Mirosław ; Wróbel
email: mwrobel@agh.edu.pl

K Pieła

Basal slip localization in zinc single crystals. The ConsidΠ Π Π Πre analyses

Keywords: crystals, deformation, mechanical testing, strain, stresses, tensile, compression user supplied): strain localization, necking, zinc zinc, single crystals, strain localization, necking, tension, compression zinc, single crystals, strain localization, necking, tension, compression

The tensile and compression tests of zinc single crystals oriented for slip in the basal slip system were performed. During the first stage of the stress-strain curve, the localized necking was typical to the strain localization in the tensile specimens. Single or multiple necks were formed along the specimen length. The range of temperature and the strain rate for the single necking of the sample was determined. It was found that the formation of such necking depends on strain hardening characteristics and can be predicted by the ConsidΠre criterion. On the other hand, propagation of the necked area along the sample length was not predictable by this criterion.

Localized sliding and specimen kinking was indicative of the strain localization observed for different specimens compressed under the same conditions, i.e., temperature and strain rate. A decrease in the compression force and in the cross-sectional area with anvils displacements produced localized sliding. On the other hand, a continuous increase in the compression force was representative of tests leading to specimen kinking.

Introduction

Early tensile tests conducted on the zinc single crystals oriented for slip in one basal slip system (soft oriented crystals) show that their mechanical characteristics as well as macrostructures essentially depend on the test temperature. The typical three-stage curve of the shear stress τ vs. shear stain γ (labeled as A, B and C, respectively, Fig. 1) was registered only for a narrow range of test temperatures (i.e., 0.40-0.55 T m where T m -the melting point), and it is replaced by a two-stage (A and B) curve at the test temperature close to 0.7 T m . This change is accompanied by a rapid decrease in the work-hardening rate at stages A and B (to values close to zero) and the increase in the range of easy glide (A) [1][2][3][4][5][6][7]. The higher test temperature (above 0.7 Tm) leads to a decrease in plasticity and an increase in the value of the 'mean' work-hardening coefficient of zinc crystals [START_REF]Kristallplastizität[END_REF][START_REF] Kajbyshev | [END_REF]. Pieła [10][11][START_REF] Pieła | Rozprawy i monografie[END_REF] showed that the temperature anomalies are closely connected with the processes of macroscopic localization of slip in the basal system, especially with the transition from single necking to crystal 'fragmentation' caused by multinecking with kink bands formation. Moreover, it was shown that the tendency toward the basal slip localization was not confined to the tensile specimens. Specimen kinking in a single broad region or in several narrow areas was typical to strain localization in the compressed zinc crystals [11,[START_REF] Pieła | Rozprawy i monografie[END_REF]. The present work investigates in detail these strain inhomogeneities during the initial stage (A) of the τ(γ) curve of zinc crystals for which deformation proceeds only in the basal slip system. The influence of deformation rate and temperature as well as the ratio of the gauge length to the sample diameter (aspect ratio) on the form of strain localization was investigated. The applicability of the ConsidΠre criterion [START_REF] Considπre | [END_REF]14] for such strain localization was tested. Verification of the applicability of that criterion for strong strain localization, such as necking, which occurred in zinc single crystal in the regime of single glide deformation, is important since some experimental results have lead to the conclusion that "ConsidΠre criterion is almost never exhibited by single crystals deformed in tension and not always by polycrystalline specimens" [15].

Experimental

The experiment was carried out on cylindrical (Ø6 mm) zinc single crystals of 99.995% purity, obtained by the Bridgman method (with the vertical gradient of the temperature). Crystals were deformed in tension or compression at constant temperature and strain rate on Instron 1115 and Instron 6025 test machines. Before deformation, each sample was carefully etched in an HCl solution in water and then chemically polished in HNO 3 solution in water.

Crystals of two initial orientations, i.e., λ o = 52 o , χ o = 38 o and λ o = 45 o , χ o = 45 o (where: λ o , χ o , -angle between the crystal axis and the normal to the basal plane of slip (0001) and the slip direction <1 12 0>, respectively) were used in tensile testing and labeled correspondingly as I and II (table 1). The ends of the tensile samples were affixed into steel rings with a zinc mold and then inserted into the grips of the tensile machine.

The initial gauge length of the tensile single crystals with orientation I was 20 mm and with orientation II was in the range of 15 -60 mm; the aspect ratios of the samples in the two orientations were 3.3 and 2.5 -10, respectively. Tensile tests of crystals with orientation I covered the range of temperatures from 373 K to 673 K and strain rates from 8x10 -4 to 8x10 -2 s -1 . The strain rate for the tensile tests of crystals with orientation II was equal to 8x10 -3 s -1 , and the tensile temperatures ranged from 373 K to 573 K.

Cylindrical single crystals (Ø6 mm) with orientation χ o = 30 o , λ o = 61 o (labeled as III) and initial length equal to 12 mm were compressed in a wide range of temperatures, 293-673 K, and strain rates from 1.3x10 -5 to 8x10 -3 s -1 . Friction between the specimens and anvils were reduced by a graphite lubricant covering the loaded ends of the specimen.

For tensile and compression tests, the total elongation divided by the initial gauge length and the elongation rate divided by the initial gauge length were used as a deformation measure and a deformation rate measure, respectively.

Slip lines produced during deformation on the polished specimens surfaces were examined by optical microscopy.

For selected specimens deformed by tension, the 0002 X-ray pole figures were measured by the use of the Cu Kα radiation on the Brucker D8 Discover goniometer. The diameter of discs from which the pole figures were measured was ca. 1 mm. Two sets of measurements were taken. For the first set, the X-ray intensities were registered for an angular position of the sample from a range of α = 0 -80 o , ∆α = 5 ο and rotation around normal direction (ND), β = 0 -360 o , ∆β = 5 ο . Measurements were performed in three points located in the necked zone, far from the neck, and also from the zone in which the neck was formed. For the other set of measurements the orientation changes were mapped in 43 points distributed along the tensile axis on the entire length of the zone were the neck was formed. The distance between the neighboring points was equal to 0.5 mm. For these measurements In the selected regions located along the gauge length of the tensile deformed single crystal the crystallographic orientations were measured by the use of the electron backscatter diffraction (EBSD) on a scanning electron microscope (SEM). The microscope used was the Philips XL-30 SEM equipped with the NORDIF EBSD hardware and the CHANNEL-HKL EBSD software for registration and fully automated indexing of the electron backscatter diffraction (EBSD) patterns.

