A The reduction in size of food particles as food is chewed B The movement of food to the stomach after food is swallowed C The, Two rods, of lengths, l1 and l2, are made from materials, whose coefficient of linear expansion are a1 and a2, respectively. Sound velocity of FeS liquids at high pressure: implications for the Moons molten outer core. Anderson, W. W. & Ahrens, T. J. If you heat the ring, will the gap become wider or narrower? 2-At 912 C, iron changes from the BCC (-Fe) to the FCC (-Fe) structure. d. first decreases and then enhances. Molodets, A. Thermodynamic potentials and non-monotonic melting curve of sodium at high pressure. The smallest possible unit cell is called the primitive cell. Calculated phase diagram of iron at pressures up to 16GPa in comparison with reference data7,11,68,69,70. 92, 81298135 (1987). Thus, it . 3. J. Geophys. Phys. A. Determining lattice points per cell in FCC. Report No. The other parameters were calculated by optimization of the PVT data (Supplementary Figures S7, S8). HC-1679 (ESRF, Grenoble, 2014). 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). Rev. Earth Planet. Face-Centered Orthorhombic11. Earth Planet. Simple Orthorhombic9. That picture shows two unit cells of the fcc lattice. Quasihydrostatic equation of state of iron above 2 Mbar. B. Wide-range multiphase equation of state for iron. The NaCl pressure standard. At pressures above approximately 10 GPa and temperatures of a few hundred kelvin or less, -iron changes into a hexagonal close-packed (hcp) structure, which is also known as -iron or hexaferrum;[15] the higher-temperature -phase also changes into -iron, but does so at a higher pressure. 43, 229236 (2016). Yield Stress, Yield Strength, and Yield Point, Elasticity and Youngs Modulus (Theory, Examples, and Table of Values), True Stress-Strain vs Engineering Stress-Strain, Stress, Strain, and the Stress-Strain Curve, What Are Shape Memory Alloys? Dependence of pressure on molar volume near the transition in iron. Reduced-activation ferritic/martensitic (RAFM) steels, primary candidate structural materials for fusion reactors, will suffer from a high dose of neutron irradiation under fusion conditions, leading to severe irradiation damages [1], [2], [3].Helium bubbles, formed from the transmutation-created helium in the iron-based alloys, have a significant deleterious effect on the . 1). Liquid iron-sulfur alloys at outer core conditions by first-principles calculations. The crystal structure is based on the Bravais lattice of the same name, with a single atom at each lattice point on the We're young materials engineers and we want to share our knowledge about materials science on this website! (The question itself is not the same as yours). Some Cr2O3 at 25C was added into it, which cause the following exothermic reaction to occur: The comparison with earlier ab initio calculations can be found in the cited papers. A. In this form it is called gamma iron (-Fe) or austenite stainless steel. Thermodynamics and Equations of State of Iron to 350GPa and 6000K. Funtikov, A. Internat. The packing fraction is the ratio of volume taken by actual atoms and the total volume of the cube. Caijuan Shi, Oliver L. G. Alderman, Chris J. Benmore, Akihiko Machida, Hiroyuki Saitoh, Katsutoshi Aoki, Andrew J. Schultz, Sabry G. Moustafa & David A. Kofke, Koutaro Hikosaka, Shoh Tagawa, Yasuo Ohishi, Konstantin D. Litasov, Tatyana B. Bekker, Konstantin E. Kuper, Scientific Reports d. does not increase at all. If youre interested in advanced crystallography or crystallography databases, you may want to check out the AFLOW crystallographic library. BCC has 2 atoms per unit cell, lattice constant a = 4R/3, Coordination number CN = 8, and Atomic Packing Factor APF = 68%. Res. & Fei, Y. Answer (1 of 2): It's thermodynamics. The fitted parameters of the EoSs for bcc-Fe, fcc-Fe, hcp-Fe, and liquid iron (Table 1) were obtained by simultaneous optimization of the experimental measurements of the heat capacity, volume and thermal expansion, adiabatic bulk modulus at room pressure, and PVT data (all references are included in the Supplementary Information). What happens to the field if the number of turns is doubled, with the length remaining the same? The best answers are voted up and rise to the top, Not the answer you're looking for? Assume that the radius of the Fe atom correspondingly changes from 0.1358 nm to 0.1381 nm. 28, 129141 (1987). Res. 90, 042505 (2007). Res. High pressure allotropes . 