These are actually primitive vectors, which you can read about in the section below. 43, 229236 (2016). ADS PhD in Materials Science Is it Worth Doing? The carbon concentration in the steel before carburization is 206.5 \ ppm and is initially uniform through the thickness of the. Phys. BCC is nearly close-packed and has an APF of 0.68. Fig. Miner. 97, 14171420 (2012). 1. Hirose, K., Labrosse, S. & Hernlund, J. At 11851667K the crystal structure of iron changes to a face-centred cubic (fcc) cell (-Fe or fcc-Fe), however, above 1667K and up to the melting temperature of 1811K, iron again has the bcc structure (-Fe). Zeitschrift fur Angewandte Physik 23, 245249 (1967). Science Lett. Rev. What is the Difference Between Allotropes and Isotopes? What is the Materials Science Tetrahedron (Paradigm)? Lu, X.-G., Selleby, M. & Sundman, B. Therefore, the hcpliquid curve overlaps the metastable fccliquid curve at pressures of about 160GPa. Molodets, A., Molodets, M. & Nabatov, S. Helmholtzfree energy of molten metals. Assume that impure copper contains only Fe, Au and Ag as impurities. What is the Difference Between Materials Science and Chemical Engineering? 233, 2432 (2014). 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 . 14. Iota, V. et al. Connect and share knowledge within a single location that is structured and easy to search. Make sure to explain clearly the different . Correspondence to 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 For a full article explaining APF, check out this link. (Simple Explanation), What Is the Difference Between FCC and BCC? Assessments of molar volume and thermal expansion for selected bcc, fcc and hcp metallic elements. The calculated volumes of fcc-Fe26,28 are plotted between bcc and fcc phases in Supplementary Figure S2. Komabayashi, T. Thermodynamics of melting relations in the system Fe-FeO at high pressure: Implications for oxygen in the Earths core. Rev. That picture shows two unit cells of the fcc lattice. To learn more, see our tips on writing great answers. 188, 114120 (2011). One more experimental dataset64 overestimates pressures by up to 6GPa compared with our data for fcc-Fe. High pressure allotropes . Kuwabara, S. Sound velocity and elastic properties of FeNi and FeNiC liquids at high pressure. 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. (Definition, Examples, and Metallurgy), The Difference Between Alloys and Composites (and Compounds), The Hume-Rothery Rules for Solid Solution. Total number of atoms per unit cell = 2. That is, 68% of the volume of the BCC unit cell is occupied by atoms and the remaining 32% is empty space. 10 and 37, whereas the EoS of Fe liquid was calculated using the standard approach38,39,40. 43, 68376843 (2016). From first-principles theory, aluminum doping drives the alloy structurally from FCC to BCC separated by a narrow two-phase region (FCC+BCC), which is well supported by our experiments. 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. b) a square with smaller area. Geophys. Face-Centered Orthorhombic11. 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. B 87, 014405 (2013). 95, 2173721742 (1990). The authors used a microscopic phenomenological model for longitudinal spin fluctuations (LSFs) based on density functional theory calculations. Solution: Each unit cell of BCC iron contains 2 atoms. (b) reduces by 4. These transitions can also be confirmed by the temperature dependence of the Gibbs energy of the fcc, hcp, and liquid iron at 125GPa (Fig. Phys. Number of atoms . 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 ) . 1.069B. b. (With Examples Beyond Carbon). The melting point of iron is experimentally well defined for pressures less than 50GPa. Miner. How to tell which packages are held back due to phased updates, Full text of the 'Sri Mahalakshmi Dhyanam & Stotram'. The A2 forms the boundary between the beta iron and alpha fields in the phase diagram in Figure 1. 18 and 20 is based on the Gibbs free energy calculations depending on temperature and pressure. Google Scholar. Res. This phenomenon is called the ductile-to-brittle transformation temperature (DBTT). Since we use the hard sphere model, each point inside the cell is either part of an atom, or part of the void.if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'msestudent_com-large-leaderboard-2','ezslot_5',124,'0','0'])};__ez_fad_position('div-gpt-ad-msestudent_com-large-leaderboard-2-0'); APF is basically the fraction of atoms to void. J. Geophys. The body-centered cubic structure has an atom at all 8 corner positions, and another one at the center of the cube. 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. Geophys. Here are the primitive vectors for the BCC unit cell. When heating iron above 912C (1,674F), its crystal structure changes to a face-centered cubic (fcc) crystalline structure. The atomic radii of iron atoms at this temperature are 0.126 and 0.129 nm for bcc and fcc, respectively. A cylindrical copper rod has resistance R. It is reformed to twice its original length with no change of volume. ADS Compute the percent volume change associated with . Among these are the potentials by Meyer and Entel (1998 Phys. Inter. (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. The position of the liquid triple point in the phase diagram of iron has been determined many times and revealed highly controversial results (Fig. 65 and 66 (Supplementary Figure S6). 