Results and discussion

Tensile tests

The typical force-elongation curves are shown in Figs. 2,3. Depending on the tensile test conditions, crystals with orientation I could be deformed up to 200-1000% (Fig. 4a). The deformation obtained in the stage A of the stress-strain curve lay between 20% to 80% of total deformation (Fig. 4b,c). Similarly, large deformations in the stage A were observed for crystals in orientation II, so both selected crystallographic orientations ensured a relatively high range of deformation occurring primarily by slip in the basal plane. This observation was confirmed by observation of the slip line pattern formed on the specimens' surfaces (Fig. 5). As was verified by selected specimens, rotation of the orientation determined from X-ray pole figures and from EBSD-patterns was the same as the rotation expected for the slip in the basal plane (Fig. 6,7). A very low strain hardening observed on the tensile curves is also typical for the slip on a single slip plane, Fig. 3.

The plastic deformation was initiated in one or more areas along the gauge length, and was initially confined to these regions. As such, single or multiple necks formed along the sample length. Single necking was expected for crystals with orientation I due to their relatively short length (i.e., 20 mm). However, it was found that single necking was observed for both crystal orientations and for crystals with significantly different lengths. Single necking corresponded to samples showing the highest elongation and the highest amount of strain in the first stage of the stress-strain curve (the A-stage of the plastic deformation). The test conditions (temperatures and strain rates) for such samples in orientation I are shown in Fig. 8. The increase in the strain rate from 8x10 -4 s -1 to 8x10 -2 s -1 shifted the temperature range of single necking from approx. 473-523 K to approx. 548-573 K. For the higher temperatures, multinecking was usually observed. It was found that there is a greater tendency toward multinecking when the strain rate decreases. This can be correlated to the increased tendency for the initiation of plastic deformation induced by local heterogeneities of the stress field occurring with decreasing strain rate. Such heterogeneity acts as a local stress concentrator. The local stress concentrations can result from imperfections in the sample surface (for example due to the surface roughness) and/or from some reasons related to microstructure (for example heterogeneity in the dislocation distribution).

Effect of the aspect ratio on the strain distribution along the gauge length of the sample is shown in Fig. 9 for crystals with orientation II. For all crystals shown in the figure, the average deformation was 100%, and the deformation rate was equal to 8x10 -3 s -1 . Single necking and the maximum local deformation were registered for the test temperature 523 K. For the higher test temperatures, the occurrence of multinecking was a typical behavior, especially for longer crystals. Susceptibility of the longer specimens to multinecking can be related to the increase in probability of a local stress heterogeneity which increases with the gauge length of the specimen.

The deformation was initially localized in the neck region, and local reduction in the cross section area of the sample increased with deformation. About 90% of deformation was localized in the neck region where the maximum reduction in the cross section area occurred. However, after some further reduction in area the basal slip plane was slightly inclined to the tensile axis and the neck deepening stopped. Continuation of the neck deepening would require an additional slip in a non-basal plane, but critical stresses for such slip are much higher then that for basal plane slip. The deformed region propagated along the gauge length of the sample until the neck ultimately vanished. The average value of the maximum reduction in cross section in the neck were equal to 52±17% and 73±8% respectively for orientations I and II; therefore, the tendency for localization of the deformation in the neck was higher for orientation II. The prominent value of local deformation resulted in stresses significantly higher than those in regions with little or no plastic deformation. For example, for one of the specimens with an average deformation of 80%, the tensile stress inside of the long neck was approximately four times larger than that acting in the region in which the neck propagated. This indicates that, due to low strain hardening, the propagation stresses are much higher than the stresses required for localization of the deformation.

Stresses acting in the area of the very deep neck are high and they could be sufficient for activation of the non-basal plane slip during high temperature deformation. Such a change in active slip systems should influence texture and microstructure. The shift of rotation axis of the texture maximum, like that shown in Fig. 6b, might have been related to the activation of the non-basal plane slip, but an occurrence of this type slip was not revealed in the microstructure (Fig. 5). However, for some specimens deformed at high temperature nonbasal plane slip cannot be excluded, so verification of the non-basal plane slip required further investigation. No increase in the deepness of the propagating neck, as was observed in our experiment, suggested that, even if the non-basal slip was activated, its amount was rather small. Nevertheless, the doubtful data were not used for analyses presented in the next chapter of our work.

Theoretical analyses of the strain localization

An understanding of the stress state is necessary for analyses of the strain localization from a mechanical point of view. Since a simple uniaxial stress can be related to the tensile test, our analyses were limited to the tensile specimens.

ConsidΠre first published the criterion for the necking of tensile rods [START_REF] Considπre | [END_REF]. According to his criterion, necking of a polycrystalline specimen, insensitive to deformation rate, requires that the following condition is satisfied: dP/dε<0, (1) or alternatively dσ/ dε < σ, (1a) where: P-tensile load, εtrue strain, σtrue flow stress. Stηwe and Toth [14] formulated the ConsidΠre criterion using the resolved shear strain γ r , the critical resolved shear stress τ rc and the Taylor factor M = (

) 2
The left hand side of the inequality (2) defines the intristic hardening (H). The right hand side of the inequality describes the geometric effects (the cross section reduction and the orientation factor changes) and defines the instability factor (S) depending on the crystallographic structure and orientation. For single crystals oriented for single slip, the value of S can be calculated from the following equation [14]:

o o o e e S λ λ χ λ λ χ ε ε 2 2 2 3 sin 1 sin cos ) cos cos 1 ( cos - - - = - = , (3)
where: χthe angle between the slip direction and the loading axis, λthe angle between the slip plane normal and the loading axes, both for the orientation after deformation ε, χ o and λ o that same angles but for the initial orientation.

