X-ray diffraction from double hexagonal close-packed crystals with stacking faults

Prasad, Bhim Bali; Lele, S.

doi:10.1107/s0567739471000111

Cited by 35 publications

(34 citation statements)

References 1 publication

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“…By analogy with Prasad & Lele (1971), we derive expressions for the boundary conditions from the equation (29) where wj represents the probability of occurrence of layers with a particular value of j at an arbitrary position in the crystal and J(m)j are the average phase factors for layers on position m in sequences originating from a layer with a particular subscript j.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…Moreover, the fault ABAB : C : ABAB in the 2H structure was called the extrinsic fault by . The names intrinsic and extrinsic faults were also used (Prasad & Lele, 1971;Lele, 1974;Pandey & Krishna, 1976) for polytypic crystals together with deformation and growth faults. According to our distinction, the name intrinsic relates in these cases to single nontwinning faults, the name extrinsic relates to double non-twinning faults and the name extrinsic in the 2H structure relates to double non-twinning-twinning faults.…”

Section: Stacking Faults In Arbitrary N-periodical Structurementioning

confidence: 99%

“…The first complete expression for the X-ray intensity distribution in reciprocal space for the simplest polytypic structure 4H with stacking faults was derived by Prasad & Lele (1971). All seven types of intrinsic faults in the 4H structure were taken into account in this theory.…”

Section: Introductionmentioning

confidence: 99%

“…This method, based on Wilson's (1942) equation, expressed the diffracted intensity directly in terms of the coefficients of the characteristic equation and the boundary conditions. Applying this method to Prasad & Lele's (1971) theory, Pandey & Krishna (1976) described the X-ray diffraction by 6H(33) structure containing all 14 possible types of intrinsic faults. Some modifications of this method and adoption to 8H(44) and nH(~) structures were presented by Michalski, Demianiuk, Kaczmarek & Zhmija (1981a, b) and some faults in 4H, 6H(33) and 8H(44) crystals were investigated (Michalski, Demianiuk, Kaczmarek & Zhmija, 1980, 1982.…”

Section: Introductionmentioning

confidence: 99%

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The diffraction of X-rays by close-packed polytypic crystals containing single stacking faults. I. General theory

Michalski¹

1988

Acta Cryst Sect A

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A general theory of X-ray diffraction by onedimensionally disordered close-packed polytypic crystals has been developed. A random distribution of all possible single stacking faults for arbitrary n-periodical structure is taken into consideration. Exact expressions for measurable parameters of changes in the intensity distribution caused by faults are given. Initial equations of the theory have been formulated by applying Holloway's [J. Appl. Phys. For the mathematical description of disorder, successive layers of the perfect structure have been denoted by an additional subscript j. The probability of occurrence of the faulted layer with subscript k after the layer with subscript j has been denoted by ajk. A set of recurrence relations is developed for average phase factors of layers with subscript j on m positions. An arbitrary sequence of layers is written in these relations by using the so-called phase-change factors (after layer with subscript j), determined by H~igg's structure symbols. Terms of the coefficients of the characteristic equation and boundary conditions which are necessary to describe the change in the intensity distribution are given for small values of ark. Finally, the shifts and broadenings of the reciprocal-lattice points and the changes in the intensity of peak maxima are derived in terms of ark.

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Section: Boundary Conditionsmentioning

confidence: 99%

Section: Stacking Faults In Arbitrary N-periodical Structurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The diffraction of X-rays by close-packed polytypic crystals containing single stacking faults. I. General theory

Michalski¹

1988

Acta Cryst Sect A

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“…In the case of hexagonal polytypes with 4H structure Prasad & Lele (1971) distinguished the following types of possible faults: intrinsic c, h, 2c, 2h, 3c, 3h, ch and extrinsic 4c and cch. The probabilities of occurrence of these faults have been denoted by the above symbols written as subscripts to a.…”

Section: Introductionmentioning

confidence: 99%

The diffraction of X-rays by close-packed polytypic crystals containing single stacking faults. II. Theory for hexagonal and rhombohedral structures

Michalski¹,

Kaczmarek²,

Demianiuk³

1988

Acta Cryst Sect A

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The general theory developed by Michalski [Acta Cryst. (1988), A44, 640-649] has been applied to the cases of hexagonal and rhombohedral structures. The symbols of stacking faults based on Zhdanov's symbols of local structure near the faults have been introduced and assigned to the formal subscripts j, k used in general theory. On this basis the regularities, according to which the faults with different subscripts j, k have the same structures, have been characterized. Then these regularities have been taken into consideration in the derivation of expressions for measurable parameters of changes (caused by faults) in the X-ray intensity distribution. The results obtained for structures 2H, 4H, 6H(33), 8H(44), 10H(55), 12H(66), 3C, 9R(12)3, 12R(13)3 and 15R(23)3 are given. Some results are compared with published data. The physical meaning of the assumption of small values of fault probabilities is discussed.

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Electron microscopic study of zinc oxide crystals microstructure crystallizing in a double hexagonal close‐packed lattice

Nowok¹

1976

Cryst Res and Technol

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X-ray diffraction from double hexagonal close-packed crystals with stacking faults

Cited by 35 publications

References 1 publication

The diffraction of X-rays by close-packed polytypic crystals containing single stacking faults. I. General theory

The diffraction of X-rays by close-packed polytypic crystals containing single stacking faults. I. General theory

The diffraction of X-rays by close-packed polytypic crystals containing single stacking faults. II. Theory for hexagonal and rhombohedral structures

Electron microscopic study of zinc oxide crystals microstructure crystallizing in a double hexagonal close‐packed lattice

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