why does iron change from bcc to fcc

When iron transforms from ferrite (bcc) to austenite (fcc) the atoms become more closely packed and the volume per atom of iron changes which generates internal stresses during the transformation. What is the difference between FCC and BCC structures? Because FCC atoms are arranged more closely together than BCC atoms, FCC metals will tend to be more dense and more stable. If youre reading this article as an introductory student in materials science, welcome! How it works: Content Filtration 6. Atoms are much more likely to slip in these directions because they are closer-packed. Its structure has been described as massive, cubic, lath-like, lenticular, subgrain-containing bundles at low C contents (i.e. The condition to occur the structural transformation was defined. Fig. Most of the elements when dissolved in iron form substitutional solid solutions such as manganese, nickel, chromium, etc. A phase may be stable at low temperatures if it has smaller specific heat than the high temperature phase. Why are FCC metals more ductile than BCC? A carbon atom has six nearest neighbour iron atoms if in an octahedral hole and four in a tetrahedral hole. When, -Fe is cooled slowly such as in furnace, small number of nuclei of -Fe form at the grain boundaries of -Fe [Fig. Iron has two different crystal structures at atmospheric pressure: the body centered cubic (bcc) and the face centered cubic (fcc). (We call this APF, and you can read more about APF here). Use music or "piano" wire. (Simple Explanation), What are Space Groups? Using Braggs law (assume first . The ability of iron to accommodate heavy interstitials, namely carbon and nitrogen, is mostly responsible for the strength and the hardening effects. A Variac supplies the adjustable AC heating current. Types of Ferrous Alloys on the Phase Diagram. The fcc lattice is both cubic and closely packed and forms more ductile materials. The iron existing between 768C to 910C, i.e., -Fe paramagnetic is sometimes called beta-iron. This is a very broad rule, however! Because, during the transition from the bcc to the fcc structure, the interatomic bond energy of a crystal is redistributed from kn = 8 bonds with nearest neighbors to kn = 12 bonds, the depth of the pair interatomic bond for an fcc crystal can be estimated by formula: D (12) = (8/12) D (8). This cookie is set by GDPR Cookie Consent plugin. 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. They occur in more or less all bcc metals, to some extent in hexagonal (hcp) metals, in many non-metallic crystals and in polymers. The cookie is used to store the user consent for the cookies in the category "Performance". This problem has been solved! In body centred cubic (bcc) metals, the slip direction is also well established to be . DBT transitions are not restricted to iron and its alloys, however, they are rather common. Now you know all the differences between FCC and BCC! Copyright 10. Does the volume increase or decrease when FCC iron changes to BCC iron? The octahedral hole in FCC-- iron is the largest hole and the largest diameter of sphere which can be accommodated here without elastic distortion is of 0.052 nm in radius, whereas largest diameter of sphere which can be accommodated in tetrahedral hole in FCC--iron is 0.028 nm in radius. FCC unit cell has 4 atoms per unit cell as compared to BCC having 2 atoms per unit cell. FCC unit cell has 4 atoms per unit cell as compared to BCC having 2 atoms per unit cell. BCC unit cell showing the relationship between the lattice constant a and the atomic radius R. Thus, if a is the length of the cube edge, then (3a) = 4R Where R is the radius of the iron atom. 1 Gauge no. Answer: d Explanation: Similar to metallic crystals, a few non-metallic crystals also change form due to temperature and pressure differences. C. comple. If a large number of carbon atoms present in dissolved state in -iron (austenite) are trapped to BCC octahedral holes by rapid cooling to temperatures below 727C, when highly supersaturated solid solution of carbon in BCC forms, the cubic structure may actually become tetragonal, particularly when carbon is more than 0.2%, which is a typical crystal structure of martensite , whose formation is the object of hardening heat treatment. 