NAA-SR-9374 METALS, CERAMICS,
AND MATERIALS 31 PAGES
EQUILIBRIUM DISSOCIATION PRESSURES
OF THE
DELTA AND EPSILON PHASES
IN THE
ZIRCONIUM-HYDROGEN SYSTEM
By J.W. RAYMOND
ATOMICS INTEI^^TIONAL A DIVISION OF NORTH AMERICAN AVIATION, INC. P.O. BOX 309 CANOGA PARK, CALIFORNIA
CONTRACT: AT(11-l)-GEN-8 ISSUED: M/̂ Y 3 2 1964
DISTRIBUTION
This repor t has been dis t r ibuted according to the
category "Meta ls , C e r a m i c s , and M a t e r i a l s " as given in
"Standard Distr ibution Lis ts for Unclassified Scientific
and Technical Repo r t s " TID-.45 00 (27th Ed. ), Feb rua ry 1,
1964, A total of 615 copies was pr inted.
ACKNOWLEDGMENT
The author wishes to expres s his apprecia t ion to
R. A. Spurling, for his a s s i s t ance in data tabulation,
and to M. E, Nathan, for in terpre ta t ions and helpful dis-
cuss ions . Acknow^ledgment also is due the efforts of
D. F . Atkins, whose pointed comnnents and c r i t i c i sms
served to spur on this investigation.
NAA-SR-9374 2
DISCLAIMER
This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.
CONTENTS
Pag
Abstract 5
I. Introduction 7
II. Exper imenta l I3
A. Mate r ia l s and P repa ra t i on I3
B. P r o c e d u r e I3
C. Discussion of E r r o r s I5
III. Resul ts 21
IV. Discussion 25
V. Conclusions 3O
References 3I
TABLES
1. Chemical Composition of Melt Stock 12
2. Composition of Hydrided Specimens 12
3. P r e s s u r e - T e m p e r a t u r e - C o m p o s i t i o n Data for Del ta-Epsi lon Zi rconium Hydride 22
FIGURES
1. Isochore Diagram (Gilbert ) g 13
2. Isochore Diagram (Atkins ) 10 14
3. Zi rconium-Hydrogen Phase Diagram (Libowitz ) H
4. Isochore Apparatus
a. Photograph I4
b. Schematic I4
5. Retort Pe rmea t ion and Leakage Under P r e s s u r e and Under Vacuum 16
6. P r e s s u r e - T e m p e r a t u r e - C o m p o s i t i o n Data for Zi rconium Hydride 20
7. Dissociat ion P r e s s u r e I sochores of Zi rconium Hydride (Expressed as H / Z r a tom rat ios) 23
NAA-SR-9374 3
FIGURES
Pag
8. Heat of Solution Coefficient (K^) of Zi rconium Hydride as a Function of Hydrogen- to-Zi rconium Atom Ratio (X) 26
9. Solubility Coefficient (K,) of Zirconium Hydride as a Function of Hydrogen- to-Zi rconium Atom Ratio (X) 26
10. Activit ies of Hydrogen and Zirconium in the Z r - H System at 600°C (Searcy and MeschilS^ 28
11. P roposed Phase Diagram of the Zirconium-Hydrogen System . . . . 29
NAA-SR-9374
4
ABSTRACT
P r e s s u r e - t e m p e r a t u r e i sochores w^ere obtained for z i rcon ium-
hydrogen al loys, spanning the H / Z r composition range of 1.430 to
1.910. The studies were confined to the t empe ra tu r e l imi ts of 300
to 900°C, and the p r e s s u r e l imi ts of 0.01 to 10.0 a tm. An e x p r e s -
sion equating equi l ibr ium dissociat ion p r e s s u r e to t empe ra tu r e and
composit ion was determined, as was the heat of solution function
over the range of composit ion studied. Based on the resu l t s of the
study, a modification to the z i rconium-hydrogen binary phase d ia -
g r a m -was proposed, involving construct ion of a single l ine, ex-
tending upward in t empera tu re from the Z r H , ^^ composition, d e -
noting onset of the 6 -• € t ransformat ion , in place of the tw^o-phase
(6+ c) region appearing on recent d i a g r a m s . It is considered that
the t-wo-phase region exists only in t e rna ry or h i g h e r - o r d e r alloy
sys t ems , general ly resul t ing from contamination w^ith oxygen, c a r -
bon, or ni t rogen.
