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Fe-P 体系热力学再优化

曹战民*

王昆鹏

乔芝郁

杜广巍

(北京科技大学,钢铁冶金新技术国家重点实验室,冶金与生态工程学院,北京100083)

摘要:

基于最新的实验热力学数据和相图数据,采用CALPHAD 技术对Fe-P 体系进行热力学再优化.其中,

溶液相(液相、α-Fe 和γ-Fe)的Gibbs 自由能用替换溶液模型描述,其余化合物(Fe 3P 、Fe 2P 、FeP 、FeP 2和FeP 4)看作严格计量比化合物.整个优化过程在Thermo-Calc ?软件包中完成,优化所得热力学数据和相图信息与实验信息吻合较好,为Fe 基合金和含P 多元合金体系的进一步优化提供了一组自洽可靠的热力学参数.关键词:

Fe-P 体系;CALPHAD 技术;相图;热力学优化

中图分类号:

O642

Thermodynamic Reoptimization of the Fe-P System

CAO Zhan-Min *

WANG Kun-Peng

QIAO Zhi-Yu

DU Guang-Wei

(State Key Laboratory of Advanced Metallurgy,School of Metallurgical and Ecological Engineering,

University of Science &Technology Beijing,Beijing 100083,P .R.China )

Abstract:The Fe-P binary system was reoptimized by means of the CALPHAD approach.The Gibbs energy descriptions of every phase in the Fe-P binary system were optimized based on the latest experimental thermodynamic and phase diagram data.The solution phase (liquid,α-Fe,and γ-Fe)was described by the substitutional solution approximation and the other phases (Fe 3P,Fe 2P,FeP,FeP 2,and FeP 4)were treated as the stoichiometric compounds.The optimization was carried out using the Thermo-Calc ?software package.The agreement of the optimized phase diagram and thermodynamic data with experimental results is good,and a self-consistent and reliable thermodynamic dataset is obtained to allow further optimization of Fe-based,P-containing multicomponent alloy systems.Key Words:Fe-P system;CALPHAD approach;

Phase diagram;Thermodynamic optimization

[Article]

http://www.wendangku.net/doc/bc5ea4ec998fcc22bcd10d87.html

物理化学学报(Wuli Huaxue Xuebao )

Acta Phys.?Chim.Sin .2012,28(1),37-43January Received:October 8,2011;Revised:November 14,2011;Published on Web:November 17,2011.?

Corresponding author.Email:zmcao@http://www.wendangku.net/doc/bc5ea4ec998fcc22bcd10d87.html;Tel:+86-136********.

The project was supported by the National Natural Science Foundation of China (50934011).国家自然科学基金(50934011)资助项目

?Editorial office of Acta Physico ?Chimica Sinica

doi:10.3866/PKU.WHXB201111172

1Introduction

Fe-P is a fundamental binary system of the Fe-based and P-containing multicomponent alloys,which are of great impor-tance for the advanced metallurgy and materials,such as stain-less steel,ultra-pure steel refining,and materials design and processing.From thermodynamic point of view,the best opti-mized parameters of the Fe-P binary system are a quite impor-tant basis for thermodynamic optimization of the Fe-based and P-containing multicomponent systems.Also,thermodynamic data of the Fe-P system with strong interactions advance a bet-ter understanding of the nature of chemical bonding and inter-

action mechanism.As pointed out by Okamoto 1in a critical as-sessment of the Fe-P system,the assessed Fe-P phase diagram was accepted primarily from Kubaschewski 2in 1982.Recently,Ohtani et al .3in 2006and Tokunaga et al .4in 2009evaluated thermodynamic parameters and calculated phase diagram of the Fe-P system in the thermodynamic analysis of the Fe-Ti-P and Fe-Nb-P systems,respectively.But,in both evaluations the valuable thermodynamic properties in the Fe-P system mea-sured by Zaitsev et al .5using differential scanning calorimetry and Knudsen effusion method with mass-spectrometric analy-sis of the gaseous phase were omitted.In order to obtain a set