In the ConsidΠre criterion the strain rate effect was neglected. Such effects should be considered for metals exhibiting significant strain rate sensitivity (as zinc), so criterion (2) should be supplemented by additional terms. Unfortunately, the data obtained in the present work were not sufficient for such analyses, so the strain rate effects were also neglected. As a consequence, we used inequalities (1, 2) derived under the additional assumption that the resolved shear stress in the activated slip system τ r is equal to the critical shear stress τ rc (the internal and external states of stress were in equilibrium, hence forward referred as the stress equilibrium condition).

The ConsidΠre criterion (inequality (1a)) is always fulfilled for a negative hardening rate (dσ/dε<0). For the positive hardening rate, the ConsidΠre criterion is used to predict the length of the macroscopically homogenous range of the plastic deformation. The ConsidΠre criterion (inequality (1)) can also predict the strain localization in the form of Lηders-band for a drop in the specimen load. In the present work, we decided to check if the criterion in the form proposed by Stηwe and Toth (inequality (2)) can predict the susceptibility for pronounced necking as was observed during single slip deformation of zinc crystals.

For orientations II and I the initial value of S was equal to 0.5 and 0.296, respectively. The effect of the resolved shear strain γ r in the basal system for the single slip deformation on the instability factor for both orientations is shown in Fig. 10. Differences in S decreased with increasing γ r , but up to a high value of shear the deformed crystals with initial orientation II had significantly higher S than those with initial orientation I. This indicates that the susceptibility to localization of strain is higher for orientation I rather than for orientation II. On the other hand, a higher maximum deformation in the neck was observed for deformed crystals with initial orientation II; therefore, as expected, the value of S is not related to deformation in the region of localized deformation (neck). Instead, the maximum deformation in the neck is determined by the crystallographic orientation that limits the maximum angle of the lattice rotation during deformation. Such rotation leads the slip direction into a position parallel to the tensile axis and the rotation angle can be higher for orientation II.

For the investigated crystals, the experimental determination of the function H(γ r ) was difficult because necking started at the very beginning of plastic deformation and the neck developed with further deformation. Generally, the function cannot be calculated directly from the tensile curve because of the tri-axial state of stress developed in the neck areas. Calculation of H(γ r ) under the assumption of uniaxial stresses is possible but can only be considered as a rough approximation. Generally, this assumption is only fulfilled for the deformation preceding necking. However, it was quite well fulfilled at the onset of necking within the areas far from the ends of relatively long, diffused necks like that observed in the crystal deformed at 523 K (Fig. 9a). This assumption significantly reduces the amount of data useful for analyses. Assuming uniaxial stresses, the resolved shear stress τ r can be calculated from the equation:

( χ + χ + λ γ χ - λ * = χ - λ = τ ε - , (4)
where A 0 -the cross-sectional areas of the undeformed crystal.

For the assumed infinitely low rate of the deformation (stress equilibrium condition), τ r from equation ( 4) is equal to τ rc and could be directly used for the calculation of H(γ r ) according to the left hand side of the inequality in (2). H(γ r ) functions were calculated for the selected relationship between the force P and extension. The force decreased with the sample extension for the initial stage of deformation when the neck was formed and then increased in the depth, as is shown in Fig. 11a. As an example the decrease in force with deformation in the initial range of the tensile curve (A1) from Fig. 11a, can be approximated by the equation: P = 0.0197-0.0002*ε + 4*10 -6 *ε 2 , where P is in kN and ε, the sample extension, is expressed in %. Fig 11b shows that for a decreasing force, H(γ r ) < S(γ r ), so the inequality (2) is fulfilled and necking is predicted by the ConsidΠre criterion. The necking condition is satisfied from zero strain so the neck was formed and increased in depth.

For the second stage of deformation (A2 in Fig. 11a), the force was nearly constant or increased with the specimen elongation depending on the test condition. Based on the experimental results, calculations for the second deformation range were performed with the assumption of the deformation under a constant tensile force equal to 2.32x10 -2 kN (i) and the P increased with ε and is approximated as: P = 1.19x10 -2 + 2x10 -4 ε (ii) and as P = 1.98x10 -2 -2x10 -4 ε+3x10 -6 ε 2 (iii). The actual increase in force is considerably smaller, and the above equation can be treated as an upper bound. Fig. 12 shows that in this case H(γ r ) > S(γ r ). The inequality in ( 2) is no longer fulfilled, so according to the ConsidΠre criterion any new neck could not be formed. As was observed, the neck propagated along the gauge length and the depth of this propagated neck was not changed.

It should be mentioned that for the ConsidΠre analysis, the stress equilibrium condition was assumed. From the Schmid law, the specimen locally deforms under the condition that τ r = τ rc . The small strain hardening effect of zinc facilitates the deformation localization. However, as τ rc increases due to strain hardening such that τ r < τ rc , the deformation must be transferred to other volume elements of the specimen where the Schmid law is satisfied. Depending on the local value of τ rc and the local stress concentrators, this can be realized by either neck propagation or by necking in another place of the specimen. Thus, the initial localization of the plastic deformation in a single slip system in the form of necking propagating along the specimen with proceeding deformation can be more akin to the Lηders type localization of plastic deformation than the typical necking observed during the last stages of tensile tests. The deformation therefore was confined primarily to the area where the neck was formed or were it propagated. In areas of the diffused necks, patterns of the slip lines indicated that the necking was not in the form of kinking and was more diffuse than slip banding, Fig. 5. Our observation confirmed that the difference in the strain along the necked crystals can be accommodated by some bending of the sample, as was predicted by Gilman [16]. Kinking (the second form of such accommodation) was observed in some crystals, particularly with low aspect ratio and/or multinecked, Fig. 13. A similar situation concerning compression and some form of the strain localization can be expected in compression tested single crystals. A detailed microscopic description of such a heterogeneous deformation is very complicated, since it requires knowledge of stress, strain and strain rate distribution on the length of deformed specimen. However, such an approach is beyond the scope of the present work. What is more, the ConsidΠre criterion is not applicable for compression tests for which the area of the compressed cross-section increases.

