Thermodynamics of formation of yttrium-magnesium intermediate phases

THERMODYNAMICS YTTRIUM-MAGNESIUM J. F. SMITH,t

D. M. BAILEY,?

OF FORMATION OF INTERMEDIATE PHASES*

D. B. NOVOTNY,f$

and J. E. DAVISON?

Three intermediate phases occur in the yttrium-magnesium system. The y-phase is isostruoturel with C&l snd has & range of homogeneity of .- 2 t&o/J. The &phase is isostructural with MgZn, and is essentially invariant in stoichiometry. The e-phase crystallizes with the a-manganese structure and a limiting stoiehiomet~ of Y,Mgza at the per&e&c temperature; at temperatures below the peritectio decomp~ition the stoichiometry is more m~esium-rich with 8 rsnge of homogeneity of N 3 at.%. The free energies of phase formation have been determined from measurement of magnesium vapor pressures over a series of alloys while the enthalpies of phese formation have been determined calorimetrieJly with a differential acid solution calorimeter. Combination of the data yield the following values for the thermodynamic functions associated with phase formation respectively of YMg, YMg, and Y,Mg,,: AFoa,s = -2.9 -& 0.2, -3.0 f 0.2, -1.9 f 0.2 k&/g atom; AHnzss = -3.0 & 0.3, -3.4 f 0.3, - 1.8 & 0.2 kcal/g atom; AS’,,, = - 0.3 & 0.4, -1.3 h 0.4, +0.4 f 0.3 eu/g atom. Both the enthalpy and entropy of formation correlate with the volume contractions which accompany phase formation. ETUDE

THERMODYNAMIQUE DE LA FORMATION DES PHASES DANS LE SYSTEME YTTRIUM-MAGNESIUM

INTERMEDIAIRES

Trois phases intermitdirtirespeuvent se former dsns le systime yttrium-magnesium. La phase y est isostructurale a C&l et a. un domaine d’homogeneite d’environ 2%&t. La phase 6 est. isostructurale & MgZn, et est essentiellement sto&hiom&rique. La. phase E cristallise dans une structure analogue it oelle du rn~gan~~ c( et peut s’etendre jusqu’8 un compose st~hiom~trique Y,Mg,, & la temperature peritectique. A des ~rnp~~tu~s inf&isures & la temperature peritectique, le composb peut s’enrichir en magnesium dsns un domaine de 3%at. Lee energies libres de formation de phases ont &e determinees par mesures de pressions de vapeurs de magnesium pour un ensemble d’allicagestandis que les enthalpies de formation ont et& d&erminees par mesures collorim&riques au collorim&re & solution a&de. Des mesures experimentales, on peut dbgeger les valeurs suivantes des fonctions thermodynamiques pour AF” 298 = -2,9 * 0,2, -3,0 & 0,2et -1,9 & 0,2 la formation des phases YMg, YMg, et Y,Mg,,: Kcal/rtt gr; AH”,,, = -3,0 & 0,3 -3,4 f 0,3 et -1,s f 0,2 Kcal/at gr; ASO,,, = -0,3 & 0,4 -1,3 + 0,4 et +0,4 f 0,3 ue/at gr. L’enthalpie et l’entropie de formation sont en correlation avec la contraction de volumes aacompagnant la formation des diverses phases. DIE THERMODYNAMIK

