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Quantification of the modulated structures in TiPdCr alloys
Author(s) -
SCHWARTZ A. J.,
PACIORNIK S.,
KILAAS R.,
TANNER L. E.
Publication year - 1995
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/j.1365-2818.1995.tb03656.x
Subject(s) - high resolution transmission electron microscopy , transmission electron microscopy , electron diffraction , diffraction , transverse plane , lattice (music) , materials science , crystal structure , lattice constant , lattice plane , crystallography , condensed matter physics , molecular physics , chemistry , physics , optics , reciprocal lattice , nanotechnology , structural engineering , engineering , acoustics
SUMMARY Ti 50 Pd (50‐x) Cr x β 2 alloys (B2, CsCl‐type crystal structure) have been investigated as part of an overall study of the systematics of phase transformation behaviour and also for the commercial applicability of the shape memory effect at elevated temperatures. The phase transformations are unique in the sense that electron diffraction and high‐resolution transmission electron microscopy of Ti 50 Pd (50‐x) Cr x alloys with x between 6 and 10 at.% reveal {110} B2 modulated structures with periodicities between 3 and 4·5 planes that vary linearly with composition. Satellites along certain <110>* lying at incommensurate positions are observed in electron diffraction patterns and are consistent with transverse lattice displacements. High‐resolution transmission electron microscopy (HRTEM) imaging usually reveals sinusoidal displacements; however, a few images appear ‘banded’ at three‐ and four‐plane intervals suggesting the possibility that three‐ and four‐plane commensurate packets combine to give the overall incommensurate satellite spacing. With the use of a newly developed technique for quantifying atomic displacements from HRTEM images, modulated phases in Ti 50 Pd 43 Cr 7 and Ti 50 Pd 42 Cr 8 alloys, where atoms are shifted from the cubic lattice sites by a transverse lattice displacement wave, have been studied. The real space displacements of the modulated structures were determined and compared to truly incommensurate and varying three‐ and four‐plane wave packet combinations by examination of the goodness of fit as assessed by the correlation coefficient for a least‐squares fit. In the cases of the Ti 50 Pd 43 Cr 7 and Ti 50 Pd 42 Cr 8 alloys, the incommensurate sine wave exhibited much better matching than the commensurate packets, indicating that these modulations are probably incommensurate.