July 20, 1937
3633
HEATC.\PACITIESOF ;\lg3Cd AND -lIgCdj
internal equilibrium. Gillespie and Perry16 have in fact observed several abnormal 0" isotherms for which no break a t all occurs. T h e second isotherm break occurs a t P d 2 H from SO to 200". T h e break occurs a t higher hydrogen concentrations a t lower temperatures possibly because of hydrogen adsorption in structural rifts and defects caused by the independent expansion of each lattice cube. Significance of the Entropy of P d ? H at OcK.I n the preceding paper? a residual entropy of 0.59 e.u. at 0°K. was compared t o the residual entropy of 0.S2 e.u. for ice on the basis that random hydrogen bonding can occur in both. In ice, each oxygen atom is surrounded by four tetrahedrally arranged hydrogen atoms. In PdH4+7Pd,only some of the palladium atoms are surrounded by four tetrahedrally arranged hydrogen atoms. For ice, however, only two hydrogen atoms are covalently bound a t one time to an oxygen atom while all four hydrogen atoms can be covalently bound to the central palladium atom. Just as random distribution of hydrogen atoms in ice is frozen into a false equilibrium a t low temperatures, the arrangement in PdzH is subject to a similar circumstance. In building a model of PdHh.'TPd, many different arrangements of the PdH4 molecules on corner lattice sites can be constructed. Actually there are five possible arrangements for the distribution in an independent lattice cube, but the cubes are not independent in the metal. T h e a-rrangenient of PdH4 molecules in one cube partially determines the arrangement in the neighboring cubes. The system is too complex to lend itself to a numerical calculation of the total number of arrangements as can be done in the case of ice. However, since each cube is equivalent to two Pd2H molecules, the (16) L J Gillespie and J. H. Perry, J P h w . Chem., 36, 3367 (1931).
[CONTRIBUTION S O . 1008 FROM
THE
experimental value of 0.59 e.u. allows the choice of two arrangements for the PdH4 molecules in each cubic lattice because SO = k In 2"j2 = l/pR In 2 = 0.69 e x .
(2)
Comparison with Free Proton Theory.-It must be remembered t h a t the degree of hydrogen bonding in palladium hydride is changing with temperature as indicated by the heat capacity curve. It is apparent t h a t the covalently bonded hydrogen model at high temperatures becomes a model of interstitial hydrogen atoms vibrating and rotating relative to the palladium lattice. This assembly of hydrogen atoms, even though the hydrogen atoms share electrons with individual palladium atoms, would be indistinguishable from the model of free protons assembled in regular monolayers as considered by Lacher." T h e straight line relation in the a-phase between hydrogen concentration and the square root of hydrogen pressure applies equally to a P d H covalently bound hydrogen model or to a free proton model. I n other words, much that has been explained in the past on the basis of free protons can also be explained by the covalently bound hydrogen. Additional investigations, particularly of neutron diffractions, will have to be conducted a t temperatures well below room temperature in order t h a t the covalently bound hydrogen model be further verified. Acknowledgments.-One of the authors (D. 31. N.) wishes to thank the Socony hlobil Oil Company for the generous provisions of the Socony Mobil Incentive Fellowship. T h e help of M r . L. F. Shultz. who produced all of the refrigerants and aided in the assembly of the apparatus, was invaluable I
(17) J. R. Lacher, Pvoc Roy. Sac ( L o n d o n ) ,161, 525 (1937).
USIVERSIT~ PARK,PA.
DEPARTMEXT O F CHEMISTRY, UNIVERSITY
O F PITTSBURGH]
Magnesium-Cadmium Alloys. VIII. Heat Capacities of MgXd and MgCds between The Standard Heats, Free Energies and Entropies of Formation and the Residual Entropies1t2
20 and 290'.
