Austenite is a metallic, non-magnetic solid solution of carbon and iron that exists in steel above the critical temperature of 1333F ( 723C). 1) is presented in Fig. (5) at T f = 1184 K: the upper curve is for bcc-Fe; the lower curve is for fcc-Fe. For these conditions, the following parameters were recommended84: V0=7.957cm3mol1, KS0=109.5GPa, (V)=92E6K1, 0=1.735, and CP=46.632Jmol1K1. Yes, that's correct. Umemoto, K. et al. The body-centered cubic structure of iron, which is called ferrite, is stable at (i) a temperature of 1,665K (1,392) or above and (ii) at 1,184K (911) or below, Iron crystal structures. Zeitschrift fur Angewandte Physik 23, 245249 (1967). 97, 14171420 (2012). & Skorodumova, N. V. Impact of magnetism on Fe under Earths core conditions. Answer (1 of 3): It's the thermodynamics of these two crystal structures. Compute the percentage volume change associated with this reaction. Res. 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. If a distance between two nearest atoms is 3.7 ? This quantity can be calculated using free-energy perturbation theory [31,36,37]. We thank the reviewers for critical comments and suggestions. Allotropes of iron - Wikipedia (c) increases by 2. (a) Calculated isentropic temperature profile started from 5882K at 328.9GPa for liquid and hcp-iron compared with the reference data95 (b) Calculated adiabatic bulk modulus along adiabats for solid and liquid iron. 16, S973S982 (2004). Res. Let's consider only one unit cell for the calculation of percentage change in the density and volume. Calphad 15, 317425 (1991). Phys. 36, 157161 (1965). Show that the reciprocal lattice of the direct FCC lattice is a BCC lattice. As was shown recently59, this scale underestimates pressure by 0.5GPa (at 1015GPa) in comparison with another NaCl EoS60. If B0=0.14, then melting of the hcp-Fe is observed at 7150K and 328.9GPa and is in agreement with the computer calculations90. (Simple Explanation), What are Space Groups? Dewaele, A. et al. B 87, 014405 (2013). What is the ratio of the. 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 values of these functions can be found in Tables S1S4. How does the number of atoms in a 27.5-gram iron ring compare to the number in a chrome ring of the same mass? Materials | Free Full-Text | A Newly Designed High-Strength Tool Steel Anderson, O. L. & Isaak, D. G. The dependence of the Anderson-Grneisen parameter T upon compression at extreme conditions. c) a rectangle with larger area. Base-Centered Monoclinic14. Austenite | Metallurgy for Dummies Dorogokupets, P. I. (b) doubles. Science 316, 18801883 (2007). When an element ejects a beta particle, the atomic number of that element (a) reduces by 1. Mao, H., Wu, Y., Chen, L., Shu, J. 42, 32393244 (1973). Belashchenko, D. K. Estimation of the thermodynamic characteristics of the Earths core using the embedded atom model. Question: Q.5. & 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. 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. Data 15, 967983 (1986). At these conditions, the entropy for liquid iron, S=114.15Jmol1K1 and hcp-Fe, S=107.2Jmol1K1, were determined from eqs 7 and 17. Allotropy of Iron: Thermodynamics and Crystal Structures | Metallurgy At 30 GPa, the dhcp phase appears in the diffraction patterns. 10 and 37 with modifications from ref. 8 4 5 u) PDF Session #15: Homework Solutions 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? The thermodynamic properties of liquid iron at a pressure of 0.1MPa calculated from our EoS (Supplementary Table S4) are in good agreement with the measured values of density84, the sound velocity (vP) and adiabatic bulk modulus84,85,86. The triple point of iron investigated by high pressurehigh temperature neutron scattering. Phys. FCC. BCC and HCP Metals - University of Rhode Island Geol. 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. PDF USNA :: United States Naval Academy The phase boundary between the different solid phases is drawn on a binary phase diagram, usually plotted as temperature versus percent iron. Thank you for visiting nature.com. The following transition can be caused by the kinetics of the transition process or the effect of fcc-Fe and hcp-Fe magnetic moment. 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 . Differentiating eq. These transitions can also be confirmed by the temperature dependence of the Gibbs energy of the fcc, hcp, and liquid iron at 125GPa (Fig. Describing complex Bravais lattice as a simple Bravais lattice with a basis. 