P. Krishna

Influence of stacking faults on the growth of polytype structures: I. Cadmium iodide polytypes

The origin of polytype structures has been attributed to spiral growth round suitable screw dislocations created in a basic structure. In deducing the different polytype structures that can result from such a mechanism, the basic structure has always been assumed to be perfect. It is shown that it is necessary to consider the possibility that the parent matrix may contain stacking faults near its surface at the time of the origin of the screw dislocation ledge. This can drastically affect the structure of the resulting polytype. The most probable fault configurations that can occur in a parent 4H or 2H structure of CdI 2 have been deduced from a calculation of the stacking fault energies. Polytype structures originating from single screw dislocations created in a faulted 2H or 4H matrix containing one of the more probable fault configurations near the surface have been deduced. It is shown that all the observedpolytype structures of CdI 2 can result from such a mechanism and represent structures with minimum, or close to minimum, stacking fault energy. There is an excellent agreement between the structures deduced on the basis of the faulted matrix model and those actually observed. It has been possible to explain the origin of the observed structure series in CdI 2 and the limitation of the Zhdanov numbers to 1, 2 and 3. It is possible to predict theoretically the more probable structures for a polytype, which greatly simplifies its structure determination.

X-ray diffraction from one-dimensionally disordered 2H crystals undergoing solid state transformation to the 6H structure. I. The layer displacement mechanism

The 2H or AB. . . close-packed structure may be transformed to 6H or ABCACB. . . structure if layer displacement faults occur preferentially on every third close-packed layer. The theory of X-ray diffraction from one-dimensionally disordered crystals undergoing the 2H → 6H structural transformation by such a layer displacement mechanism is developed. It is shown that it is necessary to consider that the faults do not occur entirely at random but prefer to occur at three-layer separations from each other in order to statistically create a 6H structure. The diffraction theory, as developed by earlier workers for 2H crystals containing a completely random distribution of stacking faults, cannot therefore be applied to the present case. An exact expression for the diffracted intensity from crystals undergoing the 2H → 6H transformation has been obtained and the different observable diffraction effects (like change in integrated intensity, peak shift, integral breadth, peak asymmetry) have been predicted.

Influence of stacking faults on the growth of polytype structures

Abstract The faulted matrix model of polytypism suggested in the preceding paper has been applied to the deduction of SiC polytypes. It is shown that all the SiC polytypes so far regarded as ‘anomalous’ can result from an appropriate screw dislocation ledge exposed in a 6H, 15R or 4H matrix. The probable fault configurations in each of these parent structures have been determined from a calculation of stacking fault energy. The most frequently occurring structure series in SiC are those which have the lowest stacking fault energy. Thus, there is an excellent agreement between the polytype structures expected on the basis of the faulted matrix model and those actually observed. The limitation of the Zhdanov numbers to 2, 3 and 4 in a polytype structure is explained. It is possible to predict the more probable structures for a polytype on the basis of the above model.

Influence of stacking faults on the spiral growth of polytype structures in mica

A systematic theoretical deduction of polytype structures of mica that can result by the spiral growth mechanism operating in faulted 1M, 2M1 and 3T basic matrices is reported. As a prerequisite, all possible intrinsic and extrinsic stacking fault configurations in each of the basic matrices have been worked out and their stacking fault energy (SFE) estimated. The deduction of polytype structures on the basis of the “faulted-matrix model” takes into account (i) the introduction of each of the low energy fault configurations in the exposed ledge of the screw dislocations, (ii) the change in the layer-position of the fault within the exposed ledge and (iii) the variation of the strength of the generating screw dislocation. At each stage, the spirally-grown polytypes are deduced for each basic structure. The most probable structures are predicted on the basis of the lowest SFE for the same strength of the screw dislocation and are then compared with the polytype structures reported in the literature. It was found that the faulted matrix model accounts successfully for the origin of all the polytype structures in mica. Furthermore, it may provide a basis for limiting the number of trial structures for determining the structures of long period polytypes.

Application of the faulted matrix model to the growth of polytype structures in mica

Following Baronnets theoretical deduction of the possible polytype structures in mica that can result from spiral growth round single screw dislocations of different Burgers vectors created in a perfect matrix, this paper reports a systematic deduction of mica polytypes on the basis of the faulted matrix model, proposed earlier by Pandey and Krishna to explain the growth of polytype structures observed in SiC, CdI2 and PbI2. All possible intrinsic and extrinsic fault configurations are worked out that can occur in the basic structures of mica, namely 1M [0], 2M1 [22] and 3T [222]. The most probable fault configurations for each basic structure are predicted by estimating the relative stacking fault energies (SFE) of all possible fault configurations. Polytype structures that can result by spiral growth round screw dislocations of different Burgers vectors originating in faulted basic structures of mica are deduced by considering the most probable fault configuration to lie at different distances from the surface at the time of the origin of the screw dislocation step. Of the various structures resulting from screw dislocations of the same Burgers vector, the structure having the lowest SFE would be more probable. The most probable series of structures so predicted are found to be in excellent agreement with those observed.

