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A simultaneous deformation and diffusion experiment: Quantifying the role of deformation in enhancing metamorphic reactions
Earth and Planetary Science Letters 278 (2009) 386–394
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Earth and Planetary Science Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e p s l
A simultaneous deformation and diffusion experiment: Quantifying the role of deformation in enhancing metamorphic reactions F. Heidelbach a,⁎, M.P. Terry a,1, M. Bystricky b, C. Holzapfel c,2, C. McCammon a a b c
Bayerisches Geoinstitut, Universität Bayreuth, Bayreuth, Germany LMTG, Observatoire Midi-Pyrénées, Université de Toulouse, Toulouse, France Institut für Funktionswerkstoffe, Universität des Saarlandes, Saarbrücken, Germany
a r t i c l e
i n f o
Article history: Received 15 July 2008 Received in revised form 5 December 2008 Accepted 9 December 2008 Available online 24 January 2009 Editor: L. Stixrude Keywords: deformation diffusion experiments ferropericlase (Mg,Fe)O
a b s t r a c t The influence of concurrent plastic deformation on a continuous Fe–Mg exchange reaction in ferropericlase/ periclase was examined as a function of strain and changing microstructure in a torsion experiment performed at 300 MPa and 1523 K. The measured Fe–Mg interdiffusion coefficient increases non-linearly by a factor of 1.2 to 1.4 (depending on composition) with increasing shear strain (up to a γ of 5.2), strain rate (up to 2.9 × 10− 4 s− 1) and decreasing grain size (from 200 μm to 80 μm). The change in diffusion is attributed to the increase in density of large-angle (N 15°) grain boundaries, whereas both subgrain boundary density and dislocation density do not correlate well with the changing diffusion coefficients. The increased diffusivity due to grain boundary diffusion does not follow any of the proposed equations for combined volume and boundary diffusion, indicating that either the effect of grain boundary diffusion has been underestimated or that there is an additional effect on diffusivity due to intracrystalline deformation (movement of dislocations and/or point defects, grain boundary migration during dynamic recrystallization) even if there is no net stress or strain in the direction of diffusion. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Metamorphic rocks are the result of chemical reactions and element exchanges by diffusional processes in the solid state. The reactions are generally driven by changing temperature and pressure conditions which the rocks are subjected to by dynamic processes like mantle convection or subduction of lithospheric plates. Observations in metamorphic rocks show that these reactions often take place dynamically, i.e. while the material is deforming concurrently (e.g. Keller et al., 2006; Terry and Heidelbach, 2006). Traditionally however, diffusion coefficients are determined experimentally under static conditions, i.e. with no deviatoric stresses present (e.g. Holzapfel et al., 2003; Mackwell et al., 2005). Deformation studies on the other hand are normally carried out on materials that are in chemical equilibrium.
⁎ Corresponding author. Bayerisches Geoinstitut, Universität Bayreuth, Universitätsstrasse 30, D-95440 Bayreuth, Germany. Tel.: +49 921 553730; fax: +49 921 553769. E-mail addresses: [email protected] (F. Heidelbach), [email protected] (M.P. Terry), [email protected] (M. Bystricky), [email protected] (C. Holzapfel). 1 Present address: Department of Geology and Geological Engineering, South Dakota School of Mines and Technology, Rapid City, USA. 2 Present address: Firma Schleifring, München, Germany. 0012-821X/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2008.12.026
Very few studies have combined both experimental approaches (e.g. De Ronde et al., 2004), demonstrating that there may be large effects on diffusivity as well as rheology. The influence of reaction-induced stress and strain (via volume change) on diffusive behaviour has been demonstrated for reaction rims of enstatite (Milke et al., 2001; Abart et al., 2004). However, the quantification of the interplay between diffusion and rheology is often difficult due to the large number of variables. For the present experiment we chose therefore a continuous exchange reaction between ferropericlase (Mg,Fe)O and periclase MgO and subjected it to a simple shear deformation geometry to provide insights into the interplay between metamorphic reactions and deformation. The sample material was chosen for its simplicity (solely interdiffusion of Fe and Mg, cubic crystal structure with isotropic diffusion and no change in the crystal structure due to the varying chemistry), its well known deformation (e.g. Stretton et al., 2001; Yamazaki and Karato, 2002; Heidelbach et al., 2003; Long et al., 2006) and diffusion behaviour (e.g. Holzapfel et al., 2003; Yamazaki and Irifune, 2003; Mackwell et al., 2005; Demouchy et al., 2007). In order to single out the effect of a deforming polycrystal on the diffusion coefficient the geometry of the deformation experiment and diffusion direction was chosen such that there was no strain in the diffusion direction and the stress in that direction was (ideally) equal to the confining pressure during the experiment. Therefore the influence of length change of the
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material or directed stresses on the resulting diffusion profiles were kept to a minimum. 2. Experimental 2.1. Sample preparation The samples were synthesized from commercially available powders of MgO and Fe2O3. The pure MgO powder was hot pressed at 1300 °C and 300 MPa for 12 h producing a dense equigrained microstructure with an average grain size of about 25 μm. The ferropericlase with a composition (Mg0.6Fe0.4)O was produced by intimately mixing the correct proportions of MgO and Fe2O3 into a powder and baking it at 1300 °C and an oxygen fugacity fO2 of 10− 9 bar buffered by a gas stream of CO/CO2 for 12 h. The sintered material was ground afterwards and also hot pressed at 1300 °C and 300 MPa for 12 h. The resulting ferropericlase had a homogeneous composition of (Mg0.6Fe0.4)O and an average grain size of about 150 μm. Both hot pressed samples showed a porosity of less than 3%. 2.2. Deformation experiment For the deformation experiment cylinders of 5 mm length and 10 mm diameter of both periclase and ferropericlase were combined into one cylinder of 10 mm length and then assembled into the torsion sample setup of the Paterson deformation rig (Paterson and Olgaard, 2000) at ETH Zürich. The deformation experiment was carried out at 1300 °C and a confining pressure of 300 MPa with the sample enclosed in a Ni sleeve. In this geometry, the shear strain varies linearly from 0 in the center to the maximum shear strain on the outer edge of the sample. 2.3. Measurement of element distribution maps and analysis of diffusion profiles Compositional data and element distribution maps were collected using the JEOL 8500 electron microprobe at Bayerisches Geoinstitut using Fe and Mg oxides as standards, an accelerating voltage of 15 keV and a beam current of approximately 15 nA. Compositional data were obtained along 9 profiles normal to the interface between periclase and ferropericlase with 2 μm step size. The profiles were measured at different distances from the center of the sample (0.173, 0.860, 1.860, 2.360, 2.860, 3.360, 3.860, 4.360, and 4.949 mm) corresponding to different local shear strains in the ferropericlase. High-resolution element distribution maps were completed using beam currents of approximately 500 nA for Fe, Mg and Ni. Regions containing elevated counts of Ni as a result of diffusion of Ni from the jacket were avoided during collection of quantitative data. Consistent with an empirically derived expression given in a previous study about interdiffusion in ferropericlase for a similar composition range (Mackwell et al., 2005) the following equation was fitted to the diffusion profile data yielding a composition-dependent diffusion coefficient:
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2.4. Microstructural analysis with SEM-EBSD The deformed sample was photographed and then cut in half along the cylinder axis; the surface of one half was polished for microstructural analysis and electron microprobe measurements. A thin section was taken off the second half for Mössbauer spectroscopy measurements. The left over piece was polished tangentially from the edge such that a section containing the shear direction was produced for microstructural observation. Both pieces intended for microstructural analysis were ground and polished down to a grain size of 0.5 μm of the diamond polishing medium. In order to remove the surface layer damaged by normal polishing the samples were additionally polished with a high pH silica solution (40 nm particle size) for about 5 h. This last step in the surface preparation allows the collection of better orientation contrast images and electron backscattering patterns (EBSPs) in the SEM. Due to the etching effect of the silica solution a slight topography was also introduced into the surface, e.g. at grain boundaries, which had to be removed again for the microprobe measurements since it affected the quantitative corrections. Finally the sample was coated with about 3 nm of carbon for the SEM-EBSD measurement in order to reduce charging. For the microstructural analysis a Leo Gemini 1530 SEM with a Schottky emitter was employed. The accelerating voltage was set to 20 keV and the probe current was about 4 nA. EBSPs and orientation contrast images were collected with a camera and detector system supplied by HKL Technology® (now Oxford Instruments®). The automated analysis of the diffraction patterns was carried out with the software package Channel 5 by the same company. Automated EBSD scans with different resolutions (=step sizes) were performed on the longitudinal (containing the shear strain profile) and tangential section of the sample (see below). 2.5. Mössbauer spectroscopy Mössbauer spectroscopy was performed on the sample in order to assure that the oxygen fugacity was homogeneous throughout the sample and no Fe3+-containing oxides were precipitated during the experiment. On the thin section set aside for Mössbauer analysis the sample slice was mounted on a glass slide using Crystalbond™ and the thin section was ground and polished to a thickness of approximately 30 μm. Three regions in the ferropericlase 2–3 mm away from the ferropericlase-periclase interface were selected for study as follows (the approximate diameter of the region is given in parentheses): (1) close to the cylinder axis (600 μm); (2) approximately 1 mm from the surrounding Ni sleeve (400 μm); (3) immediately adjacent to the
1:17 D = D01 + D02 4 XFeO expð A4 XFeO Þ: In this equation D is the diffusion coefficient, D01 and D02 are empirical diffusion parameters from Mackwell et al. (2005), A is a constant and XFeO the iron oxide fraction. In the simulation a finite difference scheme with distance divided into steps of 1 μm, time divided into steps of 1 s, and a normalized concentration was used. Details of the fitting procedure are described in Holzapfel et al. (2003). The center profile was simulated very well by using this equation, whereas some slight inconsistencies exist for the profile at the edge, where shear strain is the highest. Also there are some small problems of fitting the profile near the periclase boundary since the model was developed based on the point defect structure of Fe-bearing ferropericlase.