BY IT.lT. JOHNSTOX, K. F. STERRETT, R. S. CRAIG4 X D \\-.E. ~I-ALLACE RECEIVED~ I A R C 23,H1957
Heat capacities of hIgCd3 and MgaCd have been measured betvieen 25 and 270" using a new adiabatic calorimeter permitting a precision of 0.1 t o 0.275 in t h e measurements. Experiments \ e r e performed using a n intermittent heating technique in order t h a t equilibrium heat capacities might be obtained. The d a t a reveal a specific heat anomaly of t h e customary type for alloys undergoing order-disorder transitions, with peak values at 83.8 and 150.6' for MgCds and Mg,Cd, respectively. n'ith the aid of t h e heat capacity data, t h e standard heats, free energies and entropies of formation of t h e alloys a t 270", which were reported earlier, have been corrected t o 25'. T h e residual entropy of Mg,Cd has been found t o be 0.03 i 0.04 e.u./g. atom and the corresponding quantity for lIgCd3 has been found to be 0.16 Z!Z 0.04. T h e latter is in good agreement with t h e quantity 0.17 i 0.01 e.u. computed statistically under the assumption t h a t there is a random distribution of the observed number of Schottky defects over the lattice sites. Aqttentionis directed t o t h e large errors which can occur when the conventional continuous heating technique is used with systems undergoing configurational changes.
In Paper VI1 of this series heat capacity data for -Ilg3Cd and hIgCd3 between 12 and 320°K. (1) This work mas supported by a grant from t h e U. S. Atomic Energy Commission. ( 2 ) From a thesis submitted by W . V . Johnston in partial fulfillment of the requirements foi t h e Ph.D. degree a t t h e University of Pittsburgh, Auqust, 1955.
were p r e ~ e n t e d . ~Entropies of formation of these two substances at 270" had been determined4 earlier by the electrochemical cell method and in (3) L. W.Coffer, R. S. Craig, C. A. Krier and W . E. Wallace, THIS 76, 211 (1954). (1) F. A. Trumbore, W. E. Wallace a n d R. S. Craig, i b i d . , 74, 132
JOURNAL,
11952).
paper VI1 the two sets of data were used to evaluate the residual entropy of the compound ?.IgCd:,. 'The required thermal data above : E O " K . were taken from the literature. similar calculation for 1Ig:jCd was not possible a t t h a t time because of the unreliability of the heat capacity data for it above 320°K. I n fact the calculation for lIgCd., was not entirely satisfactory since the existing d a t a extended only to 430°K. and an extrapolation over a n interval of 110" had t o be niade. T o permit ;t satisfactory evaluation of the residual entropies of these substances a new calorimeter has been built and used t o determine their heat capacities between 20 and 290". T h e data obtained are of additional interest in t h a t ( I ) they permit reliable evaluations of the heats, free energies and entropies of formation of t h e two compounds a t 2.5' and ( 2 ) they indicate for the first time the temperature dependence of t h e eqziiiibrium heat capacities iii the region where these substaiices exhibit thermal anomalies due to order-disorder transformations. Previous studies have corisistently inxrolved the continuous heating technique yielding m n - e y u i f i b r i i m heat capacities, which for these materials differ a t some temperatures appreciably from the equilibrium values. Experimental Apparatus.