Reaction rate of combustion synthesis of an intermetallic compound

Reaction rate of combustion synthesis of an intermetallic compound

ELSEVIER Powder Technology 95 ( 1998 ) 175-181 Reaction rate of combustion synthesis of an intermetallic compound Tomohiro Akiyama *, Hiromichi Isog...

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Powder Technology 95 ( 1998 ) 175-181

Reaction rate of combustion synthesis of an intermetallic compound Tomohiro Akiyama *, Hiromichi Isogai, Jun-i~..~.i~eYagi Institutefor Advanced Materials Processing, Tohoku University, Sendal 980-77, Japan

Received 15 April 1997; revised 5 July 1997; accepted 1 August 1997

Abstract The reaction kinetics of the combustion syntl~esis of Mg,.Ni from a powder mixture of magnesium and nickel has been investigated. The physical and chemical changes of the samples ,luring the combustion synthesis were followed by scanning electron microscopy (SEM), electron probe X-ray microanalysis (EPMA), X-ray diffraction (XRD), and differential scanning calorimetry (DSC) to derive a suitable rate equation. The observations revealed that the synthesis of Mg,Ni progresses homogeneously rather than topochemically, and not through an intermediate phase, with acceleration by liquid generation of the eutectoid phase. The result was that the most reasonable expression is a

second-orderirreversibleequation,k( I -/)-', with an activationenergy of 165 kJ/mol. © 1998 Elsevier ScienceS.A. Keywords: Combustion symhesis; Kinetics; Solid-solid reactions; Hydrogen storage alloys; Intermetalliccoznpounds

Introduction A conventional arc-melting process can not control chemical composition in the ptx~duction of an intermetallic compound owing to evaporation loss. To overcome this problem, :111alternaUve route based on combustion synthesis has been proposed tbr the production of Mg~Ni alloy, one of the most promising hydrogen storage alloys. Successful laboratoryscale trials yield a high purity product, with a short processing time and reasonable energy savings, in spite of the high vapor pressure of magnesium [ 1,2]. Combustion synthesis is a process which utilizes the heat generated by exothermic reaction to sustain itself in the form of a combustion wave after external ignitioP. The exothennic heat depends upon the combination of the starting materials; for example, metal-metal reactions in general produce relatively low heat, thus sometimes requiring supplementary heat, such as preheating, for :,u~tainable combustion. Applications of combustion s~nthesis are numerous, but its reaction model has rarely been reported. This can probably be attributed to experimental problems because the ~eaction progresses very quickly, with considerable heat generation. In spite of several remarkable papers [3-6], Munir [7] reperted that the difference in the activation energy among these papers is as great as a factor of three. This suggests that a solid methodology on the reaction kinetics of combustion * Corresponding author. Tel.: + 81 22 381 0321; fax: + 81 22 384 6728; e-mail: [email protected] 0032-5910/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved PilS0032-5910(97 )03345-7

synthesis is still needed. At present, a reliable reaction rate equation is urgently needed for modeling the combustion synthesis process of several promising intermetallic compounds. The objective of this paper is to observe changes in structure of the sample during the combustion synthesis o~" Mg,Ni and to determine its reaction rate equation.

2. Experimental Cylindrical compressed powder. 100× 3 ram. of magnesium ( ,-, 177 Ixm, 99.9% purity ) and nickel (2-3 p,m, 99.9% purity) in a 2: l molar ratio was prepared as a starting sample. The detailed preparation procedure and optimal conditions are reported elsewhere I I ]. To observe how the combustion synthesis occurs, samples were heated up to different desired temperatures (723, 753 and 793 K) at the rate of 1.0 K per rain in a flowing argon atmosphere, then quenched to room temperature. A gold image furnace with a tungsten heater was used for the differential thermal analysis (DTA). during which the samples were thermally controlled very accurately by radiation from the gold-plated curved mirrors. After that. the samples were dry polished by sand papers, #800-#4000, lbr scanning electron microscope(SEM) observation and electron probe X-ray microanalysis (EPMA). Similarly, other samples, quenched shortly after reaching 715, 750 and 800 K, were prepared as powders tbr X-ray diffraction (XRD) analysis. For measuring the heat of reaction by differential scanning calorimeter (DSC), a very small piece of

7".Akiy, ma et aL t Powder 7~,ch,ohLg~"95 ~It)98} 17,~-181


the starting sample, I mg in weight, was used in order to neglect the temperature gradient within it. A feature of this ~tus is the quite high sensitivity of 0.2 p,W and its support of the modulation mode to distinguish reversible and nonreversible phenomena. The measurement conditions of this study were taken as (i) an argon atmosphere and (it) a heating rate of 0.5-10,0 K per min.

