Mechanical and Acoustic Properties of Magnesium Alloys Based (Nano) Composites Prepared by Powder Metallurgical Routs

Magnesium materials are excellent candidates for structural applications where low weight plays an important role. However, Mg and its alloys possess low stiffness and strength compared with aluminum alloys. One way to enhance the strength of Mg is to reinforce it with stronger particles or fibers of the second phase, essentially forming composite microstructures. Composites reinforced with micro-sized particulates of various materials were very often used to enhance the elastic modulus and mechanical properties. Addition of micro-particles, such as SiC, Y2O3, MgO, Al2O3 particles and CNT (carbon nanotubes) into Mg and Mg alloys has been shown to improve yield strength, modulus, hardness, fatigue and wear resistance, as well as damping properties and thermal stability (Száraz et.al., 2007, Moll et.al., 2000, Ferkel & Mordike, 2001, Trojanová et al., 1997). By scaling the particle size down to the nanometer scale, it has been shown that novel material properties can be obtained (Thostenston et al., 2005).


Introduction
Magnesium materials are excellent candidates for structural applications where low weight plays an important role. However, Mg and its alloys possess low stiffness and strength compared with aluminum alloys. One way to enhance the strength of Mg is to reinforce it with stronger particles or fibers of the second phase, essentially forming composite microstructures. Composites reinforced with micro-sized particulates of various materials were very often used to enhance the elastic modulus and mechanical properties. Addition of micro-particles, such as SiC, Y 2 O 3 , MgO, Al 2 O 3 particles and CNT (carbon nanotubes) into Mg and Mg alloys has been shown to improve yield strength, modulus, hardness, fatigue and wear resistance, as well as damping properties and thermal stability (Száraz et.al., 2007, Moll et.al., 2000, Ferkel & Mordike, 2001, Trojanová et al., 1997). By scaling the particle size down to the nanometer scale, it has been shown that novel material properties can be obtained (Thostenston et al., 2005).

Materials processing 2.1. Preparation of Mg alloys reinforced with SiC particles
The AZ91, WE54 and Mg-8Li magnesium alloys reinforced with SiC particles with were processed by a powder metallurgy method. Mixing of the matrix alloys powders with SiC microparticles (mp) was carried out first in an asymmetrically moved mixer with subsequent milling in a ball mill. The powder was capsulated in magnesium containers and extruded at 400 °C using a 400 t horizontal extrusion press. The composite samples were not thermally treated. Microstructure of the as prepared WE54/SiC composite in introduced in Fig. 1a (the micrograph was taken perpendicular to the extrusion direction). SiC mp are non-uniformly distributed in the matrix; they form in many cases small clusters. The size of sharp bounded more or less uniaxial particles was approximately 9 μm and the grain size in the matrix about 3-4 μm. Light micrographs and transmission electron micrographs showed no pores in the composite and the binding between SiC particles and the matrix was perfect. No defects were found in the vicinity of SiC particles and no chemical reaction at the interface matrix/SiC particles was observed. Microstructure of the Mg8Li/SiC composite exhibits a mixture of two phases (hexagonal close packed α phase and body centred cubic β phase). In Fig. 2 light α and darker β phase are visible together with SiC particles The X−ray analysis revealed the relation between both phases as α : β = 55 : 45. As the grain size the mean value of 5±2 μm was taken from both phases. Resulting materials contained different volume fraction of particles: AZ91 (13 vol.%), WE53 (13 vol.%) and Mg8Li (7% vol.%).

Preparation of Mg based nanocomposites and ultrafine grained materials
Microcrystalline magnesium (μ-Mg) with 3 vol.% of alumina (Al 2 O 3 ) nanoparticles (np) (μ-Mg +3nAl 2 O 3 ), μ-Mg with 3 vol.% of zirconia np (μ-Mg+3ZrO 2 ) and microcrystalline Mg (μ-Mg) were studied. Micro-scaled Mg powder having a particle diameter of about 40 μm was prepared by gas atomisation of a high purity Mg melt in Ar atmosphere containing 1% oxygen for powder passivation. Both alumina and zirconia powders with a mean particle size of 14 nm were prepared by evaporation with the pulsed radiation of a 1000 W Nd:YAG laser and subsequent condensation of the laser-induced vapor in a controlled aggregation gas. The preparation method of np is described elsewhere (Naser et al., 1997, Ferkel & Mordike, 2001). The Mg powder was mixed with ceramic np in an asymmetrically moved mixer for 8 h. The powder mixture was then milled together for 1 h in a planetary ball mill. Mixture was subsequently pre-compressed followed by hot extrusion at a temperature of 350 °C under a pressure of 150 MPa. After extrusion, the originally more or less equiaxial grains changed into elliptical grains with the long axis parallel to the extrusion direction. The grain size in the cross section was about 3 μm and in the extrusion direction 10 μm. The distribution of the np was not homogenous. The np or their agglomerates were located mainly along the grain boundaries of the resultant material. The transmission electron microscopical inspection revealed that only few particles were distributed within grains. Similar procedure was used for preparation of μ-Mg with 3 vol.% of alumina microparticles (μ-Mg+3μAl 2 O 3 ) Details of the preparation of the UFG-Mg and nanocomposite (nc) with the 3 vol.% of graphite nanopartiles (Gr np) (UFG-Mg+3nGr) was similar to the nc with the ceramic np. The microscaled Mg powder was prepared by gas atomisation of a high purity magnesium melt with argon atmosphere containing 1% oxygen for powder passivation. The Mg-powder had a median particle diameter of about 40 μm. The graphite powder used had a median particle size of 1-2 μm. The Mg powder was mixed with 3 vol.% of graphite powder in an asymmetrically moving mixer for 8 h. The powder mixtures were then milled for 8 h at 200 rpm in the planetary ball mill (Retsch, PM400) in a sealed argon atmosphere. The milling vessel of 500 ml volume was made of corundum and the milling balls (11 mm diameter) were made of hardened steel (100Cr6). The weight ratio of ball-to-powder was 10:1. The composite was encapsulated in an evacuated Mg container (70 mm in diameter), degassed at 350 °C, and extruded by the preheated (350 °C) 400 t horizontal extrusion press (outlet 14 mm). Analyses of the extruded material in an optical spark analyser (Spectrolab, Spectro Analytical Instruments) reveal no contamination of the composite by e.g. Fe from the extruder tools or milling balls, or Al from milling vessel (Ferkel, 2003). The mean grain size of specimens used was estimated, using transmission electron microscopy and X-ray profile analysis, to be about 150-200 nm. TEM of the UFG-Mg+3nGr is shown in Fig. 3.