Fig. 1. (a) Image of the sample after the experiment; Ni jacket encloses undeformed periclase (top) and deformed ferropericlase (bottom) indicating that strain is partitioned into the ferropericlase. (b) Image of a vertical section through the middle of the sample cylinder; scale bars are 5 mm.
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outer lines of α-Fe were obtained at room temperature. The spectra were fitted using the commercially available fitting program NORMOS written by R.A. Brand (distributed by Wissenschaftliche Elektronik GmbH, Germany). Spectra took one day each to collect. 3. Results 3.1. Mechanical data
Fig. 2. Stress–strain curve for the deformation experiment.
surrounding Ni sleeve (300 μm). Two of the selected regions were isolated using a “Medenbach” microscope drill, while the third region (directly adjacent to the Ni sleeve) could be removed without drilling. All three samples were removed and mounted on Mylar using clear nail varnish, and masked using a piece of 25 μm thick Ta foil (absorbs 99% of 14.4 keV gamma rays) drilled with a hole centred over the grain. The effective sample thickness was approximately 6 mg Fe/cm2. Mössbauer spectra were recorded at room temperature (293 K) in transmission mode on a constant acceleration Mössbauer spectrometer with a nominal 370 MBq 57Co high specific activity source in a 12 μm Rh matrix. The velocity scale was calibrated relative to 25 μm thick α-Fe foil using the positions certified for (former) National Bureau of Standards standard reference material no. 1541; line widths of 0.36 mm/s for the
In order to simulate deformation in combination with a cation exchange reaction, torsion experiments were used to produce a linear shear strain (γ) gradient from approximately 0 in the center of a cylindrical sample increasing outward to the edge of the sample. This geometry locally approximates simple shear deformation (Paterson and Olgaard, 2000). The juxtaposed cylinders of periclase (MgO) and of ferropericlase (Mg0.6Fe0.4O) were deformed at a shear strain rate 1.4 × 10− 4 s− 1 for 5.5 h which gave a maximum bulk shear strain of 2.7 at the edge of the sample cylinder. However, all of the strain was partitioned into ferropericlase (γ = 5.4) while the MgO was not deformed at all (Fig. 1). From Fig. 1a it appears that there is a small gradient of shear strain in the boundary region between the two materials. Microstructurally and texturally however (see below) there is a sharp boundary and no gradient is discernible such that a macroscopic strain gradient likely exists only in the Ni sleeve and not in the periclase/ferropericlase itself. The stress–strain curve (Fig. 2) shows that ferropericlase is rather weak under the experimental conditions and rapidly reaches a steady state flow after the yield point. 3.2. Element mapping and diffusion profiles The element map for iron shows a systematic broadening of the region affected by interdiffusion from the center (low strain) to the edge (high strain) of the sample (Fig. 3a). The diffusion profiles
Fig. 3. (a) Element distribution map of Fe normal to the interface between periclase (top) and ferropericlase (bottom) from the center (left) to the edge (right) of the sample. Map dimensions are 0.372 high by 5.3 mm long. White lines are the positions of the diffusion profiles normal to the interface. (b) Representative diffusion profiles determined by the electron microprobe. Note all measured Fe is assumed to be Fe2+.
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3.3. Microtextures
Fig. 4. Diffusion coefficients for different Fe contents as a function of shear strain.
become longer and the XFeO decreases for comparable distances in profiles toward the edge of the sample, shown in four representative profiles (Fig. 3b). The profiles indicate qualitatively that diffusion becomes faster and diffusion distances become longer towards the edge of the sample where shear strain is highest. The profiles are also distinctively asymmetric with the steeper side towards the periclase indicating that diffusion coefficients decrease significantly with lower iron content. Diffusion coefficients derived from the profiles at the center and close to the edge of the sample for compositions of XFeO = 0.1, 0.2 and 0.3 show a systematic nonlinear increase with increasing strain (Fig. 4). Values at the rim deviate by a factor between 1.2 and 1.4 (increasing with decreasing XFe) from those in the center.
The deformation of ferropericlase is characterized by a decrease in grain size from about 150 to 80 μm (Fig. 5). Microstructural mapping of a tangential section close to the edge of the sample (Fig. 6a) reveals an oblique grain shape preferred orientation (SPO) with the average long axis of the grain shape at about 45° to the shear plane and shear direction which is also discernible macroscopically (compare also to Fig. 1a). The boundary region between periclase and ferropericlase is marked by a sharp boundary in grain size throughout the sample (Fig. 5a, b), which coincides with the increase in Fe content (Fig. 5c, d). The crystallographic preferred orientation (CPO, Fig. 6b) shows an alignment of b110N in the shear direction and of {111} perpendicular to the shear plane indicating that deformation occurs in the dislocation creep regime. The b110N direction in the ferropericlase structure serves as Burgers vector for slip on the {100}, {110} and {111} slip planes (e.g. Yamazaki and Karato, 2002; Heidelbach et al., 2003). This CPO is therefore an indication for intracrystalline slip on the [110](111) slip system. In addition there is a texture component with a concentration of {100} oblique to the shear direction. This component also occurs in highly sheared rock salt (Armann et al., 2008) and has been interpreted as typical for grain growth. Fig. 7 shows maps of the microstructure reconstructed from detailed EBSD measurements (with a step size of 1.5 μm) covering a radial profile from the center of the sample cylinder (zero shear strain) to the edge (maximum shear strain) at four positions (γ = 0, 3.1, 4.4 and 5.1). The increase in grain/subgrain boundaries in ferropericlase can be easily recognized. The frequency of the occurrence of boundaries between neighboring points with misorientation angles ω between 1° and 15° (henceforth referred to as subgrain boundaries) and ω N 15° (henceforth referred to as grain boundaries) was measured as an area of boundaries per volume (Fig. 8). The frequency of grain boundaries
Fig. 5. Orientation contrast (OC) (a, b) and combined OC and Z contrast (c, d) images of the interface at the center (a, c) and edge (b, d) of the sample; increase in brightness in the lower part of c) and d) is due to increase in Fe content in ferropericlase.
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Fig. 6. a) EBSD orientation map of tangential section in ferropericlase (γ = 5) just below the interdiffusion region; area covers 1 mm2 and was measured with a step size of 5 μm; the shear sense is dextral; grain coloring is arbitrary according to orientation; grain (ω N 15°) and subgrain (15° N ω N 1°) boundaries are marked with black and white lines respectively; b) pole figures of magnesiowüstite from the same EBSD measurement; equal area projections are perpendicular to the shear plane (horizontal line, SP = pole to the shear plane) and containing the shear direction (SD); discrete orientation data were smoothed with a Gaussian of 15° FWHM (full width half maximum).
correlates well with the change in diffusion coefficient (Fig. 8a) suggesting that diffusion along grain boundaries has an effect on the overall diffusion coefficient. On the contrary there is no clear correlation with the frequency of subgrain boundaries (Fig. 8b). At low strains (between γ = 0 and γ = 3.1) there is a large increase in the frequency of subgrains (0.004 to ~ 0.0175 μm− 1) but no significant change in diffusion coefficient. At high strains on the other hand, a significant increase in diffusion coefficient is not accompanied by an increase in the density of subgrain boundaries (~ 0.021 μm− 1).