Compression tests

Almost all crystals compressed at 293 K and some of those compressed at 373 K and at the temperatures from 573 K to 673 K sheared more or less homogenously or barreled (Fig. 14). The changes in the shape of specimens during compression resulted not only from the eventual tendency to strain localization, but also depended on the constraints at the loaded ends, due to friction between the specimen and anvils. For deformation in one slip plane, the homogenous shearing of the specimen demonstrated frictionless conditions at the loaded ends of the specimen. In such a case, the test can be approximated as unidirectional compression. On the other hand, barreling of the specimens indicated pronounced friction that induced a complicated combined state of stress in the compressed specimen.

Some effects of the strain localization was observed for the specimens deformed at temperatures from 373 K and 423 K to 573 K and 523 K, respectively for the strain rates 8x10 -5 s -1 and 8x10 -3 s -1 . The strain localization manifested in one of two ways: as specimens kinking or as localized sliding of the specimen. Both of them indicated nearly frictionless conditions at the loaded ends of the specimens and differed in the extent of local deformation and volume of highly deformed material. For specimen kinking, the average local deformation was lower but the deformed volume was so large that the specimen bent, as representatively shown in Fig. 14a for the specimen compressed at 373 K. On the other hand, the localized sliding was limited usually to one, two or three relatively narrow and much more highly deformed areas of the specimen. Such areas were separated by effectively undeformed material, and steps were formed on the specimen (Fig. 14). Sometimes both manifestation of strain localization were formed on the same specimen. A hybrid of strain localization effects with almost homogenous shearing or barreling of the sample was also observed, but only for deformation conditions from the boundary of the region limiting observation of strain localization.

We observed the specimen kinking as the typical form of the strain localization. According to our knowledge, the term 'specimen kinking' was introduced into the literature by Orowan [17] who observed it in compressed cadmium single crystals. Earlier kinking was observed in a variety of mineral crystals [18,19] and later confirmed for metals with hcp or B2 structure (i.e., Zn and NiAl) [19][20][21]. On the other hand, the localized sliding (also referred to as the catastrophic flow) was observed in crystals with fcc [START_REF] Cottrell | The mechanical properties of materials[END_REF] and bcc [START_REF] Votava | [END_REF][25][26][27][28] structures. Formation of both types of the microstructure inhomogeneities in compressed zinc was reported in Ref. [START_REF] Pieła | Rozprawy i monografie[END_REF].

Specimen kinking is a type of reaction that compensates for the non-coaxial position of loaded faces due to their displacements by a high deformation in one slip plane, concentrated in the central part of the specimen. An increase in the compression force with anvil displacement was registered for this type of deformation. The similar character of the forcedisplacement curve was typical for tests producing nearly homogenously sheared or barreled specimens. On the other hand a decrease in the compression force with anvil displacements was typical for tests producing localized sliding and for the hybrid of them with almost homogenous shearing of the specimen, Fig. 15. The localized sliding could fulfill conditions of the ConsidΠre criterion because of the decrease in the compression force and in the local specimen cross-section area with anvil displacements. Verification of the criterion validity requires additional experiments. The deformation conditions such as that during localized sliding were not fulfilled for the tests producing kinked, nearly homogenously sheared or barreled specimens. All such forms of deformation were observed in different samples compressed under the same conditions. Therefore, it is very likely that localized sliding can be similarly explained as necks formed during the first stage of the stress-strain curve (section 3.2).

The localized sliding was promoted by the test conditions. It was observed only for some specimens deformed in a narrow range of temperatures and was favored by a lowering of the deformation rate. For the deformation rate of 1.3x10 -5 s -1 it was realized in the temperatures from 423 K up to 573 K. The increase in the deformation rate to 8x10 -5 s -1 and to 8x10 -3 s -1 narrowed the temperature range to 473-548K and 523-548 K, respectively. Other samples, deformed under the same conditions, kinked. Also Chan et al. [27] observed the localized sliding for some single crystals of Nb and believed that such a heterogeneity was not the typical form of the strain distribution over the sample volume. The above results demonstrate the sensitivity of the localized sliding to some imperfections of the tests or inhomogeneities in the sample macro-or microstructure. The decrease in tendency for sliding observed in our experiment for the higher deformation rates suggests a correlation to sample perfection rather than to errors of the deformation test itself. As was observed by Pieła [START_REF] Pieła | Rozprawy i monografie[END_REF], the tendency for the localized sliding increases with perfection of the substructure (a smaller mosaic) formed during growth of the single crystals. On the other hand, it cannot be excluded that the type of localization results from the differences in distributions of the deformation seeds within the samples, e.g. due to even fine differences in the surface roughness of the examined specimens.

Conclusions

1. During the easy glide stage of the zinc single crystals deformation, the neck was formed and initially increased in the depth. After some amount of deformation the neck deepening stopped, and the deformation proceeded by propagation of the neck along the sample length.

2. Formation of the neck can be predicted by the ConsidΠre criterion. On the other hand, the propagation of the necked area along of the gauge length during the first (easy glide) stage of the deformation is not described by this criterion.

3. The form of the ConsidΠre criterion, proposed by Stηwe and Toth [14], can be useful to predict the susceptibility of different crystallographic orientation for strain localization 4. Single necking was observed for the specimens deformed in tension in the range of temperatures approx. 473-523 K and the strain rate 8x10 -4 s -1 and was shifted to temperatures approx. 548-573 K when the strain rate increased to 8x10 -2 s -1 . A multinecking state was typical behavior for the higher temperatures, especially for the lower strain rates.

5. Localized sliding and specimen kinking were characteristic forms of strain localization for the compressed specimens. Both forms of the strain localization were revealed in specimens compressed in the temperatures from 423 K up to 573 K with the strain rate of 1.3x10 -5 s -1 . The increase in the strain rate to 8x10 -5 s -1 and to 8x10 -3 s -1 confined that range of temperatures to 473-548 K and 523-548 K, respectively.