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 It is thermodynamically stable and a fairly soft metal. Technic. B., Ahuja, R. & Johansson, B. Quasi - Ab initio molecular dynamic study of Fe melting. The measurements in Ne and Ar pressure media show an alternative deviation from our data53. Show that beta approx 3alpha, by calculating the change in volume DeltaV of a cube with sides of length L. 13.3, The reaction; 2N 2 O 5 greater than 4NO 2 + 02, shows an increase in the concentration of NO 2 by 20 * 10 ? BCC to FCC transformation in Iron (Problem discussion) Why does iron have a bcc and FCC structure? - ProfoundAdvice B. At higher pressures, the room temperature isotherm6 is consistent with our EoS of hcp-Fe (Supplementary Figure S8). BCC has 2 atoms per unit cell, lattice constant a = 4R/3, Coordination number CN = 8, and Atomic Packing Factor APF = 68%. In order to wake a sleeping child, the volume on an alarm clock is tripled. Res. D. 6. M. N. Magomedov. 2. 0.725C. J. Phys. Science Lett. Now we need to count how many atoms are in each unit cell. P.D., T.S., A.D. and K.L. B 91, 174105 (2015). 26, 206211 (1999). The fitted parameters of EoS for liquid Fe are listed in Table 1. a-e transition pathway of iron under quasihydrostatic pressure conditions. 119 (2014). Phys. Finally, the melting line of Fe measured using a synchrotron-based fast X-ray diffraction method was also proposed14. (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 pressure scales are shown in the legends to the figures. & Bell, P. Calibration of the ruby pressure gauge to 800 kbar under quasi-hydrostatic conditions. The obtained EoSs allow calculation of PVT relations and thermodynamic properties of Fe at the Earths core conditions (up to 6000K and 350GPa). Komabayashi, T. & Fei, Y. W. Internally consistent thermodynamic database for iron to the Earths core conditions. J. Appl. Allotropy of Metals (With Diagram) | Metallurgy - Engineering Notes India This is a tedious but fairly straightforward calculation. 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. Inter. Decker, D. L. High-pressure equation of state for NaCl, KCl, and CsCl. If youre interested in advanced crystallography or crystallography databases, you may want to check out the AFLOW crystallographic library. 18 and 20 is based on the Gibbs free energy calculations depending on temperature and pressure. This work was financially supported by Russian Science Foundation (No 14-17-00601) and performed under program of Ministry of education and science of Russian Federation (Project No 14.B25.31.0032). : Condens.Matter 19 326220) and by Lee et al (2012 J. Geophys. Phys. However, it was shown that at 18GPa bcc-Fe transforms into hcp-Fe and the value of the magnetic moment becomes zero46. 3.6 g/cm^3 to kg/m^3 b. Dorogokupets, P. I., Sokolova, T. S. & Litasov, K. D. Thermodynamic properties of bcc-Fe to melting temperature and pressure to 15 GPa. By submitting a comment you agree to abide by our Terms and Community Guidelines. The nearest neighbor distance is , and the next-nearest neighbor distance is (or about ). & Ponyatovsky, E. G. In Advances in Metallic Alloys V.4 Phase transformations of elements under high pressure (eds Fridlyander, J. N. & Eskin, D. G. ) 377 (CRC Press Boca Raton, Florida, 2005). BCC has 2 atoms per unit cell, lattice constant a = 4R/3, Coordination number CN = 8, and Atomic Packing Factor APF = 68%.if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[250,250],'msestudent_com-medrectangle-4','ezslot_2',143,'0','0'])};__ez_fad_position('div-gpt-ad-msestudent_com-medrectangle-4-0'); Dont worry, Ill explain what those numbers mean and why theyre important later in the article. How to tell which packages are held back due to phased updates, Full text of the 'Sri Mahalakshmi Dhyanam & Stotram'. The transformation from fcc to bcc can be considered as a homogeneous distortion, like that in figure 2. The body-centered cubic structure has an atom at all 8 corner positions, and another one at the center of the cube. Iron has a BCC structure at room temperature. We determined the density deficit of hcp-Fe at the inner core boundary (T=5882K and P=328.9GPa) to be 4.4%. Lett. The square is heated uniformly. An X-ray with a copper target is operated at 40 kV and 44 mA. 