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. B 79, 060101 (2009). 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. Use MathJax to format equations. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. The volumes for liquid iron from our EoS and that from ref. Depending on the element, the thermal energy to activate the slip systems will be different. Rev. Silicon atom density is 5 x 10^22 cm^-3. Calculate the percent change in density from BCC to FCC. b. Res. We applied the new EoS data for all Fe phases to calculate the phase diagram up to 350GPa (Figs 1, 2 and 3). What is b in terms of R? 43, 68376843 (2016). What is the Difference Between Materials Science and Chemical Engineering? But in between them, rotated by $45^\circ$, is the unit cell of the bcc lattice, stretched along the $z$ axis. B 90, 014422 (2014). 6 are in reasonable agreement with our EoS of hcp-Fe. Res. 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. Science Lett. At atmospheric pressure, three allotropic forms of iron exist, depending on temperature: alpha iron (-Fe), gamma iron (-Fe), and delta iron (-Fe). Article BCC In real space, it has a simple cubic lattice with one basis in the centre. Different structures are different as they have different arrangements of atoms in the lattice. When small pieces of material are assembled into a larger piece, the combined surface area: (a) greatly increases. That means that the body diagonal has a length of , which works out to that the lattice parameter , or side length of the cube, has a length of . Supplementary Figure S5 shows that our EoS for bcc-Fe is reliably consistent with experimental measurements49,50,51, which were obtained in quasihydrostatic conditions in He or Ne pressure media. BCC metals have a ductile-to-brittle transformation temperature (DBTT), which means that they are brittle at lower temperatures and ductile at higher temperatures. The calculated segregation energy difference between the grain boundary and the . Lithium, sodium, potassium, vanadium, chromium, iron, rubidium, niobium, molybdenum, cesium, barium, europium, tantalum and tungsten all have the BCC crystal structure. 16, S973S982 (2004). [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. 15 GPa before transforming into a high-pressure form termed -Fe discussed below. 20 are very consistent; however, entropy is consistent only at temperatures close to the melting line (Supplementary Figure S11). I am trying to find out how to check current system volume or detect system volume changed events (please note, "system" not "application" volume). The magnetic moment of the hcp-Fe is 0=0.28 at ambient conditions10. (A t. m a s s o f i r o n = 5 5. Pure iron goes through a polymorphic change from BCC to FCC upon heating at 912C. In another paper54, the measurement was performed in non-hydrostatic conditions and deviates from our data at higher pressures. 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. 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. Iron (Fe) undergoes an allotropic transformation at 912C: upon heating from a BCC ( phase) to an FCC ( phase). Strong size effect on deformation twin-mediated plasticity in body-centered-cubic iron. We've added a "Necessary cookies only" option to the cookie consent popup, FCC lattice as a stack of triangular lattices, Understanding FCC and BCC Bravais Lattices, Structure Factor for a Simple BCC Lattice. It may look like there are 9 atoms because there are 8 corners and 1 in the center, but actually the cell only intersects portions of those corner atoms. Comput. BCC also has 12 tetrahedral sites, which means that a small interstitial atom could fit in 12 positions such that it is equally surrounded by 4 FCC lattice atoms. At what temperature will the susceptibility increase to 1.9 \times 10^{-5}? Considering this, find the permeability of annealed iron at saturation. At 30 GPa, the dhcp phase appears in the diffraction patterns. Science Lett. Whereas the melting curve goes 500K higher than the experimentally determined one14 at 100200GPa. Nature 427, 339342 (2004). The Curie temperature (TC) of 1043K marks the transition to the paramagnetic state with the same structure. Therefore, the hcpliquid curve overlaps the metastable fccliquid curve at a pressure of 160GPa. The obtained EoSs allow calculation of PVT relations and thermodynamic properties of Fe at the Earths core conditions (up to 6000K and 350GPa). C. 4. 