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). Res. & Fei, Y. Calculate the temperature of the 2-mole system, which is, One heating -Ti (hcp) transforms to -Ti (bcc) at 1175 K with enthalpy of transformation equal to 4,480 J/mol. Funtikov, A. 1. Chem. Determine . [2][3][4] The outer core surrounding the solid inner core is believed to be composed of liquid iron mixed with nickel and trace amounts of lighter elements. The obtained EoSs allow calculation of PVT relations and thermodynamic properties of Fe at the Earths core conditions (up to 6000K and 350GPa). Inter. Phys. 6 are in reasonable agreement with our EoS of hcp-Fe. This is an important concept in your introductory materials science class, so if you want a full explanation of APF, check out this page. 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? (b) slightly increases. a) If a page is reduced to 80%, what percent enlargement is needed to return it to its original size? 286, 556564 (2009). Sorry, you do not have permission to ask a question, You must login to ask a question. The calculated isentrope for liquid iron from 5000K to 8000K is presented in ref. 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. (Metallurgy, How They Work, and Applications), What is the Difference Between Iron, Steel, and Cast Iron? Whereas the melting curve goes 500K higher than the experimentally determined one14 at 100200GPa. c. doubles twice. 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. Compute and compare its theoretical density with the experimental value found inside the front cover. Rev. We thank the reviewers for critical comments and suggestions. 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. How would "dark matter", subject only to gravity, behave? Physics of the Solid State What is the fractional volume change in iron as it transforms from. That is not the maximum (which is 12, found in close-packed structures), but BCC has such high stability because of its next-nearest neighbors.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'); There are 6 next-nearest neighbors, but these are only 15% farther away than the nearest-neighbors. initiated the project. 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). 3 mol liter-1 in 5 seconds. Condens. The Infona portal uses cookies, i.e. A.D., T.S. How can I get that mathematically? Phys. Phys. Earth Planet. 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. 13, 11531156 (1986). The idea being do perform an action on volume change, e.g. 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. The pressure obtained based on the compressional wave sound velocity and density measurements of bcc-Fe61 is also shown in Supplementary Figure S5 for comparison. If the diameter of a radar dish is doubled, what happens to its resolving power assuming that all other factors remain unchanged? One more important marker for calibration of the Gibbs energy for hcp-Fe and liquid Fe was the liquid triple point14. B. inversely proportional. Res. Calculate the linear density for [111] direction in . High Press. Dependence of pressure on molar volume near the transition in iron. What is the change in an e. Is there any peak shift between bulk and nano materials in XRD? Lett. Adding some elements, such as Chromium, narrows the temperature range for the gamma phase, while others increase the temperature range of the gamma phase. (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? Simple Orthorhombic9. The calculations95 indicate that the P-wave velocity is 2.5% lower than PREM at the ICB conditions and very close to PREM at the CMB. Nature 363, 534536 (1993). An alternate stable form, if it exists, may appear at pressures of at least 50GPa and temperatures of at least 1,500K; it has been thought to have an orthorhombic or a double hcp structure. The mass of the piston is such that the water exists as saturated liquid at 10.0 MPa. Phys. Zharkov, V. N. & Kalinin, V. A. Equations of State of Solids at High Pressures and Temperatures (ed. Geophys. If a distance between two nearest atoms is 3.7 ? 0.1292 nm respectively. Some Cr2O3 at 25C was added into it, which cause the following exothermic reaction to occur: How many atoms belong to the BCC cell? Lett. Describing complex Bravais lattice as a simple Bravais lattice with a basis. b.) Determine whether the following statement is true or false: The strength of a metal increases with reducing grain size. This is consistent with the packing density calculations reported in lecture that give FCC as being 74% dense and BCC 68% dense. Rev. Geol. Simple Cubic2. The structure of a denser lattice will have a better packing fraction than the other one. 2Al(l) + Cr2O3(s) = 2Cr(s) + Al2O3(s), Copyright 2021 Askmemetallurgy.com, All rights reserved. Vinet, P., Ferrante, J., Rose, J. H. & Smith, J. R. Compressibility of solids. Fei, Y. et al. At these conditions, the entropy for liquid iron, S=114.15Jmol1K1 and hcp-Fe, S=107.2Jmol1K1, were determined from eqs 7 and 17. Almost all properties . Ichikawa, H., Tsuchiya, T. & Tange, Y. Composition and state of the core. 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). 