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Intergranular pressure solution in internally wetted polycrystals: Effect of additives
Materials Science and Engineering A 495 (2008) 132–137
Intergranular pressure solution in internally wetted polycrystals: Effect of additives V. Traskine ∗ , Z. Skvortsova, A. Muralev Laboratory of Physicochemical Mechanics, Department of Chemistry, Lomonossov University, 119992 Moscow, Russia Received 23 March 2007; received in revised form 18 September 2007; accepted 24 September 2007
Abstract Wetting of grain boundaries in polycrystalline materials leads to considerable changes in their physicochemical and mechanical properties. Under a constant compressive load, internally wetted materials display an enhanced deformability; creep rate increases sometimes by several orders of magnitude. The dominant creep mechanism is known as dissolution–precipitation or pressure solution; a stress-induced excessive chemical potential provides a driving force for dissolution of material within grain contacts, diffusion through the grain boundary solution film and re-precipitation elsewhere. Sensitivity of pressure solution rate to the chemical composition of the intergranular liquid was reported earlier, but the underlying mechanisms were poorly understood. In the present work, the creep experiments were carried out on poly- or monocrystalline sodium chloride in the presence of NaCl aqueous solution (pure or containing additives such as copper, magnesium and lead chlorides, K4 Fe(CN)6 and urea). In all cases, pressure solution has been shown to be the main deformation mechanism. Creep rate decreases in the presence of additives which are known to affect the dissolution and growth processes of sodium chloride or its concentration in the brine. Rate-limiting stage (dissolution or diffusion) in various environments has been identified. © 2008 Elsevier B.V. All rights reserved. Keywords: Grain boundary wetting; Pressure solution; Sodium chloride; Dissolution rate; Diffusion; Crystal growth
1. Introduction Grain boundary (GB) wetting in the polycrystalline material can lead to significant modification of its mechanical properties. Typically, liquid layers at GBs are responsible for strength decrease and loss of ductility, which can dramatically deteriorate the material (Al–Ga, Zn–Ga, Cu–Bi, NaCl–H2 O, etc.). However, an inverse response to internal wetting may also occur; there are a variety of situations in which GB-wetted materials can display an increased ductility. A striking example is given in [1]: a zinc strip, after being wetted with gallium and placed vertically into a beaker, bent under its own weight, forming two or three windings after about 2 weeks (thus the yield stress of zinc became as low as several hundredths of its initial value). Many other cases are familiar to geologists. So, rock salt containing brine layers at GBs, contrastingly to its extreme brittleness under tensile or shear impacts, is very ductile in the Earth crust under lithostatic
∗
Corresponding author. Tel.: +7 495 939 26 31; fax: +7 495 939 26 31. E-mail address: [email protected] (V. Traskine).
0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2007.09.088
load which gives rise to hat-, dome- and mushroom-like flexures. GB wetting and behavior of GB-wetted materials attract the growing attention of physicochemists, metallurgists and geologists. Nevertheless, the underlying mechanisms (especially the rheological constitutive laws) are still poorly understood. First of all, in some cases it is difficult to discriminate between the liquid-enhanced and liquid-independent deformation mechanisms. Furthermore, the effects of liquid media on crystals plasticity are numerous and depend on many parameters, the most important being the chemical nature of the components (determining solid–liquid interface energy γ(SL) and mutual solubility), the temperature and the stress state. Low values of γ(SL), intrinsic to GB-wetted polycrystals, may facilitate plastic deformation within the grains by lowering the surface barrier to dislocation glide [2] or by increasing the surface-tobulk vacancies flow [3]. If the solubility of solid material in the intergranular liquid is not negligible, then pressure solution, aka dissolution–precipitation creep, becomes the predominant deformation mechanism. For many years, an extensive evidence has accumulated which confirms the prevalence of this mechanism in nature.
