Rosette Arms Research Articles

On gyration radius distributions of star-like macromolecules

Using the path integral approach, we obtain the characteristic functions of the gyration radius distributions for Gaussian star and Gaussian rosette macromolecules. We derive the analytical expressions for cumulants of both distributions. Applying the steepest descent method, we estimate the probability distribution functions (PDFs) of the gyration radius in the limit of a large number of star and rosette arms in two limiting regimes: for strongly expanded and strongly collapsed macromolecules. We show that in both cases, in the regime of a large gyration radius relative to its mean-square value, the PDFs can be described by the Gaussian functions. In the shrunk macromolecule regime, both distribution functions tend to zero faster than any power of the gyration radius. Based on the asymptotic behavior of the distribution functions and the behavior of statistical dispersions, we demonstrate that the PDF for the rosette is more densely localized near its maximum than that for the star polymer. We construct the interpolation formula for the gyration radius distribution of the Gaussian star macromolecule which can help to take into account the conformational entropy of the flexible star macromolecules within the Flory-type mean-field theories.

Cathodoluminescence rosettes in c-plane GaN films under Berkovich nanoindentation

In this study, the length of Berkovich nanoindentation-induced rosette arms revealed by cathodoluminescence (CL) spectroscopy was examined as a function of applied loading for the c-plane GaN thin films. Results indicated that a well-defined rosette structure with apparent six-fold symmetry extends from the center of indentation along the 〈112¯0〉 directions, suggesting that the plastic deformation is dominated by dislocation gliding on the active slip system of hexagonal GaN thin films. The length of the longest rosette arm can be satisfactorily described by the Johnson’s hemispherical hydrostatic model and gives a flow stress of ∼1.5GPa for the c-plane GaN thin films.

Indentation of Ceramics, Some Highlights

Contact mechanics is widely used to explore the mechanical properties of brittle materials while it rules the mechanical performance of industrial pieces. Elastic, plastic and brittle responses can be investigated and are highlighted. The indentation plastic zone can be decomposed into a central highly strained zone and rosette arms. The evolution of the central zone extension can be predicted by Johnson’s cavity model obtained under full load while on the other hand rosette arm extension is to be modeled considering the residual stresses from the indentation. Upon a post heat treatment, further development is obtained both experimentally and theoretically. Using large loads, elimination of cracks can be achieved using higher temperature to pass the brittle-ductile transition.

Structure of annealed nanoindentations in n- and p-doped (001)GaAs

We have studied the structure of annealed nanoindentations realized at room temperature (RT) on (001) GaAs having either n or p doping under a large range of loads Fm (between 0.5 and 50 mN). Transmission electron microscopy was used to observe systematically the nanoindentation structures. The lengths of the rosette arms were multiplied by a factor of two to three during the annealing process at 500 °C and were determined to vary with Fm, which could be modeled considering the two step thermomechanical history. While almost no anisotropy was observed before annealing (after indentation at RT), the [110] arms were observed to extend almost twice as long as the [1¯10] ones in n-doped specimens after annealing. This anisotropy was much reduced in p-doped specimens. Furthermore, almost no partial dislocations were observed whereas they were obvious in n-doped specimens before annealing.

Doping influence on the nanoindentation response of GaAs

AbstractWe have studied the nanoindentation structures realised at room temperature (RT) on (001) GaAs being either undoped, heavily n or p doped. Elastic‐plastic nanoindentations were made under a large range of loads (between 0.2 mN and 50 mN) at room temperature using a Berkovich indenter. Transmission electron microscopy (TEM) was used to observe systematically the nanoindentation structures (central zone and rosette arms) and to investigate changes in dislocations activity. The mechanical responses of all types of samples are relatively close either in terms of hardness or pop‐in load amplitude. In contrast, indentation rosette structure appears to be sensitive to doping. Perfect dislocations show long screw segments only in undoped and n‐doped specimens and this is attributed to mobility effects. Moreover, p‐doped specimens show no partial dislocations while undoped and n‐doped specimens show partial dislocations in one and both rosette arms respectively. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Nanoindentation-induced plastic deformation and fracture behavior difference between a- and c-domains of BaTiO3 single crystal