& Theory 3. I. Activation energy

Many techniques have been proposed for evaluation of the reaction rate from thermal analysis data. Among them, Ozawa's method 181 is well known as one of the most applicable. According to this method, using reaction curves obtained at different heating rates, the activation energy can be accurately determined following the prtx:edure listed in Table I: an equation for the reaction rate can be expressed Table I Pn~:udur¢Ior kinetic analys~susing DSCdata

by Eq. ( I ) under Arrhenius' law, which is rewritten in Eq. (2) in integral form. Furthermore, introducing the new reaction function G(f) and reformed time 0, Eq. (3) is a simplified version of Eq. (2). This means, theoretically, linearity between both functions. The right-hand side of Eq. (2) can be approximately solved by introducing Doyle's p function [ 9,1 O1 (see Eq, (5)), instead of an analytical integration. As a result, we can derive Eq. (6) for different heating rates ~b, by which an activation energy A E is determined from the linearity between log(6) and i IT. Once a value of the activation energy is obtained, 0, G U ) , g ( D and A are successively solved by Eqs. (2) and (3). 3,2. Rate eqttation

The equmions presented in Table 2, reviewed by Tamhanker and Doraiswamy I I I l, are selected rate equations derived from several theories. They are, essentially speaking, based on three concepts: diffusion control, chemical reaction control and order of reaction. In this study, a suitable equation is discussed for introduction in a total mathematical model of Mg-Ni combustion synthesis, based on thermal analysis data.

ASSUll~'Jliofls: 4. Results and discussion


4. i, SEM nh~'(,rrathm and chemical amdysis


I~),le'~ p fu01~'tiotl: P


k~gll~,(,~)l ~ ~-~,,ll~ql,4~f,f/.~,




s ht¢lht~J;




t (1I

Fig. I shows SEM photographs of Ihe san)pies quenched at dil'l~'u'ent temperatures, As can be seen in Fig. 2, the con'respouding EPMA line analysis revealed thai black is magnesium, white is nickel, and gray is a Iwoducl having a 2:1 nlolar ratio of 111aguesiun~ aud nickel. A green pellet was quite dense, with iio pores, caused by Ilexihle re-fornlation~ of the metallic particles ol' the raw materials. Spreading ol' a puxgluct layer with temperature was clearly observed, together with small crack generation due to thermal expansion. XRD patten)s, shown in Fig, 3, demonstrated that the reaction progresses with temperature, identifying Mg:Ni as the lin:ll major product. This also indicated direct synthesis of Mg:Ni front the Mg and Ni inixture, not through 'my intennodiate colnponleul,

logq ~! vs, I / 7" plot ,~ ~ E

4,2. Reaction ~m, mudysis

(;U ~)v,,,,OpIol ~A, ,~(,l')

The circles plotted in Fig..4. :ire DSC data measured at various heating rates, expressed in the fornl dfld'l: Here,.fis the degree of reaction evaluated from tile heat of reaction, and 7" is the absolute temtx:rature. The delinition of.f is

Nomctvdatut~,, A ,M~ .f gU') G(.f) p(x) eP

Ii~:queneyI~¢tor t s ' adivaliun el~ctgy ~J/nlol i degn:e of NaGtiun r¢~ti~m equation P2~t~ti~,~nlhn¢liol| I)oyl¢'sp funuliua rt.F¢,mlc,d Ii11~:( s ) healing rate ( KI,~)


Synthesized M g~Ni (kg) Theoretically obtainable Mg:Ni (kg)

Interestingly, the peak number and position are influenced signilicantly by the heating rate, the single peak being gradually split into two with decreasing heating rate. More impor-

7: A k h ' u m u el

rd, /I'.u'¢h'r T('('h.¢,h,,~y 95 I1(t~.~'1 175. I.%'1


Table 2 Proposed rate equations for solid-phase reaction q see review by "Famhanker and I)orai..wamy I I I I ) Reaction model ( a I Pn)duc! h~yer diffusiop, control I-D (plate) 2-D ( disk ) Yander Gi.slring el al. Zuravlev et al. Carter