Compressive stress-strain curves
Deformation tests were carried out at temperatures between room temperature and 450 °C using an INSTRON testing machine. Cylindrical specimens of 8 mm diameter and 12 mm length were used for deformation tests performed in compression. The tensile specimens exhibited a gauge length of 10 mm and gauge diameter of 6 mm. Both samples were machined with a stress axis parallel to the extrusion direction. The strain rate sensitivity parameter m has been estimated by the abrupt strain rate changes (SRC) method. SRC tests and tensile tests with a constant strain rate (ε = const.) were performed at temperatures from 300 to 450 °C. Temperature in the furnace was kept with an accuracy of ±1°C. Fig. 4    The compression yield stresses (CYS) estimated as the proof stresses at a strain of 0.002 are introduced in Table 1 (Ion et al., 1982). Another feature in the microstructure of the deformed composites is a high dislocation density. Dislocations in many cases form pile ups and tangles (see Fig. 8). Significant amount of rectangular shape fine particles was estimated distributed within the grains.   In order to obtain more detailed information concerning the deformation mechanism(-s) occurring in particle reinforced magnesium alloys based composites, acoustic emission (AE) was used. AE stems from transient elastic waves which are generated within the material during deformation due to sudden localized and irreversible structure changes like dislocation glide and twinning, which may be considered as the main deformation mechanisms in Mg and its alloys due to their hexagonal crystal structure. WE54/SiC samples were deformed in compression at room temperature. The engineering stress-time plots together with the time variation of the AE count rates are shown in Fig. 9. Two AE maxima were observed. The observed AE maximum at the onset of plastic deformation is connected with the yield point (CYS ≅ 280 MPa) and it may be ascribed to the stochastic {1012} 1010 primary twin formation in the grains unfavourably oriented for the basal slip during the very early stage of plastic deformation. These twins reorient the original lattice on 86.3° and the subsequent straining may continue by the basal slip and secondary twinning. New twins were observed in the deformed microstructure ( Fig. 10). Slim twins were observed also by the TEM as demonstrated in Fig. 8. These twins (and also dislocations visible in Fig.  8) arose very probably during extrusion of the powder material. Possible dislocation contribution to the AE signal is very probably marginal due to small grain sizes. The slip length of dislocations is very short (see dislocation tangles in the left bottom corner of the micrograph 8) and therefore the probability of pile ups formation is also very low. The mobility of dislocations is further limited due to the presence of small cuboidal particles visible in Fig. 7 and 8. The AE signal detected at the time point of ~310 s and onwards is discontinuous, and its sources may be ascribed to damage processes. Specifically, with the addition of the reinforcing phase, the geometrically necessary dislocations are generated to accommodate the plastic mismatch in the matrix. The stress concentrations in the vicinity of the reinforcing SiC particles may achieve their critical value and a breakage of particles and/or a release of cracks (decohesion) between the matrix and particles can occur. Both processes are considered as strong sources of the AE signal. The broken SiC particles and also cracks in the vicinity of particles were observed at the polished surface of the sample deformed to failure (see Fig.  11). Two main mechanisms were detected during plastic deformation: breakage of particles and decohesion in the particle−matrix interface. Based on these results we may consider localisation of the plastic deformation and fracture of the sample if the number of broken particles achieves its critical value.

High temperature properties estimated in tension
The tensile true stress−strain curves estimated for WE54/SiC samples at a strain rate of 2.8x10 -4 s -1 and various temperatures are shown in Fig. 12

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The maximum recorded elongation to failure was 99%, which shows an evidence of the enhanced plasticity, nevertheless this value remains below the bottom limit for superplastic region. SEM micrograph of the sample exhibiting the highest elongation is shown on Fig. 14 documenting the microstructure after deformation at 450 °C. Numerous cavities formed during the high temperature deformation are visible in Fig. 14. The cavitation primarily occurred at the reinforcement/matrix interfaces, which are the preferential sites for the nucleation of cavities. The density of cavities was higher near the fracture surface where elongated cavities were found. Since many of these cavities were fairly large, it is reasonable to assume that growth and subsequent coalescence and interlinkage of the cavities led to the premature failure.    Fig. 15. It is obvious that the m−values increased with increasing deformation temperature and the dependence was shifted to the higher strain rates. While at 200 °C the maximum of m was reached at ε = 4x10 -5 s -1 , at a temperature of 300 °C the maximum laid in the vicinity of the strain rate ε = 6x10 -4 s -1 . The maximum value of m estimated at 300 °C exhibited 0.46, which is close to a value of 0.5, considered as an optimal value for the superplasticity. The maximum value of m = 0.3 at 200 °C and all values of m estimated at temperatures higher for all strain rates were in the region enclosing the superplastic behaviour. The maximum ductility A = 110% was found at 300 °C and at a strain rate of 6x10 -4 s -1 , which correspond to the maximum of the strain rate sensitivity m = 0.46. Despite of relatively high values of the strain rate sensitivity m, the achieved ductility was only at the onset of the superplastic region. The observed cavities formation after high temperature deformation in WE54/SiC and Mg8Li/ SiC composites indicates the presence of some diffusion process. The activation energy Q of such rate controlling is given by the relationship (Langdon, 1994): where ε is steady−state deformation rate, A is a dimensionless constant, d is the grain size, σ is the applied stress, p is the grain size exponent, n = 1/m is the stress exponent and D 0 is the pre−exponential factor; kT has its usual meaning and R is the gas constant. The activation energy Q is a slope of the plot σ/G vs 1/T (when ε T/G is constant): The activation energy was estimated using relationship (2) for both composites to be Q(WE54/ SiC) = 114kJ/mol. The activation energy for the volume diffusion is 135 kJ/mol and for the grain boundary diffusion 92 kJ/mol (Frost & Ashby, 1982). Comparing to an experimental value of 114 kJ/mol (using rule of mixture), we may conclude that the measured activation energy consists of approximately 50% volume and 50% grain boundary diffusion. Using estimated values of m, the activation energy for Mg8Li/SiC composite was found (for the high m region) Q ≈ 87 kJ/mol. According to binary Mg-Li diagram (Nayeb-Hashemi et al., 1984), the Mg−8Li alloy at 300 °C consists of equilibrium α phase and β phase whose chemical composition are 5.7 Li and 11 Li, respectively. Owing to higher mobility of Li in β phase the Li content in β phase decreases while in the α phase increases and the volume fraction of the α phase increases at the expense of β phase. Due to grain boundary migration caused by atomic mobility, the grain size of α phase increases.
Experimentally estimated value of the activation energy Q = 87 kJ/mol indicates that the main rate controlling mechanism is the grain boundary sliding accommodated with the grain boundary diffusion with the small contribution of the lattice diffusion. The successive grain growth increases the grain size in the α phase. The diffusion accommodation of the grain boundary sliding is more difficult, which implies cavities formation.
Observed formation and growth of cavities relaxes the stress concentration caused at the particles on the sliding grain boundaries. Cavities, created by vacancy clustering, may nucleate if the stress concentration is not relieved sufficiently rapidly. Local tensile stress caused by sliding at interfaces may be written in the form (Mabuchi & Higashi, 1999): where d p is the particle diameter, ε is the strain rate, d is the grain size, D L is the lattice diffusion and D GB is the grain boundary diffusion coefficient, δ is the grain boundary width, Ω is the atomic volume. V f is the volume fraction of particles and kT has its usual meaning. The insufficiently accommodated grain boundary sliding process is the reason for cavitation and early failure of samples.
Based on our results of mechanical tests, microstructural observations and the analysis of the AE signal occurring during plastic deformation, we may conclude that the deformation processes in the powder metallurgically prepared magnesium alloys based composites are different at lower and higher temperatures. At lower temperatures (below about 150 °C), the deformation processes have following main characteristics: i. Small grain size -several micrometers -is a typical feature of the microstructure.