The plastic deformation and fracture behavior of individual a- and c-domains of (001) oriented BaTiO3 single crystal are studied with nanoindentation and atomic force microscopy. Consistent with previous observations in rocksalt and perovskite crystals, square-shaped pileups directly surround the residual indents, and rosette arm patterns extend beyond these pileups. These features have been ascribed to dislocation activities on the {110}⟨11¯0⟩ slip systems induced by nanoindentations. We observed rosette screw arms only in c-domains, inside which 90° ac-domain switching is confirmed. We conclude that indentation-induced cracks on {110}90 planes most likely nucleate by dislocation pileups on two neighboring {110}45 planes, which create a sessile dislocation. Significantly shorter cracks in the c-domain under the same indentation load suggest a higher apparent toughness of the c-domain. However, we attribute the different crack lengths to the lower crack driving force resulting from indentation-induced plasticity in c-domains rather than an inherent difference in the crack growth resistance.

Structure of nanoindentations in heavily n- and p-doped (0 0 1) GaAs

We have studied the nanoindentation structures achieved at room temperature (RT) on (0 0 1) GaAs with either n or p doping. Elastic–plastic nanoindentations were made over a wide range of loads (between 0.2 and 50 mN) at RT with a Berkovich indenter using two different orientations. Transmission electron microscopy was used to observe systematically the nanoindentation structures (central zone and rosette arms) and to investigate changes in dislocation activity. The mechanical response of both types of samples is relatively similar in terms of hardness, critical shear stress or pop-in load amplitude. In contrast, the indentation rosette structure appears to be sensitive to both doping and indenter orientation. Perfect dislocations show long screw segments only in n-doped specimens, a finding that is attributed to mobility effects. Moreover, p-doped specimens show no partial dislocations while n-doped specimens show partial dislocations in both rosette arms.

Rosette screw arms created by ac-domain structures and dislocations in barium titanate during nanoindentation

The nanoindentation in out-of-plane domains of a {001} oriented BaTiO3 single crystal was performed with a conical indenter of 0.9μm tip radius. The first pop-in occurs at 5±0.5mN load. The surface deformation was studied with atomic force microscopy and piezoresponse force microscopy. In addition to dislocation structures inside the remanent indentation, a rosette arm pattern is observed. The four identified screw arms are due to created a-domains as well as to at the free surface emerging dislocations of the {110}⟨11¯0⟩ glide system. For parts of the screw arms, a detailed analysis of the domain and dislocation structure is presented.

Observation of nanoindentation rosettes on {0001}ZnO using scanning Kelvin probe microscopy

Nanoindentation rosettes have been observed by scanning Kelvin probe microscopy on chemomechanical polished and etched {0001}ZnO while under illumination by a broadband light source. The rosette pattern consisted of a central region with a lower surface potential extending beyond the indentation and six arms emanating from this region along the ⟨112¯0⟩ directions. The length of the longest rosette arm was found to be proportional to the square root of the maximum force of indentation minus the average load at which pop-in occurred.

Nanoindentation response of a single micrometer-sized GaAs wall

Wall-patterned GaAs surfaces have been elaborated by photolithography and dry etching. The mechanical response of individual μm-sized walls was tested at different positions on the wall by nanoindentation. Overall results show that contact stiffness remains constant across the wall while total penetration drastically increases at the proximity of the free sides of the wall. Transmission electron microscopy was used to get further insight into the plastic deformation of the walls and reveals that the central-plastic zone governs the mechanical response instead of the rosette arms. The application of substrate patterning with enhanced plastic compliance is suggested in order to eliminate residual dislocations appearing in mismatched structures grown for optoelectronic devices.

