The pressure at 298K isotherm is calculated from the VinetRydberg equation42: where X=(V/V0)1/3, and =3K0/2 3/2. Res. Sokolova, T. S., Dorogokupets, P. I. Zhang, W.-J., Liu, Z.-Y., Liu, Z.-L. & Cai, L.-C. Melting curves and entropy of melting of iron under Earths core conditions. Geophys. Peculiarly, above 1,394C (2,541F) iron changes back into the bcc structure, known as -Fe. Gamma-rays pass through a 4.1 cm slab of copper. The 48 BCC slip systems are {110}<111>, {112}<111>, and {123}<111> in order of ease of activation. Standard conditions for liquid Fe were chosen at T0=1811K and P=0.1MPa. [12] When it dissolves in iron, carbon atoms occupy interstitial "holes". Belonoshko, A. 6. Meanwhile, this assumption is made based on the equilibrium thermodynamics, the shock data93 on the iron shows two phase transitions on the Hugoniot curve at pressures from 77 to 400GPa. We store cookies data for a seamless user experience. (How it Works, Applications, and Limitations), What is Materials Science and Engineering? Anzellini, S., Dewaele, A., Mezouar, M., Loubeyre, P. & Morard, G. Melting of iron at Earths inner core boundary based on fast X-ray diffraction. 1. 25, 297356 (1981). Dorogokupets, P. I., Sokolova, T. S., Danilov, B. S. & Litasov, K. D. Near-absolute equations of state of diamond, Ag, Al, Au, Cu, Mo, Nb, Pt, Ta, and W for quasi-hydrostatic conditions. How can I use it? The NaCl pressure standard. At these conditions, the entropy for liquid iron, S=114.15Jmol1K1 and hcp-Fe, S=107.2Jmol1K1, were determined from eqs 7 and 17. Funamori, N., Yagi, T. & Uchida, T. High-pressure and high-temperature in situ x-ray diffraction study of iron to above 30 GPa using MA8-type apparatus. The face-centered cubic structure has an atom at all 8 corner positions, and at the center of all 6 faces. Our thermodynamic calculations indicate a melting temperature of hcp-Fe at 5882K at 328.9GPa, and it is in a good agreement with the estimated melting temperature T=5800500K obtained from the shock wave data93 and extrapolation from the experiments14, which is T=6230500K. Figures 2 and 3 show the fccliquid melting curve and its extrapolation to high pressures. b) a square with smaller area. Dewaele, A. et al. At 1394C, -iron changes to -iron (BCC structure), the second allotropic change. & Oganov, A. R. Ruby, metals, and MgO as alternative pressure scales: A semiempirical description of shock-wave, ultrasonic, x-ray, and thermochemical data at high temperatures and pressures. The mixture adopts a lamellar structure called pearlite. (d) increases by 2. Differentiation of the thermal pressure with respect to temperature at constant volume gives the pressure slope at constant volume: The volume dependence of and q was accepted in the Altshuler form44: The volume dependence of the Einstein temperature can be expressed as: In eqs (12,13,14,15) 0 is the Grneisen parameter at reference conditions, is the Grneisen parameter at infinite compression (x=0), and is a fitted parameter. Rhombohedral5a. In the book Condensed Matter Physics by Marder I have read that an FCC lattice can be obtained by expanding a bcc lattice along one axis by a factor of $\sqrt{2}$. The calculated triple points have the following parameters: liquid is located at 5.2GPa and 1998K, at 7.3GPa and 820K, and liquid at 106.5GPa and 3787K. Most of the previous estimations plot the melting temperature of iron below the melting line obtained from our EoSs (Fig. Calculate the linear density for [111] direction in . Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Rev. An intensity level change of +1.65 dB corresponds to what percentage change in intensity? Molodets, A. Thermodynamic potentials and non-monotonic melting curve of sodium at high pressure. BCC is nearly close-packed and has great stability because of its high number of nearest neighbors and next-nearest neighbors. Earth Planet. Calibration of fitted parameters for liquid iron is considered below. Chem. Translate surface iron contamination of 1010 atoms/cm^2 into a number of monolayers. Iota, V. et al. 7, 459476 (2016). Suppose you cut a small gap in a metal ring. But in between them, rotated by $45^\circ$, is the unit cell of the bcc lattice, stretched along the $z$ axis. (b) increases by 1. Pure iron goes through a polymorphic change from BCC to FCC upon heating at 912C. Asking for help, clarification, or responding to