ii.
Early stages of the compressive plastic deformation are realised by twinning accommodated with the dislocation glide; iii.
Twin boundaries are impenetrable obstacles for the dislocation motion and contribute to a significant hardening at lower temperatures;

iv.
Breakage of particles and decohesion in the particle−matrix interfaces cause localisation of plastic deformation and failure of materials; Although the grain size of composites exhibiting 3-5 μm indicated a possibility of the occurrence of the structural superplasticity, only enhanced plasticity was estimated at higher temperatures. This fact has following reasons: i.
The values of the strain rate sensitivity parameter reached m = 0.3-0.5; ii.
The grain boundary sliding is the significant mechanism operating at higher temperatures; iii.
The stress concentrations formed at the particles on the sliding grain boundaries are the reason for the cavity formation.

iv.
Growth and subsequent coalescence and interlinkage of the cavities led to the premature failure of composites.

Microcrystalline magnesium reinforced with ceramic microparticles and nanoparticles
True stress-true strain curves obtained for microcrystalline Mg reinforced with alumina microparticles are introduced in Fig. 17a for tension and 17b for compression. A substantial difference between shapes of curves measured in tension and compression are visible. Similar curves were obtained also for microcrystalline Mg reinforced with alumina and zirconia np as it follows from Figs 18a,b and 19 a,b. It can be seen that the flow stress decreases as the test temperature is increasing. Substantial differences between curves obtained in tension and compression are obvious comparing Fig. 18a -strain curves obtained in tension are flat at temperatures above 100 °C, there is a dynamic balance between ha ing. The work hardening rate is very close to zero. Tensile/compression yield stress asymmetry was studied by M coustic emission technique . A broad maximum on the curves estimated at room temperatur s observed at a strain of about 10 %. Analysis of the acoustic emission signal revealed that during the compress °C, the maximum of the twin formation is at a very beginning of the stress-strain curve. The twin bound for dislocation motion. Therefore, twin growth caused an increase in the flow stress, which was manifested by in the acoustic emission signal. In tension, a significant twin formation was observed during the entire test. T eformation requires formation of the new interface inside of grains. The energy of twin interfaces in Mg is relativ al., 2003). This leads to an increasing difficulty of twin nucleation with decreasing grain size. This has been confi tic emission measurements (Trojanová et al., 2008).   The stress-strain curves obtained in tension are flat at temperatures above 100 °C, there is a dynamic balance between hardening and softening. The work hardening rate is very close to zero. Tensile/compression yield stress asymmetry was studied by Mathis et al. using acoustic emission technique . A broad maximum on the curves estimated at room temperature and at 100 °C was observed at a strain of about 10 %. Analysis of the acoustic emission signal revealed that during the compression tests below 200 °C, the maximum of the twin formation is at a very beginning of the stress-strain curve. The twin boundaries are obstacles for dislocation motion. Therefore, twin growth caused an increase in the flow stress, which was manifested by a rapid decrease in the acoustic emission signal. In tension, a significant twin formation was observed during the entire test. Twinning mode of deformation requires formation of the new interface inside of grains. The energy of twin interfaces in Mg is relatively high . This leads to an increasing difficulty of twin nucleation with decreasing grain size. This has been confirmed by the acoustic emission measurements (Trojanová et al., 2008).