V. Traskine et al. / Materials Science and Engineering A 495 (2008) 132–137
Therefore, the majority of works dealing with pressure solution are based on the analysis of field data or laboratory experiments on rocks and minerals (review in [4]). Other classes of materials were studied less extensively (e.g. metallic systems in [5]). The kinetics of dissolution and precipitation are extremely rapid in the NaCl–brine couple. For this reason, it became one of favorite objects for studying pressure solution [6,7], in particular as related to GB wetting in polycrystals [8,9]. Pressure solution is a complex physicochemical process driven by the stress-induced excessive chemical potential. It is achieved through a three-step process of dissolution of solid material at non-hydrostatically stressed sites, diffusion of solutes along the GBs or pore space and reprecipitation at stress-free or hydrostatically stressed sites [6,7,10,11]. The slowest of the three serial processes controls the overall deformation. The analysis of creep rate for the cases where the limiting stages are the dissolution rate (boundary regime) or the solute diffusion rate in the liquid interlayer (diffusion regime) results in the following expressions [10,12]. In the first case, the creep rate is expressed as ε˙ =
α1 κωCσ , RTd
(1)
whereas in the second case, as ε˙ =
α2 DωδCσ . RTd 3
(2)
Here, κ is the constant of dissolution rate; ω, C and D are the molar volume, concentration and diffusion coefficient of the solute, respectively; σ is the applied stress; d is a diffusion characteristic length (for polycrystals, it is assumed to be equal to the grain size); δ is the thickness of liquid interlayer; and α1 and α2 are the numerical coefficients slightly differing in different works. Dissolution and growth of crystals are well known to depend on the presence of impurities which can have a large effect on the limiting stage of these processes. Therefore, kinetics of pressure solution may also be expected to be sensitive to the chemical composition of the liquid phase. Indeed, such effects were reported earlier [13–15]. However, the atomic-scale mechanisms behind these effects are not known. In this work, pressure solution of NaCl crystals in the presence of impurities added to the brine is studied, and an attempt is made to interpret mechanisms of their influence. 2. Experimental Starting materials Analytical grade NaCl and KCl single crystals were grown from the melt. Cylindrical polycrystals of 4 mm in diameter were prepared by hot extrusion of NaCl and KCl single crystals at ∼600 or ∼500 ◦ C, respectively. After annealing at 450 ◦ C, average grain size was of 320 ± 30 m. Reagent grade urea and analytical grade potassium ferrocyanide, lead(II) chloride and cupric chloride were used as
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additives to the brine. All the solutions were brought to equilibrium with NaCl powder prior to experiments. 2.1. Experimental set-up 2.1.1. Compression of polycrystals Cylindrical polycrystalline samples of sodium or potassium chloride having the length of 15–20 mm were placed into an aqueous solution and uniaxially compressed under a static load ranging from 30 to 90 N. 2.1.2. Compression of piled single crystals NaCl monocrystalline samples (∼3 mm × 5 mm × 5 mm) were cleaved from a single crystal block and pressed together in piles of 3 crystals under a load ranging from 45 to 90 N. Crystalto-crystal contact area formed by squashed cleavage steps was measured on photographs as described in [16], and area vs. load dependence was established. Thereafter, another set of triple piles were precompressed under various loads, placed into aqueous solutions of NaCl, NaCl + urea or NaCl + K4 Fe(CN)6 and exposed to a compressive load of 45 N. 2.1.3. Indentation of single crystals NaCl single crystals were indented with a steel ball (4 mm diameter) under a load of 45 N in dry n-heptane, brine or NaCl + urea aqueous solutions. This technique makes it possible to apply a stress which smoothly decreases as the indenter penetrates the crystal [17]. In all experiments, the displacement was measured with an accuracy of ±1 m using the apparatus IZV-1. 3. Results and discussion 3.1. Effect of salt additives on pressure solution creep of NaCl Uniaxial loading of dry NaCl and KCl polycrystals (see Section 2.1.1) in air or inert medium (n-heptane) under loads up to 90 N (compressive stress of ≤7 MPa) produces no appreciable deformation. When tested in the saturated water solution at room temperature, prewetted salt samples exhibit measurable strain rates under low stresses (typically ∼10−8 s−1 at 3 MPa, which is in a good agreement with Eq. (2)). As shown earlier [14,18], the dominant mechanism of deformation of GB-wetted alkali halide polycrystals under such conditions is diffusion-controlled pressure solution creep. Arguments for this conclusion are: conformity of creep rate to Eq. (2) and closeness of activation energies of creep and diffusion in aqueous solution for each salt. Inorganic additives to NaCl solutions were chosen among the compounds which are known to be active or non-active as agents affecting NaCl crystals growth and dissolution [19]. Experiments were carried out under a load of 30 N. Despite an inevitable scatter from sample to sample which is usual for coarse grain polycrystals creep, the additive-induced changes in strain rate, at the steady state stage, were fairly reproducible. Typical fragments of strain vs. time plots are shown in Fig. 1.
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Fig. 1. Fragments of typical deformation plots for NaCl and KCl polycrystals in pure saturated water solutions (dark dots) and in the presence of additives (light dots) under a compressive load of 2.4 MPa. Concentration of additives: (a) 0.8, (b) 3, (c) 0.01, (d) 0.05, (e) and (f) 0.1 mol/l.
3.1.1. CuCl2 additives According to [19], the presence of Cu2+ ions does not affect the growth rate of NaCl at all. Our data also show the absence of any change in strain rate for the added CuCl2 concentrations up to 0.8 mol/l (Fig. 1a). 3.1.2. MgCl2 additives Creep rate of NaCl polycrystals in the presence of MgCl2 is significantly lower than without additives (Fig. 1b) and decreases to very low values with increasing MgCl2 concentration (Fig. 2a). The nature of this effect is likely to be clear, because adding MgCl2 is well known to salt out NaCl. Fig. 2b shows the same data plotted vs. NaCl content. A good linearity of the plot suggests that the pressure solution regime is diffusioncontrolled, strain rate being proportional to concentration in accordance with Eq. (2).
