Influence of Temperature upon the Diffusion Velocity of Solid Metals (The Zinc-Copper System)

In the丘rs亡part it is shown tlユ昆t the rati・o．εvelocities of di伍lsion given by We1ss is equa監to dユe ratio of coef丑cieH亡s of di｛：ftlsiOll deiined by Fick，s la、v in the 『ase of primary solid solutions． 王ll 亡he second part， the zinc。coPPer system bei：lg taken as an ex・mple， it is shown by means of・an electric・｝resist・！】ce method that the velocity of d澄hsion can exist in the case of no11－primary solid solu亡ions a正】d some of the states of diffusion h、we been examined by X－rays． In the third part it is prowd that the relation betwe合n the velocity Qf diffusion 7 and the absolute temperature T に に is given by 7；3げ一一アinstead of by Welss’formu1・・U＝灘7「with thc zillc－c。PPer system ill the r乙由ge of tempel’Lltul’e 87－3Q2。 C，、vhereβ，瓦ct andβare col）sta！lts and α罵9，52XIou degrees．

Relation be亀wee捻Diξ壬usion Ve夏ocity and Diffusion CQeMcient

In the case of metals which do not form a perfect solid solution， xve can easily see from the complexity of t’heir ediuilibritini diag＋rams that there is no such constant as the coeMcient of diffusion which is inciependeltt of the． concetitration anci time． Nevertheless， 1－1． XVeiss！ has found by microscopic examination that when samples which are both composed of the two 1〈inds of i’iietals to be t’ested， are heated at ’different temperatures， T ancl Tt， ．and one of them reaches a certain state （say A） after the ti．tne interval 1’i and another state （say B） after tg， then the other of them E lso reaches the state A after the time 1． ’ g． XVeiss：Aiin． de Chlmie， i9， 2i （Ig23＞； and 2e， 131 （1923）・ ・1 6S Chuiiro Matano interval l1ノ（which is difilerent from tl）and the state B after〆2’， and， moreover， there exists the relatlon

毒／姦ノ躍’2／～f2ノ。 （1）

Since the states A alld．B are aybitrary， the above ratiQ｛s constaDt in any state， and may be put．as． V，／V’（．7 correspondi1｝g to T and V’ to T／）． Weiss cailed 7 the velocity of di伍【sion at the tempera－ turc T．

Now we will consider what meaning the vebcity Qf di伽sion has in the caLse wherc thcre exists the coef丑cient of difFusioll Z）which is defined正）y Fick，s laxvi or by its至orm of 4if振3rent量εし1 equε沈ion

∂c ・ ：1）Ac， ∂♂ where c is the concentration， t the time and d the Lap圭ace operator．

The concentration， then， xvill be given by the forln c＝ノ「（Z）t， x，，ノ，の， where x，．7■、 lldε乱re the space coordinates which determine the pOillt where the concentration is considered， and∫ is a certa拠function2 which is determined if the boundary and initial conditions are givelL If we chOose， as in Weiss’case， the．same two sampled and heat one aLt ．．the tenlperature ク、 and the other at Ti， then the fi1’st state is reached af乞er the times ti and ll／and the other state is reached after 12 andあノ． In order to get the same stεしte at．the clifferent telnpera－ tu．res and．different intervals of time， the following・relatiO1ユs must exlst：一

C『／（Dt1， X，ア，ε） ：ゾ（」1ンtiノ， X，ア，3）， and c＝＝ノ“（Z）あ， x，夕， z）＝．／（Z）tx2ノ， x，夕，ε）， or 1）tl＝：1）’！1’ and D／，，＝：1．）’あ’， and s・ Z）’／Z）＝1、／t・’＝1・／／・’， （・） whGre l） ttn d．2つノ arg the coef慣cients of difFusioII re£erring to the temperatures 7’and T／respectively． Comparing th｛s with（1）， we have

∠フノ／2＝）二四∫ズ’／レ7； （3） i・e・the ratio Qf the coefli ci．ents of diffusion de伽1ed by Fick，s law at any two temperatures is the sarne as the ratio of the velocities Qf i． 1｛’ick： 1’ogrg． Ann． 94， sg （i8S5）・ 2・． llieinann－XVeber： Differentialgleichunsren der 1’1iysil〈 II S． 177 （lc）27）． lnlZuence of Temperature tipon the Dtffusion etc． diffusion clefiited by XVeiss solutions． i6g at those teniperatures in the case of solid