6. The decrease in the compression force and in the cross-sectional area of the deformed sample with anvil displacements was distinctive for tests producing localized sliding. The increase in compression force with anvil displacement was observed for tests producing specimen kinking and for specimens nearly homogenously sheared or barreled. Effect of the sample geometry (the length to diameter ratio) on macrostructures of zinc single crystals with orientation II elongated to 100%. Ratio length to diameter of crystals: (a) 10, (b) 2.5; strain rate 8 x 10 -3 s -1 .

Fig. 10

Changes in the instability factor S with the strain in the basal system γ r for the single slip of crystals with initial orientation I and II.

Fig. 11 Typical force (P) -elongation (ε) relationship, initial orientation II, temperature 473 K, strain rate 8x10 -4 s -1 (a) and the corresponding changes in the factor of instability S(γ r ) and in value of the intristic hardening parameter H(γ r ) with the resolved shear strain in the basal slip system γ r (b). H(γ r ) was calculated for the decreased range of the force-elongation curve (A1) which up to approx. γ r = 0.46 (ε < 25%) can be approximated by equation: P = 1.97x 10 -2 -2x10 -4 ε + 4x10 -6 *ε 2 , R 2 =0.99, where P is in kN and ε the sample elongation, expressed in %.

Relation between γ r and ε can be expressed as:

) cosχ ) χ sin ε) 01 . 0 (1 )( (1/cosλ γ 0 0 2 2 0 r - - + = Fig. 12
Changes in the factor of instability S(γ r ) and in the intristic hardening of the material H(γ r ) with the resolved shear strain in the basal slip system γ r for crystal with initial orientation II. H(γ r ) was calculated for selected experimentally determined relationship of the tensile force (P, in kN) vs. elongation (ε in %) observed for A2 deformation stage (after initial decrease in the tensile force).

Fig. 13

Slip line pattern produced during tension on the crystal surface; region of the typical kink band; orientation II, temperature 573 K, strain rate 8*10 -3 s -1 , elongation 10%. Fig. 14. Macrostructures of compressed zinc single crystals. Orientation III; strain rate: (a) 8x10 -5 s -1 , (b) 8x10 -3 s -1 .

Fig. 15

Typical compression curves with corresponding macrostructures, orientation III, strain rate 8*10 -5 s -1 for temperatures 473 K and 523 K and 1.3 *10 -5 s -1 for 423 K and 573 K. Notice that the localized sliding corresponds to a decrease in the compression force and in the local specimen cross-section area with anvil displacements.

  Basal slip localization in zinc single crystals. The Considére analyses

  ray intensities were registered for the angular position of the sample α = 0 -50 o , ∆α = 1 ο , β = -5 -20 o , ∆β = 1 ο , Fig. 6b.

  the reciprocal of the Schmid factor for the single crystals oriented for single slip): H = (1/τ rc ) *(dτ rc /dγ r ) < S = (1/M)*(1-(dM/dγ r )).

Fig. 2 Fig. 3 1 Fig. 4

 2314 Fig. 2 Force vs. elongation curves for tensile deformed single crystals with orientation I.

Fig. 5

 5 Fig. 5 Slip line pattern produced during tension on the crystal surface; region of the neck, optical microscopy, (a) bright field images, (b) image obtained by use of the Nomarski Interference Contrast; orientation II, temperature 473 K, strain rate 8*10 -3 s -1 , elongation 50% Fig. 6 0002 X-ray pole figures determined on the ED-TD cross section in different points on gauge length of the tensile single crystal, orientation I, (a) registered for angular position of the sample covered inclination α = 0 -80 o , ∆α = 5 ο and rotation around ND, β = 0 -360 o , ∆β = 5 ο , (b) position of the 0002 maximum for points no. 1-43, registered for α = 0 -50 o , ∆α = 1 ο , β = -5 -20 o , ∆β = 1 ο ; orientation II, temperature 523 K, strain rate 8*10 -3 s -1 ; EDelongation direction, ND-normal direction, TD-transverse direction. Notice a shift of rotation axis of the texture maximum (points 1-14 and 15-43).

Fig. 7 Fig. 8 .

 78 Fig. 7The results of EBSD-measurements in two regions (A and B) on the ND-ED cross-section of the tensile single crystal, orientation and the deformation conditions that same as for crystal from Fig. 6; (a) 0002-pole figure, (b) the line scan of the misorientation along ED; misorientations determined with respect to the first point of measurement (on the left side of the figures (b) and (d)), (c) typical line scan of the misorientation along ED; misorientations determined for neighboring points of measurement, (d) schematic position of investigated regions. Notice rotation of the orientation in region A and a small misorientation for the neighboring points.

  Basal slip localization in zinc single crystals. The ConsidΠ Π Π Πre analyses M. Wróbel, K. Pieła AGH University of Science and Technology 30 Av. Mickiewicza, Pl. 30-059 Kraków, Poland

Table 1 .

 1 Details of mechanical tests Typical three-stage shear stress vs. shear strain curve for tensile deformed single crystals with the soft initial orientation.

				Page 10 of 35
	Orientation	Gauge length and the aspect	Deformation	Test temperature and strain rate
	λ o /χ o (designation)	ratio (in brackets) of the sample	tension / compression
	52 o / 38 o ( I )	20 (3.3)	+ / -	373 -673 K/8*10 -4 -8*10 -2 s -1
	45 o / 45 o ( II )	15-60 (2.5-10)	+ / -	373 -573 K/8*10 -3 s -1
	30 o / 61 o ( III )	12 (2)	-/ +	293 -673 K/1.3*10 -5 -8*10 -3 s -1

http://mc.manuscriptcentral.com/pm-pml Philosophical Magazine & Philosophical Magazine Letters

Acknowledgements

The financial support of AGH, contracts no 11.11.180.792 and 11.11.180.448, is appreciated. We thank Prof. J. Bonarski from A. Krupkowski Institute of Polish Academy of Sciences for his help during X-ray measurements.