of NaCl is profound and manifold [19,20]. The growth rate as well as the dissolution rate are suppressed and the habit of the NaCl crystals changes with increasing amounts of cyanoferrate from cubic to a star-like (skeletal) growth. Significant changes in NaCl crystal growth morphology (from {1 0 0} towards {1 1 0}, {1 1 1} and {2 1 0} forms) were observed [21]. Dendritic growth was supposed to be caused by the strong adsorption of ferro-
3.1.3. PbCl2 additives Lead ions (0.01 mol/l) do not affect the steady state creep rate of sodium chloride, but produce a transient strain acceleration which starts immediately after adding PbCl2 and lasts for several hours (Fig. 1c). The increase in NaCl dissolution rate in the presence of PbCl2 reported in [19] cannot account for the observed acceleration because in the diffusion-controlled process creep rate should not be sensitive to increase in dissolution rate. More likely, the reason of strain acceleration is that sodium chloride content in its saturated Pb-containing solutions is higher than in the pure brine. Thus the crystal stress-induced dissolution in liquid interlayers should be enhanced during PbCl2 invasion, until the new equilibrium be attained. Indeed, NaCl solubility increase in mixed solutions (∼3 × 10−2 mol%) is comparable with stressinduced supersaturation C = C0 σω/RT ≈ 0.15 mol%. 3.1.4. K4 Fe(CN)6 additives Additives of 0.03–0.3 mol/l potassium cyanoferrate(II) slow down the creep of sodium chloride (Fig. 1d). It is well known that the influence of cyanoferrate(II) ions on the crystallization
Fig. 2. Creep rate of NaCl polycrystals in saturated NaCl solution with additives of MgCl2 as normalized to the creep rate of the additive-free solution, for various (a) MgCl2 and (b) NaCl concentrations. Compressive stress 2.4 MPa.
V. Traskine et al. / Materials Science and Engineering A 495 (2008) 132–137
cyanide anions on the faces of the growing salt crystals [22]. On the other hand, the [Fe(CN)]4− ion has the structure and dimensions of a hexachlorosodium [NaCl6 ]5− configuration in the NaCl lattice, and therefore the cyanoferrate(II) ion may as well pose as a NaCl nucleus in the supersaturated NaCl solution [23]. The size of such bloc nuclei is about 3000 pairs of NaCl ions per nucleus, so their diffusion coefficient should be 15–20 times lower than in pure NaCl solution. In an attempt to distinguish between adsorption- or diffusionbased mechanism of K4 Fe(CN)6 influence on NaCl pressure solution creep, we have used the experimental set-up described in Section 2.1.2. The constitutive laws for boundary- and diffusion-limited regimes (1) and (2) can be written, for this crystal-to-crystal contact geometry, as follows: dh = dt and dh = dt
4κCωF , RTA 4DCωFδ , RTβA2
(3)
(4)
where h is the height of the crystals pile, t is the time, F is the applied load, A is the total area of contacts, β is the mean contact anisotropy coefficient. The results given in Fig. 3 do not show any noticeable difference between logarithmic plot slopes for NaCl creep rate vs. contact area in pure brine (−2.01) and with K4 Fe(CN)6 additives (−2.03), which gives a support to the mechanism consisting in diffusion hindering due to large nuclei formation in the supersaturated NaCl solution. 3.2. Creep of NaCl in urea-containing solutions Urea is a widely known compound able to change NaCl crystals habit. Rom´e de l’Isle showed already in 1783 that octahedrons instead of normal cubes are formed, if rock salt is grown in the presence of urine. It was shown that formamide and urea stabilize the positively charged {1 1 1} NaCl faces by adsorption, due to amides molecular size as well as to specific charge distribution [24]. In the bulk of NaCl solutions urea is active too, forming complexes with Na+ ions [25]. Potassium chloride does
Fig. 4. Creep rate of NaCl polycrystals in saturated NaCl solution with additives of urea normalized to the creep rate of the additive-free solution, as a function of urea concentration. Compressive stress 2.4 MPa.
not exhibit any noticeable affinity to urea, neither in solid state, nor in solution. For these reasons, we made a study of NaCl and KCl rheological behavior in saturated solutions added with urea. NaCl (not KCl) polycrystals creep more slowly in urea solutions (Fig. 1e and f). Relative strain rate of NaCl falls sharply in diluted urea solutions and remains constant at higher urea contents (Fig. 4), unlike to the magnesium ions effect (Fig. 2a). It should be emphasized that NaCl solubility is known to decrease to very low values with increasing Mg+2 concentration, while it practically does not depend on the urea content. These data suggest that the coverage of NaCl surface with adsorbed urea molecules, rather than changes in diffusion rate are responsible for the effects observed. In principle, if the dissolution rate is much lower than diffusion rate, then boundary processes rather than diffusion may be expected to control the overall kinetics. The following results are likely to confirm the above assumption. 1. Activation energy EA for creep of NaCl polycrystals in ureaadded solutions grows higher at lower temperatures and decreases on heating, which is typical for change in creep regime from diffusion-controlled to dissolution-controlled mechanism (Fig. 5). This change is probably caused by urea desorption at higher temperatures. In this temperature range, the EA value of 21 ± 2 kJ/mol is close to EA for NaCl diffusion in bulk solution (19.5 kJ/mol) [26]. 2. The slope of logarithmic plots in Fig. 3 for piles of NaCl single crystals in the presence of urea is −1.04, which fits Eq. (3) describing the boundary-controlled regime. 3. Indentation technique (see Section 2.1.3) was applied to NaCl single crystals immersed in different media (Fig. 6). As found earlier, the constitutive law for diffusion-controlled regime (Eq. (2)) can be written as dh DCωFδ = , dt 2πr 2 RTh2
Fig. 3. Creep rate of piles of NaCl single crystals as a function of contact area in saturated NaCl solution (1) without additives and (2) containing 0.03 mol/l K4 Fe(CN)6 or (3) 3 mol/l urea. Applied compressive load 45 N.