(h) Phase boundary reaction control 2-D ( plme ) 3-D (disk) ( c ) Order of reaction Isl order nth order


,~ (.l')

GLf )

I/~! - In( I -J)

.f .2 ( I - . / ) In( I -./)

4](I-]') "-'~-(l-,l) ~l( 1 -.f)~:'- I! i [ ( I -J') ~1 ( 1 +1


"~~ - ( I - f l ~'~1 ~'~-( 1 -.1"1 ~ '1


+.11 1 - ( I -./) ':' l-" ( I - ~,f) - (l - f)-'" '


( I -.f) ~ - I I 2-( I +j)2,+(

2( I - f ) ),, :

I - ( I -.DI;2

3( I --.l') 2/~

I -(

I I -f) ( I -.f)"

I I/(.-

~ I-.f}2"~

i -.l'l L:'

- Ill( I -.f) I)ll(I-.f)'





~ Akiymua el M, / P{~wde~Techmd~gy ~)5( !998~ !73-181

Fip, 2. R~,sulis uf lil~

tantly, the second peak position of Mg-Ni with a eutectic lemperalur~ of 779 K was almost constant at higher temperatures (see Fig. 5): in contrast, the lirst peak position was changeable. It is also obvious that tile fraction of Ihe lit'st mode increases with decreasing heating rate, reaching as much as 96¢;{, at Ihe ~lowest heating rate of 0.5 K per lain. The.~ results revealed that the reaction between magnesium and nickel particles is driven by tw~ diffi:rent modes: socalled s~#id (',mb¢~xti~m at lower temperatures and hq,i(Ilriggercmetbusliem at 779 K with a much larger n:action rat~. Fig. 6 shows plots of Iog(d~) against I/7" h}r difl'~rent conversions. The data, obtained Ih),n live reaction curves measured at heating rates of 0.5, 1.0, 3.0, 5.0 and 10.OK per rain, showed very good linearily for any cot, version. The lines, drawn based on the least square error method, are almost parallel with constant slope, it is noteworthy that the

rate, I K/ul|in.

activation energy is unique, I'cgardless of the two reaction mectumis,ns. This is sufficient evidence to validate tIlls method and ~avc 105 kJ/tool as the activation enerBy of this system. To s¢I¢c! the 1110.',;Isuitable reaction rate equation of this system from tl)ose proposed in Table 2, all the G(.I') were plotted against # after iutroducing die value obtained for the activation e.)er~y, in order to examine the lizzearity. The resulting plots are shown in Fig. 7. Regarding tIle eight equations for G(.I) based on the concepts of product layer control and phase boundary reaction conwol, all the plotted data deviated completely fn)m linearity with 0. However. G(/) derived from the second-order reaction equation obeyed the linear relationship in Eq. (3) best for temperatures below 779 K. The second-order kinetic equation has often been reported for mixed powder reaction systems, such as ZnO + Ai_~O.~


7" Akiyama et al. / Powth,r Techmdo.+y 95 t l<~9,~'J175-I,~'I ÷












750K 0.1




t-~ 0.1




O +




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]+ II+]





I: ::0.+I



50 °

100 ° 20 (CuKct) Fig. 3. X-ray dilt'raciion rJill|t..rils of tile s;unplcs qucllchttd at'iOLis 0.( Ic


1121, in which Ilomogeneous reaction among line particles


takes place. Tile SEM photographs, shown in Fig. I, also show that tile reaction seems It> he expressed by a homogeneous model rather Ihan other typical models such as the topochemical one mentioned above, h is. therefore, concluded Ihat this n'ate equation is applicable to Ihe Mg-Ni t'eaclion system. In tile lenlpel'alttre range from rot>m lempe,'ature to 779 K, Ihe frequency factor was clearly estinlated fronl tile slope of Fig. 8 to he 5,46 x I0~: tile data tlleaSLIl'Vd at the sloxve,;t healitl~,. Colldition of 0.5 K per nlin were used




because the coutn'ihutiou of the lit'st peak wits prcdorrlirr..'tl. hl corltl'aSt, above 779 K. file gradietll oi" the ploued dala i,lcreased drastically, pn'oh~,l~ly due a> partial melting of 111c

Weight Percent HLckel t,


,o =o









i7281{ o..


