Phason Strain Research Articles

Grain growth and phason-strain field in quasicrystalline Al-Li-Cu

We report on grain growth and related structure change in single phased Al-Li-Cu quasicrystals. The icosahedral phase grains have been investigated using scanning ion microscopy and transmission electron microscopy. Regular boundaries between large grains have been observed both before and after high temperature annealing. The electron diffraction study shows that the grain growth is accompanied by a reduction of the phason-strains. The orientation relation between grains sets the 2-fold icosahedral axes parallel, and the coincidence of the planes depends on the phason strain-field. The effect of phason-strain field on these boundaries is discussed. It is proposed that the phason strain elimination can play a role in the grain growth.

Enhancement of the Icosahedral Quasicrystalline Phase Forming Ability with Be Addition to an Al62.5Cu25.5Fe12 Alloy

AbstractThe quasicrystalline phase forming ability, solidification structure, thermal stability, and phase relationships of a series of conventionally-cast Al62-xCu25.5Fe12.5Bex (x=0,1,3,5,7) alloys were investigated. Single icosahedral quasicrystalline phase was successfully obtained by partial replacement of Al with Be (7 at.%) in an Al62Cu25.5Fe12.5 alloy during crucible cooling. The I-phase in an Al55Cu25.5Fe12.5Be7 alloy has the same face-centered icosahedral structure as that in an Al62Cu25.5Fe12.5 alloy, with less phason strain. Hardness of the I-phase increases with x, i.e. from Hv 710 for x=1 to Hv 809 for x=7.

Observation of a decagonal quasicrystalline phase and quasicrystalline approximants in in situ heated thin films of the Al–Co–Cr–Fe–O system

Quasicrystalline and crystalline phase transitions observed during in situ heating in the transmission electron microscope of amorphous thin films of the Al–Co–Cr–Fe–O system have been studied. In particular, heating the film at 750°C during 2 h, grains with decagonal quasicrystalline structure were developed. This quasicrystalline phase presents a periodicity of 1.4 nm along the c-axis and its tenfold electron diffraction pattern indicates the existence of phason strains in its structure. X-ray energy dispersive spectroscopy microanalysis showed a high relative concentration of Al compared with the concentration of Cr, O and Fe in the quasicrystalline grains, and electron energy-loss spectroscopy confirmed the presence of oxygen in these grains. All this resulted in a nominal composition of Al58Cr28O17Fe5 for this phase (i.e. this is an oxygen-containing decagonal quasicrystalline phase). Cobalt was only detected in grains whose structure corresponds to crystalline phases such as Al13Co4, the well known approximant phase of the decagonal quasicrystal.

Electron diffraction analysis of plastically deformed icosahedral Al-Pd-Mn single quasicrystals

A technique is presented to determine quantitatively the phason strain fields in quasicrystals by electron diffraction analysis in a transmission electron microscope. The deviation vectors of diffraction spots from their ideal positions are measured and related to their physical and orthogonal reciprocal coordinates. Investigations have been performed on as-grown as well as plastically deformed Al-Pd-Mn single quasicrystals. It was found that the magnitudes of the shifts of the spots depend linearly on the length of the perpendicular-space component of the reciprocal coordinates, while such a correlation was not found for the respective physical-space component. This behaviour evolves more clearly with increasing plastic strain. The measured spot shifts were fitted according to a linear vector equation relating the shifts to the perpendicular reciprocal vectors. This provides the possibility of determining the entries of the first two rows of the socalled 'phason matrix'. It was found that the values of the matrix entries vary with position in a given sample and that they increase with increasing amount of plastic deformation.