-Since full descriptions of the crrliirirnetrie equipment used m:iy he found clsewliere,j,6 only ;L brief account will he given here. T h e calorimeter assembly \v:is esseiitiall\- of t h e Soutliard-Brick\vedde deEigii .i feltdepartures from conventic~n:il practici were necess:i~-! hecause of t h e higher temper:itures inviilvcd . LVires were iiisulatetl with glass 1)rnid (inst d ( i f S y l o t i ) impregnatcrl \vith either Teflon o r :i silicrine r 11. T h e r~irnplecoiitaiiier \\-as very similar t o that wliicli h been used in this Lal)cir,it o r y for w\-eral years i i i tlie 5tutly r i f iriterinctnllic coin~ j ~ i u i i tnl st ltiiv teniperaturei. I t w i 5 sc~:tlec!off using a soltier ci)niisti~igo f Pb with 5' ! A g adtled. T h i i provet1 t o be inore s:itiif;ictiir>. niecliaiiically than p u r e PI] \vliich \v:i> cirigiiially n i e d . T h e s a ~ i i p l e\vas ic,iletl r i f f in :III elicloiid cont:iincr \vliicli permitted tile sciltleriiig tii I l e cliriic under retiucetl iiressure. L%blJLit 0 . 1 z i t i i i . pressure of iieliuiii i~sclinnge gas w t s intriiduced. Ternpcr;iture-: iwre m e a < iirrd with :t cupsulc tJ-iie platiiiuin rcsiitarice tliermiirrict~r tliat hat1 1,eeri calibrntrd I)!,t h e S;itiriilal I3ure:iu i ) f Stantic ~ ~ - d s Its . fui!daiiiciit:il interv;il \v:i5 peri,idic:tll!- rcdvti~riiiirietl during tlie course i i f the work. Materials Used. -The sariiples eiii1~11iyetIwere tlii. iiiiiic ,I, h a d been tised in the earlier ~ 1 1 r k . 3They l i a t l 1iei.11 itpliere o f hcliurri \vliile not iii use. C O I I I ~ I I ~ ~\\ere ~ ~ I74.98 I I I S =k 0.04 xiid 24.98 & 11.04 Eitoitiic c , c:ttiiniuiii for I\IgCda aiitl kIg:Cd, rc\pecti\Tely. T h e c i f u n i p l e eiiiployed were: XIgCtl:. .582,2(17 g . iir g . a t o m s ; hfg,Ctl, 252.092 g . o r 5.4418 g. atoms. Method of Measurement. llgCt13 a n d Mg,Ctl uritlergo , irder--disortler tr:itisitioiis in t h e temperature range coveretl :it ahrlut 85 :itid 150", respectively. Llost of tht. heat cap;icitJ- data filralloh- in the r~rder-~tiisi~rder region Imve l w e i i obt:iirietl using t h e criiitinu~iu~heating technique. I t :ippcars that such results inay in certain regions r i f temperal u r e he sericiusl\- in error ( l o ' , o r i n i ) r c 1 due to the failuri. t i l i i i : t i i i t a i i i equilibriuiii iii tlie s:rinplc. 1)isrirtleriiig requirci 'L rc~tii.tributioii of a t i i i n i i i \ w tile p i i i i t i i n i 5 i i i t l i c 1:itticc :iii[l i h i i I I I ~ J fail t i i keep p:icc i v i i l i t h e changiiig teiiilicraturi \ v l i v ~ i c c i n t i n u ~ ~ uheating s is used. I n this e v e t i t the ineasiirrtl 11c:it czip:3eiiy is :I riijii-equilibriuiri value anti i, tlicref o r e not suitable for entropy cnlcul:iti~~ns. ~
,
M' V J o h n s t n . P h 1) T h t 5 i i . 12-ni\-Prsityof Pittsburgh. A u i . ' i i h t ,
11
liC,""t
% < a d d e 7'HlS
IOlK\'J
55.