Hetty Jolink
email: h.jolink@lumc.nl

Jan Den Hartigh

Leo G Visser

Cees Van Nieuwkoop

PHARMACOKINETICS AND

Keywords: Pancytopenia, Proguanil, Malaria, Chemoprophylaxis, Renal insufficiency

A patient known to have renal insufficiency was admitted to the hospital with fever and pancytopenia after returning from a trip to Mali. Pancytopenia was not caused by a tropical infection but was a side effect of atovaquone/ proguanil used as malaria chemoprophylaxis. High and prolonged detectable proguanil serum levels can result in bone marrow suppression in patients with renal insufficiency. This should be taken into account in a returning traveller with fever and pancytopenia.

To the Editor, An increasing number of people with chronic diseases travel to malaria endemic areas. Atovaquone/proguanil (Malarone) 250/100 mg is being used as one of the first choice agents for malaria chemoprophylaxis but is contraindicated in people with glomerular filtration rate (GFR) <30 ml/min.

We saw a 49-year old woman with diarrhoea, fever and pancytopenia after a 2-week trip to Mali. She was known to have hypertrophic cardiomyopathy and chronic renal insufficiency (estimated GFR 36-50 ml min -1 1.73 m -2 ) for which she used carvedilol, lisinopril and furosemide. She developed abdominal cramps, watery diarrhoea and fever 1 week after arrival in Mali. The symptoms arose 2 days after drinking water from a well. Four days after returning from Mali she presented in the emergency room with persisting diarrhoea, nausea and fever (38.5°C). She was still taking atovaquone/proguanil as malaria prophylaxis. On admittance we saw a dehydrated, non-acutely illappearing patient with pulse rate 70/min, blood pressure 120/70 mm Hg and a temperature of 38.3°C. Besides right lower quadrant tenderness, physical examination was unremarkable. Laboratory results revealed a pancytopenia (Hb 5.7 mmol/l, MCV 90, leucocytes 2.5×10 9 /l, thrombocytes 80×10 9 /l). There were no signs of diffuse intravascular coagulation. No previous results of blood counts were available. Serum creatinin was 279 μmol/l (eGFR 17 ml min -1 1.73 m -2 ).

The clinical diagnosis was gastroenteritis but leptospirosis, malaria, dengue and typhoid fever were also considered because of pancytopenia. Malaria thick smear and blood cultures were negative. She was rehydrated, and 2 days later she was treated with clarithromycin according to the fecal culture that grew Campylobacter jejuni. She recovered slowly, and after 2 weeks her hemoglobin level gradually increased to 8.9 mmol/l, leucocytes to 5.6×10 9 /l and thrombocytes to 150×10 9 /l. By exclusion, pancytopenia was ascribed to proguanil toxicity, likely because of deteriorated renal function by dehydration due to gastroenteritis. Afterwards, serum levels of proguanil were measured. The results are outlined in Fig. 1. The calculated half-life of proguanil was over 26 h being twice as long as in healthy subjects [START_REF] Thapar | Time-dependent pharmacokinetics and drug metabolism of atovaquone plus proguanil (Malarone) when taken as chemoprophylaxis[END_REF]. In addition, the CYP2C19 enzyme was genotyped as this is known to be involved in proguanil metabolism. The patient is heterozygotic for the defect *2 allele of CYP2C19, which is associated with a mildly decreased metabolic capacity. This may have partly contributed to the prolonged elimination half-life of proguanil (Fig. 1), but not its toxicity [START_REF] Kerb | Pharmacogenetics of antimalarial drugs: effect on metabolism and transport[END_REF].

Proguanil and its metabolite cycloguanil reduce the activity of the enzyme dihydrofolate reductase. This prevents the development of schizonts and inhibits the primary and secondary exo-erythrocytary forms of malaria [START_REF] Mckeage | Atovaquone/proguanil: a review of its use for the prophylaxis of Plasmodium falciparum malaria[END_REF]. In humans, the enzyme dihydrofolate reductase catalyzes the reduction of folic acid to dihydrofolate and tetrahydrofolate [START_REF] Fowler | The folate cycle and disease in humans[END_REF]. In healthy persons, proguanil levels are negligible for causing bone marrow suppression but sufficient for antimalarial activity as proguanil's affinity for the plasmodial enzyme is over 100 times greater than for the human enzyme [START_REF] Thorogood | The risk of antimalarials in patients with renal failure[END_REF]. However, high and prolonged detectable serum levels of proguanil and cycloguanil can also reduce the activity of the human enzyme causing depletion of intracellular tetrahydrofolate leading to anemia, leucopenia and thrombocytopenia. Proguanil is mainly metabolized by CYP2C19 to cycloguanil and 4chlorophenylbiguanide [START_REF] Thapar | Time-dependent pharmacokinetics and drug metabolism of atovaquone plus proguanil (Malarone) when taken as chemoprophylaxis[END_REF][START_REF] Thorogood | The risk of antimalarials in patients with renal failure[END_REF]. Both proguanil and cycloguanil are excreted by the kidneys and renal insufficiency is thus associated with proguanil toxicity [START_REF] Mckeage | Atovaquone/proguanil: a review of its use for the prophylaxis of Plasmodium falciparum malaria[END_REF]. Therefore atovaquone/proguanil is contraindicated in patients with a glomerular filtration rate <30 ml/min [START_REF] Mckeage | Atovaquone/proguanil: a review of its use for the prophylaxis of Plasmodium falciparum malaria[END_REF].

The development of pancytopenia due to proguanil is rare. However, pancytopenia in a returning traveller with fever will usually be ascribed to the cause of the febrile illness and thus the possibility of proguanil toxicity might be overlooked. With increasing numbers of travellers with coexisting conditions, such as renal insufficiency, going to malaria endemic areas, hematologic side-effects of proguanil might arise more frequently.