DER BILDUNG INTERMEDIARER MAGNESIUM-PHASEN

YTTRIUM-

In dem System Yttrium-Magnesium treten drei intermedi&re Phasen auf. Die y-Phase besitzt Die d-Phase besitzt gleiehe Struktur wie CsCl und hat einen Homo~nit~tsbere~ch von etwa 2 At.-%. MgZn~-Stats und ist im wesenttichen invariant beziiglich der Stochiometrie. Die e-Phase kristallisiert in der a-bin-Struktur und mit einer Grenzzus~mmensetzung Y,Mg,, bei der p~ri~kt~chen Temperstur; bei Temperaturen unterhalb der peritektisehen Zersetzung ist der M&~~siumgehalt gr(i13er, bei einem Homogenit~tsg~biet van etwa 3 At.-%. Die freien Energien der Pha~nb~dung wurden bestimmt aus Messungen des Magnesium-Dampfdrucks bei einer Reihe von Legierungen. Die Bildungsenthaipien der Phasen wurden kalorimetrisch mit einem differentiellen Kalorimeter mit sauerer Losung bestimmt. Die Verkntipfung der MeSdaten ergibt die folgenden W&e fur die mit der Phasenbildung verbundenen thermodynamischen Funktionen, der Reihe nech fiir YMg, YMg, und Y,Mg,*: A$‘“,,, = -2.9 * 0.2, -3.0 f 0.2, -1.9 & 0.2 k&/g Atom; AH”,,, = -3.0 of 0.3, -3.4 f 0.3, -1.8 & 0.2 k&/g Atom; AS’ e98 = -0.3 & 0.4, -1.3 + 0.4, to.4 f 0.3 eu/g Atom. Die Bildungsenthalpien und entropien passen zu den mit der Phasenumwandlung verbundenen Volumkontraktionen.

INTRODUCTION A ~mperatur~composition urn-magnesium

system

diagram

for the yttri-

has been proposed by Gibson

and Carlson. (I) This diagram contains three tectic compounds, y, 6, and E, with respective

peristoi-

* Received December 3, 1964; revised January 22, 1965. Contribution No. 1636. Work wae performed in the Ames Laboratory of the U.S. Atomic Energy Commission. t Institute for Atomic Research and Departments of Chemistryend Metallurgy, Iowa&ate University,Ames, Iowa. $ Now at: Monsanto Research Corp., Mound Laboratory, Miamisburg, Ohio. ACTA METALLURGICA, 2

VOL. 13, AUGUST

1965

chiometries near to YMg, Y,Mg,, and YsMgr7. Gb 1 son and Carlson reported the YMg struoture to be isomo~hous with C&l. Terekhova, S&vitskii(2) initially proposed a partial in which the most magnesium-rich YMgs, but they have subsequently

Markovs, and phase d&gram compound was accepted(3) the

Gibson and Carlson diagram. In a preliminary report(“) of the vapor pressure data for the system, it was noted that the &phase appeared to be a Laves phaset5) of the Cl4 type or a closely related structure 889

ACTA

890

while the c-phase

appeared

y-brass

related

or closely

corroborated who report YMg, that

the

to be an a-manganese,

structure.

by Kripyakevich without

isomorphous

METALLURGICA,

This has been

elaboration

that the &phase

with MgZn,

E-phase is Y,Mg,

(Cl4 structure)

with

is

structure. The present investigation was undertaken to look further at the crystallography of the intermediate associated with phase formation.

functions

The thermodynamic

measurements included independent determinations by both vapor pressure and calorimetric techniques. ALLOY

PREPARATION

diffraction

studies, all measure-

ments were made on a common alloys

were prepared

set of alloys.

from yttrium

These

and magnesium

relationships

X-RAY

y-phase

the experimental

and the indicated

yttrium and magnesium TABLE 1. Analysis Yttrium Element Y

of yttrium

crucibles.

%

These

and magnesium

Magnesium Element

99.72 0.0090 0.0075 0.0015 0.0210 0.0570 0.0100 0.0060 0.0300 0.0025

: F H 0 Ni Fe Ti Cr

crucibles

in tantalum

of

: N Fe Ca

fraction

points

pattern

second phase. bined

with

The dif-

magnesium

The lattice parameter

alloy

that

variation

a reasonable

com-

amount

of

second phase must be present before it can be observed a range of homogeneity

for the phase of

Further, if solid solubility

occurs by

the substitutional mechanism, the size difference between yttrium and magnesium would favor soluon the magnesium-rich

side of stoichiometry.

near the stoichiometric

For the &phase,

powder

specimens

composition.

for the order of one week at ~550°C.

were annealed Since the phase

is hexagonal,

are determined

two lattice parameters

from each Debye-Scherrer of the individual For

this

phase

points the

pattern and the precision is reduced

patterns

from

to

fO.007

the

65.8

A. and

66.8 at.% magnesium alloys were found to be free from extraneous lines. The data show definitely that

lid which was welded in place.