other answers. Phys. Compute the percent volume change associated with . [20], "Gamma loop" redirects here. Iron (Fe) undergoes an allotropic transformation at 912 C: upon heating from a BCC (phase) to an FCC ( phase). (5) at T f = 1184 K: the upper curve is for bcc-Fe; the lower curve is for fcc-Fe. PubMed Making statements based on opinion; back them up with references or personal experience. Stability of the body-centred-cubic phase of iron in the Earths inner core. 244, 6977 (2015). Heat capacities of -Ti and -Ti above 300 K are 33.6 and 29.5 J/mol-K, respectively. Proc. When the temperature of a coin is raised by 74^{\circ} F, the coin's diameter increases by 2.50 \times 10^{-5} m. If the original diameter is 2.10 \times 10^{-2} m, find the coefficient of linear expa, Two conductors made of the same material are connected across the same potential difference. The Bain distortion is supposed to achieve the desired volume change between the fcc and bcc crystals with the smallest strains. For fcc crystals the atoms of iron are on the cube corners and at the centres of each face of the cube. I have tried using SMTC however this is application specific volume. It was argued that hcp-Fe is likely a stable phase in the inner core of the Earth12,13,14. P-V-T equation of state for epsilon-iron up to 80GPa and 1900K using the Kawai-type high pressure apparatus equipped with sintered diamond anvils. (6) with respect to volume at constant temperature, one can obtain the thermal pressure and isothermal bulk modulus: In eqs (10, 11) is the Grneisen parameter, , and . Not to be confused with, Experimental high temperature and pressure, "The magnetic state of the phase of iron", https://en.wikipedia.org/w/index.php?title=Allotropes_of_iron&oldid=1137712070, This page was last edited on 6 February 2023, at 01:58. Earth Planet. c) a rectangle with larger area. They need thermal energy for atoms to overcome this extra distance and slip. Explain. Science 330, 359361 (2010). %PDF-1.7 4 0 obj (Identity) endobj 5 0 obj (Adobe) endobj 8 0 obj /Filter /FlateDecode /Length 102730 /Type /Stream >> stream x |UE?)s'r"N \H ( D . Science Lett. The phenomena of cavitation and cavitation erosion affect hydraulic machines, increasing their maintenance costs. 28, 129141 (1987). Annual Rev . Funtikov, A. -Fe and the A2 critical temperature are important in induction heating of steel, such as for surface-hardening heat treatments. Earth Planet. [17], The melting and boiling points of iron, along with its enthalpy of atomization, are lower than those of the earlier group 3d elements from scandium to chromium, showing the lessened contribution of the 3d electrons to metallic bonding as they are attracted more and more into the inert core by the nucleus;[18] however, they are higher than the values for the previous element manganese because that element has a half-filled 3d subshell and consequently its d-electrons are not easily delocalized. Lett. If you brought iron below room temperature, however, there would not be enough thermal energy to activate all the slip systems. If a quantity increases as a second quantity decreases and decreases as the second quantity increases, the two quantities are said to be: A. directly proportional. Supplementary Figures S5S8 show the differences between calculated pressures at different temperatures with direct experimental measurements of pressure. Dorogokupets, P. I., Sokolova, T. S. & Litasov, K. D. Thermodynamic properties of bcc-Fe to melting temperature and pressure to 15 GPa. If a toroid uses bismuth for its core, will the field in the core be (slightly) greater or (slightly) less than when the core is empty? FCC The atom in the center of a close packed plane, such as fig.3a, has six nearest neighbors in the octahedral plane above (ie B positions), and 3 below, (ie C positions). Pressures in the PVT dataset were corrected based on the self-consistent ruby pressure scale or EoSs of Au, MgO, and W31,35,36. Thus, the problem of consistent EoSs for solid phases (bcc-Fe, fcc-Fe, and hcp-Fe) and liquid iron remains extremely important. J. Geophys. Boehler, R., Vonbargen, N. & Chopelas, A. Melting, thermal-expansion, and phase-transitions of iron at high-pressures. In addition, from the obtained parameters one can calculate the coefficient of thermal expansion =(P/T)V/KT, heat capacity at constant pressure CP=CV+2TVKT, and