Some new structural and electronic characteristics of quasicrystals

The quasicrystals being based on quasiperiodic order other than crystal like periodic translational order and embodying self similarity, present unique condensed matter phases. In addition to their curious structural characteristics the paucity of translational periodicity leads to drastic deviations in their electronic behaviour as compared to crystalline counterparts. This paper describes and discusses some new developments in regard to structural and electronic aspects of quasicrystalline materials. In regard to the structural aspects, two comparatively newer features will be described. One of them relates to the observation of variable strain approximants (VSA) first found in Ti68Fe26NiSi5, qc alloys; the other relates to the structure of decagonal phases. The variable strain approximants correspond to qc phases exhibiting variable strain for the different diffraction spots for the same reciprocal lattice row (possessing linear shifts). The VSA is thought to result from variable phason strain mode locking; this in contrast to RAS which results due to linear phason mode locking. The results obtained in our laboratory on VSA will be described and discussed. Another interesting structural feature emanating in the last few years relate to the development of structural models for the decagonal phases which have nearly answered the question ‘Where are the atoms?’ for this qc variant. High resolution electron microscopy has revealed the existence of two types of atom cluster columns with a diameter of 20Å; a pentagonal cluster column and a decagonal one. The decagonal quasicrystals can be classified into three types of structures according to the space groups and symmetries and arrangements of the cluster columns. These three deca structures have been typified by: deca Al-Co-Cu, deca Al-Mn and deca Al-Fe-Pd types. Some basic features on the structures of decagonal phases as obtained recently will be outlined.Since materials owe their practical importance due to their physical behaviours, assessment of qc materials from this point of view is of imperative importance. However, the real physics/science governing properties for qc is not well understood as yet. For example, the fundamental property relating to electronic conductivity and its temperature variation has been attempted to become explicable based on (a) taking qc as disordered materials, (b) assuming qc as hierarchy of clusters and (c) bringing in new concepts governing the wave functions of electrons (critical wave functions) and some other models. However, the same results are not universally reported/reproduced by various workers. Thus the variation of electronic conductivities with temperature of Al65Cu20Ru15, Al70Pd20Re10 and other stable quasicrystals have found varied interpretations e.g. based on QIEs and power law temperature variation. Some results onσ-T and related characteristics for stable qc crystals obtained by us and also by other workers will be analysed in terms of feasible transport mechanisms.

Determination of the tiling type and phason strain analysis of decagonal quasicrystals in Al—Ni—Co alloys

Abstract From high-resolution electron micrographs of the decagonal phases of the Al72.5Co11Ni16.5 and Al70Co15Ni15 alloys, tilings are produced by connecting prominent structural features. Indexing the tiling vertices as the projection of a five-dimensional periodic lattice and investigation of the distribution of the vertices in orthogonal space gives information about the tiling model and possible phason strains. The technique also reveals domain boundaries which separate regions differing only in the amounts of linear phason strain.

Determination of the tiling type and phason strain analysis of decagonal quasicrystals in Al-Ni-Co alloys

Determination of the tiling type and phason strain analysis of decagonal quasicrystals in Al-Ni-Co alloys

Dislocation migration and phason strain relaxation in a quasicrystal

Abstract Phason flips accompanying the glide of a perfect dislocation has been examined using the Burkov model of the decagonal quasicrystal which is a pseudobinary alloy of Al and transition metals. It is shown that the glide of a perfect dislocation is difficult without producing chemical disorder. There are three extreme cases in the glide of a dislocation in quasicrystal: firstly conservative glide at a very high temperature where the complete phason relaxation occurs; secondly, glide producing chemical disorder; thirdly glide producing a stacking fault with the fault vector of the phason component of the Burgers vector.

Dislocation migration and phason strain relaxation in a quasicrystal

Dislocation migration and phason strain relaxation in a quasicrystal

X-ray Diffraction Study of the Decagonal Al<SUB>70</SUB>Ni<SUB>10</SUB>Co<SUB>20</SUB>

A decagonal Al 70 Ni 10 Co 20 single quasicrystal was studied with high-resolution X-ray diffraction. Full-widths at half-maximum (FWHM) of Bragg reflections along the longitudinal direction (L) monotonically increase with increasing of Q⊥. This result suggests that the Al 70 Ni 10 Co 20 decagonal phase has random phason strain. On the other hand, FWHM for both transverse directions T1 and T2, which are perpendicular to the L-direction in an aperiodic plane (T1) and along a periodic direction (T2), have linear Q // dependence. So the single crystal has some distortion of mosaics. Notable peak shifts from ideal Bragg peak positions were not observed.