sealed tantalum

crucibles

The

were in turn enclosed

in

The alloys were then heated to of 1 hr or more.

temperature

to facilitate homogenization

by

the heating

rocking

is believed to

is *O.OOl A or better. of the 50.8 at.%

the fact

phase boundary

were sealed under a noble gas atmosphere

1OOO’C for a period

range of homogeneity

was the only pattern free of lines from a neighboring

bility

%

with a tantalum

welded stainless steel.

were made

on samples which

It seems reasonable therefore to infer an yttrium-rich

99.60 0.0500 0.0250 0.0030 0.0040 0.0200

Mg

measurements technique

be characteristic of temperatures near the annealing temperature. The precision of the individual lattice

about 2-3 at.%.

amounts

STUDIES

had been annealed for the order of one week at ~725°C

delineated

appropriate

patterns.

DIFFRACTION

by the Debye-Scherrer

at.%

by placing

composiby X-ray

Plots of lattice parameters versus composition are shown in Fig. 1 for the y, 6, and c-phases. For the

whose purity is indicated by the analytical data in Table 1. Alloys were prepared in the range 44-94 magnesium

and analyzed were checked

with Debye-Scherrer

parameter

With the exception of the small single crystals which were used for X-ray

diffraction

Chemical analyses showed reason-

between nominal

Phase

and

an a-manganese

phases and to determine the thermodynamic

cold work effects. able accord tions.

and Evdokimenkoc6)

13, 1965

VOL.

furnace.

Agitation

The

subsequently cooled to room temperature to eight hour period. In order to enhance equilibration,

at

was achieved alloys

were

over a six

the originally

region.

variation

of either

A single crystal means

of X-ray

stoichiometry

Since

there

lattice

sition the stoichiometry

Y,Mg,

was no

parameter

is in a

detectable

with

compo-

can be considered as invariant.

of the &phase diffraction.

The

was examined crystal

by

structure

was verified as that of a Laves phase of the Cl4 type with the following structure parameters: Space Group D& - -P6,/mmc

the alloy samples

were removed from the crucibles and ground to a fine

proposed

two-phase

with

4Y at &(t(Q,6, z; 4, 8, 4-z),

z = 0.0626

powder under a helium atmosphere. The powders were again sealed in tantalum and stainless steel and annealed at temperatures slightly below their respective eutectoid or peritectic decomposition tempera-

and

tures. A small amount of sintering occurred in the powders during annealing, but the alloys were reground quite easily into powder with no apnarent __

It should be noted that this structure generates the C-centered orthorhombic symmetry reported by Gibson and Carlson if the [120] hexagonal direction

2Mg at (0, 0, 0; 0, 0, &), 6Mg at f(x,

2x, a; 22, Z, &; x, Z, 4) x = 0.8409.

SMITH

et al. :

YTTRIUM-MAGNESIUM

INTERMEDIATE

PHASES

891

V - LINES FROM A SECOND PHASE 0-

DEFINITELY PRESENT LINES FROM A SECOND PHASE NOT OBSERVED

382 3.80

‘-&--o-T

3.78 3.76

I 44

I

I 48

I

I

I

52

I 56

I

I 60

I

I 64

I .

/

I

9.80 9.75

/

76

80

84

6.037

88

92

96

COMPOSITION (at. % Mgl FIQ. 1. Lattice parameters versus composition for the three intermediate phases in the yttrium-magnesium system.

is chosen as the b axis of an orthorhombic cell. Corroboration of an invariant stoichiometry was obtained from the single crystal intensity data. These intensity data were used in ~1least-squares structure refinement with the yttrium sites in the structure treated as though occupied by a statistical atom, (z)Y + (1 - 5) Mg, with z as an adjustable parameter. This refinement minimized the discrepancy index with x = 1 in agreement with a fixed stoichiometry of YMg,. Precision lattice parameters of the e-phase were obtained from diffraction patterns taken with a backreflection camera. Precisions of the order of &0.0005 A resulted from a least-squares fit of the measured diffraction peaks with a weighting factor based on the Nelson-Riley(‘) function. Debye-Scherrer patterns were taken of the same set of alloys. The 84.6, 85.6, and 87.5 at.% magnesium alloys appeared to be