95, 2173721742 (1990). 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. 228, 114126 (2014). Lett. Altshuler, L. V., Brusnikin, S. E. & Kuzmenkov, E. A. Isotherms and Gruneisen functions for 25 metals. Phys. 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. 3) and crosses the melting curve of fcc-Fe at a temperature of 5300K and pressure of 230GPa. (Properties, Applications, and Metallurgy), Why Mercury is Used in Thermometers (and Modern Alternatives), Common Examples of Body-Centered Cubic Materials, Body-Centered Cubic Atomic Packing Factor, Interstitial Sites in Body-Centered Cubic. High Temp. Geol. 2). 2 that the FM state of fcc iron is unstable with respect to the tetragonal deformation; if one keeps the FM order the fcc iron will reconstruct spontaneously to bcc or fct phase, without essential changes of volume and magnetic moment per atom. Mechanic. What is the density of FCC -iron at 20C? Write the factors on which the change of the length of metal in linear expansion depends. Res. 5a. Inter. C. comple. Heat capacities of -Ti and -Ti above 300 K are 33.6 and 29.5 J/mol-K, respectively. Thank you for visiting nature.com. 10 in ref. Anzellini, S., Dewaele, A., Mezouar, M., Loubeyre, P. & Morard, G. Melting of iron at Earths inner core boundary based on fast X-ray diffraction. Vinet, P., Ferrante, J., Rose, J. H. & Smith, J. R. Compressibility of solids. 1) is presented in Fig. If one recalculates the data from ref. Provided by the Springer Nature SharedIt content-sharing initiative. Inter. The pressure scales are shown in the legends to the figures. 2 Experimental constraints on core composition (eds Holland, H. D. & Turekian, K. K. ) 521546 (Elsevier Pergamon, Oxford, 2003). BCC is nearly close-packed and has an APF of 0.68. Chem. The melting points are shown in Fig. 37, 721739 (2010). 49 corrected based on pressure scales31,35. During the last several years, a significant amount of new PVT data for fcc-Fe and hcp-Fe, especially at very high temperatures, have appeared6,13,25,26,27,28 and, in addition, the melting curve of Fe was shifted to higher temperatures according to measurements in ref. 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 $\sqrt{2}$. Iota, V. et al. Res. At higher pressure conditions, the metastable bcchcp curve is in the fcc-Fe or liquid stability field. 45 to obtain the correct limit of entropy at 0K. The magnetic contribution to the Helmholtz free energy can be expressed as45: where B0 is an average magnetic moment per atom, =T/T*, T* is the critical temperature (TC for ferromagnetic materials and Neel temperature TN for paramagnetic materials). Antonangeli D. et al. Now that weve written everything in terms of the radius of an atom, you can see that every face-centered cubic crystal will have the same packing factor regardless of the actual element.if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[250,250],'msestudent_com-large-mobile-banner-1','ezslot_7',126,'0','0'])};__ez_fad_position('div-gpt-ad-msestudent_com-large-mobile-banner-1-0'); As you can see, body-centered cubic crystals have 68% packing. 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. The atomic mass of Fe is 55.845 gr/mol. So it is properly described as a body-centred tetragonal lattice. These authors determined the density deficit at the inner core boundary72 to be 3.6%, whereas based on our data it would be 4.4% at T=5882K and P=328.9GPa. A given number of atoms occupy slightly . How to calculate weight of Cr2O3 addition in liquid aluminium? At high pressure and temperature, iron was found to be paramagnetic47. Given Parameter in Lattice parameter of BCC = Side of cenit cell of a Bec iron - abce = 2 . Res. Transcribed image text: 2. The pressure in this work was estimated before laser heating using the old ruby scale78. 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. -iron can dissolve considerably more carbon (as much as 2.04% by mass at 1,146C). These transitions can also be confirmed by the temperature dependence of the Gibbs energy of the fcc, hcp, and liquid iron at 125GPa (Fig. Differentiating eq. 