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(5)
(h is the indentation depth, r is the indenter radius), whence h3 should change (and really does for the pure brine [17]) as a linear function of time. The constitutive law for the boundary
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controlled regime (1) becomes dh κCωF = , dt 2πrRTh
(6)
whence h2 should be a linear function of time. Indeed, the experimental data are well linearized in h2 vs. t coordinates (Fig. 7). 4. Conclusions
Fig. 5. Arrhenius plot for NaCl polycrystals creep in saturated water solution containing 3 mol/l urea. Compressive stress 3.6 MPa.
Fig. 6. Short term deformation curves for NaCl single crystals indented with a steel ball (diameter 4 mm) under a load of 45 N (1) in n-heptane and (2) saturated aqueous solution without additives and (3) containing 3 mol/l urea.
Surprisingly enough, very few works (if any) deal with a combined study of three important phenomena: GB wetting, dissolution–precipitation creep (pressure solution) and impurities effect on crystals dissolution and growth. In this paper, we have made such an attempt. Sodium chloride has been chosen because GB wetting in NaCl polycrystals was well documented earlier. A variety of creep tests have been used to characterize the response of GB-wetted NaCl to applied loads in the presence of certain impurities known as modifiers of dissolution or growth rate and geometry. Rheological behavior of wetted GBs, as well as crystal–crystal or crystal–indenter contacts, has been found to be extremely sensitive to the chemical composition of the liquid phase. Practically in all cases, the deformation is slowed down, which is consistent with the impeding effect of most impurities on dissolution and growth of crystals and on solute diffusion. In order to identify rate-limiting process, special experimental conditions have been created under which constitutive laws are different functions of contact area for different mechanisms. The results confirm once more that, over a wide range of conditions, the creep in such polyphase systems as internally wetted polycrystals, porous materials and powders is governed by the mass transfer across solid–liquid boundaries or within the bulk of solution. A possibility of using modifiers of dissolution or diffusion rate for controlling mechanical properties of internally wetted solids seems promising from the practical point of view and worth further studying. Acknowledgements Authors wish to express their gratitude to the Russian Foundation for Fundamental Investigations (grant no. 06-03-33106-a) for financial support. References
Fig. 7. Long term deformation curve for NaCl single crystals indented with a steel ball (diameter 4 mm) under a load of 45 N in a saturated aqueous solution containing 3 mol/l urea in h2 vs. t coordinates.
[1] V. Traskine, Yu. Goryunov, G. Den’shchikova, B. Summ, Fizikokhimicheskaya mekhanika materialov 6 (1965) 643–647 (in Russian). [2] E. Shchukin, V. Savenko, L. Kochanova, P. Rehbinder, Doklady Akademii Nauk USSR 200 (1971) 406–409 (in Russian). [3] E. Glikman, Yu. Goryunov, Izvestiya Vuzov, Fizika 5 (1976) 65–72 (in Russian). [4] Z. Skvortsova, Colloid J. 66 (2004) 3–15. [5] Ya. Geguzin, V. Kibets, Fizika metallov i metallovedenie 36 (1973) 1043–1050 (in Russian). [6] C.J. Spiers, P.M.T.M. Schutjens, R.H. Brzesowsky, in: R.J. Knipe, E.H. Rutter (Eds.), Deformation Mechanisms, Rheology and Tectonics, Utrecht, Geological Society. Special Publications, 1990, pp. 215–225. [7] J.L. Urai, C.J. Spiers, H.J. Zwart, G.S. Lister, Nature 324 (1986) 554–557.