37

Acta Phys.?Chim.Sin.2012V ol.28

of self-consistent and reliable thermodynamic description for this binary system,it is necessary to reoptimize the Fe-P sys-tem with all available thermodynamic and phase equilibria da-ta using CALPHAD approach6,7and Thermo-Calc?software package.8

2Experimental phase diagram data

Due to the practical and theoretical importance many au-thors investigated the phase equilibria of the Fe-P system. Saklatwalla9firstly published the phase relationship of the Fe-P(0%-24%P,mass fraction)system.Then,Konstantinow10 and Haughton11measured the phase diagram of the Fe-P sys-tem up to24%P and32%P,respectively,and showed the exis-tence of liquid(L)phase andα-Fe,γ-Fe,Fe3P,Fe2P,FeP phas-es.The solubility of P inγ-Fe was measured by several investi-gators,including V ogel12and Roquet et al.13using metallogra-phy as well as Lorenz14and Fisher15et http://www.wendangku.net/doc/bc5ea4ec998fcc22bcd10d87.htmling magnetic mea-surements,respectively.The assessed maximum solubility of P inγ-Fe is ca0.56%at1423K.2,12The liquidus and solidus of α-Fe were measured by many researchers.9,11,16-19The quantita-tive values of solid solubility of P inα-Fe were obtained by us-ing metallography,11,12,17,20X-ray analysis,21,22precipitation hard-ening,23lattice parameter measurements,24electron probe analy-sis,25microprobe and micro-hardness tests,26and X-ray micro-analyzer.27The experimental results obtained from different in-vestigators established that three invariant reactions exist in the Fe-P system,i.e.,L?α-Fe+Fe3P,L+Fe2P?Fe3P,and L?F e2P+ FeP.But,as shown in Table1there are small differences for the temperature and composition of the invariant points.Franke et al.,28Meisel,29and Heimbrecht et al.30revealed the existence of FeP2by use of density and X-ray diffraction measurements. Holseth et al.31measured the maximum homogeneity range of FeP2from65.6%P to66.9%P and from66.2%P to67.1%P, respectively.Jeitschko et al.32synthesized monoclinic FeP4 from the elements at927to627°C using iodine as a catalyst and tin as a flux.Up to now,no experimental information about the phase relationship of the Fe-P(0%to100%P)sys-tem was reported.

3Experimental thermodynamic property data

Weibke et al.33experimentally measured the formation en-thalpies(Δf H)of Fe3P and Fe2P at908K by using an adiabatic calorimeter as well as Lewis et al.34calculated formation en-thalpies of Fe2P,FeP,FeP2at900K from their temperature de-pendences of the dissociation pressures measured by Knudsen effusion method.Based on the available thermodynamic and phase equilibria data,Spencer et al.35evaluated the thermody-namic properties of Fe3P,Fe2P,FeP,and FeP2,including heat ca-pacity(C p),mixing enthalpy(Δmix H),formation entropy(Δf S), formation enthalpy(Δf H),and Gibbs energy of formation (Δf G).As mentioned,Zaitsev et al.5measured the heat capaci-ties of iron phosphides Fe3P,Fe2P,and FeP in the temperature range of113-873K and investigated the thermodynamic prop-erties of iron phosphides(1041-1549K),bcc solid solution Fe-P(1384-1619K),and Fe-P liquid alloys(1349-1811K) by means of Knudsen effusion method with mass-spectromet-ric analysis of the gaseous phase.Then,based on the experi-mentally measured results and the second and third thermody-namic laws,Δf G-T relationships of the Fe3P,Fe2P,and FeP at 1230-1530K,Δf H,Δf S,and S (absolute entropy)at298K,as well as activities of P in liquid phase and inα-Fe were deter-mined.Little experimental thermodynamic data of FeP2and FeP4and phase relation information concerning the Fe-P (50%-100%)system existed in literature due to high volatility of phosphorus at elevated temperature.Therefore,the calculat-ed formation enthalpies of FeP2and FeP4in the Fe-P system at 298K by first-principles method3were used as initial values in the present optimization.All thermodynamic data used in the present optimization are summarized in Table2.

