal boundary by the a-phase. This trans- formation is a particularly favourable case to study, since the y-form habitually crystallizes as spherulites, the axis of elongation of the individual crystals being c, and (OlO), the optic axial plane, commonly lying in the plane of the section, so that growth of the a-sulphur across a spherulite encounters a progressively changing orientation of the y-form.EXPERIMENTAL The sulphur used was purified by the method of Bacon and Fanelli,s the starting material being B.D.H. crystalline sulphur. The films were prepared between 3 in. by 1 in. micro- scope slides and 2 in. square cover slips (no. 1). A slide with a cover slip laid on it was heated to a temperature just above the melting point of the sulphur, which was placed at the edge of the cover slip, and ran underneath by capillary action on melting. The slide was then transferred to a cold aluminium plate, and this usually resulted in the crystallization of the y-form, often as a single spherulite. In some cases the /3-form, or a mixture of the p- and y-forms appeared.The film was then re-melted and chilled as before, and the process repeated if necessary. Slides which failed to give a suitable y-film after three meltings were rejected. A typical y-film is shown in fig. 1. The slides and cover slips had been previously cleaned by prolonged immersion in hot chromic acid, followed by boiling distilled water, and then washed with conductivity water and dried at 160". In some of the experiments described below, the y-films were uncovered by stripping off the cover slip, and were then inoculated with either a single crystal, or a polycrystalline bead, of the or-form.The stripping was effected by prising up the cover slip at a corner with a razor blade, and since the slip was very thin it bent easily, leaving the sulphur attached to the slide. The inoculation was done on the stage of a polarizing microscope, and was watched with a low-power objective. The inoculating crystal or bead was mounted on a horizontal arm overhanging the stage. This arm was pivoted on jewel bearings carried in a stirrup support attached to the stage bracket of the microscope, and was counterpoised so that the crystal or bead could be lowered into very light contact with the film without splintering it. The slide was moved to the required position by means of a mechanical stage. By this method any selected point on the film could be inoculated.For the subsequent study of the orientations of the a-crystals resulting from the inoculation, the inoculating device could be swung aside, thus permitting the use of high-power objectives. RESULTS AND DISCUSSION The following experiments were carried out : (a) inoculation of uncovered y-films with (i) a single a-crystal, (ii) a polycrystalline bead, as above, followed by determination of the orientations of the resulting cc-crystals near to the site of inoculation, in relation to the c-axis of the y-form and the plane of the section; (6) inoculation of covered y-films by scratching along one edge of the cover slip with a razor blade, followed, after transformation of the whole film was complete, by determination of the orientations of the a-crystals as above in randomly dis- tributed areas mostly situated some distance from the edge inoculated.Some determinations were also made of the orientations of the a-crystals immediately adjacent to the edge inoculated, but these determinations were limited by the shattering of the film which had occurred as a result of the action of the razor blade.198 POLYMORPHIC TRANSFORMATIONS OF SULPHUR The orientations of the cc-crystals were determined from their interference figures, using the optical crystallographic data given in Groth’s Chemische Kristul- lugraphie.6 Stereographic projections of the principal low-index sections, showing the orientation of the optic axes, traces of the cleavage planes, and the true angular diameter of the interference figure given by the objective used (4 mm, N.A., 0-85), helped in identifying the sections presented.As a further aid to identification, the birefringences for these sections were calculated from the well-known relation (Ng’ - Np’) = sin 8 sin 8’(Ng - Np), where Ng’, Np’ are the greater and smaller indices of the section respectively, Ng, Np the greatest and smallest indices of the crystal, and 8, 8’ the angles made by the normal to the section with the two optic axes. From these birefringences it was often possible to confirm the identity of a section by comparing its birefringence with that of a neighbouring one whose identity was in no doubt, by using a calibrated graduated quartz wedge. c FIG. 3.