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. Saxena, S. K. & Eriksson, G. Thermodynamics of iron at extreme pressures and temperatures. There is also a full atom in the center of the cube. We store cookies data for a seamless user experience. A novel method was presented for detecting the solidliquid phase boundary of compressed iron at high temperatures using synchrotron Mssbauer spectroscopy81. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Iron-Carbon Phases | Metallurgy for Dummies Styling contours by colour and by line thickness in QGIS. J. Geophys. Lett. Materials | Free Full-Text | Degradation and Protection of Materials Alfe, D. Temperature of the inner-core boundary of the Earth: Melting of iron at high pressure from first-principles coexistence simulations. 2.6 m/s^2 to km/hr^2 c. 3.5 m^2. The triple point calculated from our data is located at P=106.5GPa and T=3787K. The EoS of liquid Fe was estimated using the following approach (eq. Phase Equilibria 3, 161165 (1982). The magnetic moment of the hcp-Fe is 0=0.28 at ambient conditions10. 1). In reciprocal space, BCC becomes an FCC structure. a) Calculate the original period in seconds. ), or their login data. Altshuler, L. V., Brusnikin, S. E. & Kuzmenkov, E. A. Isotherms and Gruneisen functions for 25 metals. 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. b) What is the change in the period in seconds? Phys. Simple Monoclinic13. Res. It becomes four times larger. Make sure to explain clearly the different steps you have undertaken to come up with the solution. At high-pressure conditions, the metastable bcchcp curve is located inside the fcc-Fe or liquid stability field. Amer. Phys. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Google Scholar. Decker, D. L. Equation of State of NaCl and Its Use as a Pressure Gauge in HighPressure Research. Volume and pressure-dependent thermodynamic properties of sodium Sakai, T., Ohtani, E., Hirao, N. & Ohishi, Y. Anderson, W. W. & Ahrens, T. J. Rev. Calculate how much thermal energy is transferred. 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. 2 Experimental constraints on core composition (eds Holland, H. D. & Turekian, K. K. ) 521546 (Elsevier Pergamon, Oxford, 2003). PubMedGoogle Scholar. 10 and 37, whereas the EoS of Fe liquid was calculated using the standard approach38,39,40. Tange, Y., Nishihara Y. The volume dependence of Gruneisen parameter of sodium has been firstly analyzed. Dewaele, A. Further complicating BCC ductility: these slip systems may not always be active. Thermodynamics and Equations of State of Iron to 350 GPa and 6000 K. Sci. The thermodynamic formalism in ref. Rev. The compressive stress in the surface layer created from the implosion of cavitation bubbles depends on the aggressiveness of the cavitation, which in turn depends on the test device . 39, L20308 (2012). You can see that, if the fcc cell dimensions are taken to be of unit length, the body-centred tetragonal cell has dimensions $\frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}} \times 1$. Res. If the mass of the bob of simple pendulum decreases, its time period will increase or decrease? Appl. Double Hexagonal Close-Packed (La-type)5. Phys. Calculate the volume change ?V/V (%) arising from the transformation of iron from FCC to BCC during cooling from 1000 C. What is the respective length change ?L/L? & Brosh, E. Experimental study and thermodynamic calculations of phase relations in the FeC system at high pressure. 1. a=b^2; a=2R. The calculated isentropic temperature profile for hcp-iron and liquid iron started from 6000K based on the reference data95 are also presented in Fig. What property is now used instead of atomic mass? The A2 forms the boundary between the beta iron and alpha fields in the phase diagram in Figure 1. (The question itself is not the same as yours). we told the simple way of calculations of relative volume change in transformation of BCC iron to FCC Iron. Earth Planet. 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 . The position of the liquid triple point in the phase diagram of iron has been determined many times and revealed highly controversial results (Fig. True or False? 0.84 g iron ore containing X percent of iron was taken in a solution containing all the iron in the ferrous state. To calculate the pressure, the Ne, NaCl-B2, and Pt pressure scales52, and the MgO pressure scale71 were used. Figures S9S11 show comparisons of the thermodynamic functions calculated by these two methods for fcc, hcp, and liquid iron. Use this information to calculate Avogadro's number. Dewaele, A. et al. 14 as more accurate. B. inversely proportional. & Huang, H. Thermal equation of state of hcp-iron: Constraint on the density deficit of Earths solid inner core. Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. At 1394C, -iron changes to -iron (BCC structure), the second allotropic change. Almost all properties . Brown, M. J. 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. Earth Planet. Rev. 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. An extrapolation to high-pressure conditions revealed the very close position of the melting curves of fcc- and hcp-Fe. How to cite this article: Dorogokupets, P. I. et al. One more experimental dataset64 overestimates pressures by up to 6GPa compared with our data for fcc-Fe. It becomes four times larger. The 298K isotherm for -Fe was calculated using the compressibility curve from ref. How does the number of atoms in a 27.5 gram iron ring compare to the number in a chrome ring of the same mass? Lett. Geodyn. Curves fccliq and bcchcp are extrapolated. 25, 297356 (1981). d. first decreases and then enhances. Annual Rev . & Garbarino, G. Low temperature equation of state of epsilon-iron. 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 authors described the second discontinuity at 243GPa as melting of the fcc-Fe. 0.1292 nm respectively. Disconnect between goals and daily tasksIs it me, or the industry? That picture shows two unit cells of the fcc lattice. Solids 54, 221227 (1993). Internet Explorer). To obtain Iron (Fe) undergoes an allotropic transformation at $912^{\c | Quizlet In solid-state chemistry, generally metals such as iron are considered to be made up of unit cells. What is \newluafunction? B-H vs M-H Hysteresis Loops: Magnetic Induction vs Magnetization (Similarities, Differences, and Points on the Graph), What is Scanning Electron Microscopy? Proc. Which of the following is a chemical change that occurs to the food? msestudent is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com. Phys. All rights reserved. B 91, 174194 (2015). Boehler, R., Vonbargen, N. & Chopelas, A. Melting, thermal-expansion, and phase-transitions of iron at high-pressures. When heating iron above 912 C (1,674 F), its crystal structure changes to a face-centered cubic (fcc) crystalline structure. At higher pressure conditions, the metastable bcchcp curve is in the fcc-Fe or liquid stability field. PNAS 115, 39163919 (2015). There are two triple points along the melting line of Fe. In an FCC structure as the name suggests atoms are present at each corner of the lattice as well as at the center of each face whereas in case of BCC structure atoms are present at each corner of the lattice and at the center of the lattice. Calculate the percentage of change in volume that occurs when BCC iron is heated and changes to FCC iron. Prashant Singh - Scientist I - Ames Laboratory | LinkedIn Fei, Y. 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. It can be emphasized that in the Supplementary Figure S8 the measurements for hcp-Fe14 deviate in the same way, but with larger scattering at 140GPa than data for fcc-Fe in Supplementary Figure S6. Google Scholar. High Temp. The calculated triple points have the following parameters: bccfcchcp is located at 7.3GPa and 820K, bccfccliquid at 5.2GPa and 1998K, and fcchcpliquid at 106.5GPa and 3787K. The melting temperature is 5882 at ICB pressure (328.9GPa). This same trend appears for ruthenium but not osmium. Calculate the linear density for [111] direction in . (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. App. (Solved) - Calculate the volume change ?V/V (%) arising from the (1 Recently, the PVT relationships for hcp-Fe in different pressure-transmitting media at 300K up to 205GPa and at 1800K up to 100GPa have been investigated6. 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. Report No. Geophys. ADS However, below its Curie temperature (TC or A2) of 771C (1044K or 1420F),[5] it becomes ferromagnetic. 55, 56 and 60 using the NaCl scale60, a better consistency with our EoS for bcc-Fe is obtained, which confirms the relevance of the experimental data mentioned above55,56. It is one of the most common structures for metals. High Temp. The wavelength of the Kα lines are 194 pm for iron and 229 pm for the unknown. Mao, H. K., Bassett, W. A. reviewed the manuscript. 