Simple Monoclinic13. B. In a property biased transistor (a) both depletion layers are equally large (b) both depletion layers are equally small (c) emitter-base depletion layer is large but base-collectorlayer is small (d) e. Over the course of the year, the right ascension of the Sun: A) decreases. So it is properly described as a body-centred tetragonal lattice. Antiferromagnetism in alloys of epsilon-Fe with Mn, Os and Ru has been observed.[16]. In this form it is called gamma iron (-Fe) or austenite stainless steel. Komabayashi, T. & Fei, Y. W. Internally consistent thermodynamic database for iron to the Earths core conditions. 10 in ref. The bcc-Fe and fcc-Fe phases are stable with liquid at the first triple point at =5.2GPa and T=1991K7, whereas hcp-Fe and fcc-Fe were found in equilibrium with liquid at the second triple point, whose location is variable in different works (e.g. Article Appl. Calculate the strength. 3. How many excess electrons are on the sock? Based on another study47, the magnet moment of both fcc-Fe and hcp-Fe approaches zero with increasing temperature and pressure. 25, 297356 (1981). 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 alloy was synthesized through a special casting process that yielded high solidification rates. So, some BCC metals are ductile at room temperature, and others are brittle. P.D., T.S., A.D. and K.L. An intensity level change of +1.65 dB corresponds to what percentage change in intensity? 8 4 5 u) 375, 244253 (2013). Calphad 29, 6889 (2005). Finally, the melting line of Fe measured using a synchrotron-based fast X-ray diffraction method was also proposed14. Cite this article. (a) Calculate the volume change associated with the change in crystal structure from BCC to FCC if at 912C the BCC unit cell had a lattice constant a = 0.293 nm and the FCC unit cell a lattice constant a=0.363 nm. (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? Calphad 31, 173185 (2007). They need thermal energy for atoms to overcome this extra distance and slip. J. Phys. High pressure allotropes . Thus, the bcc-Fe could not be stable at high pressures based on our thermodynamic model. The edge length of a body centered cubic unit cell is 390 \ pm. The enthalpy and the Gibbs free energy can be found from the following relations: H=E+PV, G=F+PV. Chem. Geophys. Determine whether the following statement is true or false: The strength of a metal increases with reducing grain size. Res. Russ. Slip systems determine many mechanical properties of materials, and is the main reason why a material will be ductile or brittle. this structural change. When heated above 916 C, iron changes its BCC crystalline form to FCC without any change in the radius of atom. Amer. Two sets of data13,67 at 250300GPa are significantly different (Supplementary Figures S8). The authors declare no competing financial interests. Desai, P. D. Thermodynamic properties of iron and silicon. 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. 6. Earth Planet. Its new resistance is equal to 2R. 121, 022018 (2008). For a full article explaining APF, check out this link. (6) with respect to temperature at constant volume one can obtain the entropy, the thermal part of the free energy and the heat capacity at constant volume: Differentiating eq. Lett. Answer to Question #175035 in Mechanical Engineering for Varun. a.) ADS Lett. The melting line of Fe in ref. When an element ejects a beta particle, the atomic number of that element (a) reduces by 1. 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. 92, 81298135 (1987). Google Scholar. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. The phenomena of cavitation and cavitation erosion affect hydraulic machines, increasing their maintenance costs. 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. At the condition of the inner core boundary (~330GPa and ~6000K), our EoS is in good agreement with the EoS obtained in ref. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/, Dorogokupets, P., Dymshits, A., Litasov, K. et al. (Simple Explanation), What Is the Difference Between FCC and BCC? Fei, Y. et al. The following comparison has also been assessed by previous studies84,95 on temperature calculations of liquid iron in the Earths core at isentropic conditions and various pressures. 282, 252257 (2009). Tsujino, N. et al. How to tell which packages are held back due to phased updates, Full text of the 'Sri Mahalakshmi Dhyanam & Stotram'. Dorogokupets, P. I. Zhang, D. et al. 18 and 20 is based on the Gibbs free energy calculations depending on temperature and pressure. Face-Centered Orthorhombic11. 