.i'Iie iiiteriiiitteiit Iieatiiig tecliiiique 1i:is liecii e i i i ~ ) Iet1 ~i~ iii t h e present stiidJ-. The s:miple is heater1 for :I carefull! incnsured i n t e r w l o f time o f 3 t o I5 minutes tiur:itioii resulting i i i :I teinpcraturi. iiicreiuent of rouglily 3'. T e i i i perature then followed until it hec:iiiic coiistcriit,5
if this riccurrd ill ;I re:i~lJliablCleiigtll o f tiirte. This \viis not feasilile ivith I\lg,,Ctl from 35 tic GO" :iiitI with l I g C d a from 31 to 95'. I n these range.. the temperature coiitiiiuetl t i l kill f(ir 1 1 1 : i i i ~ - houri after the hext i n p u t \\-as stoppctl, i i i tlicating t h a t diwrder in the >:itiiple \vas continuing ti, i l l c r w s e . Iii sriirie iiiit:iiices tlic cciurse of tlie teiiipertiturc titiie curve xrai follon.ed f i r 20 lir. :ind the sample 1i:itl n o t reacheti cr)iifiguratirinul equiiilxiuin. hi these cases a11 estr:ipi~latedf i n d temperature \\-;isfound under tlie aisuinptioii t h t t h e tciiiperaturc tends c ~ l ~ ~ ) n e n t i atoward lly the equililiinl)tii~n\rhicli Iixs 1)i:en justifietl b y rei i f tlie ortli.r-tlisiirder trarisfi)rinatii)ii i i i 1 f gCtl,. \Vitli 1Zg,Ctl tile c~tr:ipiI:itiiiiis were sliort a n t 1 error. intrc~ducedfriiin this siiurce were slight. The c ~ t r : i p o l a t i o i i ~ were not 5111>rt, howei-er, f~:irtciiiper:itiirci iiear t h e order tliwrtlcr Curie piiiiit for I\fgCdI. Equili1)r:itiiin nxi X I 5luggiili tli:it erriirs o f s c \ w a l per cent. \vere pii~sil)lc :it t c r n p e r a t u r e ~ 1,etwceii i o ;inti 80'. Acciirtliiigly tlirw tlcterrniiiatiiJii.; \ w r e t n d e o f the tot:il cliange i i i eiitli:ilp>. for MgCtl.3on 1ie:ititig it froin 30 to 100". I t \va\ cu-efull!iii:iititaiiictl a t the lo\ver teiiiper:iture fiir ;t long period ( i f time t o citahli4i equili1)riuin iiiiti:tlly. S c x r 100° cquililnrtioii occurrctl i i i :t .;hart ixriiid of tiriic ho tliat AII for t h e r \ x ! o f tciiiperxturc could be estnblisiietl q u i t c Tlic iiidividu:il Iiext capacit>-tlcteriiiiiiati(,iis !veri' (1 i!i ciiiiitruct .i provisiiiiial curve ( i f Cl, Z'Y. 7 ' . \.e \ v L i \ tlieii :itlju~tetl up\vartl ~ i r ~ i ~ ~ i ~ r t i i ~4 1i1 i ~ i l l y that tile iiitcgr:itetl lieat effect 1iIitaiiietl from t i l e curve ;igreed wit11 tiie tlircctly iiiwsurctl A f t fiir tlic 50 t < i 10ii3 iiitervxl.
Results The data for l\lgaCd were obtained in IO series or measurements involving a total of SI deteriiiinatioiis. For I l g C d . there were 1 1 series and a total of 7 1 intli~,.idualmeasureinen ts. I t was of coursc necessary to ha1.e the sample at eyuilibriuni before and after each measurement. The treatment of' the sample in the after-period has been dcscribctl above. The details o f the thermal coiitiitioniiig (li the samples prior to initiating a scries i d iiieasurcinents are too ~i~itiierousto relate here.i" 111 general the thermal treatment was such t h a t thc. sainple wis 21s near to equilibrium ;is coultl achieved experiiiientally before nieasurenierits ww beguii. I n some instances the tre:itineiit itivolvetl :I very consiclerahle amount of time :itid c;irc. For example, with hIgC& below SO" it p r o \ - d iiccessary t c i ninintaiii the sample a t tcniperature for roughly :I week for it to come to equilibriuiii. Sriioothetl values for the heat capacities arc' give11 in Table 1. Excluding the regions of slow equilibration, the precision of the measurements is 0.1 to 0.2C; as jut1g:cd frriiii the scatter of points frriiii L: smooth cun'e. Residual Entropies.--Entropics of forinntion o f riiagiiesiuni~~cadmiur~i alloys were reported earlier based 011 irieasurements iiixle using thv e1ectrocheiiiic;il cell iiiethotl. : L I ! 'The eiitropivs oi form:ttion of IIgCtl:, m t l ltg:,CcI a t 2iO' were i h l A t i w l i i t c c o n < t i i n' v
1.