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. Why? Mao, H. K., Bell, P. M., Shaner, J. W. & Steinberg, D. J. The ratio of the densities calculated here is precisely the same: 7.86 0.68 = 8.60 0.74. Sci. The inner core of the Earth is generally assumed to consist essentially of a crystalline iron-nickel alloy with structure. 84). Calculate the volume change in percentage during. Equation of state of -Fe: Reference density for planetary cores. (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. Res. D. It is reduced to 1/8th of its original value. 19) it means that B0=0.3 and this value seems to be too high for the EoS of hcp-Fe. The square is heated uniformly, as a result, it turns into a) a square with larger area. 1.231 An intensity level change of +2.00 dB corresponds to what percentage change in intensity? It is important to compare the thermodynamics of these phases calculated by different methods. and JavaScript. Elements in the same period on the Periodic Table will have the.. A. the same number of electrons B. same number of protons C. an increasing number of protons as they move across the period D. decreasing number of protons as they mov. The initial temperature in our model is 5882K at the inner core boundary (ICB) (328.9GPa) (Fig. (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. A gain of 6 dB means that the signal level or strength: a. increases very little. Later, the point was shifted back to 75GPa and 2700K74. Show that the reciprocal lattice of the direct FCC lattice is a BCC lattice. The melting curve was found to be very close to the hcpliquid curve. Article The fitted parameters of EoS for liquid Fe are listed in Table 1. Acad. True or false? Brown, M. J. & Ahrens, T. J. If you are interested in why BCC metals have different properties than FCC metals (another common structure), you should check out this article. Calphad 2, 227238 (1978). FCC unit cell has 4 atoms per unit cell as compared to BCC having 2 atoms per unit cell. Compute the percentage volume change associated with this reaction. (d) Calculated P-wave velocity along the isentrope. Belashchenko, D. K. Estimation of the thermodynamic characteristics of the Earths core using the embedded atom model. Phys. M. N. Magomedov. Round your result to 2 decimal places. Iron (Fe) undergoes an allotropic transformation at 912 C: upon heating from a BCC (phase) to an FCC ( phase). Most measurements are scattered for less than 2GPa in the 80GPa pressure range (Supplementary Figure S7). Comput. In ref. (13). Assume that the radius of the Fe atom correspondingly changes from 0.1358 nm to 0.1381 nm. In plain-carbon steel, austenite exists above the critical eutectoid temperature of 1000 K (727 C); other alloys of steel have different eutectoid temperatures. %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 . The newly measured melting line of Fe extrapolated to 330GPa reveals a temperature of about 6230500 K14. In the meantime, to ensure continued support, we are displaying the site without styles Phys. reviewed the manuscript. & Dewaele, A. Equations of state of MgO, Au, Pt, NaCl-B1, and NaCl-B2: Internally consistent high-temperature pressure scales. A square is cut out of a copper sheet. Geophys. Phys. Please enter your email address. Anderson, W. W. & Ahrens, T. J. 90, 042505 (2007). Question: Q.5. 1. The wavelength of the Kα lines are 194 pm for iron and 229 pm for the unknown. 119 (2014). PubMedGoogle Scholar. Rev. FCC-to-BCC phase transition in NaCl, Buckingham or Lennard-Jones potentials? Solid Earth 36, 958964 (2000). Funtikov, A. & Guyot, F. Thermal equation of state of iron and Fe0.91Si0.09. 16, S973S982 (2004). 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? BCC metals also tend to have a high melting point, because they have a large number of nearest neighbors and next-nearest neighbors. Article Swartzendruber, L. The Fe (Iron) System. 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. Belonoshko, A. This pressure is similar to the calculated bcc-hcp transition for pure iron . (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. The susceptibility of magnesium at 300 \ K is 1.2 \times 10^{-5} . Slip systems are the way that atoms slide past each other when deforming. Accordingly, in equation (1) for liquid Fe, the magnetic part is excluded, whereas the entropy parameter is added: The reference temperature for liquid Fe at 0.1MPa is T0=1811K. Along the reference isotherm, the pressure was calculated using eq. Huang, E., Bassett, W. A. The hcp-Fe melts at 4033K and at higher temperatures the liquid is the only stable phase. Institute of Earths Crust, SB RAS, Irkutsk, Russia, V. S. Sobolev Institute of Geology and Mineralogy SB RAS, Novosibirsk, Russia, Novosibirsk State University, Novosibirsk, Russia, You can also search for this author in At the conditions near the fcchcpliquid triple point the Clapeyron slope of the fccliquid curve is dT/dP=12.8K/GPa while the slope of the hcpliquid curve is higher (dT/dP=13.7K/GPa). At temperatures between 912 degree C and 1394 degree C, the crystal structure changes to FCC. 