0.918D. 84. Lett. If you werent sure about the difference between crystal structure and Bravais lattice, check out this article. Geophys. At 30 GPa, the dhcp phase appears in the diffraction patterns. Use MathJax to format equations. For achieving a more closed packing structure as compared to the cubic lattice, there can be two possibilities, the body-centered cubic lattice (BCC) or the face-centered cubic lattice (FCC). 1. 41, 850864 (2003). Science Lett. Annual Rev . Earth Planet. Miner. In solid-state chemistry, generally metals such as iron are considered to be made up of unit cells. What is the Difference Between Allotropes and Isotopes? Their triple point liquid is located at 81GPa and 3200K and at 330GPa the melting line is located at 5400K. Another estimation indicates a melting temperature of 6100K at 330GPa21. Res. Phys. The + phase field is, technically, the + field above the A2. Lost your password? Here are the primitive vectors for the BCC unit cell. The BCC crystal structure is not a close-packed structure since the atoms could be packed closer together. What is Atomic Packing Factor (and How to Calculate it for SC, BCC, FCC, and HCP)? Diamond Cubic3. Above the A2, the hysteresis mechanism disappears and the required amount of energy per degree of temperature increase is substantially larger than below A2. Geophys. These figures show that the entropy and molar volume of fcc- and hcp-Fe are consistent, especially at the conditions of their stability field. At 125GPa the fcc-Fe melts at 4019K, however, this point is in the stability field of the hcp-Fe. ADS All rights reserved. The position of the liquid triple point in the phase diagram of iron has been determined many times and revealed highly controversial results (Fig. J. Geophys. Only few available interatomic interaction potentials implement the phase transformation in iron by featuring a stable low-temperature bcc and high-temperature fcc lattice structure. When you increase r by a factor of 3, 1 r^2 will by a factor of . About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators . 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. Show that the FCC structure is denser than the BCC structure. Differentiating eq. The liquid iron density calculated in our study is 7.68.2% higher than PREM and the calculated one95 is 8.97.7% higher than PREM (Fig. Close. Since bainite and pearlite each contain -Fe as a component, any iron-carbon alloy will contain some amount of -Fe if it is allowed to reach equilibrium at room temperature. In any fission process, the ratio: (a) Equal to 1 (b) Greater than 1 (c) Less than 1 (d) Depends on the mass of the parent nucleus. Nature 427, 339342 (2004). 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. But above 910C, iron is called -iron with FCC crystal structure. You can read all about interstitial sites in this article, but BCC has two types of interstitial sites: octahedral and tetrahedral. Differentiating eq. Thanks for any help! What is the density of FCC -iron at 20C? Alloying elements provide solid-solution strengthening and change the allotropic transformation temperature (see Table 14-9) Limitations: Chemical reactivity with other materials at elevated temperatures; expensive ($61/kg) (difficult to extract in the pure state from its compound) At these conditions, the entropy for liquid iron, S=114.15Jmol1K1 and hcp-Fe, S=107.2Jmol1K1, were determined from eqs 7 and 17. This pressure is similar to the calculated bcc-hcp transition for pure iron . Belashchenko, D. K. Estimation of the thermodynamic characteristics of the Earths core using the embedded atom model. J. Appl. Why do we calculate the second half of frequencies in DFT? Liu, J., Lin, J.-F., Alatas, A. and K.L. (With Examples Beyond Carbon). The calculated thermodynamic properties for -Fe (fcc-Fe) are listed in Supplementary Table S2 (see also fcc-Fe.xls in Supplementary Information). Nguyen, J. H. & Holmes, N. C. Melting of iron at the physical conditions of the Earths core. 7.8 A sheet of BCC iron 1 mm thick was exposed to a carburizing gas atmosphere on one side and a decarburizing atmosphere on the other side at 725 C. After having reached steady state, the iron . The calculated thermodynamic properties for liquid Fe are listed in Supplementary Table S4 (see also liquid-Fe.xls in Supplementary Information). Inter. 