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The temperature variations of the TYS and the UTS estimated for μ-Mg and μ-Mg with ceramic mp and np are introduced in Table 3. Relatively high values of the TYS and UTS were estimated. This is also influenced by small grain size of all materials as a result of the powder metallurgical preparation route. for dislocation motion. Therefore, twin growth caused an increase in the flow stress, which was manifested by a in the acoustic emission signal. In tension, a significant twin formation was observed during the entire test. Tw deformation requires formation of the new interface inside of grains. The energy of twin interfaces in Mg is relative al., 2003). This leads to an increasing difficulty of twin nucleation with decreasing grain size. This has been confirm tic emission measurements (Trojanová et al., 2008).   The temperature variations of the CYS and the UCS are introduced in Table 4 for Mg reinforced with various types of particles. It can be seen that while the values of the CYS of all materials studied are lower, the UCS values are higher than those measured in tension. The twinning mode of deformation in the early stages of deformation is easier in the compressive straining. New interfaces formed inside the grains are impenetrable obstacles for dislocation motion and they lead to hardening which is manifested with the local maximum on the stress-strain curve. The height of this maximum estimated at RT and 100 °C agree with the UCS value. The role of twinning decreases with increasing deformation temperature. Figure 20a shows the true stress-true strain curves for UFG-Mg deformed in compression at various temperatures. Samples were deformed either to fracture or at higher temperatures to predetermined strains. A pronounced upper yield point followed by the hardening stage was observed at temperatures between room temperature and 100 °C. The stress-strain curves at temperatures higher than 150 ºC have a steady state character. Stress-strain curves measured for UFG-Mg with 3 vol. % of Gr np (UFG-Mg+3nGr) in compression are presented in Fig.  20b for various temperatures. The local maximum at the beginning of the stress strain curve was in this case observed only at ambient temperature. The temperature dependences of the CYS and UCS estimated for both materials are shown in Table 5. Both stresses decrease rapidly with increasing temperature. The yielding phenomenon is very probably caused by the avalanche release of dislocations pinned at grain boundaries. It will be shown later in the paragraph 4.2 that the amplitude dependence of the logarithmic decrement in UFG-Mg indicates this phenomenon. Acoustic emission measurements detected no signal from the deformed sample at room temperature. This indicates that no dislocation pile-ups have been formed. In order to produce a pile-up of dislocations the grains need to contain a Frank-Read source operating in a cyclic way.

Ultrafine grained magnesium
. The tensile yield stress and ultimate tensile strength estimated for various temperatures in compression.
rature variation of the CYS and the UCS are introduced in Table 4 for Mg reinforced with various types of particles. It can at while the values of the CYS of all materials studied are lower, the UCS values are higher than those measured in tensi inning mode of deformation in the early stages of deformation is easier in the compressive straining. New interfaces form the grains are impenetrable obstacles for dislocation motion and they lead to hardening which is manifested with the lo um on the stress-strain curve. The height of this maximum estimated at RT and 100 °C agree with the UCS value. The role ng decreases with increasing deformation temperature.

Ultrafine grained magnesium
20a shows the true stress-true strain curves for UFG-Mg deformed in compression at various temperatures. Samples w ed either to fracture or at higher temperatures to predetermined strains. A pronounced upper yield point followed by t ing stage was observed at temperatures between room temperature and 100 °C. The stress-strain curves at temperatu than 150 ºC have a steady state character. Stress-strain curves measured for UFG-Mg with 3 vol. % of Gr np (UFG-Mg+3nG pression are presented in Fig. 20b for various temperatures. The local maximum at the beginning of the stress strain cur this case observed only at ambient temperature. The temperature dependences of the CYS and UCS estimated for bo als are shown in Table 5. Both stresses decrease rapidly with increasing temperature. The yielding phenomenon is ve ly caused by the avalanche release of dislocations pinned at grain boundaries. It will be shown later in the paragraph e amplitude dependence of the logarithmic decrement in UFG-Mg indicates this phenomenon. Acoustic emissi rements detected no signal from the deformed sample at room temperature. This indicates that no dislocation pile-ups ha rmed. In order to produce a pile-up of dislocations the grains need to contain a Frank-Read source operating in a cyclic w  The maximum link length of a source to operate in a cyclic way becomes about D/2 (D is the separation of grain boundaries). The minimum resolved shear stress on the grain boundary due to the first loop can be written as where G is the shear modulus and b the Burgers vector of dislocations. The first term is the operating stress of the source and the second is the back stress from the first loop that is forced up against the grain boundary. If τ GB exceeds the critical stress τ c , required to an activation of an accommodating system, the first loop will escape in the grain boundary before the second loop is ejected from the source, and no pile-up will be formed (Nes et al., 2005). The stressstrain curves at temperatures higher than 150 °C exhibit a steady state character indicating a dynamic balance between hardening and softening.
It is clear that the Gr np increase the CYS. It is interesting to note that the UCS value of UFG-Mg deformed at RT is higher than that of Mg+3nGr. Values estimated at 300 °C for both materials show that the softening in the Mg+3nGr is lower than that in UFG-Mg. In the case where materials were prepared by milling, the refinement of the originally large grains into the UFG region is connected with large plastic deformation. This large plastic deformation is partially recovered during consolidation of the powder. Such mc and UFG materials usually contain a high density of dislocations in a heavy-deformation micro-structure (Mohamed, 2003). (2) UFG region (the grain size between 100 nm and 1 μm): the YS of Mg negatively deviates from the Hall-Petch relationship.
(3) Nc region (the grain size smaller than 100 nm): the slope of the yield stress dependence on the grain size is negative.
While for mc Mg the interaction of dislocations with grain boundaries and/or twin boundaries can be considered as significantly affecting plastic deformation, for UFG-Mg the dislocation pile-up mechanism loses its significance; twining and grain boundary sliding gradually contributes to plastic deformation.