L 1473

1420+_.3K o o





,!i ~0

II0 i

1073 °



1 ~K


II MgNi2- - ~ I


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r . . . . . . . .

4o Atomic


Tcnlpcralur~, T / K Fig. 4. Reaction ,';tiecurve.~estimated Iro111I)SC data.,together ,~vithpredicLcd ~.'t|t"~'es(cutcctic point. 779 K ).









+ .........



F'ig. 5. Ozawa plat for the calculalhm of activation energy.

r . . . .




,oo Hi

1: 4kiyuma el .uL I Powder Tet'imr,h.,gy q5 r 1998~ 175-181



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eutectoid phase of Mg-Ni, indicating acceleration of the reaction. This result agrees with the fact that melting makes the frequency factor larger according to collision theory and transition-state theory I 13 I. With regard to second-peak predominant data measured at the Im~est heating rate of 10 K per rain, the average slope evaluated was 2.79 X ! 0 " above 779 K. These evaluations yielded a set of reaction rates, as listed in Table 3. Here, both values of the frequency factor are smoothly connected over the temperature region of peak width 30 K. The equation gave simulation curves which ate shown by the solid curves in Fig. 4. There was relatively good agreement between the measured and si,nulated data, in particular with regard to the data at the lower heating rates, Therefore, we concluded that this rate equation ix practical enough fur simulating the ,'eactiou rate of this system, hi future, however, our attention .qlould be directed Io study in depth the reaction ,nechanisn~ of combustion synthesis with liquid genenuitm, to explain the reaction rate from the viewpoint of Inicrokinetics. This ix because there is room for

~!ii"' '


. ,I


D 0()|'~

l) (}~i14

%mperature, 117"IK-" Fig. 6. Pha~,e di~lgnml o f Ihe M g - N i ~,y~,tcm.






I &


0 '~

L f I~


~"~' ,,~++~ o~ ~ ~ + "I # ++ /


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0 0 0









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~ .......



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fl ,, .~


.......~ ..... ~i'~i~'l~ii,i,li .... ,1 2~D(disk) O Yauder(sphcze) t~ Zuravlev L'I al, v Carter ~ .........(i ijt:,~tfij~},=~!, a=!:='


,f°-^" II 8q|


secund cmicr

o o


0 0


third urdcr


411(1 L3


2I)0 t] El


=mxu:aaP~QrJa II



~ ~.2x [0 -s


I , 4 x l O '~

O!s Fig, 7, t~ ~,,,. d ( f I phil or' ',~ariuu,,, kindk: ~quations I ,,,ee 1"able 2 ) ha:,~d un the a~,sumption uf ( a ~ I)ruducl la),cr diffu~,iuu control. ( h ) ph;ise bmmdar), r~aclhm ~;~mlrt~l, ! ¢ I II~, cuucept ~1"atz order of rea¢:tiun, ( Euleclic puim, 77g K, )

T. Ak6"m.. c~ a L I Powder Te~'hm,h~gv 9.5 ! I U98~ 175- h%'l -









in this study in which the reaction mechanism was discussed by means of SEM, EMPA, XRD and DSC: its reaction rate was then lhrmulated. The loilowing conclusions were drawn. I. The combustion synthesis of this system proceeded homogeneously from the macroscopic viewpoint. 2. No intermediate phase was generated between the starting materials and Mg2Ni during the combustion synthesis, 3. Two dilti~rent reaction modes were identified at the boundary of the eutectic temperature, 779 K. 4. The activation energy of this reaction was evaluated as 165 kJ/mol, and the second-order reaction rate equation was found to be the most reasonable. The methodology used here to determine the activation energy fi'om DSC curves obtained at different heating rates can also be used lor other systems of combustion synthesis. Development of a total mathematical model of the Mg_,Ni colnbustion synthesis process with the help of the reaction n~te equation is expected in the future.