A model for the growth of anomalous polytype structures in vapour grown SiC

A number of polytype structures observed in vapour grown SiC crystals have a unit-cell which is an integral multiple of the unit-cell of the basic 6H, 15R or 4H structure. The growth of such anomalous structures cannot be understood in terms of spiral growth round a single screw dislocation in a basic matrix. However many of these polytype crystals display a single growth spiral on their (0001) face indicating that they have resulted from spiral growth round a single screw dislocation. It is shown that this anomaly can be resolved if the basic matrix is assumed to contain stacking faults near the surface at the time of the origin of the screw dislocation ledge. This possibility, overlooked in the earlier deduction of polytype structures, must be taken into consideration since vapour grown SiC crystals frequently contain a high concentration of random stacking faults, producing continuous streaks on their X-ray diffraction photographs. The most probable fault configurations that can occur in 6H, 15R and 4H structures of SiC have been deduced from a calculation of their stacking fault energy. These fault configurations are then considered to lie at different distances from the surface at the time of the origin of a screw dislocation ledge. Such a faulted ledge gives rise to polytype structures during subsequent spiral growth even if the screw dislocation has an integral Burgers vector. The most probable series of polytype structures that can result from such a faulted matrix model are deduced. It is shown that nearly all the polytype structures of SiC hitherto regarded as anomalous (such as 36H, 54H, 66H, 45R, 90R etc.) are among the expected structures and there is no need to postulate a complicated configuration of cooperating dislocations to account for their growth.

X-Ray Diffraction from One-Dimensionally Disordered 2H Crystals Undergoing Solid State Transformation to the 6H Structure. III. Comparison with Experimental Observations on Sic

The diffraction effects predicted theoretically in the preceding two papers for 2H crystals undergoing solid state transformation to the 6H structure by the layer displacement mechanism and the deformation mechanism are compared with those experimentally observed on SiC. It is shown that the observed diffraction characteristics can be explained in terms of the layer displacement mechanism and not the deformation mechanism. A simple estimate of the layer displacement fault probability in two transformed 6H SiC crystals has been made by analysing the halfwidth of the experimentally obtained intensity profiles of the 10.L reflexions. It is also shown that the presence of a small concentration of growth faults in the as-grown 2H SiC crystal does not alter the basic diffraction characteristics predicted in part I of this series of papers.

X-Ray Diffraction from One-Dimensionally Disordered 2H Crystals Undergoing Solid State Transformation to the 6H Structure. II. The Deformation Mechanism

The 2H or AB Structure may be transformed to 6H or ABCACB structure if deformation faults occur preferentially after every third close-packed layer. The theory of X-ray diffraction from one-dimensionally disordered crystals undergoing the 2H → 6H structural transformation by such a deformation mechanism is developed. For this, it is necessary to consider that the faults are not distributed entirely at random but tend to occur in such a manner as to statistically create a 6H structure. An exact expression for the diffracted intensity for crystals undergoing the 2H → 6H transformation by the deformation mechanism has been obtained and the different observable diffraction effects have been predicted. These results are very different from those obtained of 2H crystals containing an entirely random distribution of deformation faults, especially for large fault probabilities.

Direct observation of recrystallization and structural transformations in ZnS films under an electron microscope

Abstract Thin polycrystalline films of ZnS, deposited on a crystalline substrate by thermal evaporation under vacuum, were heated by the electron beam of an electron microscope, causing them to recrystallize. The recrystallization process and the structural transformations that occurred were thus observed directly. Detailed investigations reveal that the structural transformation occurs by a process of repeated microtwinning. Measurement of the average width of the resulting microtwins indicates an average of one stacking fault in every 8 to 10 layers. Polytypes of ZnS appear to be intermediate states in the phase-transformation from the cubic to the hexagonal phase and result from periodic microtwinning.

An X-ray diffraction study of faulting in single crystals of cubic ZnS grown from the vapour phase

Abstract An X-ray diffraction study is made in order to determine the nature of stacking faults present in vapour-grown cubic ZnS crystals, as well as in cubic crystals obtained by solid-state transformation from the 2H phase by thermal annealing. For this the point intensity distribution along the 10.L reciprocal lattice row of both kinds of disordered 3C crystals was recorded on a single-crystal diffractometer. The observed intensity profiles are found to be asymmetrically broadened and do not show any peak shifts, indicating that stacking faults present in both as-grown and annealed crystals are predominantly twin faults distributed randomly. The experimentally obtained intensity profiles are compared with those calculated theoretically for a random distribution of twin faults. The experimental results indicate (i) that the disordered 3C structures result by solid-state transformation of the 2H phase during the cooling of the growth furnace (ii) that they contain a random distribution of twin or growth...