Polarity influence on the nanoindentation response of GaAs

We have studied the polarity influence in the nanoindentation response of GaAs{111}. The nanoindentations were made under a large range of loads (Fmax between 0.2 mN and 50 mN) at room temperature on {111} faces of A (Ga) or B (As) character. Transmission electron microscopy (TEM) was used to observe the nanoindentation structures generated at the two polar surfaces. The indentation rosettes possess a 3-fold symmetry with arms developed along the 〈110〉 directions parallel to the surface. For a A-polar face, the rosette arms are constituted by two arms a long arm (LA, α dislocations) and a short arm (SA, β dislocations) while at the B surface only the LA (β dislocations) are formed. Furthermore, only for an A polar face microtwinning was observed to form and this is found to be in good agreement with previous observations of anisotropic microtwinning at GaAs(001) surfaces. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Absolute determination of the asymmetry of the in-plane deformation of GaAs (001)

Nanoindentation tests performed on GaAs (001) surfaces and on 4° misoriented GaAs (001) surfaces have led to the creation of anisotropic rosette arms lying along the 〈110〉 in-plane directions. One arm is always more elongated and constituted by perfect dislocations only while the shorter one shows in addition partial dislocations. Annealing of the deformed samples at 500 °C modifies the arrangement of the dislocations in the rosette arms but the asymmetry remains. Using a convergent beam electron diffraction method on plan views images obtained from indented (001) surfaces, we have determined the polarity of the samples. Experimental patterns were compared with simulated ones. The influences of several parameters were investigated and are discussed with particular attention addressed to the thickness of the samples. Before and after annealing, the longer rosette arm is constituted by α dislocations. The partial dislocations contained in the shorter rosette arm before annealing are of β type.

Polarity-induced changes in the nanoindentation response of GaAs

We studied the polarity-induced changes in the nanoindentation response of GaAs{111}. The nanoindentations were made under a large range of loads (Fmax between 0.2 mN and 50 mN) at room temperature on {111} faces of A (Ga) or B (As) character. The loading–unloading curves were compared first, with special attention addressed to pop-in events and hardness values (reported previously for microindentation). Transmission electron microscopy was used to observe the nanoindentation structures generated at the two polar surfaces. The size of the dense plastic zone generated around the indent site was found to increase linearly with √Fmax and similarly for both polar surfaces. The indentation rosettes possess a threefold symmetry with arms developed along the <110> directions parallel to the surface. Sizes were found to be very close for both polar surfaces and the entire load range. For an A-polar face, the rosette arms are constituted by two arms: a long arm (LA, α dislocations) and a short arm (β dislocations). At the B surface, only the LA (β dislocations) are formed. Furthermore, microtwinning was observed only for an A-polar face, similar to previous observations of anisotropic microtwinning at GaAs(001) surfaces.

Effects of annealing on structure of GaAs(001) nanoindentations

We have studied the changes generated by a post-annealing treatment of a nanoindentation structure realized on GaAs(001). The nanoindentations were made under a large range of loads (between 0.5 and 10 mN) at room temperature and were subsequently annealed at 500° C for 1 h. Transmission electron microscopy was used to observe the nanoindentation structures before and after annealing. The size of the dense plastic zone generated around the indent site decreased by about 20% after annealing and rosette arms propagated along the ⟨110⟩ directions parallel to the indented surface. Not only were the lengths of the rosette arms multiplied by a factor of three after the annealing process but also the arrangement and structure of the dislocations drastically changed. The hairpin dislocations starting from the side of the indents observed before annealing transformed into alignments of half-loop dislocations. Furthermore, no partial dislocations were observed after the annealing whereas some of the e could be detected before annealing.

Study by atomic force microscopy of elementary deformation mechanisms involved in low load indentations in MgO crystals

Abstract Nanoindentations have been performed at very low load in (001) MgO single crystals. The surface deformation has been investigated by atomic force microscopy, and the rosette arms pattern, induced by the glide of only a few dislocations, has been observed. Moreover, surrounding steps, oriented along the 〈100〉 directions, have been identified and associated with the early stage of the formation of the square shaped slip lines pattern commonly observed in the case of microindentation performed under very high loads. The fine structure of these surrounding steps has been resolved clearly, and a mechanism has been proposed based upon interaction between dislocations belonging, respectively, to edge and screw rosette arms and upon the activation of a 〈011〉(211) secondary glide system.