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? A body-centered cubic (bcc) unit cell contains one additional component in the center of the cube. The bcc structure is often the high temperature form of metals that are close-packed at lower temperatures. The fcc lattice is both cubic and closely packed and forms more ductile materials. You also know many common materials that take each form. The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. Above this temperature, iron transforms back . What is the crystal structure of iron? Double Hexagonal Close-Packed (La-type)5. The critical temperature observed on heating is designated as Ac, where the letter c being taken from the French chauffage-meaning heating. For example, titanium and zirconium change from CPH to BCC at temperatures of 802C and 815C respectively on heating. It is relevant to study the geometry of unit cells of a-iron and -iron crystals. What is the Materials Science Tetrahedron (Paradigm)? Why does iron have a bcc and fcc structure? What is thought to influence the overproduction and pruning of synapses in the brain quizlet? Upon heating pure Iron experiences two changes in crystal structure. At A2 temperature (768C) also called Curie temperature (named after Madam Curie), the heat change is not very conspicuous as it occurs over a range of temperatures with a maximum in the vicinity of 768C, that is, while heating pure iron from room temperature, the transformation of -iron ferromagnetic into -iron paramagnetic is spread over a range of temperatures and is not completely isothermal unlike the transformations taking place at A3 or A4. The austenite allotrope is named after Sir William Chandler Roberts-Austen (1843 . a) 308 o C b) 568 o C c) 771 o C d) 906 o C View Answer. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Simple Monoclinic13. By clicking Accept All, you consent to the use of ALL the cookies. If youre interested, we also compared FCC and HCP crystal structures here.if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'msestudent_com-medrectangle-3','ezslot_5',142,'0','0'])};__ez_fad_position('div-gpt-ad-msestudent_com-medrectangle-3-0'); The most direct difference between FCC and BCC crystals is in the atomic arrangements. Thus, I was surprized that alpha-Fe as body-centered cell has practically a higher density than the respective fcc if one uses as lattice parameters 3.656 A for fcc and 2.8664 A for bcc. However, elements like boron, carbon, nitrogen, oxygen, and hydrogen form interstitial solid solutions in -iron and -iron as their atomic sizes are sufficiently small relative to that of iron. Pure iron can have two different crystal structures as its temperature is increased from room temperature to its melting point. At this point, the carbon bonds with available iron atoms to form Fe3C, an intermetallic compound called cementite (or iron carbide). This can have a large impact in interstitial solubility. That is also the reason that transformation referring to A3 temperature shows more hysteresis than that to the A4 temperature. The alloy may form a face-centred cubic (FCC) lattice or a body-centred cubic (BCC) lattice. The first peak will thus occur when n = 1 and h 2 + k 2 + l 2 = 2, on the (110) plane. The total open space is shared by more number of sites. No worries! In the ground state the bcc -phase is stable, and at the temperature T=1184 K (A3 point), -Fe transforms into fcc -Fe, which is stable up to 1665 K (A4 point). Instead of BCC steel, you end up with body-centered tetragonal (BCT). Analytical cookies are used to understand how visitors interact with the website. The cookie is used to store the user consent for the cookies in the category "Analytics". In fact, the exact radius ratio also determines which kind of interstitial site can be occupied.if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'msestudent_com-leader-1','ezslot_7',125,'0','0'])};__ez_fad_position('div-gpt-ad-msestudent_com-leader-1-0'); The two main types of interstitial sites are octahedral and tetrahedral. 1.13, it ends in value for -Fe. The marked difference in solubility of carbon in austenite and in ferrite is of great importance in the heat treatment of steels. Why does iron change from bcc to fcc? Introduction to the Allotropy of Iron: Many of the metallic elements (even some compounds such as SiO2, quartz) exist in more than one crystal structure form depending on the external conditions of temperature and pressure, though only one crystal structure is stable under a given set of conditions. If you read a very old textbook, you may even see something called a cubic close-packed (CCP), which is another name for FCC. Slip in face centred cubic (fcc) metals is well documented to occur on {111} planes in n110m directions. Introduction to Allotropy of Iron 2. Body-Centered Cubic4. This, difference in temperatures during heating and cooling, called the thermal hysteresis, is because at the equilibrium temperature, the free energies of the two phases, one the parent phase and second the product phase, are equal. (Definition, Types, Examples). as their atomic sizes are nearer in size to that of iron. By clicking Accept All, you consent to the use of ALL the cookies. 