V. Traskine et al. / Materials Science and Engineering A 495 (2008) 132–137 [8] Yu. Filimonov, V. Traskine, Z. Skvortsova, Geophys. Res. Abstr. 5 (2003), EAE03-A-13658. [9] Z. Skvortsova, V. Traskine, Geophys. Res. Abstr. (2004), EGU-04-A01997. [10] E.H. Rutter, J. Geol. Soc. 140 (1983) 725–740. [11] J.-P. Gratier, Bull. Soc. Geol. France 164 (1993) 267–287. [12] R. Raj, J. Geophys. Res. 87 (1982) 4731–4739. [13] A. Revil, Geophys. Res. Lett. 26 (1999) 255–260. [14] Z. Skvortsova, V. Traskine, L. Lopatina, N. Pertsov, Colloid J. 56 (1994) 226–228. [15] E. Shafarenko, E. Oksenkrug, M. Tavostin, Z. Skvortsova, V. Traskine, Gazovaya promyshlennost, sept (1999) 56–58 (in Russian). [16] Z. Skvortsova, I. Kasyanova, E. Porodenko, V. Traskine, Colloid J. 69 (2007) 643–646. [17] Z. Skvortsova, I. Kasyanova, V. Traskine, Colloid J. 65 (2003) 399–404.
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[18] V. Traskine, Z. Skvortsova, L. Barrallier, P. Volovitch, A. Pertsov, Defect Diffus. Forum 258–260 (2006) 409–414. [19] S. Al-Jibbouri, J. Ulrich, J. Cryst. Growth 234 (2002) 237–246. [20] C. Rodriguez-Navarro, L. Linares-Fernandez, E. Doehne, E. Sebastian, Growth 243 (2002) 503–516. [21] R. Boistelle, R. Kern, R. Weiss, C. R. Acad. Sci. 254 (1962) 1829. [22] R.K. Sapre, Indian J. Technol. 6 (1968) 219. [23] A. Glasner, M. Zidon, J. Cryst. Growth 21 (1974) 294–304. [24] N. Radenovi´c, W. van Enckevort, E. Vlieg, J. Cryst. Growth 263 (2004) 544–551. [25] K. Sulaymankulov, Carbamide Compounds with Inorganic Salts, Ilim, Frunze, 1971 (in Russian). [26] J. Kestin, H.E. Khalefa, R.J. Correia, J. Phys. Chem. Refer. Data 10 (1981) 71–87.
Intergranular pressure solution in internally wetted polycrystals: Effect of additives V. Traskine ∗ , Z. Skvortsova, A. Muralev Laboratory of Physicochemical Mechanics, Department of Chemistry, Lomonossov University, 119992 Moscow, Russia Received 23 March 2007; received in revised form 18 September 2007; accepted 24 September 2007
Abstract Wetting of grain boundaries in polycrystalline materials leads to considerable changes in their physicochemical and mechanical properties. Under a constant compressive load, internally wetted materials display an enhanced deformability; creep rate increases sometimes by several orders of magnitude. The dominant creep mechanism is known as dissolution–precipitation or pressure solution; a stress-induced excessive chemical potential provides a driving force for dissolution of material within grain contacts, diffusion through the grain boundary solution film and re-precipitation elsewhere. Sensitivity of pressure solution rate to the chemical composition of the intergranular liquid was reported earlier, but the underlying mechanisms were poorly understood. In the present work, the creep experiments were carried out on poly- or monocrystalline sodium chloride in the presence of NaCl aqueous solution (pure or containing additives such as copper, magnesium and lead chlorides, K4 Fe(CN)6 and urea). In all cases, pressure solution has been shown to be the main deformation mechanism. Creep rate decreases in the presence of additives which are known to affect the dissolution and growth processes of sodium chloride or its concentration in the brine. Rate-limiting stage (dissolution or diffusion) in various environments has been identified. © 2008 Elsevier B.V. All rights reserved. Keywords: Grain boundary wetting; Pressure solution; Sodium chloride; Dissolution rate; Diffusion; Crystal growth
1. Introduction Grain boundary (GB) wetting in the polycrystalline material can lead to significant modification of its mechanical properties. Typically, liquid layers at GBs are responsible for strength decrease and loss of ductility, which can dramatically deteriorate the material (Al–Ga, Zn–Ga, Cu–Bi, NaCl–H2 O, etc.). However, an inverse response to internal wetting may also occur; there are a variety of situations in which GB-wetted materials can display an increased ductility. A striking example is given in [1]: a zinc strip, after being wetted with gallium and placed vertically into a beaker, bent under its own weight, forming two or three windings after about 2 weeks (thus the yield stress of zinc became as low as several hundredths of its initial value). Many other cases are familiar to geologists. So, rock salt containing brine layers at GBs, contrastingly to its extreme brittleness under tensile or shear impacts, is very ductile in the Earth crust under lithostatic
∗
Corresponding author. Tel.: +7 495 939 26 31; fax: +7 495 939 26 31. E-mail address: [email protected] (V. Traskine).