2Al(l) + Cr2O3(s) = 2Cr(s) + Al2O3(s), Copyright 2021 Askmemetallurgy.com, All rights reserved. Geol. Iron (Fe) undergoes an allotropic transformation at 912 C: upon heating from a BCC (phase) to an FCC ( phase). Data 15, 967983 (1986). S. I. Novikova, Thermal Expansion of Solids (Nauka, Moscow, 1974 . At this transition, the heat capacity of Fe has a characteristic -shape form with a maximum at TC9,10. (d) is reduced to one-quarter its original value. This form of carbon saturation is exhibited in stainless steel. The ratio of density of the crystal before heating and after heating is [atomic weight of F e =56 ]A. The Curie temperature (TC) of 1043K marks the transition to the paramagnetic state with the same structure. The initial temperature in our model is 5882K at the inner core boundary (ICB) (328.9GPa) (Fig. I r. Supplementary Figures S1S4 show the temperature dependence of the isobaric heat capacity, the volume coefficient of thermal expansion, molar volume, adiabatic and isothermal bulk modulus for bcc-Fe, fcc-Fe, and hcp-Fe at 0.1MPa calculated from our EoSs in comparison with direct experimental measurements and reference data. Science 236, 181182 (1987). B. 143144, 455467 (2004). A square is cut out of a copper sheet. Compute the percent volume change associated with . The body-centred position is empty. Geol. 93, 091904 (2008). [10][11] The maximum solubility of carbon is about 0.02 wt% at 727C (1,341F) and 0.001% at 0C (32F). 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. Adding a few parts per million of dopant atoms to silicon can increase its conductivity by a factor of a million. Miner. 4). Pressures in the PVT dataset were corrected based on the self-consistent ruby pressure scale or EoSs of Au, MgO, and W31,35,36. 43, 229236 (2016). 362, 143150 (2013). Please briefly explain why you feel this question should be reported. , so there is one full corner atom. Answer (1 of 3): It's the thermodynamics of these two crystal structures. Createyouraccount. Accompanying this transformation is a change in the atomic radius of Fefrom rBCC= 0.12584 nm to rFCC = 0.12894 nmand, in addition a change in density (and volume). 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. Author links open overlay panel Ligong Zhao a 1, Guoxujia Chen a 1, He Zheng a b c, Shuangfeng Jia a, Kaixuan Li a, Renhui Jiang a, Lei Li a, Ying Zhang a, Huayu Peng a, Peili Zhao a, Ziyang Huang a . [8][9] It has a hardness of approximately 80 Brinell. Find the permeability of annealed iron at saturation. Science Lett. Make sure to explain clearly the different steps you have undertaken to come up with the solution. Get access to this video and our entire Q&A library, When impurities are added to an elastic substance, its elasticity (a) Increases (b) Decreases (c) Becomes zero (d) May increase or decrease. One more experimental dataset64 overestimates pressures by up to 6GPa compared with our data for fcc-Fe. In the presence of impurities and deviations from stoichiometry, the diffusion rate of ions in ionic crystals: a. enhances. Interstitial sites are the spaces inside a crystal where another kind of atom could fit. Alf, D., Voadlo, L., Price, G. D. & Gillan, M. J. Melting curve of materials: theory versus experiments. The Helmholtz free energy of solid phases can be expressed in its classical form41 as: where U0 is the reference energy, E0(V) is the potential (cold) part of the free energy at the reference isotherm T0=298.15K, which depends only on V, Fth(V, T) is the thermal part of the free energy, which depends on V and T, Fe(V, T) is the free electrons contribution to the Helmholtz free energy, which also depends on V and , and Fmag(T) is the magnetic contribution, depending on T only. The magnetic moment10,37 of bcc-Fe is B0=2.22. Please briefly explain why you feel this answer should be reported. Dorogokupets, P. I., Dymshits, A. M., Sokolova, T. S., Danilov, B. S. & Litasov, K. D. The equations of state of forsterite, wadsleyite, ringwoodite, akimotoite, MgSiO3-perovskite and postperovskite and phase diagram of the Mg2SiO4 system at pressures to 130 GPa. J. Geophys. After the passage of 140 amperes for 482.5 sec, the mass of anode decreased by 22.260 g and the cathode increased in mass by 22.011. Sciences 41, 657691 (2013). It becomes four times larger. Choose the best answer to the following. Therefore, the hcpliquid curve overlaps the metastable fccliquid curve at pressures of about 160GPa. Res. The calculated segregation energy difference between the grain boundary and the . By what percent is the radius of 239 92 U greater than the radius of 232 92 U? B) increases. 91, 74857494 (1986). 