2 Interstitial sites of FCC Interstitial sites of BCC. Gamma-iron, silver, gold, and lead have fcc structures. The Curie change is not regarded as an allotropic transformation as there is no change in either the crystal structure or lattice parameter. HCP metals are the most brittle. Describing complex Bravais lattice as a simple Bravais lattice with a basis. A vertical scale (meter stick) placed behind the wire may help to make its motion more evident. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators . Iron has two different crystal structures at atmospheric pressure: the body centered cubic (bcc) and the face centered cubic (fcc). There are eight in number per unit cell. We talk about these structures under the field of crystal lattices. However, you may visit "Cookie Settings" to provide a controlled consent. The volume of atoms in a cell per the total volume of a cell is called the packing factor. bcc pillars is often weaker than in fcc metals,47,48 and depends on the particular material48-50 and the crystal-lographic orientation of the pillar . What is the shape of BCC and FCC in iron? B. inversely proportional. However, tetrahedral sites are larger in BCC, and BCC has more tetrahedral and octahedral sites. Why does iron have a BCC and FCC structure? engineeringenotes.com All rights reserved. Between 912 and 1,394 C iron is in its fcc order . When iron first solidifies 1539 c. It is in the form of B..C.C structure. And, thus, the critical temperatures are designated as Ac2, Ac3 and Ac4. However, above room temperature, the steel switches to the gamma phase, which also has an FCC (face-centered cubic) crystal structure. When heated above 916 C, iron changes its BCC crystalline form to FCC without any change in the radius of atom. Diamond Tetragonal (White Tin)8. That is why all metals must melt at sufficiently high temperatures, because the liquid has no long-range structure and has higher entropy than any solid phase, that is, the term T.S overcomes the H0 term in the normal free energy equation. This demonstration has been around for some time (see Sutton, for example). The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. Nearly all elements have FCC, BCC, or HCP structures. Infact BCC has more slip systems around 48 more than FCC. As the current is increased, the wire will heat up, expand, and sag. Iron is ferromagnetic (attracted to magnets), but only within a certain temperature range and other specific conditions. The key difference between BCC and FCC is that the coordination number of BCC is 8 whereas the coordination number of FCC is 12. Effect of Pressure on Allotropy of Iron: As the pressure is increased, the -Fe -Fe transition temperature is lowered, whereas -Fe Fe transition temperature is raised. At room temperature, BCC iron has all 5 slip systems activated, which is why it is ductile. Iron atoms are arranged in a body-centered cubic pattern (BCC) up to 1180 K. Above this temperature it makes a phase transition to a face-centered cubic lattice (FCC). Newtonian MechanicsFluid MechanicsOscillations and WavesElectricity and MagnetismLight and OpticsQuantum Physics and RelativityThermal PhysicsCondensed MatterAstronomy and AstrophysicsGeophysicsChemical Behavior of MatterMathematical Topics, Size: from small [S] (benchtop) to extra large [XL] (most of the hall)Setup Time: <10 min [t], 10-15 min [t+], >15 min [t++]/span>Rating: from good [] to wow! Explanation: Pure iron exists in three allotropic phases of iron, iron, and iron. We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. 8 Why FCC is more ductile than BCC and HCP? Geometry of BCC and FCC Crystal Structures of Pure Iron: Pure iron has essentially two crystal structures, one BCC and the other FCC. Thus, BCC structure of a-iron is more loosely packed than that of FCC -iron, and that is why density of FCC -iron is 8.14 g/cm3 at 20C and 7.87 g/cm3 for -iron. For example, it has been shown that martensite has a BCC structure in the low carbon range up to 0.6mass% C. What are the limitations on the use of the iron-iron carbide diagram? Overall, we call the slip system {111}<110>. The BCC phase is known as the alpha or ferrite phase of iron; the FCC phase is known as the gamma or austenite phase. (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? Octahedral sites are much bigger in FCC than in BCC. BCC crystals have 48 slip systems but still only 5 are independent. A small weight suspended from the middle of the wire by a paper clip also aids visibility. Find the reciprocal lattice vectors for the bcc and fcc structures and calculate the primitive volume for each. Triclinic. Ferrite. 