Determination of Diffuslon Veloclty by Resistance Method

Genera／ co／iSi’def’aX！b／z ρ／ t／i e 〃2．eal乃od．・ 「～Veiss！ 11as determined the veloclty of cliffusion of various iiietals and N． X）V． Ageew and O． 1． Vher2’ hic ve determinecl that o£ aluminium ancl iron． by microscopic means， but the velocity ’of diffusion can be dete．rinined froni the chcc nge in the electrlca！ resistance of the samples examiRed． As iR the previous experiment3 carriecl out in the case o£． px’i｛nary solid solutions， tal〈e two samples inacte of two 1〈・inds of meta！s in the forin of foils， aRd heat theni at the different temperatuires T and 1”i， then measure the electrical resistance of them at the same temperature Tt （〈T）． The concentration c of the one ．metal will be given by c ＝f（x，’ t） at T， and c＝g（x， 1） at Tt， x’vhere f and g are zml〈nown functions， t the time， and ．x the space tt．Qordinate which is perpendicular to tlie ｛lat surface of the s．ample． lf the sanie state be reachecl at the times t and ti in ’the respective cases as XVeiss supposed，・tl’ien tke relation c； 一一f （x， t） ＝ g （x， lt） must exist and． the el’e c’ trica！ resi stance of the sampies has also・the same value． Conversely， if the resistance of many 1〈inds of saniples of the same pair of metals be measured， and tlte time intervals x・vhich are necessary to bring the resistance to the sanie va£“e be compared， and i．f． the series of tinie rtttios have a constant value． in ecftch case， ’we can say that XVeiss’ coikception is correct apd the veloci．ty of dififusion exists． To illustrate this． method the author has ． chosen the system of zinc and copper， althoug）’h the diffusion pheiioinena of this system have alz’eady been studi．ed by XVeiss“ ancl S． ．］IL． llloyt：’ by microscopic examination ancl by C． F． IEIcam6 by the X－ray method with larsre sins，le－crys．tals ot’ copl）er， but in any case the velocitY of diffusiolt has not yet been giv en．

乃’od？t・ctib／l q／3α〃～rP／eg・〃ie’l／i・Ot／〈ゾ〃leas～lr6？〃16・’ 7Zt a7zalの6Pa7αXZdS ： 1’t． XVeiss， loc． cit． 1．Nlr． ’XV’． tN．geew and （：）． 1． Vher： Jour・ lnst． iTN・ietals， 44， 83 （lg3i）・

C． Xi・latano： ’arhese ILN’［emoirs， i4， 123 （i93i）・ 1－1． ’iiX・T’ eiss， ioc． cit．

S． L． 1－loyt： ．X．mer． lnst 2Niin． L）v｛et． ］：， ng． Tech． iJubl．， 128， 1 （it）2S）．

C． F・． Elam； Jour． lnst． 1“gletals． 45， 217 （lg3i）． 170 ChuiiTo Matano

As in the previous papert the samples were made in the forin o£ foils by aiternate electropiating with copper and zinc． A wax surface covered with graphite was first p1ated wi，th coppev in the electroplat－ in．o．’ solution； I oo c c． of water containinsr 4，3s gms， of caustic soda， 2．609ms． of copPer sulphate and エ3．oo gms． of R．ochelle salt． T’heii zinc ancl copper ！ciyers were added alternately， but as the above so－ lutioii used for copper was not suitable for zinc objects， the followiRg solutions were usegl： for’zinc， i oo c．c． of wc｝ter contai．ning 2，20 f．’｝’ms． of sodium citrate and 3．s2 gms． of．zinc chloride； and for copper， ioo c．c． of water containing 2．i2 ．o’ins． of soditnn bisulphite， ・i．7s s．ms・ of copper acetate and 2．i2・ g’nis． of potassium cyanide． After a suitable thicl〈ness had been obtained， the foils were peeled off ancl cut into stri．ps cdbout o．i cm． in breadth and i，s cms． in ieng’th． ’Ilrlie time for eic ch piating’， the current densky， the number of layers anci． the total t2iicl〈ness of the foils are tabulatecl in Table 1．

’rable 1

Foi1