ISSN 1061-933X, Colloid Journal, 2007, Vol. 69, No. 5, pp. 643–646. © Pleiades Publishing, Ltd., 2007. Original Russian Text © Z.N. Skvortsova, I.V. Kas’yanova, E.V. Porodenko, V.Yu. Traskine, 2007, published in Kolloidnyi Zhurnal, 2007, Vol. 69, No. 5, pp. 684–687.
Deformation at the Contacts of Sodium Chloride Crystals in the Presence of Water Z. N. Skvortsova, I. V. Kas’yanova, E. V. Porodenko, and V. Yu. Traskine Department of Chemistry, Moscow State University, Vorob’evy gory, Moscow, 119992 Russia Received November 2, 2006
Abstract—The processes taking place at the intergrain contacts during powder pressing in dissolving media are studied. The threshold stress corresponding to a change in the mechanism (the transition from the dislocation glide to the recrystallization creep) of sodium chloride deformation in the presence of its saturated aqueous solution is determined. An equation is proposed for describing the variations in the compaction rate of powders in the course of their deformation. DOI: 10.1134/S1061933X0705016X
INTRODUCTION The deformation of solids under the influence of liquid media can be facilitated by an accelerated mass transfer through the liquid phase along the gradients of applied stresses. This process, which is, as a rule, accompanied by matter reprecipitation at unstressed sites, is denoted as the recrystallization creep (pressure solution or dissolution–precipitation creep). The rheological characteristics of solids deformed under such conditions have been studied intensively throughout recent decades, mainly as applied to tectonic, metamorphic, and technogenic processes that occur in the Earth’s crust. Sodium chloride, which is widely distributed in nature and represents a convenient model material, is a common object of investigations [1, 2]. In some works (for example, see [3]), the pressing of NaCl powders in saturated aqueous solutions, which provides for rather a high deformation rate and allows one to model the processes of salt seam formation, is used as a test method. However, the uncertain geometry of grain contacts and porous space, together with the possibility of the realization of other deformation and fracture mechanisms make the obtained results difficult to interpret. The aim of this work is to determine the conditions under which the dissolution–precipitation creep becomes a predominant mechanism of sodium chloride powder compaction in the presence of water, as well as to describe the process quantitatively. EXPERIMENTAL Uniaxial Compression of Single Crystals Contacting along Cleavage Planes When studying the processes accompanying powder pressing, it is rather difficult to estimate the area of
interparticle contacts, which determine the real stress values. To solve this problem, a method was developed for studying the deformation at the contacts of sodium chloride single crystals. Single crystal prisms of sodium chloride approximately 2.5 mm high with a square base area of 15−25 mm2 were cut out from large single crystals along the cleavage plane. The profilometric measurements showed that the sample surface had a characteristic stepped relief with an average cleavage step height of 30 µm. The prisms were placed between two single crystals of larger sizes with a turn around their vertical axes by 45° to avoid their coalescence. The whole system was then exposed to a constant load from 10 to 90 N in either a dry heptane or a saturated aqueous NaCl solution (Fig. 1). The shift ∆h of the upper support under load F was measured with an accuracy of 1 µm as depending on time t using an IZV-1 instrument. The contacts were flattened (the average height of the steps decreased, and the contact area enlarged) over the initial 24 h; in the absence of water, deformation ceased following this step, while in a saturated solution, it continued at a constant, although much lower, rate. When a fixed load was applied, the deformation rate at the stage of the steady state creep was virtually independent from the average crystal size, i.e., macroscopic contact area S. An analogous effect was found also in [4]. As an explanation, the authors [4] proposed a complex scheme of passage between diffusion and kinetic modes of mass transfer through the solution, with no account for the fact that crystal size does not necessarily determine the real contact area. In order to establish the dependence of real final contact area Ä on the applied load, we performed a special series of experiments. A drop of Quintol glue was placed in air into a gap between the single crystals prior to loading. Over a
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Adobe Photoshop software package. The contact area was found to be directly proportional to the applied load with a proportionality coefficient of ≈0.05 MPa–1.