8 Which is more ductile, HCP or fcc lattice? From 912 to 1,394 C (1,674 to 2,541 F) alpha iron undergoes a phase transition from body-centred cubic (BCC) to the face-centred cubic (FCC) configuration of gamma iron, also called austenite. A face-centered cubic (fcc) unit cell contains a component in the center of each face in addition to those at the corners of the cube. The cookies is used to store the user consent for the cookies in the category "Necessary". For example, FCC metals, Cu, Au, Ag, are usually soft and ductile, which means they can be bent and shaped easily. Thus, it can be generalised that whenever a phase change occurs, the more close-packed structure usually exists at low temperatures, whereas the more open structure is stable at the higher temperatures. Which is more ductile, HCP or fcc lattice? The Debye characteristic temperature of -iron (FCC) is lower than that of -iron (BCC) and this is mainly responsible for the -Fe to -iron transformation. Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. What is the Difference Between Crystal Structure and Bravais Lattice, How to Read Hexagonal Miller-Bravais Indices. For an elemental crystal, there exist a number of methods to calculate this quantity, such as the This phase is non-magnetic. Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. How long do you leave diatomaceous earth down for bed bugs? If there are at least 5 independent slip systems, the metal is ductile! The interstitial holes in BCC -iron (also called ferrite) are much smaller, which explains the very limited solubility of carbon in it. 3C (0.008-2.14wt%) Microstructures of iron -ferrite austenite. We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. Iron atoms are arranged in a body-centered cubic pattern (BCC) up to 1180 K. The transition from BCC to FCC results in an 8 to 9% increase in density, causing the iron sample to shrink in size as it is heated above the transition temperature. Nitrogen (r = 0.072 nm) too sits in octahedral holes in austenite and ferrite but causes lesser strains in the lattices as its atomic radius is smaller than carbon and thus, the solid solubility of nitrogen in iron is more than carbon as shown in table 1.8. Iron atoms are arranged in a body-centered cubic pattern (BCC) up to 1180 K. Above this temperature it makes a phase transition to a face-centered cubic lattice (FCC). Phase transitions are one of the most fundamental phenomena of matter. BCC metals are infact stronger than FCC metals. Face-Centered Orthorhombic11. (Metallurgy, How They Work, and Applications), What is the Difference Between Iron, Steel, and Cast Iron? And, thus there are 2 tetrahedral holes per atom in FCC structure. Using a laser to melt and re-solidified the cube, the structure changes to a solid 100% delta ferrite BCC structure. A sample of bcc metal with the lattice parameter a = 0.33nm was placed in a X-ray diffractometer using incoming x-rays with = 0.1541nm. However, the comparison of atomic size of carbon with the available interstitial holes (these are much smaller) makes it clear that carbon forms interstitial solid solutions with -iron, called austenite and with -iron called ferrite. 2. You already know that unit cells of metals are not fully packed (74% for FCC and 68% for BCC), which means they have some empty space. Iron atoms are arranged in a body-centered cubic pattern (BCC) up to 1180 K. The transition from BCC to FCC results in an 8 to 9% increase in density, causing the iron sample to shrink in size as it is heated above the transition temperature. Also the crystal tolerates larger shear strains (from these distortions) than dilatations (from the symmetrical substitutional defects). These transformations occur below the equilibrium temperature during cooling and above it during heating, and that is why the temperature of transformation during cooling is designated by the symbol, Ar (A letter is for arrest), where the letter V being taken from the French refroidissement meaning cooling. The 48 BCC slip systems are {110}<111>, {112}<111>, and {123}<111> in order of ease of activation. [] or not rated [], Copyright 2023 The President and Fellows of Harvard College, Harvard Natural Sciences Lecture Demonstrations, Temperature and Thermal Properties of Matter. If youre reading this article because youre taking a class on structures, you may be interested in my other crystallography articles. Iron atoms are arranged in a body-centered cubic pattern (BCC) up to 1180 K. The transition from BCC to FCC results in an 8 to 9% increase in density, causing the iron sample to shrink in size as it is heated above the transition temperature. . This state has low entropy as well as minimum internal energy, which makes BCC structure stable in iron at low temperatures. The sagging wire will rise a few centimeters, halt momentarily and drop two to three centimeters, and then continue rising back to its original height. In this article we will discuss about:- 1. Terms of Service 7. What is the Difference between Materials Science and Materials Engineering?, What is Yield in Materials? Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors. As a rule of thumb, atoms that fit in interstitial sites should be less than 15% of the size of atoms in regular sites. (For example, cobalt and iron can both be FCC when heavily alloyed, especially with nickel). If you dont understand Miller Indices, this next section will be hard to follow.if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[250,250],'msestudent_com-box-4','ezslot_3',121,'0','0'])};__ez_fad_position('div-gpt-ad-msestudent_com-box-4-0'); FCC crystals are close-packed along the {111} planes, and the <110> direction within that plane. There are two main types of interstitial holes called octahedral and tetrahedral holes in FCC and BCC irons. The terms BCC and FCC are used to name two different arrangements of crystalline structures. It will be impossible to get 3 . We also use third-party cookies that help us analyze and understand how you use this website. What Is Magnetic Hysteresis and Why Is It Important? 2 The wire will glow red hot. The relative magnitude of the free energy value governs the stability of a phase, that is, the phase having lowest free every in any temperature range is the stable phase. Before uploading and sharing your knowledge on this site, please read the following pages: 1. Thus, BCC structure of a-iron is more loosely packed than that of FCC -iron, and that is why density of FCC -iron is 8.14 g/cm3 at 20C and 7.87 g/cm3 for -iron. What are Alloys? This cookie is set by GDPR Cookie Consent plugin. 2 How HCP BCC and FCC metals have different ductility? These cookies ensure basic functionalities and security features of the website, anonymously. It's pretty counterintuitive because you'd expect the tighter FCC packing structure would leave less room for carbon . With increasing temperature, all crystal variants will increase in energy. The electronic specific heat of BCC iron is greater than FCC iron above about 300C and becomes sufficiently greater at higher temperatures to make it stable again above 1394C. The iron-carbon phase diagram is widely used to understand the different phases of steel and cast iron. Additionally, none of the BCC planes are as close-packed as the FCC planes, which generally means that BCC metals dont slip as easily (stronger, but less ductile). Smaller atoms can fit in these spaces. Therfore interstitial gap in BCC is much smaller than that of FCC. There are 6/2 + 12/4 = 6 octahedral site positions per unit cell in the BCC crystal structure. After freezing of pure iron, there are three thermal arrest temperatures (excluding freezing temperature), also called critical temperatures, and are designated as A4 (where the letter A being taken from the French word arret-meaning arrest), A3 and A2, associated with the -iron -Fe, -Fe -Fe (paramagnetic) and -paramagnetic to -ferromagnetic transformations respectively. As -Fe (FCC) is a close-packed structure, it resists the pressure more than -Fe, or -Fe (BCC) which are more open structures (less densely packed), and that is why the area of stabilisation of -Fe increases with the increase of pressure. 1.16 illustrates that there are 8 tetrahedral holes per unit cell. FCC materials have more slip systems, or ways for dislocations to move, than BCC materials. When the temperature reaches 910 C , another . Make sure the Variac has a slow-blow fuse. The bcc lattice, although cubic, is not closely packed and forms strong metals. It does not store any personal data. In FCC -iron, octahedral holes are large sized than tetrahedral holes and thus carbon atoms sit in these symmetrical octahedral holes even though some uniform lattice expansion takes place. As it continues to cool back to room temperature the wire shrinks back to approximately its original length. 