(If
CVLIT\P
neiw : ~ ~ l i i c \ e ~Iln i r . i ( . ! i r c
TABLE
HEAT C A P A C I T I E S O F C", cal./deg. g. a t o m MgCdl hlgiCd
7.06 7 . 10 7.39 8.01
6.01 6.01 6.10 6 90
9.05
7 .00
1 u . 88 12.11 1 3 . 9s 16.28 21 .01 !ma x .) 9.18 7.46 6.98 6 . $I( I r j 88 6.88 A 88 6.88
7.16 7.25 7.35 7.47
7.59 7 72 7 87 8.23 8.70 9.11 9 91 12.23
1
MgCdj T, OK.
AND
MgiCd
CP cal./deg. g. a t o m MgCds MgaCd I
415
6 . 8 8 16.68 6.89 19.98 . . 27.35 (max.) 6.89 18.02 425 6.90 7.40 430 6.91 7 1 0 4111 6.93 7.03 150 46) R.95 6 . 9 9 ii . 9 X (i.96 470 380 7 00 6 .94 490 7.02 6.93 ,500 7 . 01 6.94 510 7.07 6.97 7.10 6 . 9 3 520 580 7.13 6 . 9 4 7.17 6.98 540 6.99 513.16 7.18
freezing-in of the configuration in a very striking way (Fig. 1). The Cp values rise with temperature as if they will reach the Dulong-Petit limit a t about 300°K. However, a t about 310°K. there is a sudden rise in C, followed b y a small maxi-
120 123.8
found t o be 1.04 and 0.91 e.u., respectively." Using the heat capacity data for the pure metals reported in the following paperI3 together with earlier data from this Laboratory for the low temperature regionla one computes entropies a t 270" to be 11.33 e.u. for N g and 16.28 e.u. for Cd. From these data one calculates the entropies of lIgCdri arid Mg:jCcl to be 16.14 and 13.65 e.u., respectively. The data in the present paper together with previously published results3 permit the calculation of S2:(,3 - .Suo;.i;. for the two compounds. These entropy increments are found to be 13..X e.u. for ?rZg,,Cd and lq5.9fi e.u. for MgCd3, from which one computes the residual entropies to be 0.1 1 and 0 18 e.u. for the respective compounds. For reasons which shall now be indicated the quantities so computed represent t h a t which may be called the uncorrected values. T h e compounds are formed upon cooling the Corresponding magnesium-cadmium solid solution, the solution being the stable form a t high temperatures. Since the transitions are second order and are spread out over a temperature range, progressive reduction of the temperature of the systems results in an accompanying configurational change. For the present purpose the configuration of the system can be represented by the Bragg-iirilliamsI5 order parameter s . As temperature approaches O"K., s tends to unity corresponding to the situation in which each magnesium atom occupies a rnagnesiuni site in the lattice and each cadmium atom, a cadmium site. However, in practice mobility is lost before perfect configurational order is achieved, .c is frozen-in a t some value slightly less than unity and the compound is left with a residual entropy. 'The heat capacity data for Mg3Cd show this (12) D a t a are expressed throughout this paper o n a per gram a t o m Ilasi. T h e y e d a t a therefore reier tti the entropy change accompanying t h r f r m a t i o n of one gram atom u i alluy from t h e component metals I 131 IV C> S n h a , I;. f; Sterrrtt, K . S . CraiK iind W .l i . IVallacc. 'I'tIlS J O r K s A ' . 79, :3i1:i7 1 l9d7! ( 1 - l i K S . Craig. cl t i / , i b i d , 76, 238 (19.74). f 1 . i ) I V . I.. R i a ~ : l :and I: J . \l"illiams, Prof. R o y . .Sfif. (T,ondoiz), 14SA, ii