4Thermodynamic models and optimization 4.1Reference states

As reference states for the investigated system,the pure sol-id elements in their stable states at298.15K and105Pa(stable element reference,SER)were chosen.The Gibbs energy of the element i withΦphase appears in the following form:

0GΦ

i

()T=GΦ

i

(T)-H SER

i

(298.15K)

=a+bT+cT2+dT3+eT-1+fT ln T+gT-9(1)

where H SER

i

is the enthalpy of the element i in its SER state at 298.15K and105Pa;T is the absolute temperature in K;GΦi(T) is the Gibbs energy of the element i;0GΦi(T)is the molar Gibbs energy of the element i with the structure ofΦreferred to the enthalpy of its stable state at298.15K and105Pa,which is de-noted by GHSER i when the element i is in its stable state.Dif-ferent sets of coefficients a to g used in different temperature ranges in Eq.(1)and compiled by the SGTE(Scientific Group Thermodata Europe)database36were chosen.The used lattice stability parameters for Fe and P are summarized in Table3. 4.2Stoichiometric intermetallic compounds

In the Fe-P system intermetallic compounds Fe3P,FeP,and FeP4belong to the stoichiometric phases.Even small solubility of P in Fe2P and FeP2was reported,31,37Fe2P and FeP2were also approximately treated as intermetallic compounds.The Gibbs energy per mole Fe3P,Fe2P,and FeP is given as:

0GΦ

m

(T)=a+bT+∫298.15K

T

C p d T-T∫298.15K

T C p d T(2) where C p is isobaric molar heat capacity,the coefficients of a and b will be optimized usingΔf H 298.15K,S 298.15K as initial values. The measured values of C p reported by Zaitsev et al.5were also used in the present optimization.

The Gibbs energy per mole FeP2and FeP4can be expressed as follows:

0G Fe m P n

m

(T)=m GHSERFe+n GHSERP+Δf G Fe m P n(3)

where0G Fe m P n

m

(T)denotes the standard Gibbs energy of forma-

38

CAO Zhan-Min et al.:Thermodynamic Reoptimization of the Fe-P System No.1

tion per mole formula of Fe m P n.Due to the lack of experimen-tal data of heat capacities,by applying to the Neumann-Kopp rule,Δf G Fe m P n can be given as follows:

Δf G Fe m P n=a+bT(4) where the parameters a and b were to be evaluated in the pres-ent work.

4.3Solution phases

There are three solution phases in the Fe-P system,i.e.,liq-uid phase,bcc(α-Fe),and fcc(γ-Fe).The Gibbs energy of the solution phase in the Fe-P system is described as follows:

0GΦ

m

=x Fe0GΦFe(T)+x P0GΦP(T)+RT(x Fe ln x Fe+x P ln x P)+E GΦm(5) where E GΦm is excess molar Gibbs energy,which can be ex-pressed by Redlich-Kister polynomial38as,

E G

m

=x Fe x Pé

?

ù

?

L0+()

x Fe-x P L1+()

x Fe-x P2L P(6) where L i(i=0,1,2,…)are the i-order interaction parameters of liquid phase in the Fe-P system and are expressed as tempera-ture dependent terms as follows:

39

40

Acta Phys.?Chim.Sin.2012V ol.28

c N

CAO Zhan-Min et al.:Thermodynamic Reoptimization of the Fe-P System No.1

L i=a i+b i T+c i T ln T(7)

where a i,b i,and c i are model parameters to be optimized based

on the experimental data in this study.

5Optimization procedure and results

Based on the lattice stability parameters of Fe and P in Table

3cited from references36as well as the experimental phase dia-

gram and thermodynamic property data summarized in Ta-

bles1and2,all the values of the model parameters for the

phases in this system were optimized by use of the PARROT

module,which works by minimizing the square sum of the dif-

ferences between the experimental data and calculated values, in the Thermo-Calc?software package developed by Sundman et al.8In the optimization procedure,each selected experimen-tal value has been given a weight according to the reliability and compatibility of the experimental data.The weight can be changed to achieve a satisfactory description of most of the ex-perimental data.The optimized thermodynamic parameters for all condensed phases in the Fe-P system are summarized in Table4.The calculated temperatures and compositions of all invariant reactions in this system are compared with the experi-mental data in Table1.