Speidel (1967), we calculated a log fO2 value of approximately −10.5, which is close to the Fe–FeO buffer at those conditions and approximately 4 log units below the Ni–NiO buffer. These results indicate that the Fe3+ concentration in ferropericlase remained close to the original value achieved during synthesis, and did not change during the course of the deformation experiment. 4. Discussion 4.1. Comparison of diffusion data with previous studies
3.4. Mössbauer spectroscopy The Mössbauer spectra taken from different regions of the ferropericlase are similar to each other (Fig. 9) and were fitted using a model reported in the literature to determine Fe3+/ΣFe (Dobson et al., 1998). All regions yielded a value in the range 4–6% Fe3+/ΣFe, showing that there was no gradient of fO2 in the sample. Using the data of
The diffusion coefficients measured in this study for practically undeformed ferropericlase (in the center of the torsion cylinder) can be directly compared to data published in the literature. The length scale of the diffusion profiles in the low shear strain region is on the order of the grain size so that these data are comparable to the single crystal data measured by Mackwell et al. (2005) under atmospheric
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Fig. 7. Detailed EBSD orientation maps for measurement of the frequency of grain and subgrain boundaries; from left to right the shear strain γ equals 0, 3.1, 4.4 and 5.1; maps were measured with a step size of 1.5 μm; small angle (1°b ω b 15°) boundaries in red, large angle (ω N 15°) boundaries in black; measurements with a low confidence index are shown as grey pixels.
pressure, different oxygen fugacities and temperatures between 1320 and 1400 °C. Entering our experimental conditions (temperature and oxygen fugacity) into their empirical relationship yields Fe–Mg interdiffusion coefficients which are 15% (XFeO = 0.1), 25% (XFeO = 0.2) and 33% (XFeO = 0.3) lower than our diffusion coefficients measured in the center of the torsion cylinder. While discrepancies of 15 to 20% could be explained by experimental errors in temperature, oxygen fugacity, time and/or composition, they cannot be due to the pressure difference in the experiments (1 atm vs. 0.3 GPa) since that would cause a much smaller change (less than one percent) and would also mean a decrease (instead of an increase) in interdiffusion coefficient with increasing pressure (Holzapfel et al., 2003). The difference in the diffusion coefficients can be explained by the grain boundaries that are still present even at low strains whereas Mackwell et al. (2005) performed their experiments on true single crystals. Based on this assumption, we used the volume diffusion coefficients extrapolated from their equation to estimate grain boundary diffusion coefficients via the equation DEff = DV + πδ/d DGB where DEff, DV and DGB are the effective, volume and grain boundary diffusion coefficients respectively, δ the grain boundary thickness and d the grain size (e.g. Van Orman et al., 2003). The resulting values for δD GB are approximately 0.3–1 × 10 − 19 (XFeO = 0.1), 2–3.5 × 10 − 19 (XFeO = 0.2) and 0.9–1.1 × 10− 18 (XFeO = 0.3) m3/s (Table 1); assuming a grain boundary thickness δ of about 1 nm grain boundary diffusion is 3 to 4 orders of magnitude faster than volume diffusion for the same Fe content. The variability of these values for each composition reflects the fact that the increase in DEff is not linear with increasing grain boundary density in our data (Fig. 8a).
The δDGB values can be compared with literature data for oxygen and magnesium grain boundary diffusion in MgO from Frost and Ashby (1982) and Van Orman et al. (2003). Frost and Ashby (1982) derived a boundary diffusion coefficient for oxygen from the MgO creep experiments of Passmore et al. (1966) yielding a δDGB value of 1.758 × 10− 23 m3/s. This is 3 to 4 orders of magnitude slower than the estimated Fe–Mg grain boundary interdiffusion rates in our sample. Comparison with the high pressure (25 GPa) and temperature (2273 K) data of Van Orman et al. (2003) requires extrapolation of our values using the pressure and temperature dependence of volume diffusion in ferropericlase (Holzapfel et al., 2003). This extrapolation results in δDGB values that are about 1 order of magnitude faster than at our experimental conditions, i.e. in the range between 10− 19 to 10− 17 m3/s. This in turn is about 1 to 2 orders of magnitude faster than the self diffusion values for magnesium in MgO boundaries measured by Van Orman et al. (2003). The faster boundary coefficients in our study are likely due to the increased point defect concentration that comes with the presence of iron in ferropericlase and also affects the grain boundary structure. In addition, the three studies are not directly comparable, since we measured concentration-driven Fe/Mg interdiffusion coefficients whereas the oxygen diffusion values of Frost and Ashby (1982) are derived from stress driven diffusion in deformation experiments and the values of Van Orman et al. (2003) are self diffusion coefficients. 4.2. The effect of deformation on diffusion coefficients The results of the combined deformation–diffusion experiment show that there is a clear increase in the Fe/Mg interdiffusion coefficient
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The correlation between diffusion coefficient increase and grain boundary density (which is equivalent to the inverse grain size) does not follow a linear trend as would be expected from theoretical considerations (e.g. Kaur et al., 1995). The plot of these parameters (Fig. 8a) rather indicates an exponential relationship, especially for high Fe contents. The number of data points here is quite small though, such that fitting an exponential equation is not warranted. Also, it is not clear if this strong increase is only an effect of the grain boundary density or if there is a second factor such as the strain or strain rate. Ruoff and Balluffi (Balluffi and Ruoff, 1962; Ruoff, 1967) have proposed a formulation for the influence of strain or strain rate
Fig. 8. Frequency of large angle (a; ω N 15°) and small angle (b; 1° b ω b 15°) grain boundaries with increasing shear strain as a function of diffusion coefficient for Fe in ferropericlase with different Fe content; values of shear strain are next to symbols.
with increasing shear strain. Since the torsion geometry approximates simple shear deformation on a local scale and the diffusion direction is perpendicular to the shear direction, deformation of the diffusion profiles themselves can be excluded as a reason for this change. In addition the stress in the diffusion direction is equal to the confining pressure so that it cannot be responsible for the observed effect on diffusion. The oxygen fugacity as determined indirectly by Mössbauer spectroscopy via the Fe3+ concentration remains constant throughout the shear strain profile and is therefore also excluded as an explanation. The only parameter showing a reasonable correlation with the change in diffusion coefficient with increasing strain is the density of large angle grain boundaries (Fig. 8) which enhances the importance of the faster grain boundary diffusion and therefore increases the bulk diffusivity in ferropericlase. Another possible explanation for the increased diffusivity could be pipe diffusion as a result of the increase in dislocation density likely to accompany deformation in the dislocation creep regime. Dislocation density is well correlated with stress. In dislocation creep described by a power law, the stresses in the torsion cylinder increase rather rapidly at the center and level out towards higher shear strains at the rim of the sample cylinder (Paterson and Olgaard, 2000). However, a different trend is observed for the change in diffusion coefficient, with a relatively small change at low shear strains and a rapid increase towards higher shear strains. Enhanced diffusion along dislocation lines appears therefore as an unlikely explanation for the observed change.
Fig. 9. Top: optical micrograph indicating the regions in ferropericlase that were studied using Mössbauer spectroscopy. The width of the sample is 10 mm. Bottom: room temperature Mössbauer spectra taken from each region. Absorption due to Fe3+ is shaded black.