Based on this case history, we recommend such chemoprophylaxis should be discontinued once a traveller presents with pancytopenia. In addition, this case highlights the importance of pre-travel counselling in subjects with renal insufficiency especially once travellers' diarrhoea occurs.

Open Access This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. Fig. 1 Elimination curve of proguanil levels in the patient compared to elimination curve of healthy subjects [START_REF] Thapar | Time-dependent pharmacokinetics and drug metabolism of atovaquone plus proguanil (Malarone) when taken as chemoprophylaxis[END_REF]. Extensive metabolizers have normal metabolic capacity of CYP2C19, a key enzyme involved in the metabolization of proguanil to cycloguanil. Poor metabolizers have decreased metabolic capacity of CYP2C19. The expected elimination curve of the patient would be between the curves of poor and extensive metabolizers, but because of impaired excretion due to renal insufficiency the elimination curve is shifted to the right. T=0: time of last tablet of atovaquone/proguanil


Anca -Luiza

Salvatore Marino

Andrei Th Ionescu

Anca-Luiza Alexe-Ionescu

Gaetano Nicastro

Giuseppe Strangi

Nicola Scaramuzza
email: scaramuzza@fis.unical.it

Statistical analyses of repolarisation current of a PZT film deposited on ITO electrode with different thermal treatments

Keywords: ferroelectrics, PZT, statistical physics PZT film, repolarisation current, thermal treatments, Ferroelectric properties PACS: 77.00.00, 42.70.Mp, 77.90.+k, 03.75.Hh, 81.20.Fw

. In the present work the polarization current of a PZT film (PbZ r0,47 T i0,53 O 3 ), obtained by sol-gel synthesis and deposited by spin coating on ITO (indium tin oxide) electrode, has been studied. The different behaviour showed by such a system when the support electrode is previously submitted to a thermal treatment could be attributed to the change of the electrical properties of the ITO layer. In particular, a higher negative charge in the conductive band of the ITO electrode seems to be responsible of a higher order in the ferroelectric film.

Introduction

PZT is a well known material for its ferroelectric properties that are suitable for a large number of applications as non-volatile ferroelectric memories, sensors [START_REF] Takasu | The Ferroelectric Memory and its Applications[END_REF][START_REF] Lionel | Ferroelectric active sensors[END_REF] and so on [START_REF] Van Den Ende | Piezoelectric and mechanical properties of novel composites of PZT and a liquid crystalline thermosetting resin[END_REF][START_REF] Zhang | Study of a deformable micro-mirror based on PZT films[END_REF][START_REF] Shvartsman | Nonlinear local piezoelectric deformation in ferroelectric thin films studied by scanning force microscopy[END_REF][START_REF] Dawbwr | Physics of thin-film ferroelectric oxides[END_REF][START_REF] Zhu | Investigation the effects of the excess Pb content and annealing conditions on the microstructure and ferroelectric properties of PZT (52-48) films prepared by sol-gel method[END_REF][START_REF] Liu | Domain configuration and interface structure analysis of sol-gel-derived PZT ferroelectric thin films[END_REF]. Recently, thin films of PZT have been used to create asymmetric nematic liquid crystal cells (ANLC) in order to obtain a polarity sensitive electrooptical response. The advantage of such cells consists in controlling both ON and OFF states by an external field, consequently reducing the switching time [START_REF] Bruno | Morphological and electrical investigations of lead zirconium titanate thin films obtained by sol-gel synthesis on indium tin oxide electrodes[END_REF]. The electro-optical response obtained with ANLCs containing PZT thin films was very interesting in terms of response time, contrast and rectifying effect. Such behaviour had been ascribed to the ferroelectric nature of the PZT film and to the interlayer phenomena occurring at the PZT-ITO interface that are responsible for a favoured orientation of the PZT nanodomains and, consequently, for the polar sensitive response of the liquid crystal layer. In this work the repolarisation current of PZT thin film obtained by sol-gel synthesis has been studied in two different cases. In the first case the PZT film has been deposited on an ITO electrode deprived of whatever thermal treatment and subsequently submitted to a heating of 600°C for 1h in order to ensure the transition to the ferroelectric perovskite phase. In the second case the ITO electrode has been previously submitted to a thermal treatment of 700°C in order to induce a change of its electric properties, then covered by the sol-gel process and eventually heated at 600°C for 1h. Interesting conclusions have been drawn from the

Experimental setup

The repolarisation currents of PZT film were investigated using the setup described in Fig. 1. The ITO substrate is connected to the output of a voltage source (Wavetek Universal Waveform Generator model 195). The signal applied to the electrode was a triangular wave with a 1s period. The upper electrode of cylindrical shape and 1 cm in diameter was placed with one of its optically polished bases directly in contact to the PZT film (the contact pressure was provided by the very weight of the copper cube). This electrode is connected to the ground by a rather small and well known resistor (100Ω). The voltages drop on this resistor, measured and recorded by a high input impedance oscilloscope (Agilent Infiniium 54832D MSO), is directly proportional to the electric current through the PZT film. To minimize the noise, the measuring setup (substrate, PZT film, upper electrode, and the measuring resistor) was surrounded by a grounded Faraday cage (not shown in the figure). Another channel of the oscilloscope was used to visualize and record the applied triangular wave, this last one also serving to trigger the oscilloscope. For each frequency two sets of data have been recorded, allowing representing currents and voltages versus time. The digitized sets of data are amenable to several kind of mathematical processing (for instance: peak area integration, smoothing, curve fitting, etc.). All the measurements have been performed at room temperature. We have used a rather large upper electrode because we are concerned of repolarization measurements. The repolarization is controlled by the electric field in the PZT and, therefore, we tried to create a thin planar condenser between the ITO substrate and the polished copper surface. We are not interested in having good ohmic contacts on totp of PZT free surface, on the contrary. Actually, the ohmic current is very small as one can easily see from Fig. 2, analyzing the slopes of the currents for the two regimes of the triangular signal (increasing and decreasing). On the other hand, the dielectric displacement current change is quite evident at the time instants where the two regimes of the triangular signal change the slopes. On top of this two currents there appear the ferroelectric repolarization currents manifested as two narrow peaks.