single phase though in the pattern of the 87.5 at.% alloy there was a questionable trace in the background which could be attributable to the neighboring second phase. It seems evident from the lattice parametercomposition plot that the range of homogeneity near the annealing temperature of 525°C is about 84-87 at. o/Omagnesium. This composition range includes the 85 at.% magnesium composition associated with the originally proposed(l) stoichiometry of YsMg,, but is slightly more magnesium-rich than the 82.6 et.% magnesium of the stoichiometry Y,Mgs4 proposed by the Russian workers.(@ Examination of the a-manganese structure indicates that a composition range 82.6-86.2 at.% magnesium, corresponding to the limits Y,Mgs4 and Y,Mg,,, could be achieved if the twofold set (OOO,#) could be occupied by either magnesium or yttrium atoms. A single crystal of the s-phase was examined

ACTA

892

METALLURGICA,

VOL.

13, 1965

COMPOSITIONlata % Mg 1 FIG. 2. Temperature-composition

diagram

by means of X-ray diffraction. The data were found to be in rough accord with & stoichiometry of Y5Mgz4 in the u-manganese structure. However, significantly better agreement between calculated and observed intensities was achieved with the twofold set (OOO,#) occupied on the average by 1.5 yttrium atoms and 0.5 ma~esium atoms. Refined structural parameters are as follows : Space Group T$ - - i43m with two atoms (1.5 Y, 0.5Mg) at (0, 0, 0) + B.C., plus 8 Y at (zzz;

EZ;

ZxZ; E&x) + B.C. with x = 0.3126,

24 Mg at (xX.2; .2Xx; x2x; zxz; ZEx; xzzi!; xzz; zxz; zzx; E&J; .zZZ; ZzE) + B.C. with 2 = 0.3605 and z = 0.0259, and 24 Mg as above with x = 0.0857 and z = 0.2805. The indicated composition is 83.6 at.% magnesium and should correspond to a point on the magnesiumrich boundary of the phase in the temper&n-e region 567-605’C since the crystal was grown in the twophase region of liquid plus compound. A comparison of this m&gnesium-rich phase boundary at elevated temperature with the magnesium-poor phase boundary at lower temperature indicates an increasing stability

for the yttrium-magnesium

system.

toward the magnesium-poor side with increasing ternperature. On this basis it seems likely that the limiting stoichiometry Y,Mgz4 should be the phase composition at the peritectio decomposition temperature 605°C. Incorporation of the present X-ray diffraction results with the original results of Gibson and Carlson leads to the modified phase diagram which is shown in Fig. 2. VAPOR

PRESSURE

MEASUREMENTS

Magnesium vapor pressures were measured over the yttrium-magnesia system by the Knudsen effusion method.(@ The vapor pressures were determined from the weight loss of a Knudsen effusion cell as a function of time at fixed temper~tu~. This technique obviates solid angle calculations, consideration of oondensing efficiency, or additional analytical procedures. The &ppar~tus and technique have been described in more d&&I in previous papers.@J’J) Verification of the negligibility of the yttrium contribution to the vapor pressures measured over yttrium-magnesium alloys was achieved by spectrographic analysis of the condensate which had been washed from the walls of the effusion chamber with acid. This analysis indicated that only a trace amount of yttrium was present. A graphical display of the experimental points is shown in Fig. 3 while an analytical representation of the data as determined by a least-squares fit is shown

SMITH

et

YTTRIUM-MAGNESIUM

al.:

I

I

1

INTERMEDIATE

PHASES

893

Y(K) + 2% (4 72 JWQ%

,’

AP” = (+) RT In P1P11/(Po)2

= -2.97 + 0.95+ (0.3j, 1.2)x IOWT; (5) 5Vd + 24Mg (~)FttY$fg&), AP” = (2~) RT In (.r)5(P11)5(P111)141(P0)2* = -2.04

1.3) x 10-V.

(6)

The quoted uncert&i~ties include a contribution from the uncertainties in the vapor pressure of pure msgnesium as well as from the uncertainties of the present measurements. The net uncertainties in computed values of AF” from equations (4), (5), and (6) based only on the scatter in the present m~surements sre respectively jO.16, fO.18 and fO.16 kcal/g atom of compound.