F
1 (a) 3 2 (100) (b)
Fig. 1. Schematic representation of the uniaxial loading of a system of single crystals: (a) side view and (b) top view; (1) and (2) Vaseline oil and a glue protecting the upper and lower contacts from (3) NaCl aqueous solution.
period of 24 h, the glue hardened, after which the crystals were dissolved in water and the film was studied under a microscope. The size of holes corresponding to the sites of the direct contact between crystals were determined from photographs of the films using the
ε, % 10
Powder Pressing Wetted sodium chloride powders (a particle size of 120–200 µm) with a water content of about 20 wt %, which corresponded to the complete filling of the porous space, were pressed in a cylindrical matrix with a channel diameter of 12 mm. The height h0 of a powder column before pressing was approximately 20 mm. The powders were pressed in the two following modes: (1) with a stepwise increase in the load on the die from 3 to 45 N and (2) with a stepwise decrease in the load after a sample was exposed to a load of 45 N for 24 h, which provided the relative deformation ε = –∆h/h0 ≈ 0.1. In the experiments of the first series, each increase in the load caused rapid deformation followed by a stage of steady-state creep (Fig. 2). At this stage, the deformation rate decreased as the load was increased (Fig. 3, curve 1). In the experiments of the second series, a constant creep rate was immediately established after each reduction in the load that remained unchanged for a long time. In this case, the creep rate was directly proportional to the load (Fig. 3, curve 2). RESULTS AND DISCUSSION It is evident that at the first stage of the deformation of single crystals and powders of NaCl that occur almost identically in different media, well studied dislocation mechanisms of plastic flow are realized. This is possible when stresses exceed the yield stress ê* of a deformation-hardened material, the values of which are known to be close to 20 MPa [5], i.e., near the value
5 ε × 106, s–1 3
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Fig. 2. Typical deformation curves resultant from powder pressing in the increasing pressure mode: pressing stress P = (1) 0.2, (2) 0.6, (3) 1.0, (4) 1.4, and (5) 2.3 MPa.
0
0
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Fig. 3. Deformation rate of a wetted NaCl powder vs. load F curves measured in the modes of a stepwise (1) increase and (2) decrease in the load. COLLOID JOURNAL
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found for single crystals. In other words, the deformation of single crystals in a nondissolving medium must stop when the contact area increases to Ä = F/P*. Therefore, the experiments were carried out in two stages as described: first, a preset contact area between single crystals was formed during their 24 h exposure to load F1, and, second, the samples were tested in the presence of a saturated aqueous NaCl solution under another load F2 ≤ F1, i.e., at a known real stress of P = F2/A. The pattern of the deformation curves and the order of creep rate magnitude (several µm/day) indicate that the deformation is realized via the dissolution–precipitation creep mechanism. This is corroborated by calculations analogous to those described in [6] for another test method (the impression of a spherical indenter on NaCl single crystals). It can be shown that the deformation, the rate of which is limited by diffusion or dissolution, must obey the following relations, 4Dc 0 ωFδ dh ------ = ----------------------2 dt RTα A
(1)
κc 0 ωF dh ------ = ----------------, 2RTA dt
(2)
or
respectively, where D and Ò0 are the diffusion coefficient and solubility of the salt in water, respectively; ω is the molar volume of the salt; δ is the average thickness of a liquid interlayer; κ is the dissolution rate constant; α < 1 is the average coefficient of anisometry in the contacts; R is the gas constant; and T is temperature. Experimental data processing in logarithmic coordinates confirms that the dh/dt and A–2 values are proportionally related to each other (the correlation coefficient is 0.99) (Fig. 4). The line slope and the proportionality coefficient are of –2.02 and 1.4 × 10–22 m5/s, respectively. Substituting D = 1.3 × 10–9 m2/s [7] and δ = 10–7 m [1, 8] into Eq. (1), we obtain a close value of the coefficient (about 10–22 m5/s with deviations within one order of magnitude depending on the α values) for a load of F = 45 N; this suggests that the dissolution–precipitation creep is realized in the diffusion mode, when the system of single crystals is deformed. Different patterns of the dependences of NaCl powder deformation on a load imposed under the regimes of stepwise increase and decrease (Fig. 3) are well explained within the framework of the scheme used to analyze the deformation of a system of single crystals. Let us assume that the response to the increase in the load is the rapid enlargement of the intergrain contact areas, which takes place until the stress at the contacts decreases to the yield stress of the salt (in the first series at the onset of each test cycle, though only at the beginning of the experiment in the second series). In the first COLLOID JOURNAL
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log(dh/dt) [µm/min] –2.4
–2.8
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0.4 0.5 logA [mm2]
Fig. 4. Deformation rate of a system of NaCl single crystals vs. contact area A in the presence of a saturated aqueous NaCl solution.