-(a) Net used to plot orientations of a-crystals ; (b) optic orientation of y-sulphur, showing presumed orientation of s8 rings.By these means it was possible to determine the orientations of the axes of the optical indicatrix in relation to the c axis of the original y-crystals and the plane of the section to within say k 10”. The distributions of these orientations were then found by plotting two axes of the optical indicatrix, namely, those correspond- ing respectively to the principal refractive indices Np (see above) and N,,, (the principal intermediate refractive index) * on the stereographic quarter net shown in fig. 3(a). The NS (north-south) diameter of the net represents the c-axis of the y-form, and the primitive quarter circle the plane of the section. All results plotted were pooled in this one quadrant of the usual circle, since it was assumed that two poles in different quadrants but making the same angles with the NS diameter and with the centre of the projection represented structurally equivalent relative orienta- tions of the two forms.Thus, for example, poles actually plotting at P’ and P” (see figure), which are both at an angle w to the NS diameter and 4 from the centre, were placed at P. The justification for this procedure was that (i) a-sulphur is orthorhombic and the indicatrix axes and crystallographic axes therefore * The symbols Np, Nm and Ng have been used for the principal refractive indices instead of the more usual a, and y, to avoid confusion with the designations of the three forms of sulphur.C . BRISKE AND N . H . HARTSHORNE 199 coincide (Np = a, Nm = 6, Ng = c).Moreover it belongs to the highest sym- metry class, so that all sections having the same indices are structurally equivalent ; (ii) y-sulphur is pseudo-orthorhombic, for its p-angle is 8 8 r and the extinction angle N p : c is only ly (hence the parallel extinction cross seen in fig. 1).6*7 Furthermore the birefringence of y-sulphur is strong and negative, which shows that the Sg rings must be arranged parallel to one another with their planes normal to c, or approximately so, as shown in fig. 3(b). The sections of the net, numbered 1 to 7, are projections of equal areas on the surface of the sphere in the corresponding spherical projection. If therefore the orientations of the cc-crystals had been quite random, these areas should have TABLE PERCENTAGES OF a-CRYSTALS HAVING (i) THE Np AXIS, (ii) THE Nnl AXIS, OF THE OPTICAL INDICATRIX IN THE DIFFERENT SECTIONS OF THE NET IN FIG.3 exDeriment and total number of crystals studied (in brackets) section of net inocn. by crystal (332) inocn. by bead (241) inocn. of covered films at edge crystals at edge (65) crystals in randomly situated areas (272) Np Nm 23.8 56.6 3.9 7.5 4.5 7.5 1.5 0 2.4 0 6.1 0 57.8 28.3 N p N m 28.2 63.1 2.9 2.9 2.5 5-4 0 2.1 0-8 1.2 7.9 1.2 57.7 24.1 Np N", 40-0 46.1 0 6.2 23.1 15.4 4.6 0 3.1 0 3.1 0 26.2 32.3 Np Nm 22-8 54.0 2.9 6.3 19-9 21.7 6.3 0 0.7 0 8.1 0 39.3 18.0 been approximately equally populated with poles representing any one axis of the indicatrix, since the number of crystals studied in each experiment was quite large. The actual distributions, given in table 1, show that this was far from being the case.In all experiments, the percentage of crystals with the N7,L axis plotting in section 1 was high (46.1 to 63-1 %), indicating a strong tendency for the NgNp plane, i.e. the optic axial plane, to become orientated approximately normally or at a large angle to the c axis of the original y-phase. In the first two experi- ments (inoculation by crystal and bead respectively) the figures indicate also a marked tendency for the Np axis to orientate vertically, or at a small angle (< 31") to the vertical (section 7 ) . The fairly close correspondence between these distribu- tions will be noted, and is discussed later. In the last two experiments (inoculation of covered films at the edge), the percentages of crystals with the ATp axis in section 7 are much smaller, but there is an increase in the population of section 3, both by this axis and by the N,,, axis.It will also be noted that sections 2,4, 5 , and 6, i.e. those corresponding to large angles with the c ( y ) axis and the plane of the section are either sparsely populated, or avoided altogether. Table 2 shows the distribution of cc-crystals having one of the two axes Nm and Np in section I , i.e. parallel or at a small angle to c(y), and the other in either section 3 or section 7. Such crystals present " centred " interference figures (two optical symmetry planes vertical), or are inclined at small angles, i.e. up to the angular limits of these net sections, to these centred positions.cc-Sulphur is optically positive, and so the Np axis is the obtuse bisectrix. The indicatrix axis normal to the centred section is given in brackets in each column heading of the table. The totals in the penultimate column show that the majority of the crystals are distributed among these categories. A striking consequence of this tendency to adopt orientations so simply related to that of the y-form is demon- strated by fig. 2, which shows the film in fig. 1 after having been completely trans- formed to cc-sulphur. The film still displays a marked extinction cross with arms parallel to the vibration directions of the polars. On rotating the polars in unison200 POLYMORPHIC TRANSFORMATIONS OF SULPHUR the cross rotated in sympathy, though it was not as complete throughout the operation as that shown in the figure, since not all the crystals had achieved the same degree of conformity with the general tendencies expressed in table 2.This persistence of the parallel extinction cross has been observed on a number of transformed films. TABLE 2.