22 24 26 2.8 3.0

CALORIMETRIC

3.2 341.0

f 0.97 + (0.3 f

I

I 1.2

I I.1

14

1.3

Free energy values are normally obtained from vapor pressure me&surements with good reliability. However, it is recognized that minor systematic errors in a vapor pressure determination may reflect appreciable inaccuracies in enthalpy and entropy values although the corresponding free energy values rem&n quite acceptable. Even in the absence of such systematic errors, the resolution of v&lues for enthalpy and entropy terms solely from vapor pressure data ordinarily occurs with a precision almost an order of magnitude poorer than the precision of the associated free energy values. On this basis a separate determin~tion of enth~~~~ indoor entropy is desir&ble, and in the present experiments a determination of enthalpies of formation for the three intermediate phases in the yttrium-magnesium system was undertaken with a differential acid solution calorimeter. The experimental procedure consisted of measuring the difference between the heats of solution of an alloy and an equivalent mixture of the constituent elements in a 2.5 N HCl solution. The calorimeter design allowed the escape of evolved hydrogen only after thermal equilibration with the solvent through a heat exchanger, and the problem of solvent evaporation wss minimized by covering the solvent with an immiscible layer of mineral oil. A detailed description of the calorimeter will be included in a subsequent

1

I.5

d/Tf”K)

FIG. 3. Vapor pressures measured over yttriummagnesium alloys.

in Table 2. It may be seen that the vapor pressures are compatible with the proposed phase diagram. The standard free energies for the following reactions may be written: mg(y) 2 Mg (g) + YWd, AF” = -RT In (ar)(P’)/(a,);

(1)

mg2@) ZMg (g) + =@g 0% AP” = -RT In ~u~)(~~~)~(~~);

(2)

YPg&) * Mg tg) + YMg, (Q, AF” = -RT In (ad)(P1’r)/(a,).

(3) Since the maximum solid solubilities for all phases are ~3 at.% or less, no appreciable error will be intr~uced by approxim&ting the activities of the solid phases as unity. Combination of this approximation with the vapor pressure data for pure magnesium allows the derivation of the following free energies of form&ion in kcal/g atom of compound from the measured partial pressures; Y(a) + Mg (s) ?rtYMg (Y) AF” = 8 RT In (PI/PO) = -2.77 f 0.80 - (0.1 f

1.0) x 10-327;

MEASUREMENTS

(4)

TABLE 2. Linear representation of measured vapor pressures log,,P(torr) = A/T _.

Tamperrature range (“K)

Over phase

Pressure PI PII

PII1 P”

region

Y+Y& YMg + YMi,

YMg, + Y&&s, pure Mg

B

-A 8760 8290 7780 7750

f f & ”

220 140 90 130

8.64 f 8.91 f 8.78 & 8.f19 _c

+ B

0.21 0.18 0.12 0.19

741-922 718-913 688-837 626-818

-

=

ACTA

894

METALLURGICA,

VOL.

13,

1965

c-2

N

5 0 -CALORIMETRIC

X-VAPOR

t

s”

5”

5”

i

i

i”

DATA

PRESSURE DATA

MOLE

FRACTION OF MAGNESIUM

FIG. 4. Heat of formation a8 a function of composition for yttriummagnesium alloys.

publication.

The calorimeter

ments on the intermetallic -AH&,,

of 3.14 f

was tested by measure-

phase CaMg,.

0.21 kcal/g

and is in quite satisfactory

atom

A value of

was

agreement

obtained

with the value

3.23 f 0.10 kcal/g atom determined by King Kleppaol) by means of tin solution calorimetry. Calorimetric

measurements

yttrium-magnesium

average

of several

composition;

vapor

range

The experimental values are each point representing the

measurements

at the indicated

pressure values are included

the figure for comparison.

equations

(4), (5), and (6) at 298’K

obtain values of -2.8, respectively

for AF&,

such an evaluation the associated

-2.9,

and -1.9

reactions

in

The dashed line in Fig. 4

and Y,Mg,;

assumes that

is zero.