38, 272276 (1967). Dorogokupets P. I., Sokolova T. S., Dymshits A. M. & Litasov K. D. Thermodynamic properties of rock-forming oxides, -Al2O3, Cr2O3, -Fe2O3, and Fe3O4 at high temperatures and pressures. Make sure to explain clearly the different . Antonangeli D. et al. =88GPa and =2800K17 or =98.5GPa and =3712K14). If the change in their lengths are the same for the same change in temperat. Fitting parameters for our EoS for liquid iron were calculated using the following assumptions (as a starting point for calculations): (i) the Gibbs energy of -Fe and liq-Fe must be the same at 1811K and 0.1MPa; (ii) the entropy of liquid Fe increases by 7.626Jmol1K1 upon melting9 in comparison with the entropy of -Fe; (iii) the melting line of Fe was taken from ref. Why? Stability of bcc, fcc and hcp crys-tal structures as a function of canonical d-band lling was discussed some time back by Pettifor3 and Ander-sen et al..4,5 These authors showed that without ferro-magnetism the ground state of Fe would be hcp, just as for its nonmagnetic and isoelectronic 4dand 5dcounter-parts, Ru and Os. Volume 144, 1 May 2023, Pages 235-242. The authors fixed the triple point at P=98.5GPa and T=3712K. The pressures were estimated from the EoS of hcp-Fe49 and KCl83. Most of the ab initio estimations provide higher melting temperatures of Fe at 330 GPa compared with our data: 6700600K87, 6370100K88, 6900400K89, 71007200K90, 6325K91, and 6345K92. Phys. How can I get that mathematically? At high-pressure conditions, the metastable bcchcp curve is located inside the fcc-Fe or liquid stability field. Let the switch be closed at t = 0. Nature 401, 462464 (1999). The volume of the unit cell is . You can see a useful picture of this in a question posted on Chemistry StackExchange. Strssle, T., Klotz, S., Kunc, K., Pomjakushin, V. & White, J. S. Equation of state of lead from high-pressure neutron diffraction up to 8.9 GPa and its implication for the NaCl pressure scale. Science Lett. 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. Google Scholar. If you increase the multiplicity by a factor of 10, how much does the scaled entropy, S/k, change? The density of iron is 7. Stability of the body-centred-cubic phase of iron in the Earths inner core. In this study, a newly developed high-strength cast Fe81Cr15V3C1 (wt%) steel with a high resistance against dry abrasion and chloride-induced pitting corrosion is presented. J. Geophys. 119, 41644177 (2014). When heating iron above 912C (1,674F), its crystal structure changes to a face-centered cubic (fcc) crystalline structure. Condens. 5a. The phase boundary between the different solid phases is drawn on a binary phase diagram, usually plotted as temperature versus percent iron. Pure iron goes through a polymorphic change from BCC to FCC upon heating at 912C. 90, 042505 (2007). Lett. (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? To understand slip system directions, you will need to be familiar with Miller Indices notation. e. It becomes one-fourth as large. (c) halves. In reciprocal space, BCC becomes an FCC structure. Nature 424, 10321034 (2003). The thermodynamic formalism in ref. Metallic iron changes from BCC to FCC form at 9100C. View the full answer. Basinski, Z. S., Hume-Rothery, W. & Sutton, A. L. The lattice expansion of Iron. Equation of state of pure iron and Fe0.9Ni0.1 alloy up to 3 Mbar. However, under the Earths core conditions (P 360GPa, T 6000K) Fe acquires a substantial local magnetic moment47, up to 1.3B. What Is Magnetic Hysteresis and Why Is It Important? Thermodynamics and Equations of State of Iron to 350GPa and 6000K. Get the most important science stories of the day, free in your inbox. Anderson, O. L. & Isaak, D. G. The dependence of the Anderson-Grneisen parameter T upon compression at extreme conditions. The idea being do perform an action on volume change, e.g. Solution: Each unit cell of BCC iron contains 2 atoms. CAS True or false? Calculate the percentage of change in volume that occurs when BCC iron is heated and changes to FCC iron. Nishihara, Y. et al. The pressure in these works was calculated using ruby30,35 and Au52 pressure scales and in the pressure range of 015GPa these scales give consistent results. It is possible to convert Fick's law into a form that is useful when the concentration is zero at one end of the diffusion channel ( C 1 = 0 ) . The Definitive Explanation. 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. KS for hcp-Fe is almost identical to the PREM at the Earths inner core conditions. Martensite is not shown in the equilibrium phase diagram of the iron-carbon system . What is the Difference Between Materials Science and Chemical Engineering? The iron density, adiabatic bulk modulus and P-wave velocity calculated up to 328.9GPa at adiabatic temperature conditions started from 5882K (outer/inner core boundary) were compared with the PREM and calculated model95. Rhombohedral5a. Solids 54, 221227 (1993). A. By submitting a comment you agree to abide by our Terms and Community Guidelines. HC-1679 (ESRF, Grenoble, 2014). Science 340, 464466 (2013). Tectonophys. At first, the periodic table placed the elements in order of increasing atomic mass. Geophys. 65 and 66 (Supplementary Figure S6). Inter. Iron has a BCC structure at room temperature. Its face-centred cubic (FCC) structure allows it to hold a high proportion of carbon in solution. Dorogokupets, P. I. P-V-T Equations of state of MgO and thermodynamics. When an element ejects an alpha particle, the atomic number of the resulting element (a) reduces by 2. Phys. Unchanged c. Double d. Increase four times. 