"H/Zr - the atom ratio of hydrogen to zirconium
NAA-SR-9374
5
I. INTRODUCTION
While the z i rconium-hydrogen constitution d iagram has , in genera l , been 1-15 quite adequately defined in previous invest igat ions, contradic tory r e su l t s in
the i sochores presen ted by Gilbert and Vetrano and Atkins, and in subsequent 13 18
work of Atkins and the i so the rm data of Libowitz, indicate incomplete
definition of the p re s su re -compos i t i on - t empera tu re ( P - C - T ) re la t ionships in the
6-f region of the b inary . Exact kno'wledge of the P - C - T rela t ionships in these
regions is of grea t significance, as this information is d i rect ly involved in the
determinat ion of the SNAP reac tor fuel p a r a m e t e r s : hydrogen redis t r ibut ion,
dissociat ion p res su re -c l add ing s t rength re la t ionships , etc . The investigation
was undertaken in an at tempt to es tabl ish more definitely the P - C - T re la t ion-
ships for the 6-€ phases .
Quantitative represen ta t ion of the dissociat ion p r e s s u r e can bes t be
accomplished by means of an equation of the genera l form
log P = K j + K 2 / T , . . . ( 1 )
T being the absolute t e m p e r a t u r e , K , , a factor express ing the p r e s s u r e
dependence of the solubility of the gas in the solid phase , and K-, a coefficient
relat ing to the heat of solution of the gas in the solid phase .
F r o m a plot of log p r e s s u r e vs r ec ip roca l t e m p e r a t u r e , the functional
relat ionship between Equation 1 and the composit ion p a r a m e t e r (X) may be
de termined (X represen t ing , in this sys tem, the hydrogen- to -z i rcon ium atom
rat io) . The genera l equation for the family of curves ( isochores) express ing
this relat ionship is given by
log P = A + B X - Y , • • -(2)
where A, B, and C a r e constants , the other p a r a m e t e r s retaining thei r
previous ident i t ies .
Regarding the isochore plot, C, the heat of solution coefficient, may be
determined from the slope of the i sochores ; a n e c e s s a r y requis i te for a constant
heat of solution being an invariant i sochore slope, for the concentra t ions
considered. Conversely , a var ia t ion in slope neces sa r i l y impl ies a concentrat ion
NAA-SR-9374 7
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dependence of the heat of solution. The solute concentrat ion or solubility d e -
pendence on p r e s s u r e (i. e. , coefficient B in Equation 2) is evidenced in the
spacing of the i sochores , p re s su re -dependen t solubility giving r i s e to nonuni-
form spacing of i sochores of equal inc rements of composit ion.
Considering once again Equation Z, if X is plotted vs log P , at constant
t e m p e r a t u r e , the slope of the result ing curve or i so the rm defines the coeffi-
cient B. The slope of the i so the rms so plotted re la tes to the physical mechan-
i sm of solution of the gas in the solid phase . In dilute solution (i. e. , X — 0),
the slope is 2, indicating that dissolution of hydrogen in z i rconium is a tomic,
r a the r than molecu la r , in na tu re . This is as would be predic ted from Siever t ' s
law for a b imolecular gas . The implication is that, at constant t e m p e r a t u r e ,
the concentrat ion of hydrogen in the solid phase will be proport ional to the square
root of the ambient hydrogen p r e s s u r e . To the extent that concentrat ion depend-
ence on p r e s s u r e obeys this re la t ionship, the activity coefficient of hydrogen
dissolved in the solid phase w îll be constant at unity. How^ever, depar ture from
ideality ( i . e . , the i so the rm slope / 2 ) w îll resu l t when, due to increas ing solute
concentrat ion, the activity coefficient depar t s from unity. A change in slope or
deviation from l inear i ty of the i s o t h e r m s , or a change of spacing of the i s o -
chores , may then be in te rpre ted as a concentrat ion dependence of the activity of
hydrogen in solid solution.
The major a r e a of d i sagreement in the works of Gilber t , Vetrano and 12 13
Atkins, and the subsequent work of Atkins lay in the spacing of the i sochores
of the 6 - e region, relat ive to the two-phase /3 - 6 equi l ibr ium l ine. Specifi-
cally, the i sochores of Vetrano and Atkins, and Gilbert (see Figure 1), exhibited
a p rogress ive ly increas ing change in spacing with increas ing hydrogen concen-
t ra t ion (i. e. , B continuously increasing w^ith hydrogen concentrat ion, in Equa-
tion 2). However, Atkins, in his subsequent work, repor ted an i sochore map
that w^ould requ i re anomalous behavior of the act ivi t ies in this region (i. e. , the
condensing of the i sochores at composit ions between Z r H , , and Z r H , j.) (see
F igure 2).
While such behavior would be inconsistent in a t rue binary one-phase region,
it must be considered that two dist inct phases , (fee) 6 and (fct) c, coexist '
over the composit ion range of approximately 1.65 to 1.75 H / Z r (see F igure 3).
''The heat of solution must be independent of concentration, for this to be str ict ly true.