X-ray analysis
Deformed UFG-Mg samples were investigated by the high resolution X-ray diffraction peak profile analysis. The diffraction profiles are evaluated by assuming that peak broadening is caused by small crystallites and strain caused by dislocations. The Williamson-Hall plots (integral breadth β vs. sinϑ, where ϑ is the Bragg angle) were constructed. The measured physical profiles are fitted by theoretical profiles calculated on the basis of well-established profile functions of size and strain. Both strain and strain anisotropy are accounted for by the dislocation model of lattice distortions (Wilkens, 1970;Ungár & Borbely, 1996). In a crystal containing dislocations, the mean square strain is done by Wilkens (1970) where ρ is the density of dislocations and b is their Burgers vector, C is the dislocation contrast factor, f(η) is the Wilkens function, where η = L/R e (R e is the effective outer cut-off radius of dislocations), L is the Fourier length defined as L = na 3 (a 3 = λ/2(sinϑ 2 -sinϑ 1 )), n are integers starting from zero, λ is the wavelength of X-rays and (ϑ 2 -ϑ 1 ) is the angular range of the measured diffraction profile. In the case of hexagonal polycrystals, where dislocations with various Burgers vectors take place in deformation, the average contrast factor may be obtained by the weighted linear combination of the individual contrast factors for the active sub slip systems: where N is the number of the different activated sub slip systems, C i is the average dislocation contrast factor corresponding to the ith sub slip system and f i are the fractions of the particular sub slip systems by which they contribute to the broadening of a specific reflection. The average contrast factors for a single sub slip system (hk.ℓ) in hexagonal crystals are (Dragomir & Ungár, 2002): .0 1 2 where x = (2/3)(ℓ/ga) 2 , q 1 and q 2 are parameters depending on the elastic properties of the material, C hk.0 is the average contrast factor corresponding to the hk.0 type reflections, g is the absolute value of the diffraction vector and a is the lattice constant in the basal plane. The q 1 and q 2 parameters and the values of C hk.0 have been calculated for hexagonal crystals and compounds in (Dragomir & Ungár, 2002). Two Burgers vectors types were taken into account: a = 1 3 2 110 and c + a = 1 3 2113 . Using the scheme described by Kužel & Klimanek (1989), it is possible to take for the number N of sub-slip systems in eq. (12) with the <a> or <c+a> Burgers vector N a = 4 and N c + a = 5, respectively. Once the Burgers vector types are determined, the value of C hk .0 b 2 and the dislocations density ρ can also be calculated; for further details see (Kužel & Klimanek, 1989). The experimental values of q 1 and q 2 denoted as can be estimated by the whole profile fitting procedure (details see (Kužel, 1998)).
The Williamson-Hall plots in terms of the integral breadth β vs. the magnitude of the reciprocal lattice vector G (G represents sinϑ) are shown in Figs. 22 for samples deformed at various temperatures. Circles correspond to the values calculated from the experimental data (Kužel, 1998). Squares correspond to the values calculated on the basis of the model (Dragomir & Ungár, 2002). The fitting procedure allows to estimate the density of basal <a> dislocations, the density of <c+a> dislocations and the grain size depending on the testing temperature. The results are given in Table 6. From Table 6 it follows that the basal dislocation density decreases with increasing deformation temperature, while the fraction of <c+a> dislocations is constant. The grain size growth has been also observed with increasing deformation temperature. Máthis et al., (2004) used the similar method to study the evolution of the dislocation density with the Burgers vector of different types as a function of the testing temperature in a coarse grained Mg. They found that at room temperature and at 100 °C, the dominant dislocations are <a> or mainly basal dislocations.  Table 6. Basal dislocation density ρ <a>, density of <c+a> dislocations ρ <c+a> and grain size estimated for various deformation temperatures. e described by Kužel & Klimanek (1989), it is possible to take for the number N of sub-slip systems in eq. (12) with the < Burgers vector N a = 4 and N c a  = 5, respectively. Once the Burgers vector types are determined, the value of h C e dislocations density  can also be calculated; for further details see (Kužel & Klimanek, 1989). The experimental values denoted as can be estimated by the whole profile fitting procedure (details see (Kužel, 1998) (Kužel, 1998). Squares correspond to the values calculated on the basis of the model (Dragomir & Ungár, ting procedure allows to estimate the density of basal <a> dislocations, the density of <c+a> dislocations and the grai ding on the testing temperature. The results are given in Table 6. From Table 6 it follows that the basal dislocation de ses with increasing deformation temperature, while the fraction of <c+a> dislocations is constant. The grain size growt lso observed with increasing deformation temperature. Máthis et al., (2004) used the similar method to study the evol dislocation density with the Burgers vector of different types as a function of the testing temperature in a coarse grained ound that at room temperature and at 100 °C, the dominant dislocations are <a> or mainly basal dislocations. her temperatures, the fraction of <a> dislocations decreases, whereas the fraction of <c+a> dislocations increases. The fra dislocations remains practically unchanged. The average total dislocation density increased considerably with stra red to the value in the as-cast state.

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At higher temperatures, the fraction of <a> dislocations decreases, whereas the fraction of <c +a> dislocations increases. The fraction of <c> dislocations remains practically unchanged. The average total dislocation density increased considerably with strain as compared to the value in the as-cast state.
However, with increasing deformation temperature, the increment of the dislocation density decreased strongly in the plastically deformed sample. The concomitant increase of the fraction of <c+a> dislocations and the decrease of the average dislocation density with increasing deformation temperature can be explained by the dynamic recovery mechanism/-s. The results obtained in our study for UFG-Mg exhibit similar decrease in the basal dislocation density. The fraction of the <c+a> dislocations in UFG Mg remains constant, while it increases in the coarse grained material. This is very probably caused by the different deformation mechanisms in the UFG-material.