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. Lett. What is the density of FCC -iron at 20C? The calibration of the Gibbs energy of hcp-Fe was performed using the triple point11, the transition at room temperature68,69,70, and considering the slope of the transition14 (Fig. Molodets, A., Molodets, M. & Nabatov, S. Free energy of liquid diamond. However, it was shown that at 18GPa bcc-Fe transforms into hcp-Fe and the value of the magnetic moment becomes zero46. Toward a mineral physics reference model for the Moons core. When a bimetallic strip is cooled, will the strip bend toward the side with the smaller coefficient of linear expansion or the side with the larger coefficient of linear expansion? & Tatsumi, Y. Combustion, Explosion and Shock Waves 35, 185190 (1999). Asking for help, clarification, or responding to other answers. Earth Planet. In reciprocal space, BCC becomes an FCC structure. Boehler, R., Vonbargen, N. & Chopelas, A. Melting, thermal-expansion, and phase-transitions of iron at high-pressures. 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? The phase boundary between the different solid phases is drawn on a binary phase diagram, usually plotted as temperature versus percent iron. The position of the triple point was estimated at 75GPa and 2500K73. Redox-structure dependence of molten iron oxides, Hexagonal Close-packed Iron Hydride behind the Conventional Phase Diagram, Electronic correlations and transport in iron at Earths core conditions, No system-size anomalies in entropy of bcc iron at Earths inner-core conditions, Melting phase relations in FeSiH at high pressure and implications for Earths inner core crystallization, Superionic iron alloys and their seismic velocities in Earths inner core, Stability and nature of the volume collapse of -Fe2O3 under extreme conditions, Viscosity of hcp iron at Earths inner core conditions from density functional theory, (Fe,Ni)2P allabogdanite can be an ambient pressure phase in iron meteorites, http://creativecommons.org/licenses/by/4.0/, Core origin of seismic velocity anomalies at Earths coremantle boundary, Stratification in planetary cores by liquid immiscibility in Fe-S-H, Thermal conductivity of iron and nickel during melting: Implication to the planetary liquid outer core, Compressional wave velocity for iron hydrides to 100 gigapascals via picosecond acoustics, Equations of state of clino- and orthoenstatite and phase relations in the MgSiO3 system at pressures up to 12 GPa and high temperatures. ADS What is the unknown material? If the change in their lengths are the same for the same change in temperat. Now we need to count how many atoms are in each unit cell. 0.1292 nm respectively. d. first decreases and then enhances. 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. How many excess electrons are on the sock? 7.12 An FCC iron-carbon alloy initially containing 0.35 wt% C is exposed to an oxygen-rich and virtually carbon-free atmosphere at 1400 K (1127 C . An monatomic ideal gas at 300 K has a volume of 15 liters at a pressure of 15 atm. Triclinic. In this work, we propose updated EoSs for Fe phases based on a formalism from our recent publications29,30,31,32,33,34,35,36. fcc = DF Fe!fcc +DF Fe!X DFFe!X. Quasihydrostatic equation of state of iron above 2 Mbar. Earth Planet. The body-centered cubic cell belongs to space group #229 or , Strukturbericht A2, and Pearson symbol cI2. J. Phys. Decker, D. L. Equation of State of NaCl and Its Use as a Pressure Gauge in HighPressure Research. Boehler, R., Santamara-Prez, D., Errandonea, D. & Mezouar, M. Melting, density, and anisotropy of iron at core conditions: new X-ray measurements to 150 GPa. The calculated entropy at pressure 0.1MPa is very close to the reference data9. The Clapeyron slope (T/P)S for hcp-Fe differs significantly for both the liquid Fe and the calculated model95. If you are interested in primitive cells, you can read all about them in this article. 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. Zarkevich, N. A. & 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. If you heat the ring, will the gap become wider or narrower? a cubic bcc lattice is created without the need to change the volume of the bct cell. At 125GPa the fcc-Fe melts at 4019K, however, this point is in the stability field of the hcp-Fe. The melting line of Fe determined in ref. Supplementary Figures S5S8 show the differences between calculated pressures at different temperatures with direct experimental measurements of pressure. CAS 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. (c) Calculated density along the 5882K isentrope. By registering, you agree to the Terms of Service and Privacy Policy .*. Problem #2 . so if you want a full explanation of APF, check out this page. Based on this result and the Lindemann criterion of melting we derived the analytical expression of volume-dependent melting temperature. Choose the best answer to the following. Sciences 41, 657691 (2013). [20], "Gamma loop" redirects here. Equation of state of pure iron and Fe0.9Ni0.1 alloy up to 3 Mbar. Dorogokupets, P. I. P-V-T Equations of state of MgO and thermodynamics. 244, 6977 (2015). The equation for the Helmholtz free energy for liquid metal can be rewritten38,39,40. B 85, 214105 (2012). 14 because our EoS of liquid iron is based mainly on these data. (Crystal Structure, Properties, Interstitial Sites, and Examples), What is the Difference Between FCC and HCP? J. Appl. Lett. The melting line of Fe in ref. [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. Google Scholar. Liquid iron-sulfur alloys at outer core conditions by first-principles calculations. b) What is the change in the period in seconds?
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