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. The adiabatic bulk modulus for liquid Fe is about 3.04.5% lower than the PREM and the calculated95 KS is 3.19.0% higher than the PREM (Fig. The body-centered cubic lattice is a cube with an atom on each corner and another in the volumetric center of the cube. Please briefly explain why you feel this answer should be reported. Q.5. ADS , so there is one full corner atom. Composition and state of the core. Thus, the problem of consistent EoSs for solid phases (bcc-Fe, fcc-Fe, and hcp-Fe) and liquid iron remains extremely important. What happens to the volume occupied by the sphere? This point was also placed at 100GPa and 2700K1. Komabayashi, T. Thermodynamics of melting relations in the system Fe-FeO at high pressure: Implications for oxygen in the Earths core. Figure 7 - FCC to BCT . Res. Sci Rep 7, 41863 (2017). C. comple. 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 idea being do perform an action on volume change, e.g. Phys. 3, 129166 (2012). The structure of iron in Earths inner core. 1. In order to wake a sleeping child, the volume on an alarm clock is tripled. Calculate the linear density for [111] direction in . Please enter your email address. This form of carbon saturation is exhibited in stainless steel. If the thickness of a uniform wall is doubled, the rate at which heat is conducted through the wall is A. doubled B. increased by a factor of four C. decreased by a factor of four D. cut in half E. unchanged, If the voltage of X-ray tube is doubled, the intensity of X-rays will become: a. 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. Solution: Each unit cell of BCC iron contains 2 atoms. Ishimatsu, N. et al. I have tried using SMTC however this is application specific volume. The + phase field is, technically, the + field above the A2. Many metals such as iron, chromium, tungsten, molybdenum, and vanadium have the BCC crystal structure at room temperature. B. inversely proportional. 91, 46734676 (1986). In the first approximation, the entropic parameter is independent of volume. Chem. D. It is reduced to 1/8th of its original value. Translate surface iron contamination of 1010 atoms/cm^2 into a number of monolayers. If you are interested in primitive cells, you can read all about them in this article. The flux through a closed surface surrounding the sock is 17 kNm^2/C. How to cite this article: Dorogokupets, P. I. et al. Phys. [20], "Gamma loop" redirects here. a. Russ. 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? Lett. The Atomic Packing Factor (APF) is essentially the density of the unit cell. Calculate the relative volume change from BCC to FCC crystal structure (12 POINTS) b. When you increase r by a factor of 3, 1 r^2 will by a factor of . Phase diagram and melting curve of iron obtained using the data of static and shock-wave measurements. Google Scholar. Use this information to calculate Avogadro's number. The differences would be defined by reference points chosen by different authors. & 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. J. Geophys. Why? Find the permeability of annealed iron at saturation. Its new resistance is equal to 2R. Question #173485. Miner. To understand slip system directions, you will need to be familiar with Miller Indices notation. Article In the past, the paramagnetic form of -iron was known as beta iron (-Fe). You can see a useful picture of this in a question posted on Chemistry StackExchange. The measurements in Ne and Ar pressure media show an alternative deviation from our data53. Iron (Fe) undergoes an allotropic transformation at 912 C: upon heating from a BCC (phase) to an FCC ( phase). J. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc. PubMedGoogle Scholar. The volume of a sphere is . An intensity level change of +2.00 dB corresponds to what percentage change in intensity? I also mentioned atomic packing factor (APF) earlier in this article. Therefore the coordination number of FCC structures is 6 + 3 + 3 = 12. Inter. Kohlhaas, R., Dunner, P. & Schmitz, P. N. Uber die temperaturabhangigkeit der gitterparameter von Eisen, Kobalt und Nickel im bereich hoher temperaturen. Phys. First, two partial derivatives of the Gibbs energy allow calculation of the entropy and volume . 