Amplitude dependence of internal friction
The damping measurements were carried out in a vacuum (about 30 Pa) at room temperature.
The specimens fixed at one end were excited into resonance by a permanent magnet fixed at the free side of the bending beam and a sinusoidal alternating magnetic field. The internal friction was characterised by the logarithmic decrement δ of the free decay of the vibrating beam δ = ln (A n /A n+1 ), where A n and A n+1 are the amplitudes of a free decay of vibrations after n and (n+1) cycles, respectively. The resonance frequency ranged from 130 to 160 Hz. The strain amplitude dependences of the logarithmic decrement were measured. The specimens were annealed step by step at increasing temperatures up to 500 °C for 0.5 h and after each annealing cycle quenched into water of room temperature. The annealing at higher temperatures was performed in an argon atmosphere to avoid oxidation. The damping measurements were carried out immediately after heat treatment and quenching at room temperature. Figure 23 shows the logarithmic decrement plotted against the logarithm of the maximum strain amplitude for μ-Mg+3nZrO 2 samples. The logarithmic decrement was measured before (as received -as rec) and after step by step annealing at increasing upper temperature of the cycle. It can be seen that the measured strain dependence of the logarithmic decrement exhibits two regions and can be expressed as where δ 0 is the amplitude independent component (or only weakly dependent on the maximum strain amplitude) found in the first region, for lower strain amplitudes. In the second region, for higher strain amplitudes, the component δ H (ε) depends on the strain amplitude (amplitude dependent internal friction -ADIF); it increases with increasing strain amplitude. The upper temperature of the thermal cycling influences the logarithmic decrement. In the case of the μ-Mg+3nZrO 2 composite, the thermal treatment influences mainly the amplitude independent component of the decrement. It is important to note that very high values of damping in the amplitude independent component -in order of 10 -2 -were obtained. The strain amplitude dependences of the logarithmic decrement for μ-Mg+3nAl 2 O 3 are given in Figures  24. Figure 24a shows the strain amplitude dependence of the logarithmic decrement for specimens annealed up to 300 ºC. Figure 24b shows the strain amplitude dependence of the logarithmic decrement for specimens annealed at temperatures between 300 and 500 ºC. The thermal cycling influences mainly the amplitude dependent component δ H that increases with increasing upper temperature of the cycle, if the upper temperature is between room temperature and 300 ºC. For the upper temperature between 300 and 500 ºC, the δ H component decreases with increasing upper temperature. es. The logarithmic decrement was measured before (as received -as rec) and after step by step annealing at increasing u rature of the cycle. It can be seen that the measured strain dependence of the logarithmic decrement exhibits two regions expressed as 0 H δ + δ ( ε), (8) δ0 is the amplitude independent component (or only weakly dependent on the maximum strain amplitude) found in the , for lower strain amplitudes. In the second region, for higher strain amplitudes, the component δH(ε) depends on the s tude (amplitude dependent internal friction -ADIF); it increases with increasing strain amplitude. The upper temperatu ermal cycling influences the logarithmic decrement. In the case of the μ-Mg+3nZrO2 composite, the thermal treatm nces mainly the amplitude independent component of the decrement. It is important to note that very high value ing in the amplitude independent component -in order of 10 -2 -were obtained. The strain amplitude dependences o thmic decrement for μ-Mg+3nAl2O3 are given in Figures 24. Figure 24a shows the strain amplitude dependence o thmic decrement for specimens annealed up to 300 ºC. Figure 24b shows the strain amplitude dependence of the logarit ent for specimens annealed at temperatures between 300 and 500 ºC. The thermal cycling influences mainly the ampli dent component δH that increases with increasing upper temperature of the cycle, if the upper temperature is between r rature and 300 ºC. For the upper temperature between 300 and 500 ºC, the δH component decreases with increasing u rature. train amplitude dependences of the logarithmic decrement measured in UFG-Mg after thermal cycling are given in Fi nly a slight influence of thermal cycling on the δ versus ε curves can be observed. Figure 25b shows the plots of δ versus Mg+3nGr. It can be seen that the thermal cycling causes a slight decrease of the logarithmic decrement at small s tudes. The δH component changes only very slightly with increasing temperature of the cycle. Figure 26 shows the s tude dependence of the logarithmic decrement for various materials before annealing (as received). The value of the cr εc at which the logarithmic decrement begins to increase with strain amplitude depends on annealing temperature a ds on the kind of particles. The strain amplitude dependences of the logarithmic decrement measured in UFG-Mg after thermal cycling are given in Figure 25a. Only a slight influence of thermal cycling on the δ versus ε curves can be observed. Figure 25b shows the plots of δ versus ε for UFG-Mg+3nGr. It can be seen that the thermal cycling causes a slight decrease of the logarithmic decrement at small strain amplitudes. The δ H component changes only very slightly with increasing temperature of the cycle. Figure 26 shows the strain amplitude dependence of the logarithmic decrement for various materials before annealing (as received). The value of the critical strain ε c at which the logarithmic decrement begins to increase with strain amplitude depends on annealing temperature and it depends on the kind of particles.  It is generally accepted that the δ 0 component is connected with the material microstructure and the amplitude dependent component δ H is due to an interaction of dislocations with point defects (e.g. solute atoms). The dislocations contribute to the damping capacity by the motion of vibrating dislocation lines. Particulates (Al 2 O 3 , ZrO 2 , Gr), as secondary phases, may improve the damping capacity of alloys. The particles in a composite may cause an increase in the dislocation density as a result of thermal strain mismatch between the ceramic particles and the matrix during preparation and/or thermal treatment. The difference between the coefficients of thermal expansion (CTE) of the particles and the matrix may create the thermal residual stresses after cooling from the processing temperature to room temperature. The thermal stresses are also generated during heat treatment and when composites are heated and cooled through a temperature range (thermal cycling). In generally, there are biaxial or triaxial stress fields located near the reinforcement-matrix interface. The amplitudes of the stress field decrease with increasing distance from the interface. In a simple one-dimensional model, the thermal stresses σ TS , produced by a temperature change ΔT, at the interface are given by (Chawla, 1991)