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! Is martensite a BCC? In any crystal structure, there are small holes in between the usual atoms into which smaller interstitial atoms may sit to form interstitial solid solution. The solubility of carbon in iron essentially depends on the crystal structure in which iron exists (and also the temperature). FCC metals tend to be more ductile than BCC metals because of their different slip systems. Although BCC has more total room for interstitial atoms, FCC has the largest particular interstitial site (octahedral). In general, alloys with these metals will have the same crystal structure as the most common element. Hope you'll find our explanations and tips useful! The parent phase may transform if its temperature is changed where the product phase has lower free energy. Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. Thus, tetrahedral holes are not preferred sites in -iron (also ferrite) for carbon but prefer smaller octahedral holes. This cookie is set by GDPR Cookie Consent plugin. Then, when considered the net total of spheres in a BCC unit cell, it has 2 spheres because one corner has 1/8 th of spheres. There is, however, no cold shortness for fcc metals. The temperature range of Curie transformation is unaffected by the variations in cooling, or heating rate and always occurs over the same temperature range. 1.12 (b) 4] is smaller than of - Fe [Fig. It precipitates out as a discrete structure and the. At very high pressure, a fourth form exists, called epsilon iron (-Fe). c-axis tries to become larger than -axis. The cookie is used to store the user consent for the cookies in the category "Performance". Accordingly, for BCC metals the lattice friction stress is higher at low temperatures and decreases as temperature is raised. What is the density of FCC -iron at 20C? It is also true of nitrogen in iron. Volume Change During BCC to FCC Iron transformation//Calculation of Volume change in transformations Metallurgical facts 4.45K subscribers Subscribe 4K views 2 years ago Physical Metallurgy. Depending on the element, the thermal energy to activate the slip systems will be different. What does it mean that the Bible was divinely inspired? If you are interested in more details about any specific crystal structure, I have written individual articles about simple crystal structures which correspond to each of the 14 Bravais lattices: 1. There are 8 octahedral site positions per unit cell in the FCC crystal structure.There are (64)/2 = 12 octahedral site positions per unit cell in the BCC crystal structure. A face-centered cubic crystal structure will exhibit more ductility (deform more readily under load before breaking) than a body-centered cubic structure. The lattice parameter of -iron increases with the increase of temperature due to increase of thermal vibrations, increase of vacancies etc., which also means increase in the size of the interstitial holes too. This cookie is set by GDPR Cookie Consent plugin. Gamma-iron unit cell has greater lattice parameter than -iron unit cell, but atomic packing factor of FCC is 0.74, that is, 26% of the volume of unit cell is unoccupied by atoms; and is 0.68 in BCC, that is, 32% of the volume of unit cell is unoccupied by atoms. At this. It is thermodynamically stable and a fairly soft metal. This is not true for BCC. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". Set the Variac voltage to 0, switch on the Variac, and then increase the voltage slowly to about 95 volts. The presence of carbon in octahedral hole in BCC -iron causes tetragonal distortion of lattice, and this large strain permits ferrite to accommodate only a limited number of carbon atoms, and thus, the lattice remains essentially body centred cubic. In the ground state the bcc -phase is stable, and at the temperature T=1184 K (A 3 point), -Fe transforms into fcc -Fe, which is stable up to 1665 K (A 4 point). FCC and BCC crystal structure also have different arrangements of interstitial sites. As -iron having FCC structure is a close-packed structure (APF = 0.74) and -iron (BCC) is more loosely packed (APF = 0.68), the FCC structure has large sized interstitial holes but fewer in number as compared to BCC structure which has small sized interstitial holes but inter-connected large number of them, the diffusion of both substitutional and interstitial solute takes place faster in ferrite than in austenite, and that is why activation energy is less for a particular element diffusing in -iron than it is for the same element diffusing in - iron. Thus, super-cooling during cooling cycle and superheating during heating cycle, become necessary to bring about the changes resulting in the thermal hysteresis, which can be reduced by slow heating and cooling rates and increased with faster rates of heating and cooling. Therefore, considering that three significant digits should be used in all calculations, the answer will be a = 4R / 3 a = 4 (0.124 nm) / 3 a = 0.287 nm

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