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 $\sqrt{2}$. Science 316, 18801883 (2007). Mao, H. K., Bassett, W. A. The function f() can be written as: The value of the parameter p changes from p=0.4 (for bcc-Fe) to p=0.28 for other Fe polymorphs. The solution required X mL of a potassium dichromate solution for the oxidation of iron content to the ferric state. If the X-ray tube current is reduced to 40 mA, what will be the percent change in the number of Cu K x-rays that are produced by the x-ray. An monatomic ideal gas at 300 K has a volume of 15 liters at a pressure of 15 atm. The nearest neighbor distance is , and the next-nearest neighbor distance is (or about ). Note that the radius of the largest nucl, A 0.840 \ m long brass pendulum experiences a 21.0^oC temperature increase. J. Geophys. This is an important concept in your introductory materials science class, so if you want a full explanation of APF, check out this page. Nature 363, 534536 (1993). The extrapolation of this line from the low-pressure data (Fig. In addition, a wide-range multiphase equation of state (EoS) to 10 TPa and 105K was calculated24. Rev. Geochem. The calculated volumes of fcc-Fe26,28 are plotted between bcc and fcc phases in Supplementary Figure S2. if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[250,250],'msestudent_com-banner-1','ezslot_4',123,'0','0'])};__ez_fad_position('div-gpt-ad-msestudent_com-banner-1-0');If you wanted to describe the face-centered cubic crystal with math, you would describe the cell with the vectors. In plain-carbon steel, austenite exists above the critical eutectoid temperature of 1000 K (727 C); other alloys of steel have different eutectoid temperatures. Assessments of molar volume and thermal expansion for selected bcc, fcc and hcp metallic elements. : Condens.Matter 19 326220) and by Lee et al (2012 J. Base-Centered Monoclinic14. (a) Calculate the radius of ^{58}\textrm{Ni}, one of the most tightly bound stable nuclei. (13). At the standard conditions (T=298.15K and P=1bar), iron is a ferromagnet and has a body-centred cubic (bcc) structure (-Fe or bcc-Fe). Belonoshko, A. d. It becomes one-half as large. Article Vinet, P., Ferrante, J., Rose, J. H. & Smith, J. R. Compressibility of solids. (The question itself is not the same as yours). Sola, E. & Alfe, D. Melting of Iron under Earths Core Conditions from Diffusion Monte Carlo Free Energy Calculations. Describing complex Bravais lattice as a simple Bravais lattice with a basis, Implement Seek on /dev/stdin file descriptor in Rust, Linear regulator thermal information missing in datasheet, Follow Up: struct sockaddr storage initialization by network format-string. You will receive a link and will create a new password via email. 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. Brown, M. J. b) Estimate the, The ratio of the radii of the nuclei _{13}Al^{27} and _{52}Te^{125} is approximately (a) 6:10 (b) 13:52 (c) 40:177 (d) 14:73. 7, 459476 (2016). Most measurements are scattered for less than 2GPa in the 80GPa pressure range (Supplementary Figure S7). This work is licensed under a Creative Commons Attribution 4.0 International License. Convert: a. Phys. Therefore, the hcpliquid curve overlaps the metastable fccliquid curve at a pressure of 160GPa. . The beta designation maintains continuity of the Greek-letter progression of phases in iron and steel: -Fe, -Fe, austenite (-Fe), high-temperature -Fe, and high-pressure hexaferrum (-Fe). As was shown recently59, this scale underestimates pressure by 0.5GPa (at 1015GPa) in comparison with another NaCl EoS60. 1.Introduction. In some sense, this allows BCC crystals to act as though they have 14 bonds, which is higher than the maximum of 12. Calphad 2, 227238 (1978). 3). These EoSs should be consistent with the phase diagram of iron, including the melting curve and with PVT, thermochemical, and sound velocity data at 0.1MPa. Rev. 22). What is the Difference Between Polymorphism and Allotropy? The reduction of germanium tetrachloride with lithium aluminum hydride gives a) digermane b) di and tri germanes c) monogermane d) mixture of all germanes. 18) decreases with increase of temperature and pressure up to 1.51.6 at 100GPa and 30004000K (Supplementary Table S2). Isothermal compression of face-centered cubic iron. Calculated phase diagram of iron at pressures up to 16GPa in comparison with reference data7,11,68,69,70. There is also a full atom in the center of the cube. -Fe and the A2 critical temperature are important in induction heating of steel, such as for surface-hardening heat treatments.
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