-Mg+3nZrO
where Δα is the mismatch of the CTE values between the reinforcements and the matrix, E F and E M are the values of the Young's modulus for the reinforcement and the matrix, respectively and f is the volume fraction of the reinforcement. The CTE of the matrix is much higher than that of the reinforcement. Thus after cooling, the tensile thermal residual stresses are created in the matrix. The thermal stresses may relax around the matrix-reinforcement interface by emitting dislocation. An increase in the dislocation density near reinforcement has been calculated as (Arsenault & Shi, 1986, Dunand & Mortensen, 1991: where t is the minimum dimension of reinforcement, b is the magnitude of the Burgers vector of dislocations and B is a geometrical constant (depending on the aspect ratio). The newly formed dislocations may be sources of the higher damping capacity because of the motion of vibrating dislocation lines under cycling loading. According to the Granato-Lücke theory (Granato, & Lücke, 1981), weak and strong pinning points restrict motion of dislocations in their glide plane. At low strain amplitudes (stresses), dislocation bows out between the weak pinning points, leading to the amplitude independent logarithmic decrement. The dislocation remains anchored at the strong pinning points. At higher strain amplitudes, the force exerted on the weak pinning points becomes higher than the binding force of the weak pinning points. The dislocation segments break away from some weak pinning points within longer dislocation segments. This leads to a drastic instantaneous increase in the dislocation strain and thus giving rise to the level of the logarithmic decrement. The amplitude dependent component of the decrement depends on the dislocation density, length of shorter and longer dislocation segments. At temperatures higher than 0 K, the breakaway of shorter dislocation segments is thermally activated. During thermal cycling, new dislocations are created due to the difference in the CTEs (see Eq. (10)). An increase in the dislocation density, while the number of weak pinning points remains constant, increases effectively the length of dislocation segment between weak pinning points and hence the δ H component should increase, which is observed. The higher temperature of the cycling, the higher the dislocation density and the higher increase in the effective length of the shorter dislocation segments. The critical strain ε c at which the decrement becomes to be amplitude dependent is determined by the interaction energy between dislocations and the weak pinning points and the distance between the pinning points. As the distance between weak pinning point increases with the upper temperature, the dislocations can break away from the weak pinning point under lower critical stress and thus, the value of ε c should decrease with increasing upper temperature, which is observed. The values of ε c for a composite are proportional to the yield stress of the composite matrix. It should be consider that the value of ε c can be influenced by the thermal stresses due to the difference in CTEs for both components of the composite. In mc and UFG Mg no new dislocations are created during thermal cycling. Hence, it is expected only a slight influence of the thermal cycling on the δ versus ε curves, which is in agreement with experimental results. Interfaces may contribute to the damping behaviour of composite materials. Due to a large difference in the coefficients of thermal expansion between the particles and the matrix, high thermal residual stresses are created around the particles. The thermal stresses with temperature can relax and plastic zones of tangled dislocation are formed. Their average radius depends on the difference in CTEs, particles radius and the change of temperature. The higher the matrix yield stress, the smaller radius of the plastic zones (Dunand & Mortensen, 1991). Plastic zones may also contribute to the damping behaviour.
The contribution of interfaces to internal friction depends on the character of interfacial bonding. The interface damping should be considered. The internal friction of a composite with the perfectly bonded interface (interface is incoherent) depends on the shape of particles, their volume fraction and the magnitude of local stress at the particle-matrix interface.
Assuming that all the particles have the same diameter, the logarithmic decrement is given as (Zhang et al., 1994a) where V p is the volume fraction of particles and ν is the Poisson ratio of the matrix. The effect of the perfectly bonded interfaces on the damping behaviour becomes more significant at high temperatures; in Mg based composites this could be above 150 ºC. The matrix becomes relatively soft relative to the nanoparticles. Hence, the internal friction at the interface may be thermally activated.
In the case of weak bonding at the interface, interfacial slip (sliding at the interface) may occur. In this case, the frictional energy loss caused by the sliding at interfaces may become a primary source of damping. The damping component due to interfacial slip under the applied stress amplitude σ 0 can be expressed as (Zhang et al., 1994a) where κ is the friction coefficient between both components of the composite, σ r is the radial stress at the particle-matrix interface corresponding to the stress amplitude σ 0 , ε 0 is the strain amplitude corresponding to σ 0 . The critical interface strain ε cr corresponding to the critical interface shear stress τ cr is the strain at which the sliding on the on interface begins. E C is the elastic modulus of the composite. For weakly bonded interfaces, the critical strain ε cr is assumed to be much lower than the strain amplitude ε 0 and then 2 0 3 . 2 The stress concentration factor σ r /σ 0 has been reported to be 1.1-1.3 (Zhang et al., 1994b). The model does not take into account possible effects of temperature or frequency on damping and therefore the predictions of the model may be taken only as the first approximation. Very high values of δ 0 for mc and nc Mg reinforced by zirconia np and Gr np are very probably caused by interfacial slip due to weak bonding between particles and matrix. The effect of an additional damping due to the influence of particle can be clearly seen in Figure 26. Therefore, the effect of an additional damping due to the influence of particles may be estimated. The measured increase in δ 0 due to the addition of ZrO 2 np to μ-Mg and Gr np to UFG-Mg is about 0.008-0.009 ( Figure 26). Taking for the friction coefficient a typical value of ~0.08, the relation (10) predicts a value for an additional damping owing to interfaces of δ 0i = 0.04. The discrepancy between the predicted and measured value may be caused by a non-uniform strain state in specimens because they were subjected to bending in experiment. Hence, the stress (strain) level can reach its critical value at which the interface sliding starts only in some region of the measured specimen. Accordingly, the measured interface-damping component is lower than the predicted value. High values of the decrement component δ 0 obtained for mc and UFG-Mg are very probably caused by grain boundary sliding support by diffusion processes. On the other hand, the observed decrease in the amplitude independent component of μ-Mg +3nAl 2 O 3 comparing with μ-Mg may be explained according to the following way: Np situated in grain boundaries prevent the grain boundary sliding which contribute significantly to the amplitude independent component of decrement.

Temperature relaxation spectrum of internal friction
The temperature dependent internal friction (TDIF), internal friction spectrum, is the temperature or frequency dependence of damping. Internal friction spectra were measured in a DMA 2980 (TA Instruments) apparatus in a single heating and cooling process. Measurements were performed at various frequencies from 0.1 up to 2 Hz. Throughout the measurements the strain amplitude was 1.2x10 -4 . The heating as well as cooling rate was 1 K/min.  The internal friction in a material is a result of internal processes, which occurs during alternating stress cycles imposed on it and these processes originate from the interactions among structural components in the material. The presence of point, line, and planar defects within a stressed material often causes the internal friction to occur because of the atomic movement, rearrangement, or realignment of the defects under the application of a stress. These techniques can be used to characterize types of structure defects. Figure 27 shows the temperature dependence of the internal friction IF=tanφ (Nowick & Berry. 1972) measured at 0.1 Hz during heating (heating rate 1 K/min.). Two peaks showing different intensities have been found: the weak low temperature peak (P1) and the more intense high temperature peak (P2). It can be seen that both peaks shift to a higher temperatures with increasing frequency, indicating that they may be relaxations peaks. The curves introduced in Fig. 27 were measured during one heating course in the multifrequent mode. The internal friction peaks are assumed to be imposed by a background IF b expressed by where k is the Boltzmann constant, T is the absolute temperature, A, B, and C b are constants. After subtracting the background by using a fitting program PeakFit, the peak temperature T P was estimated for the both relaxation peaks. The temperatures of both peaks estimated for various frequencies are given in Table 7. The peak widths are broader than that for a Debye peak, characterised by a single relaxation time. The internal friction peak appears at the condition ωτ = 1 (Nowick & Berry. 1972), with where ω is the angular frequency (= 2πf, f is the measuring frequency), τ is the mean relaxation time, τ 0 is the pre-exponential factor, and ΔH is the mean activation enthalpy.