60 o 40


: A=5.46x108








2 x l 0 -a


I , 4 x ] O -'I

O/s (b)

1 i


second order

80 -



61) -

11 ....a~'e~_ 0



I IxlO










2x i()-8


Ols Fig, 8. I)¢lerlllilial,ion o1' I11¢ l'l'cqut311¢y fat;it." A i,I the l,elnl~eralur,2 rallg,2:., I~elow alld above l,he eulccli¢ pOilll 1779 K I Ior a heal,illg ral,e of llt} 0.5 all,d (1~1 I0 K/Ill,ill. "t'~thle 3

Kiile(i¢ i~arl~alnelCl'r• eslilnaled Il'Oln I)S(' dala

• 31 ¸ tltd"/[t": '4 ¢~'11 ~ ( ~°~'h'~' ) ~qLl

.~1: ~" Ih5 '~ Ill' ,limt~l

A~ + Ut, "°A~ II '17'

A, 1;,, + ,.%T< I' ,.t~ ~5.4(~X Ill ~' ~, o, I

1;,, =

77 t) K

imp:ovemcnt in the simuhuion results of Ihe second reaction mode above 779 K. 5. Conclusions The kinetics of the combustion synthesis of Mg2Ni, as one example of an intermelallic cotnpotmd, has been investigated

I I I T. Akiyama. H. Isogai and J. Yawl, Combustion s xnl,hesis o! 111;.l~lleSjtlm nickel, 1111. J. SHS (Self-i~rop,'lgaling t4igh-tcnq~:rvtuw Synl,hesis) 4 11995) 69. 121 I-I. Isogai. T. Akiyvma and J. Yagi. ('umhusfion synthesis ~1 Mg?Ni and Mg:NiH4. J. Jpll. lllsl.. Met,.. 2 f 1996) b(}. [ 31 SD. I)ulmlead. D.W. Readey. C.E. Semler .',nd J.B. I-hill. Kinetics of col|11'~u,',;liq.m~.yn,l,hwsis in file Ti-C an,d Ti-C°Ni ,,),stem, J. Anl, ('ermu, St..',, 72 (1989) 2318, 141 S.D, l)unrnead ar,.l Z,A, Mt,ifii', TcInl',:I'alm'¢ pr,nlil¢ mmly,,i'., in ,.'L,llbtisli~ul sVrllh¢,, I, Th¢,nry alld hilekgnILllld..I, Alh, ('l~'|ra|'ll, S()I~',, 75 I I~92~ 175. j 51 A, llil',ino, l"r,...',:s,', SilllUhlli,~ll ilild irmdel ,,inlllJalh',ll of't',t1111Illl'.,liLlll ~,yl~lll¢,",is ,al Ni,AI inlerlu¢lallic L:,,mq',,mmd,,, ,I, ,llm, IrL',l, M,:I,, 50, ~ 1992) 1435. I/~l tl. Rt~d¢ .'rod V. Itlavacek. Delaik.'d kineliCs , f lilallilllll m i m i c ,,,y111hesis. Aft?hE .I., 41 1191)5 ) 377, 171 Z,A, Ml,111ir. Rem,'lioll, ,.,yntl1¢sis l'q'oces,',,¢,',,: incdli11|iSln~, ,11d clrqm:leristics. M¢I~,II. A, 23 (1092) '7. 181 T, O,,':rvv:1. A llt:w rn,clhod ,td' armly,'~in,g lherm~z,gnr,, irli,clri~: dim,, Bull, Chem, S,,',c, Jim,, 38 i It)65) 1881, I'91 C,D. l).yl¢. Kirlcl,ic analyst,,, ,td' lhernlogravinlelri¢ dala. ,I, Apl'fl l.)cflyln. Sci., 0 11962) 039. I lU] ('.1). Doyle. Series allproMlnalit'q|s 0,, Ilk' eql,lilli~,1 of ll'lermugravim¢Iri¢ dal,,a, Natpre, 207 ( 1'9051 2q0, I I I I S.S. Taluhanker and I.,K. Dorai,~wamy, Arm.lysi,,., ul ,,,olid-,,,olid l'¢aclion,,.,: .'i reeler,'. Al(,hl~ J.. 25 11979) 561, I12] D . L l:h'an,,,ou. KiIlelicn al|d n]t.,chani,',m of rea¢liol| h¢lW¢¢ll ~,ii()al~d AI.tL, J, Am, Cer:ml,. Sot,, 48 11905) 1529, 1131 g.J. lalidler. I¢,eaction Rate ginetics--I,'undame.tals ;.nd Al~plicafi.ns (Japanese ve|'sion, h Hirokawa. I t)72. p. 41.