F. Heidelbach et al. / Earth and Planetary Science Letters 278 (2009) 386–394 Table 1 Effective and grain boundary diffusion coefficients as a function of iron content and shear strain (DEff) (grain boundary density (δDGB)); DEff are derived from the experimental diffusion profiles and δDGB are estimated using the extrapolated DV values of Mackwell et al. (2005) (see text) Diffusion coefficient DEff [m2/s], δDGB [m3/s]
XFeO = 0.1
XFeO = 0.2
XFeO = 0.3
DEff (γ = 0.2) DEff (γ = 3.1) DEff (γ = 4.4) DEff (γ = 5.0) DV (extrapolated from Mackwell et al., 2005) δDGB (γ = 0.2) δDGB (γ = 3.1) δDGB (γ = 4.4) δDGB (γ = 5.0)
1.36 × 10− 14 1.42 × 10− 14 1.52 × 10− 14 2.04 × 10− 14 1.16 × 10− 14
5.38 × 10− 14 5.48 × 10− 14 6.00 × 10− 14 7.08 × 10− 14 4.02 × 10− 14
1.67 × 10− 13 1.70 × 10− 13 1.83 × 10− 13 2.09 × 10− 13 1.13 × 10− 13
3.35 × 10− 20 3.95 × 10− 20 4.73 × 10− 20 1.01 × 10− 19
2.31 × 10− 19 2.16 × 10− 19 2.57 × 10− 19 3.53 × 10− 19
9.31 × 10− 19 8.46 × 10− 19 9.20 × 10− 19 1.11 × 10− 18
on diffusion in metal alloys, which yields a linear (strain) or quadratic (strain rate) relationship depending on the diffusion mechanism (vacancy or pipe diffusion). Since vacancy diffusion appears to be the most likely bulk diffusion process in ferropericlase we should also find a linear dependance of the diffusion coefficient on strain. However, as shown in Fig. 4, this is clearly not the case. Also, the observed diffusion data cannot be explained by a combination of grain boundary diffusion and strain since both linear effects should again yield a linear dependency. A probable explanation for the nonlinear relationship between strain and the bulk diffusion coefficient is the migration of grain boundaries. There is evidence in metal alloys for two different mechanisms by which diffusivity may be enhanced by migrating grain boundaries. The first mechanism involves a higher diffusion coefficient (several orders of magnitude) in the moving grain boundary that is suggested to be the result of long-range atomic jumps in grain boundaries (Smidoda et al., 1978). This is not always the case; experimental results for several metal alloy systems show that the diffusion coefficients for static and migrating grain boundaries are similar within an order of magnitude (Zieba, 2003). The second mechanism involves a model with a fixed grain boundary diffusion coefficient (Ruoff and Balluffi, 1963) in which the effectiveness of boundary migration in enhancing diffusivity will depend upon the number of atoms visited by the migrating grain boundary. The model is described by the equation DT/D0T = 1 +gDB/D0T where DT is the bulk diffusivity, D0T is the lattice diffusion coefficient, DB is the grain boundary diffusion coefficient and g is the fraction of atoms swept by grain boundaries. In this model, as the velocity of grain boundaries increases so will the diffusivity by increasing the number of atoms visited by the grain boundary. Clearly, grain boundaries are mobile in the deforming part of our sample: the grain size reduction due to increasing deformation and dynamic recrystallization involves some grain boundary migration and, in the zone of the diffusion gradient, grain boundaries become increasingly mobile with increasing Fe content. The latter is nicely visible along the boundary between periclase and ferropericlase which coincides with a drastic increase in grain size throughout the diffusion profile (Fig. 5). However, it is very difficult to get an estimate of the grain boundary velocity in this region since it is relatively small and contains a gradient in composition. 5. Conclusions The results of this study show that deformation has an influence on the diffusion of atoms through a solid even if there is no net stress or strain in the direction of diffusion. The most likely cause for the observed increase in diffusion coefficients with strain is the increase in large angle grain boundaries which serve as pathways for grain boundary diffusion. This effect appears to be relatively small (a factor of 1.2 to 1.4 with decreasing Fe content), since the change in grain size
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between undeformed and deformed material was quite moderate in our case. However, the influence of grain boundaries on the overall diffusion coefficients will increase rather dramatically as a function of decreasing grain size. In addition, the small effect observed in this study already causes a significant increase in the diffusion length scale. The contribution of grain boundary diffusion will therefore be significant in regions of the Earth's Interior with small grain sizes, e.g. where phase transformations occur or where relatively high stresses cause a drastic grain refinement by dynamic recrystallization. This is most likely the case in the boundary regions, e.g. the transition zone between upper and lower mantle or the D" layer at the core mantle boundary. In order to characterize the diffusive behaviour in these regions it is likely not sufficient to rely solely on the volume diffusion properties (e.g. Holzapfel et al., 2003), since these will give only minimum estimates of diffusive exchange rates. The non-linear increase in the diffusion coefficient with increasing strain and grain boundary density in our experiment probably cannot be accounted for by these effects alone since theory predicts that they both have a linear relationship with diffusion. A possible explanation for the non-linearity may be the mobility of grain boundaries which causes an additional increase in diffusivity. It is clear from the microstructures in our sample that boundaries become increasingly mobile with higher Fe content. Since the interdiffusion region in our sample is rather narrow a quantification of the grain boundary velocity is not feasible. Acknowledgements We would like to thank H. Schulze for diligent sample preparation. The manuscript benefited from constructive reviews of James van Orman and an anonymous reviewer. FH gratefully acknowledges financial support through the EU Marie Curie research training network ‘c2c’ under contract MCRTN-CT-2006-035957. References Abart, R., Kunze, K., Milke, R., Sperb, R., Heinrich, W., 2004. Silicon and oxygen self diffusion in enstatite polycrystals: the Milke et al. (2001) rim growth experiments revisited. Contrib. Mineral. Petrol. 147, 633–646. Armann, M., Burlini, L., Kunze, K., Burg, J.-P., 2008. Changes in microstructure and CPO as a function of increasing shear strain — torsion experiments on synthetic rock salt. Geophys. Res. Abstr. 10, A–06920. Balluffi, R.W., Ruoff, A.L., 1962. Enhanced diffusion in metals during plastic deformation. Appl. Phys. Lett. 1, 59–60. Demouchy, S., Mackwell, S.J., Kohlstedt, D.L., 2007. Influence of hydrogen on Fe–Mg interdiffusion in (Mg,Fe)O and implications for Earth's lower mantle. Contrib. Mineral. Petrol. 154, 279–289. De Ronde, A.A., Heilbronner, R., Stünitz, H., Tullis, J., 2004. Spatial correlation of deformation and mineral reaction in experimentally deformed plagioclase–olivine aggregates. Tectonophysics 389, 93–109. Dobson, D.P., Cohen, N.S., Pankhurst, Q.A., Brodholt, J.P., 1998. A convenient method for measuring ferric iron in magnesiowüstite (MgO–Fe1 − xO). Am. Mineral. 83, 794–798. Frost, H.J., Ashby, M.F., 1982. Deformation-mechanism maps. The Plasticity and Creep of Metals and Ceramics. Pergamon, Oxford. 166 pp. Heidelbach, F., Stretton, I., Langenhorst, F., Mackwell, S., 2003. Fabric evolution during high shear-strain deformation of magnesiowüstite (Mg0.8Fe0.2O). J. Geophys. Res. B108, ECV4–1–14. Holzapfel, C., Rubie, D.C., Mackwell, S., Frost, D.J., 2003. Effect of pressure on Fe–Mg interdiffusion in (FexMg1 − x)O, ferropericlase. Phys. Earth Planet. Inter. 139, 21–34. Kaur, I., Mishin, Y., Gust, W., 1995. Fundamentals of grain and interphase boundary diffusion. Wiley, Chichester. 512 pp. Keller, L.M., Abart, R., Wirth, R., Schmid, D.W., Kunze, K., 2006. Enhanced mass transfer through short-circuit diffusion: Growth of garnet reaction rims at eclogite facies conditions. Am. Mineral. 91, 1024–1038. Long, M.D., Xiao, X., Jiang, Z., Evans, B., Karato, S.-i., 2006. Lattice preferred orientation in deformed polycrystalline (Mg,Fe)O and implications for seismic anisotropy in D". Phys. Earth Planet. Inter. 156, 75–88. Mackwell, S., Bystricky, M., Sproni, C., 2005. Fe–Mg interdiffusion in (Mg,Fe)O. Phys. Chem. Miner. 32, 418–425. Milke, R., Wiedenbeck, M., Heinrich, W., 2001. Grain boundary diffusion of Si, Mg, and O in enstatite reaction rims: a SIMS study using isotopically doped reactants. Contrib. Mineral. Petrol. 142, 15–26. Passmore, E.M., Duff, R.H., Vasilos, T., 1966. Creep of Dense, Polycrystalline Magnesium Oxide. J. Am. Ceram. Soc. 49, 594–600. Paterson, M.S., Olgaard, D.L., 2000. Rock deformation tests to large shear strains in torsion. J. Struct. Geol. 22, 1341–1358.
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Ruoff, A.L., 1967. Enhanced diffusion during plastic deformation by mechanical diffusion. J. Appl. Phys. 38, 3999–4003. Ruoff, A.L., Balluffi, R.W., 1963. Strain-enhanced diffusion in metals. II. Dislocation and grain-boundary short-circuiting models. J. Appl. Phys. 34, 1848–1853. Smidoda, K., Gottschalk, W., Gleiter, H., 1978. Diffusion in migrating interfaces. Acta Metall. 26, 1833–1836. Speidel, D.H., 1967. Phase equilibria in the system MgO–FeO–Fe2O3: the 1300 °C isothermal section and extrapolations to other temperatures. J. Am. Ceram. Soc. 50, 243–248. Stretton, I., Heidelbach, F., Mackwell, S., Langenhorst, F., 2001. Dislocation creep of magnesiowüstite. Earth Planet. Sci. Lett. 194, 229–240. Terry, M.P., Heidelbach, F., 2006. Deformation-enhanced metamorphic reactions and the rheology of high-pressure shear zones, Western Gneiss Region, Norway. J. Metamorph. Geol. 24, 3–18.