-PERCENTAGE DISTRIBUTIONS OF a-CRYSTALS SHOWING CENTRED, OR APPROXIMATELY CENTRED INTERFERENCE FIGURES, WITH ONE VIBRATION DIRECTION PARALLEL TO C(y) crystals crystals crystals crystals with with with with N,,, in 1, N,,, in I, N,,, in 7, N,,, in 3. total crystals Npin7 Nph3 Npin 1 Npinl Ngin 1 (obtuse (acute (optic (acute bisectrix) bisectn'x); normal) bisectrix) 0' with expt. inoculation by crystal 48.2 2.1 23-2 0.3 73.8 6.6 inoculation by bead 53.5 2.1 22.4 4-1 82.1 0.8 inoculation at edge: crystals at edge 21.6 21.6 30.8 9.2 83.2 1.5 random areas 26.5 19.5 14.7 8.1 68.8 7.7 In the last column of table 2 are the percentages of crystals having the Ng axis in section 1.These of course differ from those just discussed in having Nm and Np normal to c(y). The percentages are all small, and so there is evidently a tendency to avoid this orientation. An explanation of this is suggested by the structure of cc-sulphur determined by Warren and Burwell.8 In this structure the planes of the s8 rings are all parallel to the N, axis, but are near 45" to the N,,, and Np axes. Therefore if the Ng axis were aligned with the c-axis of the y-form (see fig. 3(6)), the rings would have to turn through about 90" to fit on to the a-structure, whereas a much smaller rotation would be involved if either the N,,, or Np axis were parallel to c(y).The tendency to preserve the orientations established on inoculation, in particular the parallelism between the Nm axis and the c(y) axis which is shown by the figures for the last two experiments in tables 1 and 2, and by the persistence of the extinction cross (fig. 1 and 2), shows that a-crystals advancing across a y-spherulite and encountering a progressively changing orientation of the y- crystals are subjected to what may be described as a " steering " effect by the y-crystals. A detailed example, one of several observations, is shown in fig. 4. In this, an area of cc-crystals, all showing a centred acute bisectrix figure with N,,, parallel to c(y), maintains this relationship over a change of direction of the y-needles of more than 90". Detailed microscopic examination of the area has shown that the change in the orientation of the a-phase is partly continuous and partly discontinuous, i.e.it consists of a series of slightly misaligned blocks, some of which are curved crystals, showing a wave of extinction passing from one end to the other as the section is rotated between crossed polars. This steering effect is imperceptible in the crossing of a single y - y crystal boundary, even when there is a very marked change in the orientation of the y-phase, as for example, at the boundary between two spherulites. Table 2 shows that the crystals produced by inoculation with a crystal or bead at single points included very few which presented acute bisectrix type sections (columns 3 and 5), as compared with those resulting from inoculation by scratching at the edge, and that these contained far fewer obtuse bisectrix type sections (column 2) than the former. Whether this is fortuitous, or due to the different methods of inoculation is not known.It may be noted, however, that the fully transformed films resulting from point inoculation by crystal or bead developed many crystals showing acute bisectrix type figures at places distant from the sitesC . BRISKE AND N . € I . HARTSHORNE 20 1 of inoculation, but it has not yet been possible to ascertain whether they resulted from spontaneous nucleation, or as the result of a gradual change in the orientation of the original crystals. B 0 FIG. 4.-" Steering * ' effect, showing change of orientation of a-crystals in sympathy with change in direction of c(y). 0 = centre of original y-spherulite, OA, OB, OC = original y-needles. Finally the correspondence between the distributions of the orientations re- sulting from the crystal and bead inoculations may be noted with some interest (tables 1 and 2). In the former the crystals used were bipyramids bounded by { 11 11, and they were mounted on the inoculating device so that when in contact with the y-film, the c axis of the crystal made an angle of about 65" with the film. Now this axis is the acute bisectrix of a-sulphur, so that if the orientation of the crystal had any effect on the mechanism of the inoculation, a large proportion of inclined acute bisectrix figures was to be expected. As already stated, these were almost completely absent, and the results were very similar to those obtained with a polycrystalline bead. This raises the question as to how exactly a crystalline inoculant acts in a solid-solid transformation. 1 Hartshorne and Roberts, J. Clzern. SOC., 1951, 1097. 2 Hartshorne and Thackray, J. Chern. SOC., 1957, 212. 3 Bradley, Hartshorne and Thackray, Nature, 1954, 173,400. 4 Bradley, Proc. Roy. Soc., A, 1951, 205, 553. 5 Bacon and Fanelli, Ind. Eng. Chem., 1942,34, 1043. 6 Groth, Clzernische Kristallographie (W. Engelmann, Leipzig, 1906), vol. I. 7 Sekanina, Z. Krist., 1931, 80, 174. 8 Warren and Burwell, J, Chern. Physics, 1934, 89, 195. G*