series, the real stress appears to be constant and equal to the yield stress, while the diffusion path elongates from one cycle to another. In the second series, the stress decreases from one cycle to another and the diffusion path remains practically unchanged. For a quantitative description of the obtained data, we should allow for an increase in the intergrain contact area with a degree of powder deformation ε. For a rather low degree of compaction (ε ≤ 10%), these values may be considered proportional to one another. This allows one to propose an equation for the deformation rate of the powders analogous to that used for polycrystals [1, 9] with the introduction, however, of a correction factor ε2 that takes into account the dependence of both the stress at a contact and the mass flow coming into the solution on the degree of deformation. Dc 0 ωδP -, ε˙ = -------------------3 2 RT d ε
(3)
where P is the stress as calculated for the matrix cross section and d is the average grain size. Figure 5 shows that the corresponding calculation according to Eq. (3) makes it possible to combine both groups of results, the slope of the straight line being equal to the calculated value within one order of magnitude. It should be noted that Eq. (3) corresponds to the empiric formula derived in [3] by fitting the parameters that describe the deformation of rock salt powders in solutions. Thus, the obtained results allow us to distinguish between the stress regions in which single crystals and sodium chloride powders undergo deformation by dislocation mechanisms (in air or in the presence of water) and by the dissolution–precipitation creep mechanism (only in the presence of water). It is shown that the mechanism changes at stresses of approximately
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ε × 106, s–1 2.0
ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research, project no. 06-03-33106a. 1
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REFERENCES 1.2 2
0.8 0.4 0
0
50
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200 250 P/ε2, MPa
Fig. 5. Experimental data on powder pressing as measured in the modes of a stepwise (1) increase and (2) decrease in the load and presented in Eq. (3) coordinates.
20 MPa which, according the literature data, corresponds to the initial stress of dislocation glide or the yield stress of NaCl.
1. Urai, J.L., Spiers, C.J., Zwart, H.J., and Lister, G.S., Nature (London), 1986, vol. 324, p. 554. 2. Brodsky, N.S. and Munson, D.E., Abstracts of Papers, 32nd US Symp. “Rock Mechanics as a Multidisciplinary Science”, Oklahoma, 1991, Roegiers, J.-C., Ed., Rotterdam: Balkema, 1991, p. 703. 3. Spiers, C.J., Schutjens, P.M.T.M., Brzesowsky, R.H., et al., in Deformation Mechanisms, Rheology and Tectonics, Knipe, R.J. and Rutter, E.H., Eds., Geological Society Special Publication, 1990, vol. 54, p. 215. 4. Martin, B. and Röller, K., Tectonophysics, 1999, vol. 308, p. 299. 5. Munson, D. and Devries, K., Abstracts of Papers, 7 Int. Congress on Rock Mechanics, Aachen, 1991, vol. 1, p. 127. 6. Skvortsova, Z.N., Kas’yanova, I.V., and Traskine, V.Yu., Kolloidn. Zh., 2003, vol. 65, p. 399. 7. Kestin, J., Khalefa, H.E., and Correia, R.J., J. Phys. Chem. Ref. Data, 1981, vol. 10, p. 71. 8. Skvortsova, Z.N., Kolloidn. Zh., 2004, vol. 66, p. 5. 9. Geguzin, Ya.E. and Kibets, V.I., Fiz. Met. Metalloved., 1973, vol. 36, p. 1043.
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