Investigation of phason strains in decagonal Al-Pd-Mn single quasicrystals by means of x-ray diffraction

A careful examination of the peak profiles, peak shifts and peak separations of Bragg reflections, which are inherent in the disordering of quasicrystal, is carried out using an x-ray diffraction method for decagonal Al-Pd-Mn single quasicrystals. The full widths at half-maximum (FWHM) of the Bragg reflections along the longitudinal direction (L) have no or -dependence whereas those for both transverse directions, which are perpendicular to the L direction in an aperiodic plane and with a periodic axis, have linear -dependence. Notable peak shifts and separations of Bragg reflections are observed. The absolute values of the shifts are found to be proportional to . The peak shifts and separations are analysed in terms of linear phason strains.

Modifications 7 And 8 Of Decagonal AI-Co-Ni

AbstractBesides the six established decagonal states of the Al-Co-Ni quasicrystal two more modifications have been discovered by means of transmission electron microscopy. One is a pentagonal quasicrystal with a superstructure found in specimens with a very high Co-content and quenched from the highest possible temperature lying within the stability field of decagonal Al-Co-Ni. Its electron diffraction patterns are characterized by a 5-fold rotation axis as a unique symmetry element as well as superstructure reflections similar to those of a related decagonal phase. The other is a one-dimensional quasicrystal closely related to decagonal Al-Co-Ni. The modulation length of 61 Å along the periodic direction in its pseudo 10-fold diffraction patterns can be assumed to be caused by a strong linear, uniform, phason strain in the material.

Bulk Mechanical Properties Of Quasicrystals

AbstractElastic moduli, anharmonicity, hardness and high temperature plastic behavior of icosahedral and decagonal quasicrystals are reviewed. Elastic properties are discussed in relation to the bonding nature of the quasicrystals. The plastic deformation behavior at high temperatures is discussed based on the characteristics of the dislocation mechanism in the quasiperiodic lattice. A Peierls potential, a phason relaxation and a dragging stress due to production of a defect field are considered as the controlling factors for the thermally activated dislocation glide; a dislocation in quasiperiodic lattice is accompanied not only by the elastic (phonon) strain field but also by the phason strain field which is difficult to be relaxed completely with the dislocation glide.

Phason Strain In AL70NI10CO20 Decagonal Quasicrystal

AbstractThe peak broadening and peak positions of Bragg reflections in a single-phase decagonal Al70Ni10Co20 quasicrystal has been studied by the synchrotron X-ray diffraction technique at SPring-8. Full-widths at half-maximum (FWHM) of the Bragg reflections along the longitudinal direction (L) and transverse direction (TI) which is perpendicular to L-direction in an aperiodic plane have linear Q⊥, dependence. This means that the Al70Ni10Co20 decagonal phase has random phason strains. On the other hand, another transverse direction (T2), which is perpendicular to the aperiodic plane, have linear Q, dependence. So the single crystal has some distortion of mosaics to the periodic layer stacking. Notable peak shifts from ideal Bragg peak positions were not observed.

On the energy ratio between the phonon and the phason part of dislocations in icosahedral Al-Pd-Mn quasicrystals

Abstract Using two different ansatze for the energy of quasicrystal dislocations the phonon strain energy is related to the phason strain energy by means of the strain energy ratio. The possible ranges for this ratio are determined while a new type of dislocation dissociation is proposed. This reaction describes the dissociation of a perfect dislocation into two other also perfect dislocations. Based on recent experimental observations the energy ratio due to phason and phonon strain of dislocations with Burgers vectors along twofold directions is calculated. Also recent experimental observations of partial dislocations are considered. Implications for the mechanisms stabilizing the quasicrystalline structures are discussed.