adiabatic bulk modulus KS=KT+VT(KT)2/CV, which can also be compared with direct experimental measurements. Melting of compressed iron by monitoring atomic dynamics. Nature 363, 534536 (1993). However, below its Curie temperature (TC or A2) of 771C (1044K or 1420F),[5] it becomes ferromagnetic. Calculate the volume change ?V/V (%) arising from the transformation of iron from FCC to BCC during cooling from 1000 C. What is the respective length change ?L/L? (Crystal Structure, Properties, Interstitial Sites, and Examples), Comparison of SC, BCC, FCC, and HCP Crystal Structures, Double Hexagonal Close-Packed (La-type) Unit Cell, Close-Packed Rhombohedral (Sm-type) Unit Cell, 17 Metals With the Highest Melting Points (and Why), Refractory Metals (Definition, Examples, and Applications), What Are Superalloys? Tsujino, N. et al. Phase diagram and melting curve of iron obtained using the data of static and shock-wave measurements. 1. Zhang, D. et al. If the magnetic moment for hcp-Fe is 0=0.04 and TN=67K (see eqs 19,20,21), the hcpliquid curve shifts to higher temperatures and crosses the fccliquid curve at the temperature of 5300K and pressure of 230GPa. At room temperature, BCC iron has all 5 slip systems activated, which is why it is ductile. 2. The DFT calculations in this study enable us to understand how different amounts of H change the unit-cell volume of fcc FeH x alloy and then . Inter. A square is cut out of a copper sheet. 1). One more experimental dataset64 overestimates pressures by up to 6GPa compared with our data for fcc-Fe. True or false: The value of the RC time constant decreases when C decreases. Internet Explorer). However, when dealing with mathematical descriptions of crystals, it may be easier to describe the unit cell in the smallest form possible. At high pressure and temperature, iron was found to be paramagnetic47. Phys. 49 corrected based on pressure scales31,35. Note that the radius of the largest nucl, A 0.840 \ m long brass pendulum experiences a 21.0^oC temperature increase. Question #173485. The initial temperature in our model is 5882K at the inner core boundary (ICB) (328.9GPa) (Fig. Slip systems are the way that atoms slide past each other when deforming. Science Lett. Do roots of these polynomials approach the negative of the Euler-Mascheroni constant? Alf, D., Voadlo, L., Price, G. D. & Gillan, M. J. Melting curve of materials: theory versus experiments. Many metals such as iron, chromium, tungsten, molybdenum, and vanadium have the BCC crystal structure at room temperature. For the Nozomi from Shinagawa to Osaka, say on a Saturday afternoon, would tickets/seats typically be available - or would you need to book? Phys. 228, 114126 (2014). Res. -iron can dissolve considerably more carbon (as much as 2.04% by mass at 1,146C). Why do small African island nations perform better than African continental nations, considering democracy and human development? If I_0 is 92 mR/h, the HVL for an isotope is 0.47 cm, and the thickness of the shield is 1.51 cm, what will be the intensity after the beam has passed through the shield? c. doubles twice. 92, 81298135 (1987). J. Phys. We determined the density deficit of hcp-Fe at the inner core boundary (T=5882K and P=328.9GPa) to be 4.4%. Phys. Sokolova T. S., Dorogokupets P. I., Dymshits A. M., Danilov B. S. & Litasov K. D. Microsoft excel spreadsheets for calculation of P-V-T relations and thermodynamic properties from equations of state of MgO, diamond and nine metals as pressure markers in high-pressure and high-temperature experiments. [rank_math_html_sitemap]. Medvedev, A. When an element ejects an alpha particle, the atomic number of the resulting element (a) reduces by 2. Chem. The volume of a sphere is . reviewed the manuscript. The values of these functions can be found in Tables S1S4. B 91, 174105 (2015). An intensity level change of +2.00 dB corresponds to what percentage change in intensity? Zarkevich, N. A. Based on these data, the adiabatic bulk modulus at the ICB conditions is consistent with isentropes of 7000K and at the ICB with isentropes of 5000K (see Fig. The lower value of the hcp-Fe magnetic moment seems to be more realistic. The magnetic moment of the hcp-Fe is 0=0.28 at ambient conditions10. : Condens.Matter 19 326220) and by Lee et al (2012 J. , so there is one full corner atom. In the book Condensed Matter Physics by Marder I have read that an FCC lattice can be obtained by expanding a bcc lattice along one axis by a factor of $\sqrt{2}$. Total number of atoms per unit cell = 2. 