Light Metal Alloys Applications 192
 is the angular frequency (= 2f, f is the measuring frequency),  is the mean relaxation time, 0 is the pre-exponential is the mean activation enthalpy.  29. Background subtracted low (a) and high (b) temperature peaks after a prestraining of 2.55%.
Low temperature peak 28 shows the semilogarithmic plot of the frequency versus reciprocal value of peaks temperatures TP (estimated fo so called Arrhenius plots. From the slope and intercept of the straight line, the mean activation enthalpy for th rature peak H has been obtained and its value is 1.160.05 eV. as the low temperature peak may have a dislocation nature, prestraining of the sample at low temperature should inf ight of the peak. Therefore, the samples were deformed by rolling. Deformation by rolling at room temperature (  es the strength of the low temperature peak, as it is obvious from Figure 29a (the peak was extracted from the in spectrum subtracting the background damping). However, the peak is stronger only in the first run after prestrain ond and third run, the height of the peak is approximately the same as in the as-prepared state, and the height is low first run. rain amplitude dependent component of the logarithmic decrement ( Figure 25a) indicates free dislocation loops al. IF peaks estimated in the second and third heating and cooling runs are practically the same. Beside this o tion population, the prestraining of the sample produced new dislocations which were practically completely rec the heating course of measurements. Owing to small grain size the grain boundaries were very probably the sources s of the newly created dislocations. As mentioned above, the dominant deformation mode in magnesium is the bas of a dislocations. The secondary conservative slip may be realised by motion of a dislocations on prismat idal planes of the first kind. Couret & Caillard (1984a,b) studied by TEM prismatic glide in magnesium over a rature range. They have reported that the screw dislocations with the Burgers vector of 1 / 3 1120     are able to gl tic planes and their mobility is much lower than the mobility of edge dislocations. The deformation is controlled lly activated glide of those screw dislocation segments. A single controlling mechanism has been identified as the F mechanism. This mechanism assumes a dissociated dislocation on a compact plane (0001) that joints together along a Lr producing double kinks on non-compact plane. Dislocations in very small grains are pinned at the grain boundari the reason why this dislocation population is so stable. On the other hand, the newly created dislocations during cold ly slightly pinned and they are recoverable during heating part of the measurement cycle.
High temperature peak gh temperature peak was observed at a temperature of ≈ 345 °C (0.5Hz). The cold prestraining of the sample did no ength of the high temperature peak, as it can be seen from Figure 29b. Position and height of the peak are very stable g as well as cooling. The activation energy was obtained from the frequency dependence of the peak temperature (Arr  Figure 28 shows the semilogarithmic plot of the frequency versus reciprocal value of peaks temperatures T P (estimated for both peaks) so called Arrhenius plots. From the slope and intercept of the straight line, the mean activation enthalpy for the low temperature peak ΔH has been obtained and its value is 1.16±0.05 eV.

Low temperature peak
As far as the low temperature peak may have a dislocation nature, prestraining of the sample at low temperature should influence the height of the peak. Therefore, the samples were deformed by rolling. Deformation by rolling at room temperature (ε ≈ 2.55%) increases the strength of the low temperature peak, as it is obvious from Figure 29a (the peak was extracted from the internal friction spectrum subtracting the background damping). However, the peak is stronger only in the first run after prestraining. In the second and third run, the height of the peak is approximately the same as in the as-prepared state, and the height is lower than in the first run.
The strain amplitude dependent component of the logarithmic decrement ( Figure 25a) indicates free dislocation loops in the material. IF peaks estimated in the second and third heating and cooling runs are practically the same. Beside this original dislocation population, the prestraining of the sample produced new dislocations which were practically completely recovered during the heating course of measurements. Owing to small grain size the grain boundaries were very probably the sources as well as sinks of the newly created dislocations. As mentioned above, the dominant deformation mode in magnesium is the basal slip; glide of <a> dislocations. The secondary conservative slip may be realised by motion of <a> dislocations on prismatic and pyramidal planes of the first kind. Couret & Caillard (1984a,b) studied by TEM prismatic glide in magnesium over a wide temperature range. They have reported that the screw dislocations with the Burgers vector of 1 / 3 112 0 are able to glide on prismatic planes and their mobility is much lower than the mobility of edge dislocations. The deformation is controlled by the thermally activated glide of those screw dislocation segments. A single controlling mechanism has been identified as the Friedel-Escaig mechanism. This mechanism assumes a dissociated dislocation on a compact plane (0001) that joints together along a critical length L r producing double kinks on non-compact plane. Dislocations in very small grains are pinned at the grain boundaries and this is the reason why this dislocation population is so stable. On the other hand, the newly created dislocations during cold rolling are only slightly pinned and they are recoverable during heating part of the measurement cycle.

High temperature peak
The high temperature peak was observed at a temperature of ≈ 345 °C (0.5Hz). The cold prestraining of the sample did not affect the strength of the high temperature peak, as it can be seen from Fig. 29b. Position and height of the peak are very stable during heating as well as cooling. The activation energy was obtained from the frequency dependence of the peak temperature (Arrhenius plot) to be 1.77±0.05 eV (see Figure 28).
The presence of the high temperature peak in magnesium has been reported by Kê (Kê, 1947). He described this peak as being related to the grain boundary relaxation.
Grain boundaries in materials with the small grain size contain a dense network of overlapping grain boundary dislocations. Grain boundary sliding is realized by the slip and climb (providing a maintenance of vacancy sources and sinks) of the grain boundary dislocations. Since both modes of the grain boundary dislocation motion must occur simultaneously, the slower one will control the grain boundary sliding. The climb mode involves jog formation and grain boundary diffusion and both modes of the grain boundary dislocation movement may be affected by the interaction of the grain boundary dislocations with impurities segregated in grain boundaries. According to Lakki et al. (1998) the activation energy for such process can be expressed as ΔH = ΔH j + ΔH GB , where ΔH j and ΔH GB are the activation enthalpies for the jog formation and the grain boundary diffusion, respectively. The activation enthalpy for grain boundary diffusion in the coarse grained magnesium is 0.95 eV (Frost & Ashby, 1982). Comparing with the estimated activation enthalpy value of 1.77 eV, the possible jog formation energy should be approximately 0.8 eV, which seems to be a reasonable value. Taking into consideration that the surface of grains was passivated during the milling by 1% of oxygen in a protective argon atmosphere; therefore, MgO particles in the grain boundaries may influence the grain boundary diffusion characteristics.