Van Orman, J.A., Fei, Y.W., Hauri, E.H., Wang, J.H., 2003. Diffusion in MgO at high pressures: constraints on deformation mechanisms and chemical transport at the core-mantle boundary. Geophys. Res. Lett. 30. doi:10.1029/2002GL016343. Yamazaki, D., Karato, S., 2002. Fabric development in (Mg,Fe)O during large strain, shear deformation: implications for seismic anisotropy in Earth's lower mantle. Phys. Earth Planet. Inter. 131, 251–267. Yamazaki, D., Irifune, T., 2003. Fe–Mg interdiffusion in magnesiowüstite up to 35 GPa. Earth Planet. Sci. Lett. 216, 301–311. Zieba, P., 2003. Diffusion along migrating grain boundaries. Interface Sci. 11, 51–58.
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Earth and Planetary Science Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e p s l
A simultaneous deformation and diffusion experiment: Quantifying the role of deformation in enhancing metamorphic reactions F. Heidelbach a,⁎, M.P. Terry a,1, M. Bystricky b, C. Holzapfel c,2, C. McCammon a a b c
Bayerisches Geoinstitut, Universität Bayreuth, Bayreuth, Germany LMTG, Observatoire Midi-Pyrénées, Université de Toulouse, Toulouse, France Institut für Funktionswerkstoffe, Universität des Saarlandes, Saarbrücken, Germany
a r t i c l e
i n f o
Article history: Received 15 July 2008 Received in revised form 5 December 2008 Accepted 9 December 2008 Available online 24 January 2009 Editor: L. Stixrude Keywords: deformation diffusion experiments ferropericlase (Mg,Fe)O
a b s t r a c t The influence of concurrent plastic deformation on a continuous Fe–Mg exchange reaction in ferropericlase/ periclase was examined as a function of strain and changing microstructure in a torsion experiment performed at 300 MPa and 1523 K. The measured Fe–Mg interdiffusion coefficient increases non-linearly by a factor of 1.2 to 1.4 (depending on composition) with increasing shear strain (up to a γ of 5.2), strain rate (up to 2.9 × 10− 4 s− 1) and decreasing grain size (from 200 μm to 80 μm). The change in diffusion is attributed to the increase in density of large-angle (N 15°) grain boundaries, whereas both subgrain boundary density and dislocation density do not correlate well with the changing diffusion coefficients. The increased diffusivity due to grain boundary diffusion does not follow any of the proposed equations for combined volume and boundary diffusion, indicating that either the effect of grain boundary diffusion has been underestimated or that there is an additional effect on diffusivity due to intracrystalline deformation (movement of dislocations and/or point defects, grain boundary migration during dynamic recrystallization) even if there is no net stress or strain in the direction of diffusion. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Metamorphic rocks are the result of chemical reactions and element exchanges by diffusional processes in the solid state. The reactions are generally driven by changing temperature and pressure conditions which the rocks are subjected to by dynamic processes like mantle convection or subduction of lithospheric plates. Observations in metamorphic rocks show that these reactions often take place dynamically, i.e. while the material is deforming concurrently (e.g. Keller et al., 2006; Terry and Heidelbach, 2006). Traditionally however, diffusion coefficients are determined experimentally under static conditions, i.e. with no deviatoric stresses present (e.g. Holzapfel et al., 2003; Mackwell et al., 2005). Deformation studies on the other hand are normally carried out on materials that are in chemical equilibrium.
⁎ Corresponding author. Bayerisches Geoinstitut, Universität Bayreuth, Universitätsstrasse 30, D-95440 Bayreuth, Germany. Tel.: +49 921 553730; fax: +49 921 553769. E-mail addresses: [email protected] (F. Heidelbach), [email protected] (M.P. Terry), [email protected] (M. Bystricky), [email protected] (C. Holzapfel). 1 Present address: Department of Geology and Geological Engineering, South Dakota School of Mines and Technology, Rapid City, USA. 2 Present address: Firma Schleifring, München, Germany. 0012-821X/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2008.12.026
Very few studies have combined both experimental approaches (e.g. De Ronde et al., 2004), demonstrating that there may be large effects on diffusivity as well as rheology. The influence of reaction-induced stress and strain (via volume change) on diffusive behaviour has been demonstrated for reaction rims of enstatite (Milke et al., 2001; Abart et al., 2004). However, the quantification of the interplay between diffusion and rheology is often difficult due to the large number of variables. For the present experiment we chose therefore a continuous exchange reaction between ferropericlase (Mg,Fe)O and periclase MgO and subjected it to a simple shear deformation geometry to provide insights into the interplay between metamorphic reactions and deformation. The sample material was chosen for its simplicity (solely interdiffusion of Fe and Mg, cubic crystal structure with isotropic diffusion and no change in the crystal structure due to the varying chemistry), its well known deformation (e.g. Stretton et al., 2001; Yamazaki and Karato, 2002; Heidelbach et al., 2003; Long et al., 2006) and diffusion behaviour (e.g. Holzapfel et al., 2003; Yamazaki and Irifune, 2003; Mackwell et al., 2005; Demouchy et al., 2007). In order to single out the effect of a deforming polycrystal on the diffusion coefficient the geometry of the deformation experiment and diffusion direction was chosen such that there was no strain in the diffusion direction and the stress in that direction was (ideally) equal to the confining pressure during the experiment. Therefore the influence of length change of the
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material or directed stresses on the resulting diffusion profiles were kept to a minimum. 2. Experimental 2.1. Sample preparation The samples were synthesized from commercially available powders of MgO and Fe2O3. The pure MgO powder was hot pressed at 1300 °C and 300 MPa for 12 h producing a dense equigrained microstructure with an average grain size of about 25 μm. The ferropericlase with a composition (Mg0.6Fe0.4)O was produced by intimately mixing the correct proportions of MgO and Fe2O3 into a powder and baking it at 1300 °C and an oxygen fugacity fO2 of 10− 9 bar buffered by a gas stream of CO/CO2 for 12 h. The sintered material was ground afterwards and also hot pressed at 1300 °C and 300 MPa for 12 h. The resulting ferropericlase had a homogeneous composition of (Mg0.6Fe0.4)O and an average grain size of about 150 μm. Both hot pressed samples showed a porosity of less than 3%. 2.2. Deformation experiment For the deformation experiment cylinders of 5 mm length and 10 mm diameter of both periclase and ferropericlase were combined into one cylinder of 10 mm length and then assembled into the torsion sample setup of the Paterson deformation rig (Paterson and Olgaard, 2000) at ETH Zürich. The deformation experiment was carried out at 1300 °C and a confining pressure of 300 MPa with the sample enclosed in a Ni sleeve. In this geometry, the shear strain varies linearly from 0 in the center to the maximum shear strain on the outer edge of the sample. 2.3. Measurement of element distribution maps and analysis of diffusion profiles Compositional data and element distribution maps were collected using the JEOL 8500 electron microprobe at Bayerisches Geoinstitut using Fe and Mg oxides as standards, an accelerating voltage of 15 keV and a beam current of approximately 15 nA. Compositional data were obtained along 9 profiles normal to the interface between periclase and ferropericlase with 2 μm step size. The profiles were measured at different distances from the center of the sample (0.173, 0.860, 1.860, 2.360, 2.860, 3.360, 3.860, 4.360, and 4.949 mm) corresponding to different local shear strains in the ferropericlase. High-resolution element distribution maps were completed using beam currents of approximately 500 nA for Fe, Mg and Ni. Regions containing elevated counts of Ni as a result of diffusion of Ni from the jacket were avoided during collection of quantitative data. Consistent with an empirically derived expression given in a previous study about interdiffusion in ferropericlase for a similar composition range (Mackwell et al., 2005) the following equation was fitted to the diffusion profile data yielding a composition-dependent diffusion coefficient:
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2.4. Microstructural analysis with SEM-EBSD The deformed sample was photographed and then cut in half along the cylinder axis; the surface of one half was polished for microstructural analysis and electron microprobe measurements. A thin section was taken off the second half for Mössbauer spectroscopy measurements. The left over piece was polished tangentially from the edge such that a section containing the shear direction was produced for microstructural observation. Both pieces intended for microstructural analysis were ground and polished down to a grain size of 0.5 μm of the diamond polishing medium. In order to remove the surface layer damaged by normal polishing the samples were additionally polished with a high pH silica solution (40 nm particle size) for about 5 h. This last step in the surface preparation allows the collection of better orientation contrast images and electron backscattering patterns (EBSPs) in the SEM. Due to the etching effect of the silica solution a slight topography was also introduced into the surface, e.g. at grain boundaries, which had to be removed again for the microprobe measurements since it affected the quantitative corrections. Finally the sample was coated with about 3 nm of carbon for the SEM-EBSD measurement in order to reduce charging. For the microstructural analysis a Leo Gemini 1530 SEM with a Schottky emitter was employed. The accelerating voltage was set to 20 keV and the probe current was about 4 nA. EBSPs and orientation contrast images were collected with a camera and detector system supplied by HKL Technology® (now Oxford Instruments®). The automated analysis of the diffraction patterns was carried out with the software package Channel 5 by the same company. Automated EBSD scans with different resolutions (=step sizes) were performed on the longitudinal (containing the shear strain profile) and tangential section of the sample (see below). 2.5. Mössbauer spectroscopy Mössbauer spectroscopy was performed on the sample in order to assure that the oxygen fugacity was homogeneous throughout the sample and no Fe3+-containing oxides were precipitated during the experiment. On the thin section set aside for Mössbauer analysis the sample slice was mounted on a glass slide using Crystalbond™ and the thin section was ground and polished to a thickness of approximately 30 μm. Three regions in the ferropericlase 2–3 mm away from the ferropericlase-periclase interface were selected for study as follows (the approximate diameter of the region is given in parentheses): (1) close to the cylinder axis (600 μm); (2) approximately 1 mm from the surrounding Ni sleeve (400 μm); (3) immediately adjacent to the
1:17 D = D01 + D02 4 XFeO expð A4 XFeO Þ: In this equation D is the diffusion coefficient, D01 and D02 are empirical diffusion parameters from Mackwell et al. (2005), A is a constant and XFeO the iron oxide fraction. In the simulation a finite difference scheme with distance divided into steps of 1 μm, time divided into steps of 1 s, and a normalized concentration was used. Details of the fitting procedure are described in Holzapfel et al. (2003). The center profile was simulated very well by using this equation, whereas some slight inconsistencies exist for the profile at the edge, where shear strain is the highest. Also there are some small problems of fitting the profile near the periclase boundary since the model was developed based on the point defect structure of Fe-bearing ferropericlase.