93, 091904 (2008). For greater pressures, published data (as of 2007) put the --liquid triple point at pressures that differ by tens of gigapascals and 1000K in the melting point. If the mass of the bob of simple pendulum decreases, its time period will increase or decrease? Body-Centered Cubic is one of these 14 Bravais lattices and also occurs as a crystal structure. Similarly, the A2 is of only minor importance compared to the A1 (eutectoid), A3 and Acm critical temperatures. Supplementary Figure S12 shows isochores of liquid Fe calculated from our EoS and plotted in comparison with PVT data calculated by ab initio molecular dynamics simulations95,96. This inconsistency is probably due to the differences in the EoSs. A.D., T.S. B 79, 060101 (2009). Appl. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/, Dorogokupets, P., Dymshits, A., Litasov, K. et al. Silicon atom density is 5 x 10^22 cm^-3. (Simple Explanation), What are Space Groups? The study94 based on new measurements of sound velocity and reassessment of previously obtained shock data established the melting temperature of the iron between 5100500K at P=2253GPa and 6100500K and P=2603GPa on the Hugoniot curve. It is one of the most common structures for metals. The contribution of this part to entropy, internal energy, heat capacity, pressure, isothermal bulk modulus, and pressure slope at constant volume can be estimated as: It should be emphasized that if the electronic contribution to the Helmholtz free energy is not equal to zero, the thermal Grneisen parameter: will be different from the Grneisen parameter calculated from eq. Calculate the volume change associated with the change in crystal structure. (Definition, Examples, and Metallurgy), The Difference Between Alloys and Composites (and Compounds), The Hume-Rothery Rules for Solid Solution. Lett. and JavaScript. Rev. High Press. Its new resistance is equal to 2R. In the first approximation, the entropic parameter is independent of volume. 1.) Dorogokupets, P. I. If B0=0.14, then melting of the hcp-Fe is observed at 7150K and 328.9GPa and is in agreement with the computer calculations90. Calculate the relative volume change from BCC to FCC crystal structure (12 POINTS) b. (13). Magnetically, -iron is paramagnetic at high temperatures. [6][7] Even though the slight tetragonal distortion in the ferromagnetic state does constitute a true phase transition, the continuous nature of this transition results in only minor importance in steel heat treating. Cite this article. It is thermodynamically stable and a fairly soft metal. W is the prototype for BCC. An extrapolation to high-pressure conditions revealed the very close position of the melting curves of fcc- and hcp-Fe. B-H vs M-H Hysteresis Loops: Magnetic Induction vs Magnetization (Similarities, Differences, and Points on the Graph), What is Scanning Electron Microscopy? The ratio of density of the crystal before heating and after heating is [atomic weight of F e =56 ]A. The authors6 used a third-order BirchMurnaghan EoS to fit the parameters on the room temperature isotherm with a fixed initial density 0=8.2695gcm3 and obtained K0=172.7GPa and K0=4.79. So, some BCC metals are ductile at room temperature, and others are brittle. The metastable line bcchcp-iron was also calculated at high pressures. How does the number of atoms in a 27.5-gram iron ring compare to the number in a chrome ring of the same mass? Zhang, J. 2023 Copyright Materials Science & Engineering Student, link to Hexagonal Close-Packed (HCP) Unit Cell, link to Face-Centered Cubic (FCC) Unit Cell, Prince Ruperts Drops: The Exploding Glass Teardrop, Chemical Tempering (Chemically Strengthened Glass), 13 Reasons Why You Should Study Materials Science and Engineering. How many excess electrons are on the sock? Fei, Y. et al. High pressure allotropes . Sorry, you do not have permission to ask a question, You must login to ask a question. The hcp-Fe melts at 4033K and at higher temperatures the liquid is the only stable phase. (b) slightly increases. The A2 forms the boundary between the beta iron and alpha fields in the phase diagram in Figure 1. BCC has 2 atoms per unit cell, lattice constant a = 4R/3, Coordination number CN = 8, and Atomic Packing Factor APF = 68%. (b) reduces by 4. Chem. The segregation effects of Co and Cr on the bcc Fe 3 [1 1 0] (1 1 1) grain boundary cohesion are investigated based on the Rice-Wang thermodynamics model by the first-principles DMol method within the framework of density functional theory. Correspondence to This form of carbon saturation is exhibited in stainless steel. Mechanism of the -d phase transformation in iron. A cylindrical copper rod has resistance R. It is reformed to twice its original length with no change of volume. (Applications, History, and Metallurgy), Thermal Barrier Coatings (TBCs): Materials, Manufacturing Methods, and Applications, Hastelloy C-276 (Composition, Properties, and Applications), Magnetic Materials: Types of Magnetism, Applications, and Origin of Magnetism, Which Metals Are Magnetic? If entropy and molar volume (pressure) are comparable in different EoSs, then the Gibbs energy will be similar and deviations in calculated lines in equilibrium phase diagram would be negligible. To understand slip system directions, you will need to be familiar with Miller Indices notation. True or False? The calculated thermodynamic properties for -Fe (hcp-Fe) are listed in Table S3 (see also hcp-Fe.xls in Supplementary data). CAS B. Wide-range multiphase equation of state for iron. The calculated thermodynamic properties for -Fe (fcc-Fe) are listed in Supplementary Table S2 (see also fcc-Fe.xls in Supplementary Information). At 25 GPa, the unit-cell volume of the fcc phase . (With Examples Beyond Carbon). When heated, it transforms from BCC to FCC at 1185 K. The atomic radii of iron atoms at this temperature are 0.126 and 0.129 nm for bcc and fcc, respectively. (2) with respect to volume, we obtain the bulk modulus at reference isotherm T0=298.15K and its pressure derivative: The potential energy at the 298K isotherm is: The thermal part of the Helmholtz free energy can be expressed via the Einstein model, which coincides with the Debye model at the high-temperature limit43: where is the characteristic temperature depending on volume, which is related to the Debye temperature (D) via =0.75 D; n is the number of atoms in the chemical formula of the compound, and R is the gas constant. 2. FCC iron is more closely packed than BCC suggesting that iron contracts upon changing from BCC to FCC. The high-pressure phases of iron are important as models for the solid parts of planetary cores. What Is Magnetic Hysteresis and Why Is It Important? Choose the best answer to the following. Combustion, Explosion and Shock Waves 35, 185190 (1999). However, the more scattered data62 deviate by 2 to +4GPa at 298K isotherm and significantly overestimate pressures at high temperatures. Please briefly explain why you feel this user should be reported. Strong size effect on deformation twin-mediated plasticity in body-centered-cubic iron. Id recommend reading Kelly & Knowles, Crystallography and Crystal Defects if you want to prove this, and if you want to prove that only 5 of these are independent. W is the prototype for BCC.if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'msestudent_com-medrectangle-3','ezslot_6',142,'0','0'])};__ez_fad_position('div-gpt-ad-msestudent_com-medrectangle-3-0'); The Body-Centered Cubic (BCC) unit cell can be imagined as a cube with an atom on each corner, and an atom in the cubes center. 2). 447, 7283 (2016). S. I. Novikova, Thermal Expansion of Solids (Nauka, Moscow, 1974 . When heated above 916 C, iron changes its BCC crystalline form to FCC without any change in the radius of atom. The calculated melting lines of iron from the bcc, fcc, and hcp phases are shown in Figs 1, 2 and 3. If the diameter of a radar dish is doubled, what happens to its resolving power assuming that all other factors remain unchanged? Iron atoms arrange themselves in one of two stable crystal structures called the body-centered cubic structure and the face-centered cubic structure. 2-At 912 C, iron changes from . & Litasov, K. D. Self-consistent pressure scales based on the equations of state for ruby, diamond, MgO, B2-NaCl, as well as Au, Pt and other metals to 4 Mbars and 3000 K. Russ. Thats almost as much as a close-packed crystal (which has APF = 74%).if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[336,280],'msestudent_com-large-mobile-banner-2','ezslot_10',147,'0','0'])};__ez_fad_position('div-gpt-ad-msestudent_com-large-mobile-banner-2-0'); The conventional BCC cell that I have shown you is a conventional unit cell, not a primitive unit cell. Double Hexagonal Close-Packed (La-type)5. 