. In Fig. 2 The peak height variation as function of the time, measured for both polarities of the applied voltage, is shown in Fig. 3, while in Fig. 4 are shown the same measurements for the ITO electrode submitted to a previous thermal treatment at 700°C. Comparing these results it is evident that in the first case a higher correlation between the experimental data is present, in particular the peak height occurring during the negative polarity of the applied voltage. Such difference could be attributed to a higher order of the ferroelectric nanodomain orientation in the first case with respect to the second case.

Results and discussion

In Fig. 5 are showed the histograms related to the value of the applied voltage at which the repolarisation switches appear both for positive and negative polarity when the ITO electrode has not been thermally treated. It is possible to notice that for negative polarity (ITO negatively charged) the distribution of voltage values at which the polar switch happens, within a quite narrow range, centres around 33V. On the contrary, for positive polarity the distribution is rather wide and centres on 18V.

In Fig. 6 the switching time histograms of the ferroelectric repolarisation are reported both for positive and negative polarization of the ITO not thermally treated. In this case also it is possible to notice a remarkable difference between the opposite polarities. In fact, for negative polarity the switching time distribution has a narrow range cantered around 0.02s, while for positive polarity the switching time distribution is wider and cantered on 0.04s. What can be deduced by these data is that when the ITO electrode is negatively charged the ferroelectric repolarisation appears in a faster and cooperative way that when the ITO electrode is positively charged. The same histograms have been drawn for the sample in which the ITO electrode has been previously annealed at 700°C. The histograms related to the value of the applied voltage at which the repolarisation switch happens for both positive and negative polarity are reported in Fig. 7. A remarkable difference from the precedent case is that now the required voltage to command the polar switch is higher. In fact, for positive polarity, the distribution is cantered on 60V while, for the negative one, around 43V, moreover, the two distributions are not so different in width as the preceding ones. As the ferroelectric switching time is concerned (see fig. 8), in the last case we still observe narrowed distribution for negative polarity respect to the positive one, but the average switching time is similar, in fact both positive and negative polarity distributions are cantered around 0.01s.

Conclusions

In this work the switching properties of PbZr 0.47 Ti 0.53 O 3 (PZT) ferroelectric films were studied. Such films was obtained by sol-gel synthesis and deposited on ITO covered glass substrates by spin coating deposition and submitted to a thermal treatment at 600°C for one hour to ensure the transition to the perovskite phase. The analysis of the repolarisation current was effectuate on two different kinds of samples: in one of them the bottom electrode was previously submitted to a thermal treatment at 700°C in order to induce a structural modification of the ITO layer, while in the other one the substrate was thermally untreated. From the statistical analysis can be deduced that, in the case of the sample having the ITO electrode untreated, the polar switch occurring when the ITO electrode is negatively charged appears in a faster and cooperative way than the ITO electrode is positively charged. This difference was less evident for the other sample, moreover, even in this last case, an increased value of the voltage at which the ferroelectric switch happen was observed for both polarities. Such information, together with the distribution shapes, suggests that the structure modification induced on the ITO film by the thermal treatment is responsible of a higher disorder of the nanodomain polarization. A possible explanation of this behaviour should take into account the influence of the annealing on the ITO charge carriers. In particular, we can imagine the fact that ITO/PZT interface is not just a geometric dividing plane but it allows injection of electrons into the PZT film. For instance, with negative polarity applied to ITO side of the sample not only the ITO film has got an influx of electrons but also the PZT. As both zirconium and titanium are transition metals there are d-type orbitals that can accept extra electrons. The twin potential walls, typical for ferroelectric materials, go deeper and the potential barrier increase (see fig. 9). On the contrary, the positive potential extracts electrons also from PZT and the barrier lowers permitting the electric dipoles to flip over at a smaller voltage. This synergic bond mechanism [START_REF] Huheey | INORGANIC CHEMISTRY: PRINCIPLES OF STRUCTURE AND REACTIVITY[END_REF] is consistent to the nefelauxetic effect seen in transition metal complexes as an auxiliary contribution to the usual ionic ligand field.

When the ITO substrate was previously treated up, its electrical properties worsen, the permeability of electrons to PZT diminishes and the histograms cannot show clearly the effect.

  behaviours of the repolarisation current showed by these samples.

  is reported the voltage-current vs time plot. The two peaks of the current flowing trough the PZT (open circle) that appear in correspondence of around +40V and -29V of the applied voltage (black line) are due to the switch of the ferroelectric dipole. Since the applied signal includes 200 cycles we have 400 repolarisation switches (200 for positive polarity and 200 for negative one) that are enough to do statistical analyses. From such measurement has been possible to carry out information about the intensity of the repolarisation current (peak height), the voltage value at which the repolarisation switches happens and the repolarisation switching time (peak width measured at the base).

  Figure captions

Fig. 1

 1 Fig.1 Repolarization current setup . r is the measuring resistor.

Fig. 2 1

 2 Fig.2 1 s part out of the 200 s plot. The black line is the applied voltage, the open

Fig. 3

 3 Fig.3 Peaks height as function of time (sample with the substrate previously

Fig. 4

 4 Fig.4 Peaks height as function of time (sample with the substrate previously treated).

Fig. 5

 5 Fig.5 Voltage value histograms at which the repolarization happens. Positive polarity

Fig. 6 Fig. 7

 67 Fig.6 Switching time histograms. Positive polarity (a), negative polarity (b). (Sample

Fig. 8

 8 Fig.8 Switching time histograms. Positive polarity (a), negative polarity (b). (Sample

Fig. 9

 9 Fig.9Twin potential walls for a ferroelectric material in an ideal symmetric condition

  fig. 1 163x110mm (500 x 500 DPI)

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Acknowledgements

The authors are greatly indebted to Professor R. Bartolino for his helpful discussions. Page 9 of 23 http://mc.manuscriptcentral.com/pm-pml Philosophical Magazine & Philosophical Magazine Letters