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. This phenomenon is called the ductile-to-brittle transformation temperature (DBTT). All BCC metals have a DBTT. However, when dealing with mathematical descriptions of crystals, it may be easier to describe the unit cell in the smallest form possible. Find the length of the side of the original square. Nature 363, 534536 (1993). The resulting fine, multiphase microstructure is composed of martensite, retained austenite and a network of complex carbides. Dorogokupets, P. I. At 0.1MPa the calculated entropy20 of solid phases of Fe decreases much faster than in our EoSs. The equations of state for solid (with bcc, fcc, and hcp structures) and liquid phases of Fe were defined via simultaneous optimization of the heat capacity, bulk moduli, thermal expansion, and volume at room and higher temperatures. ), or their login data. Phys. C) stays the same. Klotz, S., Le Godec, Y., Strassle, T. & Stuhr, U. Res. 408, 155162 (2014). Austenite, also known as gamma-phase iron (-Fe), is a metallic, non-magnetic allotrope of iron or a solid solution of iron with an alloying element. At high pressures, the present EoS of fcc-Fe averages out the experimental measurements14,17, where pressures were calculated using the EoS of hcp-Fe49. The primary phase of low-carbon or mild steel and most cast irons at room temperature is ferromagnetic -Fe. The ratio of the population. The extrapolation of this line from the low-pressure data (Fig. The thermodynamic formalism in ref. Body-centered cubic iron-nickel alloy in Earths core. The calculated molar volume of fcc-Fe at 0.1MPa is consistent with measurements in ref. 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? 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. Sodium has bcc packing. USA 104, 91829186 (2007). In the meantime, to ensure continued support, we are displaying the site without styles bcc!fcc from DFFe+X bcc! Phys. Phys. 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. 27, 431446 (2007). Antiferromagnetism in alloys of epsilon-Fe with Mn, Os and Ru has been observed.[16]. These unit cells may have different structures such as FCC(face-centered cubic), BCC(body-centered cubic) and HCP(hexagonal closed packed structure). Umemoto, K. 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. 4.1) 4.2} 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 11131. According to the small temperature difference between the melting lines of hcpliquid and fccliquid, there might be a possible fcchcp transition in a very narrow temperature range. The electronic properties are studied for Co/Fe and Cr/Fe systems. Phys. One mole of copper at a uniform temperature of 0C is placed in thermal contact with a second mole of copper which, initially, is at a uniform temperature of 100 C. High Press. 0.1292 nm respectively. Phys. A student kept his 9.0 V, 5.6 W radio turned on at full volume from 4.00 P.M. until 3.00 A.M. Rubidium forms the positive Rb+. Boehler, R. The phase diagram of iron to 430 kbar. The calculated thermodynamic properties (P, T, x=V/V0, , S, CV, CP, KT, KS, th, K, and Gibbs energy, G) for -Fe (bcc-Fe) are listed in Supplementary Table S1 (see also bcc-Fe.xls in the Supplementary Information). 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). d) a r. The susceptibility of magnesium at 300 K is 1.2 \times 10^{-5}. By what percent is the radius of 239 92 U greater than the radius of 232 92 U? In this work, the volume and pressure effects on thermodynamic quantities including Gruneisen parameter and melting temperature of sodium have been studied of to 65 GPa. For a full article explaining APF, check out this link. (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 . Tateno, S., Hirose, K., Ohishi, Y. Phys. Amer. If you are interested in why BCC metals have different properties than FCC metals (another common structure), you should check out this article. If I_0 is 95 mR/h, the HVL for an isotope is 0.42 cm, and the thickness of the shield is 1.39 cm, what will be the intensity after the beam has passed through the shield? Mild steel (carbon steel with up to about 0.2 wt% C) consist mostly of -Fe and increasing amounts of cementite (Fe3C, an iron carbide). For a silicon crystal doped with boron, what must be if at t = 300 k the electron concentration drops below the intrinsic level by a factor of? Among these are the potentials by Meyer and Entel (1998 Phys. B. Yes, that's correct. ADS Geophys. J. Geophys. We store cookies data for a seamless user experience. Technic. Zhang, J. Internet Explorer). 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.
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volume change of iron from bcc to fcc