Rosette Microstructure in Indented (001) GaAs Single Crystals and the α/β Asymmetry

The characteristic features of the dislocation microstructure that develops around indentations performed at room temperature on (001) GaAs single crystals are analysed by High Voltage Transmission Electron Microscopy. It is shown that perfect rosette dislocations (with Burgers vector parallel to the surface) are nucleated deeply in the crystal and never merge at the sample surface. Perpendicular rosette arms have similar lengths, which raises the question of the α/β asymmetry. Twins are present in one rosette arm only; twinning dislocations are nucleated on — or very close to — the indented surface. These results are discussed in connection with previously reported results.

Vickers indentation on the {001} faces of ZnS sphalerite under UV illumination and in darkness. Crack patterns and rosette microstructure

Vickers microhardness indentations are performed on the (001) surface of ZnS sphalerite single crystals in darkness and under UV illumination, close to the band absorption edge. For low applied loads, the crack length and the rosette size confirm the hardening effect of illumination (positive photoplastic effect) that causes a lowering of the dislocation mobility. For high applied loads the positive photoplastic effect is masked by a strong workhardening in the highly strained zone. In darkness as well as under irradiation, perpendicular rosette arms have the same length, showing that α and β perfect dislocations have similar mobilities at variance with III-V compounds. However, the observed asymmetry in the dissociation behaviour suggests that partial dislocations have different mobilities.

Indentation-induced dislocations and microtwins in GaSb and GaAs

Abstract The {100} and (110) faces of n-type GaSb and the {110) face of n-type GaAs have been indented at room temperature and 200°C, and the plastic zone around the microindents has been investigated by transmission electron microscopy. In both materials, indentation rosettes with approximate twofold symmetry form around the indents. In general, the rosettes consist of dislocations and microtwins. The rosette arms in n-type (001) GaSb are only slightly asymmetric along the two (110) directions, with the longer arms corresponding to α-type dislocations. This implies that the mobility of α-dislocations in GaSb is higher than the mobility of β dislocations. In both GaSb and GaAs, the 90° perfect and partial dislocations have the highest mobility. Based on the experimental results, it is proposed that, in both GaSb and GaAs, perfect dislocations nucleate on the indentation facets as half-loops with Burgers vectors parallel to the propagation directions of the rosette arms. On the other hand, twinning dislocations nucleate on the indentation surface as partial dislocation half-loops. A mechanism for indentation twinning is proposed whereby the step created by surface nucleation of a dislocation half-loop acts as a preferential site for nucleation of the next half-loop on an adjacent (1 l 1) plane.

Transmission electron microscope investigation of indentation induced dislocation configurations on the (001) GaSb face

Abstract Dislocation configurations induced by room temperature microindentations on the (001) face of GaSb (undoped and Te-doped) have been studied using high voltage transmission electron microscopy. Perfect and partial dislocations could be found in all four arms of the dislocation rosette around the indent. Microtwins and rarely single stacking faults are associated with the partials. Contrary to other binary III–V compounds, an “inverse” glide prism along the [1[unk]0]/[[unk]10] rosette arms is created and it is bounded by {111}B planes which diverge away from the surface. Under high stress – low temperature conditions plastic deformation in undoped as well as n-doped GaSb proceeds by the movement of mobile α-dislocations, whereas β-dislocations are almost immobile. The reasons for the observed slip asymmetry of the dislocation rosette are discussed and a model for the formation of microtwins is proposed.

Microtwinning in GaAlAs and GaInAs due to indentation at room temperature

Abstract Microindentation at room temperature has been studied, by transmission electron microscopy, for GaAlAs and GaInAs with a range of compositions. Both p-type and n-type alloys have been investigated with particular reference to the formation of microtwins. A change of doping from n-type to p-type in GaAlAs results in microtwin formation along perpendicular 〈110〉 rosette arms. This is also observed in n-type GaInAs alloys.