Fig. 1. (a) Image of the sample after the experiment; Ni jacket encloses undeformed periclase (top) and deformed ferropericlase (bottom) indicating that strain is partitioned into the ferropericlase. (b) Image of a vertical section through the middle of the sample cylinder; scale bars are 5 mm.
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outer lines of α-Fe were obtained at room temperature. The spectra were fitted using the commercially available fitting program NORMOS written by R.A. Brand (distributed by Wissenschaftliche Elektronik GmbH, Germany). Spectra took one day each to collect. 3. Results 3.1. Mechanical data
Fig. 2. Stress–strain curve for the deformation experiment.
surrounding Ni sleeve (300 μm). Two of the selected regions were isolated using a “Medenbach” microscope drill, while the third region (directly adjacent to the Ni sleeve) could be removed without drilling. All three samples were removed and mounted on Mylar using clear nail varnish, and masked using a piece of 25 μm thick Ta foil (absorbs 99% of 14.4 keV gamma rays) drilled with a hole centred over the grain. The effective sample thickness was approximately 6 mg Fe/cm2. Mössbauer spectra were recorded at room temperature (293 K) in transmission mode on a constant acceleration Mössbauer spectrometer with a nominal 370 MBq 57Co high specific activity source in a 12 μm Rh matrix. The velocity scale was calibrated relative to 25 μm thick α-Fe foil using the positions certified for (former) National Bureau of Standards standard reference material no. 1541; line widths of 0.36 mm/s for the
In order to simulate deformation in combination with a cation exchange reaction, torsion experiments were used to produce a linear shear strain (γ) gradient from approximately 0 in the center of a cylindrical sample increasing outward to the edge of the sample. This geometry locally approximates simple shear deformation (Paterson and Olgaard, 2000). The juxtaposed cylinders of periclase (MgO) and of ferropericlase (Mg0.6Fe0.4O) were deformed at a shear strain rate 1.4 × 10− 4 s− 1 for 5.5 h which gave a maximum bulk shear strain of 2.7 at the edge of the sample cylinder. However, all of the strain was partitioned into ferropericlase (γ = 5.4) while the MgO was not deformed at all (Fig. 1). From Fig. 1a it appears that there is a small gradient of shear strain in the boundary region between the two materials. Microstructurally and texturally however (see below) there is a sharp boundary and no gradient is discernible such that a macroscopic strain gradient likely exists only in the Ni sleeve and not in the periclase/ferropericlase itself. The stress–strain curve (Fig. 2) shows that ferropericlase is rather weak under the experimental conditions and rapidly reaches a steady state flow after the yield point. 3.2. Element mapping and diffusion profiles The element map for iron shows a systematic broadening of the region affected by interdiffusion from the center (low strain) to the edge (high strain) of the sample (Fig. 3a). The diffusion profiles
Fig. 3. (a) Element distribution map of Fe normal to the interface between periclase (top) and ferropericlase (bottom) from the center (left) to the edge (right) of the sample. Map dimensions are 0.372 high by 5.3 mm long. White lines are the positions of the diffusion profiles normal to the interface. (b) Representative diffusion profiles determined by the electron microprobe. Note all measured Fe is assumed to be Fe2+.
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3.3. Microtextures
Fig. 4. Diffusion coefficients for different Fe contents as a function of shear strain.
become longer and the XFeO decreases for comparable distances in profiles toward the edge of the sample, shown in four representative profiles (Fig. 3b). The profiles indicate qualitatively that diffusion becomes faster and diffusion distances become longer towards the edge of the sample where shear strain is highest. The profiles are also distinctively asymmetric with the steeper side towards the periclase indicating that diffusion coefficients decrease significantly with lower iron content. Diffusion coefficients derived from the profiles at the center and close to the edge of the sample for compositions of XFeO = 0.1, 0.2 and 0.3 show a systematic nonlinear increase with increasing strain (Fig. 4). Values at the rim deviate by a factor between 1.2 and 1.4 (increasing with decreasing XFe) from those in the center.
The deformation of ferropericlase is characterized by a decrease in grain size from about 150 to 80 μm (Fig. 5). Microstructural mapping of a tangential section close to the edge of the sample (Fig. 6a) reveals an oblique grain shape preferred orientation (SPO) with the average long axis of the grain shape at about 45° to the shear plane and shear direction which is also discernible macroscopically (compare also to Fig. 1a). The boundary region between periclase and ferropericlase is marked by a sharp boundary in grain size throughout the sample (Fig. 5a, b), which coincides with the increase in Fe content (Fig. 5c, d). The crystallographic preferred orientation (CPO, Fig. 6b) shows an alignment of b110N in the shear direction and of {111} perpendicular to the shear plane indicating that deformation occurs in the dislocation creep regime. The b110N direction in the ferropericlase structure serves as Burgers vector for slip on the {100}, {110} and {111} slip planes (e.g. Yamazaki and Karato, 2002; Heidelbach et al., 2003). This CPO is therefore an indication for intracrystalline slip on the [110](111) slip system. In addition there is a texture component with a concentration of {100} oblique to the shear direction. This component also occurs in highly sheared rock salt (Armann et al., 2008) and has been interpreted as typical for grain growth. Fig. 7 shows maps of the microstructure reconstructed from detailed EBSD measurements (with a step size of 1.5 μm) covering a radial profile from the center of the sample cylinder (zero shear strain) to the edge (maximum shear strain) at four positions (γ = 0, 3.1, 4.4 and 5.1). The increase in grain/subgrain boundaries in ferropericlase can be easily recognized. The frequency of the occurrence of boundaries between neighboring points with misorientation angles ω between 1° and 15° (henceforth referred to as subgrain boundaries) and ω N 15° (henceforth referred to as grain boundaries) was measured as an area of boundaries per volume (Fig. 8). The frequency of grain boundaries
Fig. 5. Orientation contrast (OC) (a, b) and combined OC and Z contrast (c, d) images of the interface at the center (a, c) and edge (b, d) of the sample; increase in brightness in the lower part of c) and d) is due to increase in Fe content in ferropericlase.