can be taken as representative

to

kcaljg atom

for YMg, YMg,,

implicitly

AC,

Alternatively,

enthalpy values indicated in equations

were made on fourteen

alloys in the composition

48-90 at.% magnesium. shown in Pig. 4 with

and

evaluating

for the

(4), (5), and (6)

of the mean temper-

ature of the range of measurement, difference between these enthalpy

800°K,

and the

values and the cal-

orimetric values leads to average AC, values of +0.5, +0.9,

and -0.6

c&l/g atom deg for the respective

re-

actions. These AC, values can be combined with values of AF&, to yield the respective values of

represents the least-squares fit to the calorimetric data with the form of the line being based on the

may be noted that the two sets of values for AF&,

arguments

are in essential agreement,

advanced

by Kubaschewski

concerning

the expected

formation

as a function

systems.

The enthalpies

solid constituent

contour

and Evanso2)

of the enthalpy

of composition of phase formation

elements are indicated

of

in binary from the

by this least-

squares fit to be -3.02 & 0.34, -3.40 f 0.28, and -1.76 f 0.14 kcal/g atom respectively for YMg, YMg,

and Y,Mg,,. The agreement of these values with the vapor pressure values is within the precision of the latter and lends credence to both determinations. the enthalpy

measurements

values

from

the calorimetric

are of better precision and are believed

to be more reliable than the enthalpy values from the vapor pressure measurements, combination of the free energy values from the vapor pressure measurements with enthalpy values from the calorimetric measurements should yield entropy values which are somewhat better than those derived solely from the vapor pressure data.

The combination

was made by first

-3.1,

combined

and

-1.8

kcal/g

atom

for AF&,.

It

and the mean values were

with the calorimetric

data to obtain

the

entropy values which are shown in Table 3. The

electronegativity

magnesium tendency

values(i3)

for yttrium

and

are both 1.2 so that there should be little

for the occurrence

of ionic character in the

bonding interactions, and the small values enthalpies of formation of the intermediate

for the phases

are in accord with such a lack of ionic contribution. Volume YMg,,

DISCUSSION Since

-2.9,

contractions and 0.8%

of

1.8%

for

YMg,

for Y5Mgz4 accompany

3.2%

for

phase for-

mation, and the trend in these numbers parallels that TABLE 3. Thermodynamic functions for the formation of yttrium-magnesium intermediate phases from the pure solid elements

Phase =‘Mg YMg, Y,Mgz,

-A-F,“,, (kcal/g atom) 2.9 l 0.2 3.0 * 0.2 1.9 f 0.2

--a%,, (kcal/g atom) 3.0 f 0.3 3.4 + 0.3 1.8 A 0.2

As:,, (eu/g atom) -0.3 -1.3 +0.4

* 0.4 * 0.4 _c 0.3

SMITH

et al.:

YTTRIUM-MAGNESIUM

INTERMEDIATE

PHASES

895

TABLE 4. Comparison of enthalpy of formation with work function of the variable component for some Laves phases of magnesium

MgX, MgNi, MgCu, MgZn, Mgco,

Group A --dH%, (kc&l/g etom) 4.63 2.67 2.61 1.9

shown by the enthalpies of formation. To the extent that the volume contractions are indicative of atomic packing efficiency, the data support the view that the bonding is primarily non-directional metallic in character. The entropies of formation are also in qualitative accord with the volume contractions, since as a first approximation one would expect vibrational amplitudes, and hence entropies, to decrease with available volume. Further, the small positive entropy of formation for Y5Mgz4 might indicate a oonfigurational contribution which would be in accord with a, temperature dependence of the yttrium-rich boundary of the phase (see Fig. 2). However, interpretation of the entropy values must be viewed sceptically because of the small magnitudes and limited preoisions. It may also be noted that estimates of the enthalpies of formation from the crystal structure data by the method of Kubaschewskio4) give values of -5.4 kcal/g atom for YMg, -1.9 kcal/g atom for YMgs, and -3.8 kcal/g atom for YGMg,,. While these estimated values indicate the correct order of magnitude they do not show 8 system~tie ~l~tionship to the observed values. Laves phases containing magnesium are of two types, MgX, and XMg,, and in a previous publication(l5) it was observed that the enthalpies of formation of the compounds within a given type show s. systematic trend with the work functions of the X components. The present data for YMgz when combined with the work function of yttriumo6) fit with the previously noted trends which are shown in Table 4. Such a systematic trend between enthalpy of formation and work function is not too surprising if it is remembered that the work function is a measure of the electronic energy levels in the sense of being a sum of the electronic ground state energy plus the Fermi energy; these two energy terms in the Wigner-Seitz approximation are dominantly responsible for the cohesive energy of a metal. Miohaelson(17) has pointed out the generally parallel variation between work functions and the first ionization potentials of the elements, and this variation indicates a systematic sensitivity of the electronic