Unusual structural modification in theTi68Fe26Ni1Si5squasicrystalline phase

We report here the formation of a class of materials in the rapidly solidified ${\mathrm{Ti}}_{68}$ ${\mathrm{Fe}}_{26}$ ${\mathrm{Ni}}_{1}$ ${\mathrm{Si}}_{5}$ system based on transmission electron microscopic exploration of the electropolished melt-spun ribbons. The phase reported here pertains to a modification of the icosahedral phase leading to tetrahedral symmetry with no discernible periodicities, unlike those of earlier known rational approximant phases. The analysis of the selected area diffraction patterns of these phases revealed variable linear phason strains in the shifted spots of undistorted twofold reciprocal rows. The experimentally observed reciprocal vectors in these directions have been suggested to arise owing to their dependence on both the physical and pseudospace components vis-`a-vis that of the icosahedral phase. It has been argued that such a dependence may arise owing to the presence of the nonlinear motif having components in both the spaces in the higher-dimensional structural description.

Calculation and illustration of section-projection diagrams of quasicrystals

On the basis of cut and projection description of quasicrystals, a method for calculating section-projection diagrams of quasicrystals is developed and applied to decagonal quasicrystals. Firstly, a section-projection diagram parallel to the quasiperiodic plane of perfect decagonal quasicrystal is calculated. By using the existing elastic displacement field formulae, section-projection diagrams parallel to the quasiperiodic plane of a decagonal quasicrystal containing a straight dislocation along periodic direction have been calculated when only phason strain and both phason and phonon strains are introduced respectively.

Phason strains on growth, stability and structure of icosahedral phases

Growth, stability and structure of icosahedral (i-) phases have been studied by electron diffraction and X-ray diffraction in relation with the phason strains. Three alloy systems; AlPdCr, AlPdMn and AlCuV were chosen in this study. An i- Al 72Pd 25Cr 3 grain has been analysed to have a phason matrix toward to a tetragonal or orthorhombic structure. Stability of the i-phases correlated with the phason relaxation was discussed in Al-Pd-Mn system. A quenched i-Al 74Pd 17Mn 9 close to but containing significant phason strains, revealed that the phason relaxation induced by precipitation of crystalline phases upon annealing. Phason disorder dominated by the chemical composition was evidenced in a composition study in Al-Pd-Mn system. A high density random phasons characterized the icosahedral glass phase was observed in AlCuV alloys.

Phason-strain analysis of the twinned approximant to the decagonal quasicrystalAl70Co15Ni15: Evidence for a one-dimensional quasicrystal

In high-resolution x-ray diffraction sometimes a pronounced splitting of the strongest Bragg reflections in decagonal ${\mathrm{Al}}_{70}$ ${\mathrm{Co}}_{15}$ ${\mathrm{Ni}}_{15}$ is observed. So far, this has been interpreted as evidence for a twinned (micro-)crystalline state with large lattice parameters. In the present paper we show that the metrics can be perfectly reproduced by modeling a twinned one-dimensional quasicrystal rather than a twinned three-dimensional crystalline phase. The split peak positions can easily be reproduced by application of a linear phason strain on the ideal decagonal quasicrystal and subsequent fivefold twinning. New high-resolution x-ray-diffraction data are used in this analysis. An anisotropic broadening of all investigated reflections leads us to suggest a nonlinear phason-strain component.

Effect of boron additions on Al-Cu-Fe icosahedral quasicrystals

Abstract The structure, stability and phase relationships of a series of Al63-x Cu25Fe12B x alloys, with x ranging from 0 to 2, were investigated in this study. Increasing x resulted in a change in the solidification behaviour and microstructural scale. While the face-centred icosahedral (fci) phase was observed to be the primary solidification product in each of the samples, proportionately more AlFe (β) was observed as x increased and, for x = 1 and 2, Al2Cu appeared. Also, the relative amount of phason strain present in the fci phase increased as x increased.