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Fig. 6. a) EBSD orientation map of tangential section in ferropericlase (γ = 5) just below the interdiffusion region; area covers 1 mm2 and was measured with a step size of 5 μm; the shear sense is dextral; grain coloring is arbitrary according to orientation; grain (ω N 15°) and subgrain (15° N ω N 1°) boundaries are marked with black and white lines respectively; b) pole figures of magnesiowüstite from the same EBSD measurement; equal area projections are perpendicular to the shear plane (horizontal line, SP = pole to the shear plane) and containing the shear direction (SD); discrete orientation data were smoothed with a Gaussian of 15° FWHM (full width half maximum).
correlates well with the change in diffusion coefficient (Fig. 8a) suggesting that diffusion along grain boundaries has an effect on the overall diffusion coefficient. On the contrary there is no clear correlation with the frequency of subgrain boundaries (Fig. 8b). At low strains (between γ = 0 and γ = 3.1) there is a large increase in the frequency of subgrains (0.004 to ~ 0.0175 μm− 1) but no significant change in diffusion coefficient. At high strains on the other hand, a significant increase in diffusion coefficient is not accompanied by an increase in the density of subgrain boundaries (~ 0.021 μm− 1).
Speidel (1967), we calculated a log fO2 value of approximately −10.5, which is close to the Fe–FeO buffer at those conditions and approximately 4 log units below the Ni–NiO buffer. These results indicate that the Fe3+ concentration in ferropericlase remained close to the original value achieved during synthesis, and did not change during the course of the deformation experiment. 4. Discussion 4.1. Comparison of diffusion data with previous studies
3.4. Mössbauer spectroscopy The Mössbauer spectra taken from different regions of the ferropericlase are similar to each other (Fig. 9) and were fitted using a model reported in the literature to determine Fe3+/ΣFe (Dobson et al., 1998). All regions yielded a value in the range 4–6% Fe3+/ΣFe, showing that there was no gradient of fO2 in the sample. Using the data of
The diffusion coefficients measured in this study for practically undeformed ferropericlase (in the center of the torsion cylinder) can be directly compared to data published in the literature. The length scale of the diffusion profiles in the low shear strain region is on the order of the grain size so that these data are comparable to the single crystal data measured by Mackwell et al. (2005) under atmospheric
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Fig. 7. Detailed EBSD orientation maps for measurement of the frequency of grain and subgrain boundaries; from left to right the shear strain γ equals 0, 3.1, 4.4 and 5.1; maps were measured with a step size of 1.5 μm; small angle (1°b ω b 15°) boundaries in red, large angle (ω N 15°) boundaries in black; measurements with a low confidence index are shown as grey pixels.
pressure, different oxygen fugacities and temperatures between 1320 and 1400 °C. Entering our experimental conditions (temperature and oxygen fugacity) into their empirical relationship yields Fe–Mg interdiffusion coefficients which are 15% (XFeO = 0.1), 25% (XFeO = 0.2) and 33% (XFeO = 0.3) lower than our diffusion coefficients measured in the center of the torsion cylinder. While discrepancies of 15 to 20% could be explained by experimental errors in temperature, oxygen fugacity, time and/or composition, they cannot be due to the pressure difference in the experiments (1 atm vs. 0.3 GPa) since that would cause a much smaller change (less than one percent) and would also mean a decrease (instead of an increase) in interdiffusion coefficient with increasing pressure (Holzapfel et al., 2003). The difference in the diffusion coefficients can be explained by the grain boundaries that are still present even at low strains whereas Mackwell et al. (2005) performed their experiments on true single crystals. Based on this assumption, we used the volume diffusion coefficients extrapolated from their equation to estimate grain boundary diffusion coefficients via the equation DEff = DV + πδ/d DGB where DEff, DV and DGB are the effective, volume and grain boundary diffusion coefficients respectively, δ the grain boundary thickness and d the grain size (e.g. Van Orman et al., 2003). The resulting values for δD GB are approximately 0.3–1 × 10 − 19 (XFeO = 0.1), 2–3.5 × 10 − 19 (XFeO = 0.2) and 0.9–1.1 × 10− 18 (XFeO = 0.3) m3/s (Table 1); assuming a grain boundary thickness δ of about 1 nm grain boundary diffusion is 3 to 4 orders of magnitude faster than volume diffusion for the same Fe content. The variability of these values for each composition reflects the fact that the increase in DEff is not linear with increasing grain boundary density in our data (Fig. 8a).
The δDGB values can be compared with literature data for oxygen and magnesium grain boundary diffusion in MgO from Frost and Ashby (1982) and Van Orman et al. (2003). Frost and Ashby (1982) derived a boundary diffusion coefficient for oxygen from the MgO creep experiments of Passmore et al. (1966) yielding a δDGB value of 1.758 × 10− 23 m3/s. This is 3 to 4 orders of magnitude slower than the estimated Fe–Mg grain boundary interdiffusion rates in our sample. Comparison with the high pressure (25 GPa) and temperature (2273 K) data of Van Orman et al. (2003) requires extrapolation of our values using the pressure and temperature dependence of volume diffusion in ferropericlase (Holzapfel et al., 2003). This extrapolation results in δDGB values that are about 1 order of magnitude faster than at our experimental conditions, i.e. in the range between 10− 19 to 10− 17 m3/s. This in turn is about 1 to 2 orders of magnitude faster than the self diffusion values for magnesium in MgO boundaries measured by Van Orman et al. (2003). The faster boundary coefficients in our study are likely due to the increased point defect concentration that comes with the presence of iron in ferropericlase and also affects the grain boundary structure. In addition, the three studies are not directly comparable, since we measured concentration-driven Fe/Mg interdiffusion coefficients whereas the oxygen diffusion values of Frost and Ashby (1982) are derived from stress driven diffusion in deformation experiments and the values of Van Orman et al. (2003) are self diffusion coefficients. 4.2. The effect of deformation on diffusion coefficients The results of the combined deformation–diffusion experiment show that there is a clear increase in the Fe/Mg interdiffusion coefficient
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The correlation between diffusion coefficient increase and grain boundary density (which is equivalent to the inverse grain size) does not follow a linear trend as would be expected from theoretical considerations (e.g. Kaur et al., 1995). The plot of these parameters (Fig. 8a) rather indicates an exponential relationship, especially for high Fe contents. The number of data points here is quite small though, such that fitting an exponential equation is not warranted. Also, it is not clear if this strong increase is only an effect of the grain boundary density or if there is a second factor such as the strain or strain rate. Ruoff and Balluffi (Balluffi and Ruoff, 1962; Ruoff, 1967) have proposed a formulation for the influence of strain or strain rate
Fig. 8. Frequency of large angle (a; ω N 15°) and small angle (b; 1° b ω b 15°) grain boundaries with increasing shear strain as a function of diffusion coefficient for Fe in ferropericlase with different Fe content; values of shear strain are next to symbols.
with increasing shear strain. Since the torsion geometry approximates simple shear deformation on a local scale and the diffusion direction is perpendicular to the shear direction, deformation of the diffusion profiles themselves can be excluded as a reason for this change. In addition the stress in the diffusion direction is equal to the confining pressure so that it cannot be responsible for the observed effect on diffusion. The oxygen fugacity as determined indirectly by Mössbauer spectroscopy via the Fe3+ concentration remains constant throughout the shear strain profile and is therefore also excluded as an explanation. The only parameter showing a reasonable correlation with the change in diffusion coefficient with increasing strain is the density of large angle grain boundaries (Fig. 8) which enhances the importance of the faster grain boundary diffusion and therefore increases the bulk diffusivity in ferropericlase. Another possible explanation for the increased diffusivity could be pipe diffusion as a result of the increase in dislocation density likely to accompany deformation in the dislocation creep regime. Dislocation density is well correlated with stress. In dislocation creep described by a power law, the stresses in the torsion cylinder increase rather rapidly at the center and level out towards higher shear strains at the rim of the sample cylinder (Paterson and Olgaard, 2000). However, a different trend is observed for the change in diffusion coefficient, with a relatively small change at low shear strains and a rapid increase towards higher shear strains. Enhanced diffusion along dislocation lines appears therefore as an unlikely explanation for the observed change.
Fig. 9. Top: optical micrograph indicating the regions in ferropericlase that were studied using Mössbauer spectroscopy. The width of the sample is 10 mm. Bottom: room temperature Mössbauer spectra taken from each region. Absorption due to Fe3+ is shaded black.