As shown in Fig.1and Table1,Schürmann?s experimental result19of the reaction L?α-Fe+Fe3P are lower than others?. Haughton11pointed that in the low-phosphorous alloys un-der-cooling of the eutectic was very marked,and this may ac-count for the extraordinary shape given to the eutectic line by Schurmann.19Therefore,the calculated liquidus and solidus as well as temperatures and compositions of all invariant reac-tions in the Fe-P(0%-50%P)system agree well with the ex-perimental data,especially reported in some references11,18,26,27

Table4Optimized thermodynamic parameters of the Fe-P system

temperatures in K,and L is dimensionless parameter.

1Fe-P phase diagram calculated by the present thermodynamic description with the experimental data Fig.2Calculated standard formation enthalpy at298K(a) and900K(b)in the Fe-P system and comparison with

the literature data

3Calculated mixing enthalpy of liquid at1809K in the Fe-P system with the literature data

41

Acta Phys.?Chim.Sin .2012

V ol.28

and the previous results assessed by Okamoto 1and Ohtani et al .3As the part of Fe-P (50%-100%P),there is no experimen-tal information compared with calculated phase diagram.But,if compared the present calculated phase diagram with the pre-vious assessed one,3the former is a little more reasonable than the latter.

Fig.2compares the calculated values of formation enthalpies of the Fe-P system at 298and 900K in this study with the liter-ature data.Obviously,the present calculated values are in good agreement with measured 5and evaluated 35data at 298K as well as with measured data at 900K.33,34However,the values evaluated by Ohtani et al .3and Tokunaga et al .4and predicted using first-principles calculations 3are more negative than the experimental measured data.5

Fig.3presents the calculated Δmix H of liquid Fe-P system at 1809K compared with the experimental data.3,4,35It is clear that the present calculated values agree well with evaluated data by Spencer et al .35

It can be seen from Fig.4and Fig.5that agreement between present calculated heat capacities and absolute entropies of Fe 3P,Fe 2P,and FeP with measured data 5is better than the one between previous evaluated data 3,4with measured data.5

6Conclusions

Based on all available experimentally measured thermody-

namic properties and phase diagram data,the Fe-P system,which is a significant binary one of the Fe-based and P-contain-ing multicomponent alloys,was reoptimized by CALPHAD ap-proach and Thermo-Calc ?software package.The agreement between the optimized Fe-P (0%-50%P)phase diagram and experimentally measured data is good enough.The calculated Fe-P (50%-100%P)phase diagram is a little more reasonable than previously assessed one.The comparison of calculated for-mation entropies of the Fe-P system at 298and 900K,calculat-ed mixing entropies of the Fe-P system at 1809K as well as calculated heat capacities of Fe 3P,Fe 2P,and FeP in this study with the measured data available from literature remains fairly good.An obtained thermodynamic description with self-consis-tency describing all the phases in the Fe-P system is better than that of the previous assessment.References

(1)Okamoto,H.Bulletin of Alloy Phase Diagrams 1990,11,404.(2)Kubaschewski,O.Iron-Binary Phase Diagrams ;Springer-Verlag:Berlin,1982;pp 84-86.

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International 2009,49,947.(5)Zaitsev,A.I.;Dobrokhotova,Z.V .;Litvina,A.D.;Mogutnov,B.M.J.Chem.Soc.Faraday Trans .1995,91,703.(6)Kaufman,L.;Bernstein,http://www.wendangku.net/doc/bc5ea4ec998fcc22bcd10d87.htmlputer Calculation of Phase Diagrams ;Academic Press:New York,1970.

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(9)Saklatwalla,B.J.Iron Steel Inst.1908,77,92.(10)Konstantinow,N.Z.Anorg.Chem.1910,66,209.(11)Haughton,J.L.J.Iron Steel Inst.1927,115,417.(12)V ogel,R.Arch.Eisenhüttenwes.1929-1930,3,369.

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4Calculated heat capacity of Fe 3P (a),Fe 2P (b),and FeP (c)with the literature

data

5

Calculated absolute entropy in the Fe-P system with the

literature data

42

CAO Zhan-Min et al.:Thermodynamic Reoptimization of the Fe-P System No.1

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