0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2007.09.088
load which gives rise to hat-, dome- and mushroom-like flexures. GB wetting and behavior of GB-wetted materials attract the growing attention of physicochemists, metallurgists and geologists. Nevertheless, the underlying mechanisms (especially the rheological constitutive laws) are still poorly understood. First of all, in some cases it is difficult to discriminate between the liquid-enhanced and liquid-independent deformation mechanisms. Furthermore, the effects of liquid media on crystals plasticity are numerous and depend on many parameters, the most important being the chemical nature of the components (determining solid–liquid interface energy γ(SL) and mutual solubility), the temperature and the stress state. Low values of γ(SL), intrinsic to GB-wetted polycrystals, may facilitate plastic deformation within the grains by lowering the surface barrier to dislocation glide [2] or by increasing the surface-tobulk vacancies flow [3]. If the solubility of solid material in the intergranular liquid is not negligible, then pressure solution, aka dissolution–precipitation creep, becomes the predominant deformation mechanism. For many years, an extensive evidence has accumulated which confirms the prevalence of this mechanism in nature.
V. Traskine et al. / Materials Science and Engineering A 495 (2008) 132–137
Therefore, the majority of works dealing with pressure solution are based on the analysis of field data or laboratory experiments on rocks and minerals (review in [4]). Other classes of materials were studied less extensively (e.g. metallic systems in [5]). The kinetics of dissolution and precipitation are extremely rapid in the NaCl–brine couple. For this reason, it became one of favorite objects for studying pressure solution [6,7], in particular as related to GB wetting in polycrystals [8,9]. Pressure solution is a complex physicochemical process driven by the stress-induced excessive chemical potential. It is achieved through a three-step process of dissolution of solid material at non-hydrostatically stressed sites, diffusion of solutes along the GBs or pore space and reprecipitation at stress-free or hydrostatically stressed sites [6,7,10,11]. The slowest of the three serial processes controls the overall deformation. The analysis of creep rate for the cases where the limiting stages are the dissolution rate (boundary regime) or the solute diffusion rate in the liquid interlayer (diffusion regime) results in the following expressions [10,12]. In the first case, the creep rate is expressed as ε˙ =
α1 κωCσ , RTd
(1)
whereas in the second case, as ε˙ =
α2 DωδCσ . RTd 3
(2)
Here, κ is the constant of dissolution rate; ω, C and D are the molar volume, concentration and diffusion coefficient of the solute, respectively; σ is the applied stress; d is a diffusion characteristic length (for polycrystals, it is assumed to be equal to the grain size); δ is the thickness of liquid interlayer; and α1 and α2 are the numerical coefficients slightly differing in different works. Dissolution and growth of crystals are well known to depend on the presence of impurities which can have a large effect on the limiting stage of these processes. Therefore, kinetics of pressure solution may also be expected to be sensitive to the chemical composition of the liquid phase. Indeed, such effects were reported earlier [13–15]. However, the atomic-scale mechanisms behind these effects are not known. In this work, pressure solution of NaCl crystals in the presence of impurities added to the brine is studied, and an attempt is made to interpret mechanisms of their influence. 2. Experimental Starting materials Analytical grade NaCl and KCl single crystals were grown from the melt. Cylindrical polycrystals of 4 mm in diameter were prepared by hot extrusion of NaCl and KCl single crystals at ∼600 or ∼500 ◦ C, respectively. After annealing at 450 ◦ C, average grain size was of 320 ± 30 m. Reagent grade urea and analytical grade potassium ferrocyanide, lead(II) chloride and cupric chloride were used as
133
additives to the brine. All the solutions were brought to equilibrium with NaCl powder prior to experiments. 2.1. Experimental set-up 2.1.1. Compression of polycrystals Cylindrical polycrystalline samples of sodium or potassium chloride having the length of 15–20 mm were placed into an aqueous solution and uniaxially compressed under a static load ranging from 30 to 90 N. 2.1.2. Compression of piled single crystals NaCl monocrystalline samples (∼3 mm × 5 mm × 5 mm) were cleaved from a single crystal block and pressed together in piles of 3 crystals under a load ranging from 45 to 90 N. Crystalto-crystal contact area formed by squashed cleavage steps was measured on photographs as described in [16], and area vs. load dependence was established. Thereafter, another set of triple piles were precompressed under various loads, placed into aqueous solutions of NaCl, NaCl + urea or NaCl + K4 Fe(CN)6 and exposed to a compressive load of 45 N. 2.1.3. Indentation of single crystals NaCl single crystals were indented with a steel ball (4 mm diameter) under a load of 45 N in dry n-heptane, brine or NaCl + urea aqueous solutions. This technique makes it possible to apply a stress which smoothly decreases as the indenter penetrates the crystal [17]. In all experiments, the displacement was measured with an accuracy of ±1 m using the apparatus IZV-1. 3. Results and discussion 3.1. Effect of salt additives on pressure solution creep of NaCl Uniaxial loading of dry NaCl and KCl polycrystals (see Section 2.1.1) in air or inert medium (n-heptane) under loads up to 90 N (compressive stress of ≤7 MPa) produces no appreciable deformation. When tested in the saturated water solution at room temperature, prewetted salt samples exhibit measurable strain rates under low stresses (typically ∼10−8 s−1 at 3 MPa, which is in a good agreement with Eq. (2)). As shown earlier [14,18], the dominant mechanism of deformation of GB-wetted alkali halide polycrystals under such conditions is diffusion-controlled pressure solution creep. Arguments for this conclusion are: conformity of creep rate to Eq. (2) and closeness of activation energies of creep and diffusion in aqueous solution for each salt. Inorganic additives to NaCl solutions were chosen among the compounds which are known to be active or non-active as agents affecting NaCl crystals growth and dissolution [19]. Experiments were carried out under a load of 30 N. Despite an inevitable scatter from sample to sample which is usual for coarse grain polycrystals creep, the additive-induced changes in strain rate, at the steady state stage, were fairly reproducible. Typical fragments of strain vs. time plots are shown in Fig. 1.