F. Heidelbach et al. / Earth and Planetary Science Letters 278 (2009) 386–394 Table 1 Effective and grain boundary diffusion coefficients as a function of iron content and shear strain (DEff) (grain boundary density (δDGB)); DEff are derived from the experimental diffusion profiles and δDGB are estimated using the extrapolated DV values of Mackwell et al. (2005) (see text) Diffusion coefficient DEff [m2/s], δDGB [m3/s]
XFeO = 0.1
XFeO = 0.2
XFeO = 0.3
DEff (γ = 0.2) DEff (γ = 3.1) DEff (γ = 4.4) DEff (γ = 5.0) DV (extrapolated from Mackwell et al., 2005) δDGB (γ = 0.2) δDGB (γ = 3.1) δDGB (γ = 4.4) δDGB (γ = 5.0)
1.36 × 10− 14 1.42 × 10− 14 1.52 × 10− 14 2.04 × 10− 14 1.16 × 10− 14
5.38 × 10− 14 5.48 × 10− 14 6.00 × 10− 14 7.08 × 10− 14 4.02 × 10− 14
1.67 × 10− 13 1.70 × 10− 13 1.83 × 10− 13 2.09 × 10− 13 1.13 × 10− 13
3.35 × 10− 20 3.95 × 10− 20 4.73 × 10− 20 1.01 × 10− 19
2.31 × 10− 19 2.16 × 10− 19 2.57 × 10− 19 3.53 × 10− 19
9.31 × 10− 19 8.46 × 10− 19 9.20 × 10− 19 1.11 × 10− 18
on diffusion in metal alloys, which yields a linear (strain) or quadratic (strain rate) relationship depending on the diffusion mechanism (vacancy or pipe diffusion). Since vacancy diffusion appears to be the most likely bulk diffusion process in ferropericlase we should also find a linear dependance of the diffusion coefficient on strain. However, as shown in Fig. 4, this is clearly not the case. Also, the observed diffusion data cannot be explained by a combination of grain boundary diffusion and strain since both linear effects should again yield a linear dependency. A probable explanation for the nonlinear relationship between strain and the bulk diffusion coefficient is the migration of grain boundaries. There is evidence in metal alloys for two different mechanisms by which diffusivity may be enhanced by migrating grain boundaries. The first mechanism involves a higher diffusion coefficient (several orders of magnitude) in the moving grain boundary that is suggested to be the result of long-range atomic jumps in grain boundaries (Smidoda et al., 1978). This is not always the case; experimental results for several metal alloy systems show that the diffusion coefficients for static and migrating grain boundaries are similar within an order of magnitude (Zieba, 2003). The second mechanism involves a model with a fixed grain boundary diffusion coefficient (Ruoff and Balluffi, 1963) in which the effectiveness of boundary migration in enhancing diffusivity will depend upon the number of atoms visited by the migrating grain boundary. The model is described by the equation DT/D0T = 1 +gDB/D0T where DT is the bulk diffusivity, D0T is the lattice diffusion coefficient, DB is the grain boundary diffusion coefficient and g is the fraction of atoms swept by grain boundaries. In this model, as the velocity of grain boundaries increases so will the diffusivity by increasing the number of atoms visited by the grain boundary. Clearly, grain boundaries are mobile in the deforming part of our sample: the grain size reduction due to increasing deformation and dynamic recrystallization involves some grain boundary migration and, in the zone of the diffusion gradient, grain boundaries become increasingly mobile with increasing Fe content. The latter is nicely visible along the boundary between periclase and ferropericlase which coincides with a drastic increase in grain size throughout the diffusion profile (Fig. 5). However, it is very difficult to get an estimate of the grain boundary velocity in this region since it is relatively small and contains a gradient in composition. 5. Conclusions The results of this study show that deformation has an influence on the diffusion of atoms through a solid even if there is no net stress or strain in the direction of diffusion. The most likely cause for the observed increase in diffusion coefficients with strain is the increase in large angle grain boundaries which serve as pathways for grain boundary diffusion. This effect appears to be relatively small (a factor of 1.2 to 1.4 with decreasing Fe content), since the change in grain size
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between undeformed and deformed material was quite moderate in our case. However, the influence of grain boundaries on the overall diffusion coefficients will increase rather dramatically as a function of decreasing grain size. In addition, the small effect observed in this study already causes a significant increase in the diffusion length scale. The contribution of grain boundary diffusion will therefore be significant in regions of the Earth's Interior with small grain sizes, e.g. where phase transformations occur or where relatively high stresses cause a drastic grain refinement by dynamic recrystallization. This is most likely the case in the boundary regions, e.g. the transition zone between upper and lower mantle or the D" layer at the core mantle boundary. In order to characterize the diffusive behaviour in these regions it is likely not sufficient to rely solely on the volume diffusion properties (e.g. Holzapfel et al., 2003), since these will give only minimum estimates of diffusive exchange rates. The non-linear increase in the diffusion coefficient with increasing strain and grain boundary density in our experiment probably cannot be accounted for by these effects alone since theory predicts that they both have a linear relationship with diffusion. A possible explanation for the non-linearity may be the mobility of grain boundaries which causes an additional increase in diffusivity. It is clear from the microstructures in our sample that boundaries become increasingly mobile with higher Fe content. Since the interdiffusion region in our sample is rather narrow a quantification of the grain boundary velocity is not feasible. Acknowledgements We would like to thank H. Schulze for diligent sample preparation. The manuscript benefited from constructive reviews of James van Orman and an anonymous reviewer. FH gratefully acknowledges financial support through the EU Marie Curie research training network ‘c2c’ under contract MCRTN-CT-2006-035957. References Abart, R., Kunze, K., Milke, R., Sperb, R., Heinrich, W., 2004. Silicon and oxygen self diffusion in enstatite polycrystals: the Milke et al. (2001) rim growth experiments revisited. Contrib. Mineral. Petrol. 147, 633–646. Armann, M., Burlini, L., Kunze, K., Burg, J.-P., 2008. Changes in microstructure and CPO as a function of increasing shear strain — torsion experiments on synthetic rock salt. Geophys. Res. Abstr. 10, A–06920. Balluffi, R.W., Ruoff, A.L., 1962. Enhanced diffusion in metals during plastic deformation. Appl. Phys. Lett. 1, 59–60. Demouchy, S., Mackwell, S.J., Kohlstedt, D.L., 2007. Influence of hydrogen on Fe–Mg interdiffusion in (Mg,Fe)O and implications for Earth's lower mantle. Contrib. Mineral. Petrol. 154, 279–289. De Ronde, A.A., Heilbronner, R., Stünitz, H., Tullis, J., 2004. Spatial correlation of deformation and mineral reaction in experimentally deformed plagioclase–olivine aggregates. Tectonophysics 389, 93–109. Dobson, D.P., Cohen, N.S., Pankhurst, Q.A., Brodholt, J.P., 1998. A convenient method for measuring ferric iron in magnesiowüstite (MgO–Fe1 − xO). Am. Mineral. 83, 794–798. Frost, H.J., Ashby, M.F., 1982. Deformation-mechanism maps. The Plasticity and Creep of Metals and Ceramics. Pergamon, Oxford. 166 pp. Heidelbach, F., Stretton, I., Langenhorst, F., Mackwell, S., 2003. Fabric evolution during high shear-strain deformation of magnesiowüstite (Mg0.8Fe0.2O). J. Geophys. Res. B108, ECV4–1–14. Holzapfel, C., Rubie, D.C., Mackwell, S., Frost, D.J., 2003. Effect of pressure on Fe–Mg interdiffusion in (FexMg1 − x)O, ferropericlase. Phys. Earth Planet. Inter. 139, 21–34. Kaur, I., Mishin, Y., Gust, W., 1995. Fundamentals of grain and interphase boundary diffusion. Wiley, Chichester. 512 pp. Keller, L.M., Abart, R., Wirth, R., Schmid, D.W., Kunze, K., 2006. Enhanced mass transfer through short-circuit diffusion: Growth of garnet reaction rims at eclogite facies conditions. Am. Mineral. 91, 1024–1038. Long, M.D., Xiao, X., Jiang, Z., Evans, B., Karato, S.-i., 2006. Lattice preferred orientation in deformed polycrystalline (Mg,Fe)O and implications for seismic anisotropy in D". Phys. Earth Planet. Inter. 156, 75–88. Mackwell, S., Bystricky, M., Sproni, C., 2005. Fe–Mg interdiffusion in (Mg,Fe)O. Phys. Chem. Miner. 32, 418–425. Milke, R., Wiedenbeck, M., Heinrich, W., 2001. Grain boundary diffusion of Si, Mg, and O in enstatite reaction rims: a SIMS study using isotopically doped reactants. Contrib. Mineral. Petrol. 142, 15–26. Passmore, E.M., Duff, R.H., Vasilos, T., 1966. Creep of Dense, Polycrystalline Magnesium Oxide. J. Am. Ceram. Soc. 49, 594–600. Paterson, M.S., Olgaard, D.L., 2000. Rock deformation tests to large shear strains in torsion. J. Struct. Geol. 22, 1341–1358.
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