Taking the model of interstitial alloy AB with a body-centred cubic structure and the condition of absolute stability for the crystalline state, we derive analytic expression for the temperature of the limit of absolute stability for the crystalline state, the melting temperature, and the equation for the melting curve of this alloy using the statistical moment method. The results allow us to determine the melting temperature of alloy AB under pressure as well as at zero pressure. In limit cases, we obtain the melting theory of main metal A with a body-centred cubic structure. The theoretical results are numerically applied for alloys FeH, FeSi and FeC using different potentials.
Physical Sciences | Physics Doi: 10.31276/VJSTE.61(2).17-22 On the melting of interstitial alloys FeH, FeSi and FeC with a body-centred cubic structure under pressure Nguyen Quang Hoc1, Nguyen Thi Hoa2, Tran Dinh Cuong1*, Dang Quoc Thang1 Hanoi National University of Education, Vietnam University of Transport and Communications, Hanoi, Vietnam Received 18 October 2018; accepted 21 December 2018 Abstract: Taking the model of interstitial alloy AB with a body-centred cubic structure and the condition of absolute stability for the crystalline state, we derive analytic expression for the temperature of the limit of absolute stability for the crystalline state, the melting temperature, and the equation for the melting curve of this alloy using the statistical moment method The results allow us to determine the melting temperature of alloy AB under pressure as well as at zero pressure In limit cases, we obtain the melting theory of main metal A with a body-centred cubic structure The theoretical results are numerically applied for alloys FeH, FeSi and FeC using different potentials Keywords: absolute stability of the crystalline state, interstitial alloy, statistical moment method Classification number: 2.1 Introduction the following phenomenological equation: Alloys in general, and interstitial alloys in particular, are widely used in material technology and science Therefore, they are of particular interestto T many researchers m A B Pm P0 ∆Tm [T0 ( Pm − P0 )] = A + B ( Pm − P0 ) (1.3) (1.3) P0 ) of materials under T0 ( Pm (MT) where Tm and T0 are the MT at pressures Pm and P0, The melting temperature , and A and B are constants pressure is a crucial state physics Pand Whereproblem Tm and T0inaresolid the MT at pressures m and Prespectively, 0, respectively, ΔT m Tm T0 , and A and B (1.3) allows us to determine the MT of crystal at material science [1, The MT of crystal is usually is the Equation are 2] constants Equation (1.3) allows us to determine the MT of crystal at high pressures Theoretically, it is necessary to use the solid-liquid equilibrium to determine the MT of Simon experimental equation: high pressures crystal However, this does not allow us to explicitly express the MT According to some Pm − P0 Theoretically, necessary = (Tm −researchers, T0 )c − the temperature corresponding(1.1) to the absolute stability limit it foriscrystalline stateto at ause the solid-liquid a to determine MTauthors of crystal However, this pressure Therefore, accordingthe to the certain pressure (Ts) is close to the MT at the same equilibrium of [4], thethe melting curve of crystala coincides the curve representing absolute express stability the MT According where Tm is the MT, Pm is melting pressure, and c arewith does not allow us to the explicitly limit for the crystalline state Accordingly, the self-consistent phonon-field method and the one- corresponding to constants, P0 and T0 are the pressure and the temperature, to some researchers, the temperature particle distribution function are used to investigate the MT However, the results are not respectively, of the triple point on the phase diagram the absolute stability limit for crystalline state at a certain consistent with experiments This has led some scientists to conclude that the MT can never be (Ts) is have closeused to the thecorrelation MT at the same pressure found limit for solid phase pressure Other researchers Normally, when theusing valuetheofstability P0 is small, wethe can write Therefore, according to state the authors effect to calculate the temperature of the absolute stability limit for the crystalline Althoughof [4], the melting equation (1.1) in the form: the results of this are more exact, they are limited at curve low pressures of crystal coincides with the curve representing the In support of the statistical moment method absolute (SMM), N.stability Tang and V.V.for Hung 5] show state Accordingly, limit the [4, crystalline Pm c (1.2) = (Tm − T0 )that − 1we can, in fact, determine the MT using the solid phase of crystal First, they determine the the self-consistent phonon-field method and the onea absolute stability temperature (Ts) at different pressures using the SMM and then carry out the particle distribution function are used to investigate the MT regulation in order to find Tm from Ts The results of the SMM correspond better with However, the results are not consistent with experiments However, equation (1.2) cannot describe melting of experiments than those of otherthe methods crystal at high pressures Kumari, et al [3] have introduced This has led some scientists to conclude that the MT can The content of the research Analytical results *Corresponding author: Email: trcuong1997@gmail.com In the model of the interstitial alloy AB, which has a body-centred cubic (BCC) structure, the large atoms A are in the peaks and the centre of the cube, and the smaller interstitial atoms B are in the centres of the cube faces In [6-11], we derived the analytic expressions for the nearest (the of Science, neighbour distance, the cohesive energy and the alloy parameters for atoms B, A,Vietnam and A1Journal JUne 2019 • Vol.61 Number Technology and Engineering to atom main atom A which is closest to atom B) and A2 (the main atom A which is second closest B) 17 Physical Sciences | Physics m never beTfound using the A B P0 limit for the solid phase a= P,0) + y AB ( P, T ) Pmstability AB ( P, T ) a AB ((1.3) Tm P ) ( T P A have B Pm used P0 the correlation effect to m Other0 researchers (1.3) P0 ) T ( Pm the a ( P,0) = ( P,0) + cB a′A ( P,0), a′A ( P,0) = 3aB ( P,0) Where Tm0and T0 are the MT at of pressures Pm and stability P0, respectively, (1 −Acand calculate temperature the absolute limit forΔT B ) a AB m TmAB T0 , and Where T and T are the MT at pressures P and P , respectively, , and A and B Δ T T T m m m pressures the crystalline state Although results ofthethis more mat high are constants Equation (1.3) allows us the to determine MTare of crystal y AB ( P,T ) = − 7cB ) y A ( P,T ) + cB yB ( P,T ) + 2cB y A1 ( P,T ) + 4cB y A2 ( P,T ) (2.4) (1the are constants Equation allows determine the MT ofequilibrium crystal at high Theoretically, it(1.3) is necessary toto use the solid-liquid to pressures determine MT of exact, they are limited at lowuspressures necessary to use equilibrium to determine the MT of crystal Theoretically, However, thisit is does not allow us the to solid-liquid explicitly express the MT According to some InHowever, supportthis of does the statistical moment method (SMM), The free energy of interstitial alloy AB with concentration crystal not allow us to explicitly express the MT According to some researchers, the temperature corresponding to the absolute stability limit for crystalline state at a N pressure Tangtheand Hung [4, MT 5] show that we can, in fact,