Group B XMg,

--dH%, (k&/g atom) 4.8 3.4 3.23

3.5 3.1 2.9

::‘s

2.7 2.5

energy levels to potential field. Thus a correlation of work functions with enthalpies of formation in a defined crystalline environment, wherein the symmetry end magnesium contribution to the potential field is essenti&lly fixed, is not likely to be fortuitous. ACKNOWLEDGMENTS

The authors wish to thank Mr. F. A. Schmidt for providing the pure elemental yttrium and magnesium which were used for alloy preperation and Mr. E. D. Gibson for providing the single crystals which were used in the X-ray diffraction portion of the investigation. Appreciation is also extended to Dr. C. V. Banks and members of the analytical chemistry group for the chemical analyses on the yttrium-magnesium alloys. Finally the assistance of Mr. J. E. Pahlmsn in connection with the calorimetric measurements and Mr. D. L. Anderson in connection with the X-ray measurements is gratefully acknowledged. REFERENCES 1. E. D. Gmso~ and 0. N. CAEISON, Tptx;ns.Amer. Sot. Meals 52,1084 (1960). 2. V. F. TEREKHOVA, I. A. MAREOVAand E. M. SAVITSKIX, Zmlhur. Neorg. Khim. 5, 235 (1960). 3. E. M. SAVITSKII, V. F. TEREKHOVA,I. A. MARKOVAand R. F. FILIMONOVA,Metalloved. i Term. Obrabotka Metall. 9, 42 (1962). 4. J. l?. SMITH, in T&?rmodynamics of Nuclea? Materials, p. 271. International Atomic Energy Agency, Vienna (1962). 5. It. L. BERRY and G. V. RAYNOR, Acta Cry& 6, 1’78 (1953). 6. P. I. KRIPYAKEVICHand V. I. EVDOKSXENKO,Dopovi& Akad. Nauk Ukr. R.S.R., No. 12, 1610 (1962). 7. J. B. NELSON and D. P. RILEY, Proc. Phy8. Sot. Land. 57, 160 (1945). 8. M. KNUDSEN, Ann. Php. Lpz. 28, 999 (1909). 9. 5. F. SMITH snd R. L. SMYTHE, Acta Bet. 7, 261 (1969). IO. J. F. SXITE and J. I,. CHRISTIAN,A& Met. 8,249 (1960). il. R. C. KINU and 0. J. KLEPPA, Acta Met. 12, 87 (1964). 12. 0. KUBASGHEWSEI and E. LL. EVANS, Me~~~rg~~~ Thermochemistry, 3rd Ed., pp. 197-200. Pergamon Press, New York (1958). 13. I?. LAVES, in Theory of Alloy Phases, pp. 131-132. Amer. Sot. for Metals, Clevelsnd, Ohio (1956). 14. 0. KUBASCHEWSRI,The Physical Chem&m of Metallic So&&ions and Intwmetilic Compounds, Vol. I, Paper 3C. H.M.S.O., London (1969). 15. J. F. SBIITH,in N&ear Me~llur~, VoI, X, p. 397, edited by J. T. WABER, P. Crrronr and W. N. MINER. Edwards Bros., Ann Arbor, Mich. (1964). 16. K. A. GSCHNEIDNER,Rare Earth Alloys, p. 53. Van Nostrand, New York (1961). 17. H. B. MICHAELSON,J. Appl. Phys. RX, 536 (1950).