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. Figure 5d shows that the calculated P-wave velocity for liquid iron is 5.45.7% lower than PREM and consistent with the calculated estimations84. Oxidation of Metals 86, 58015808 (1999). so if you want a full explanation of APF, check out this page. If you are interested in primitive cells, you can read all about them in this article. At 125GPa the fcc-Fe melts at 4019K, however, this point is in the stability field of the hcp-Fe. e. It becomes one-fourth as large. Google Scholar. We prepared gold quasi-BCC nanolattices with beam diameters of 117 5 nm, 86 4 nm, 69 4 nm, and 34 2 nm, and the corresponding relative densities are 0.48, 0.29, 0.20, and 0.49 . However, when dealing with mathematical descriptions of crystals, it may be easier to describe the unit cell in the smallest form possible. In this form it is called gamma iron (-Fe) or austenite stainless steel. The contribution of free electrons to the Helmholtz free energy in the simplest form can be expressed as41: where the parameter e0 denotes the electronic contribution to the Helmholtz free energy, g is an electronic analogue of the Grneisen parameter, and x=V/V0. High Press. Chem. Adding a few parts per million of dopant atoms to silicon can increase its conductivity by a factor of a million. c. It is unchanged. Thus, it . -iron can dissolve considerably more carbon (as much as 2.04% by mass at 1,146C). Iron has BCC structure at room temperature. At temperatures between 912 49 corrected based on pressure scales31,35. The extrapolation of this line from the low-pressure data (Fig. rev2023.3.3.43278. 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. (d) is unchanged. Transcribed image text: 2. ADS Rhombohedral Close-Packed (Sm-type)6. Earth Planet. Thus, direct experimental measurements of the melting line of Fe and the liquid triple point indicate about 40GPa uncertainty in pressure and about 1000K uncertainty in temperature. The 1.069B. 3) and crosses the melting curve of fcc-Fe at a temperature of 5300K and pressure of 230GPa. Therefore, the hcpliquid curve overlaps the metastable fccliquid curve at a pressure of 160GPa. 49, 32763283 (1978). 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). KS for hcp-Fe is almost identical to the PREM at the Earths inner core conditions. Dinsdale, A. T. SGTE data for pure elements. Comput. (Definition, Examples, and Metallurgy), The Difference Between Alloys and Composites (and Compounds), The Hume-Rothery Rules for Solid Solution. Estimate the proportion of boron impurity which will increase the conductivity of a pure silicon sample by a factor of 100.Assume that each boron atom creates a hole and the concentration of holes in pure silicon at the same temperature is 7\times10^{15}. A discontinuity in sound velocities of iron at 200GPa may mark the transition of hcp-iron to fcc iron. An intensity level change of +2.00 dB corresponds to what percentage change in intensity? Lett. At moderate and high pressures, such extrapolation provides reliable results with a close agreement with reference data20. Phys. The structure of iron in Earths inner core. -Fe and the A2 critical temperature are important in induction heating of steel, such as for surface-hardening heat treatments. Show that the reciprocal lattice of a direct BCC lattice is an FCC lattice. & Johnson, D. D. Coexistence pressure for a martensitic transformation from theory and experiment: Revisiting the bcc-hcp transition of iron under pressure. 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. ADS Desai, P. D. Thermodynamic properties of iron and silicon. For the Nozomi from Shinagawa to Osaka, say on a Saturday afternoon, would tickets/seats typically be available - or would you need to book? Explain. Therefore the coordination number of FCC structures is 6 + 3 + 3 = 12. The phenomena of cavitation and cavitation erosion affect hydraulic machines, increasing their maintenance costs. The density, adiabatic bulk modulus and P-wave velocity of liquid Fe calculated up to 328.9GPa at adiabatic temperature conditions started from 5882K (outer/inner core boundary) were compared to the PREM seismological model. 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. 84, 36383641 (2000). Phase diagram and melting curve of iron obtained using the data of static and shock-wave measurements. Phys. theoretical grounds.
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