52, 456466 (2014). Mechan. ADS Body-centered cubic iron-nickel alloy in Earths core. Vinet, P., Ferrante, J., Rose, J. H. & Smith, J. R. Compressibility of solids. (a) Calculate the radius of ^{58}\textrm{Ni}, one of the most tightly bound stable nuclei. Provided by the Springer Nature SharedIt content-sharing initiative. (b) What is the ratio of the radius of ^{58}\textrm{Ni} to that of ^{528}\textrm{Ha}, one of the largest nuclei ever made? What is the Materials Science Tetrahedron (Paradigm)? Figure 5b shows adiabatic bulk modulus and density for solid and liquid iron calculated from our EoSs in comparison with PREM72 and the calculated model95. The newly measured melting line of Fe extrapolated to 330GPa reveals a temperature of about 6230500 K14. When the area of an expanding square, in square units, is increasing three times as fast as its side is increasing, in linear units, the side of the square is what? I also mentioned atomic packing factor (APF) earlier in this article. An aluminum plate has a length of 0.13 m and a width of 0.12 m at 23^{\circ}C. The plate is uniformly heated to 236^{\circ}C. If the linear expansion coefficient for aluminum is 2.3 \times 10^{-5}/^{\circ}C, what is the change in the area of the plate as. Differentiating eq. At what temperature will the susceptibility increase to 1.8 \times 10^{-5}? You can read all about interstitial sites in this article, but BCC has two types of interstitial sites: octahedral and tetrahedral. 1. In situ X-ray diffraction studies of iron to Earth-core conditions. b. Thank you for visiting nature.com. For SC, BCC, and FCC crystal structures, the respective values of n are 1, 2, and 4, whereas the expressions for a (since VC = a3) are . When heating iron above 912C (1,674F), its crystal structure changes to a face-centered cubic (fcc) crystalline structure. Phys. The susceptibility of magnesium at 300 \ K is 1.2 \times 10^{-5} . Swartzendruber, L. The Fe (Iron) System. Geochem. ADS Thanks for any help! The 298K isotherm for -Fe was calculated using the compressibility curve from ref. Half b. It has a simple cubic lattice of length ##\frac{2\pi}{a}## with 4 atoms in total. (d) is reduced to one-quarter its original value. All other trademarks and copyrights are the property of their respective owners. The Definitive Explanation. 2 and the pressure was determined using the ruby scale82 with corrections for thermal pressure (note that at Fig. These unit cells may have different structures such as FCC(face-centered cubic), BCC(body-centered cubic) and HCP(hexagonal closed packed structure). (d) Calculated P-wave velocity along the isentrope. The BCC crystal structure is not a close-packed structure since the atoms could be packed closer together. 6 5 p m.. All rights reserved. By submitting a comment you agree to abide by our Terms and Community Guidelines. 119 (2014). Composition and state of the core. In addition, the magnetic contribution to the Helmholtz free energy was calculated according to ref. Iron is a major component of the Earths core, therefore knowledge of its PVT relations and thermodynamic properties is extremely important1,2,3,4,5,6. Write copper, steel, rubber, and glass in the increasing order of their elasticity. The pressure in this work was estimated before laser heating using the old ruby scale78. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. The thermodynamic formalism in ref. Belashchenko, D. K. Estimation of the thermodynamic characteristics of the Earths core using the embedded atom model. The square is heated uniformly, as a result, it turns into a) a square with larger area. The high-frequency alternating magnetic field of induction heating heats the steel by two mechanisms below the Curie temperature: resistance or Joule (I2R) heating and ferromagnetic hysteresis losses. Ichikawa, H., Tsuchiya, T. & Tange, Y. Inter. J. Geophys. How to determine interplanar spacing for BCC/FCC crystals? Steel is typically austenitized at 9001000C before it is quenched and tempered. To learn more, see our tips on writing great answers. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy.
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