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Fig. 1. Fragments of typical deformation plots for NaCl and KCl polycrystals in pure saturated water solutions (dark dots) and in the presence of additives (light dots) under a compressive load of 2.4 MPa. Concentration of additives: (a) 0.8, (b) 3, (c) 0.01, (d) 0.05, (e) and (f) 0.1 mol/l.
3.1.1. CuCl2 additives According to [19], the presence of Cu2+ ions does not affect the growth rate of NaCl at all. Our data also show the absence of any change in strain rate for the added CuCl2 concentrations up to 0.8 mol/l (Fig. 1a). 3.1.2. MgCl2 additives Creep rate of NaCl polycrystals in the presence of MgCl2 is significantly lower than without additives (Fig. 1b) and decreases to very low values with increasing MgCl2 concentration (Fig. 2a). The nature of this effect is likely to be clear, because adding MgCl2 is well known to salt out NaCl. Fig. 2b shows the same data plotted vs. NaCl content. A good linearity of the plot suggests that the pressure solution regime is diffusioncontrolled, strain rate being proportional to concentration in accordance with Eq. (2).
of NaCl is profound and manifold [19,20]. The growth rate as well as the dissolution rate are suppressed and the habit of the NaCl crystals changes with increasing amounts of cyanoferrate from cubic to a star-like (skeletal) growth. Significant changes in NaCl crystal growth morphology (from {1 0 0} towards {1 1 0}, {1 1 1} and {2 1 0} forms) were observed [21]. Dendritic growth was supposed to be caused by the strong adsorption of ferro-
3.1.3. PbCl2 additives Lead ions (0.01 mol/l) do not affect the steady state creep rate of sodium chloride, but produce a transient strain acceleration which starts immediately after adding PbCl2 and lasts for several hours (Fig. 1c). The increase in NaCl dissolution rate in the presence of PbCl2 reported in [19] cannot account for the observed acceleration because in the diffusion-controlled process creep rate should not be sensitive to increase in dissolution rate. More likely, the reason of strain acceleration is that sodium chloride content in its saturated Pb-containing solutions is higher than in the pure brine. Thus the crystal stress-induced dissolution in liquid interlayers should be enhanced during PbCl2 invasion, until the new equilibrium be attained. Indeed, NaCl solubility increase in mixed solutions (∼3 × 10−2 mol%) is comparable with stressinduced supersaturation C = C0 σω/RT ≈ 0.15 mol%. 3.1.4. K4 Fe(CN)6 additives Additives of 0.03–0.3 mol/l potassium cyanoferrate(II) slow down the creep of sodium chloride (Fig. 1d). It is well known that the influence of cyanoferrate(II) ions on the crystallization
Fig. 2. Creep rate of NaCl polycrystals in saturated NaCl solution with additives of MgCl2 as normalized to the creep rate of the additive-free solution, for various (a) MgCl2 and (b) NaCl concentrations. Compressive stress 2.4 MPa.
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cyanide anions on the faces of the growing salt crystals [22]. On the other hand, the [Fe(CN)]4− ion has the structure and dimensions of a hexachlorosodium [NaCl6 ]5− configuration in the NaCl lattice, and therefore the cyanoferrate(II) ion may as well pose as a NaCl nucleus in the supersaturated NaCl solution [23]. The size of such bloc nuclei is about 3000 pairs of NaCl ions per nucleus, so their diffusion coefficient should be 15–20 times lower than in pure NaCl solution. In an attempt to distinguish between adsorption- or diffusionbased mechanism of K4 Fe(CN)6 influence on NaCl pressure solution creep, we have used the experimental set-up described in Section 2.1.2. The constitutive laws for boundary- and diffusion-limited regimes (1) and (2) can be written, for this crystal-to-crystal contact geometry, as follows: dh = dt and dh = dt
4κCωF , RTA 4DCωFδ , RTβA2
(3)
(4)
where h is the height of the crystals pile, t is the time, F is the applied load, A is the total area of contacts, β is the mean contact anisotropy coefficient. The results given in Fig. 3 do not show any noticeable difference between logarithmic plot slopes for NaCl creep rate vs. contact area in pure brine (−2.01) and with K4 Fe(CN)6 additives (−2.03), which gives a support to the mechanism consisting in diffusion hindering due to large nuclei formation in the supersaturated NaCl solution. 3.2. Creep of NaCl in urea-containing solutions Urea is a widely known compound able to change NaCl crystals habit. Rom´e de l’Isle showed already in 1783 that octahedrons instead of normal cubes are formed, if rock salt is grown in the presence of urine. It was shown that formamide and urea stabilize the positively charged {1 1 1} NaCl faces by adsorption, due to amides molecular size as well as to specific charge distribution [24]. In the bulk of NaCl solutions urea is active too, forming complexes with Na+ ions [25]. Potassium chloride does
Fig. 4. Creep rate of NaCl polycrystals in saturated NaCl solution with additives of urea normalized to the creep rate of the additive-free solution, as a function of urea concentration. Compressive stress 2.4 MPa.
not exhibit any noticeable affinity to urea, neither in solid state, nor in solution. For these reasons, we made a study of NaCl and KCl rheological behavior in saturated solutions added with urea. NaCl (not KCl) polycrystals creep more slowly in urea solutions (Fig. 1e and f). Relative strain rate of NaCl falls sharply in diluted urea solutions and remains constant at higher urea contents (Fig. 4), unlike to the magnesium ions effect (Fig. 2a). It should be emphasized that NaCl solubility is known to decrease to very low values with increasing Mg+2 concentration, while it practically does not depend on the urea content. These data suggest that the coverage of NaCl surface with adsorbed urea molecules, rather than changes in diffusion rate are responsible for the effects observed. In principle, if the dissolution rate is much lower than diffusion rate, then boundary processes rather than diffusion may be expected to control the overall kinetics. The following results are likely to confirm the above assumption. 1. Activation energy EA for creep of NaCl polycrystals in ureaadded solutions grows higher at lower temperatures and decreases on heating, which is typical for change in creep regime from diffusion-controlled to dissolution-controlled mechanism (Fig. 5). This change is probably caused by urea desorption at higher temperatures. In this temperature range, the EA value of 21 ± 2 kJ/mol is close to EA for NaCl diffusion in bulk solution (19.5 kJ/mol) [26]. 2. The slope of logarithmic plots in Fig. 3 for piles of NaCl single crystals in the presence of urea is −1.04, which fits Eq. (3) describing the boundary-controlled regime. 3. Indentation technique (see Section 2.1.3) was applied to NaCl single crystals immersed in different media (Fig. 6). As found earlier, the constitutive law for diffusion-controlled regime (Eq. (2)) can be written as dh DCωFδ = , dt 2πr 2 RTh2
Fig. 3. Creep rate of piles of NaCl single crystals as a function of contact area in saturated NaCl solution (1) without additives and (2) containing 0.03 mol/l K4 Fe(CN)6 or (3) 3 mol/l urea. Applied compressive load 45 N.
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(5)
(h is the indentation depth, r is the indenter radius), whence h3 should change (and really does for the pure brine [17]) as a linear function of time. The constitutive law for the boundary
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controlled regime (1) becomes dh κCωF = , dt 2πrRTh
(6)
whence h2 should be a linear function of time. Indeed, the experimental data are well linearized in h2 vs. t coordinates (Fig. 7). 4. Conclusions
Fig. 5. Arrhenius plot for NaCl polycrystals creep in saturated water solution containing 3 mol/l urea. Compressive stress 3.6 MPa.
Fig. 6. Short term deformation curves for NaCl single crystals indented with a steel ball (diameter 4 mm) under a load of 45 N (1) in n-heptane and (2) saturated aqueous solution without additives and (3) containing 3 mol/l urea.
Surprisingly enough, very few works (if any) deal with a combined study of three important phenomena: GB wetting, dissolution–precipitation creep (pressure solution) and impurities effect on crystals dissolution and growth. In this paper, we have made such an attempt. Sodium chloride has been chosen because GB wetting in NaCl polycrystals was well documented earlier. A variety of creep tests have been used to characterize the response of GB-wetted NaCl to applied loads in the presence of certain impurities known as modifiers of dissolution or growth rate and geometry. Rheological behavior of wetted GBs, as well as crystal–crystal or crystal–indenter contacts, has been found to be extremely sensitive to the chemical composition of the liquid phase. Practically in all cases, the deformation is slowed down, which is consistent with the impeding effect of most impurities on dissolution and growth of crystals and on solute diffusion. In order to identify rate-limiting process, special experimental conditions have been created under which constitutive laws are different functions of contact area for different mechanisms. The results confirm once more that, over a wide range of conditions, the creep in such polyphase systems as internally wetted polycrystals, porous materials and powders is governed by the mass transfer across solid–liquid boundaries or within the bulk of solution. A possibility of using modifiers of dissolution or diffusion rate for controlling mechanical properties of internally wetted solids seems promising from the practical point of view and worth further studying. Acknowledgements Authors wish to express their gratitude to the Russian Foundation for Fundamental Investigations (grant no. 06-03-33106-a) for financial support. References
Fig. 7. Long term deformation curve for NaCl single crystals indented with a steel ball (diameter 4 mm) under a load of 45 N in a saturated aqueous solution containing 3 mol/l urea in h2 vs. t coordinates.
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