NAA-SR-9374 9
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+ \ / 1 Zr(/3) N. ^ / ^ I
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1 1
1
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j-HYDRIDE (tetragonal)
1 06 08 10 12 14
HYDROGEN CONTTENT (H/Zr)
za
7635-4704
F i g u r e 3 . Z i r c o n i u m - H y d r o g e n P h a s e D i a g r a m (Libow^itz •'•'*)
Al though a v a i l a b l e e v i d e n c e i n d i c a t e s t ha t the t w o - p h a s e 5 + e e q u i l i b r i u m d o e s
not e x i s t m u c h above r o o m t e m p e r a t u r e , one m a y p o s t u l a t e t h a t a " m e m o r y -
e f fec t " of the 6 + € l o w - t e m p e r a t u r e e q u i l i b r i u m r e s u l t e d in the a p p a r e n t l y
a n o m a l o u s b e h a v i o r of the a c t i v i t y coef f ic ien t ( i s o c h o r e spac ing ) r e p o r t e d 13
by A t k i n s . T h i s a n a l y s i s b e c o m e s e s p e c i a l l y s ign i f i can t , in l ight of t h e fac t 16
tha t Edw^ards and L e v e s q u e , in t h e i r s t u d i e s on t h e t e r n a r y s y s t e m , z i r c o n i u m -
o x y g e n - h y d r o g e n , r e p o r t t ha t the ex ten t of t h e 6-€ tw^o-phase r e g i o n i s r e l a t i v e
to the oxygen c o n c e n t r a t i o n . Atk ins r e p o r t e d t h e a v e r a g e oxygen con ten t of
h i s h y d r i d e d s a m p l e s to be c o n s i d e r a b l y h i g h e r t h a n tha t of the s t a r t i n g
m a t e r i a l s , wh ich w a s g iven a s 0.10 wt %. T h e z i r c o n i u m s a m p l e s u s e d by
G i l b e r t c o n t a i n e d 0.005 wt % O.
N A A - S R - 9 3 7 4
11
TABLE 1
CHEMICAL COMPOSITION OF MELT STOCK
Element
A l
B
C
Ca
Cd
CI
Co
C r
p p m
40
II. EXPERIMENTAL
A. MATERIALS AND PREPARATION
All specimens used in this investigation were p repa red by double consumable -
elect rode a rc -me l t ing of compacted r eac to r grade z i rconium sponge. Chemical
analyses of the melt stock and hydrided specimens a r e given in Tables 1 and 2.
Subsequent to extrusion and swaging to 1/2 in. in d iamete r , the rod was
machined to 3/8 in. in d iamete r , to minimize surface contamination, and then ^i
cut into 1-in. cy l inders . These were chemical ly polished and vacuum annealed _5
at 950° C and 10 t o r r for 24 h r , to e l iminate poss ib le e r r o r due to the p re sence
of volatile const i tuents . The samples were then repol ished, weighed, and
identified. Hydriding was accomplished by adding ca l ibra ted amounts of
pre-pur i f ied hydrogen to the specimen contained in an evacuated r e to r t at
900° C. This was followed by furnace cooling to room t e m p e r a t u r e . After
hydriding, the sanaples were reweighed, composit ions calculated, and all data
recorded .
B. PROCEDURE
The dissociat ion p r e s s u r e data were obtained with the i sochore appara tus ,
shown in F igure 4. The hydrided samples , approximately 3/8 in. in d iameter
by 1 in. long, were placed in the mull i te sample chamber . Solid mull i te rod was
then inse r ted above the specimen in the chamber to minimize void volume,
and the r e to r t was evacuated to < 1/i. Subsequent to evacuation, the r e to r t was
isolated, the p r e s s u r e sensing t r ansduce r sys tem was zeroed, and the r e to r t
was inser ted in a wire-wound re s i s t ance furnace and brought up to t e m p e r a t u r e .
Specimen t empe ra tu r e was measu red with a Chromel -Alumel thermocouple ,
located in the heat sink, outside and adjacent to the r e t o r t wall and posit ioned
at the sample midspan. When equil ibr ium had been establ ished, p r e s s u r e and
t empera tu re data (in t e r m s of output voltages of the p r e s s u r e t r ansduce r and
thermocouple) were recorded , and the operat ion repeated at other t e m p e r a t u r e s .
The r e to r t was a l te rna ted between tw ô furnaces during a run to confirm the
*45 H2O, 45 HNO3, 10 HF (voI%) t< 10 ppm total impurities
NAA-SR-9374 13
a. Photograph
7568-18328
b . Schematic
TO VACUUM PUMP
FURNACE''
PRESSURE TRANSDUCER
THERMOCOUPLE TO POTENTIOMETER
-SAMPLE
7635-4705
Figure 4. Isochore Apparatus
NAA-SR-9374
14
rel iabi l i ty of the t e m p e r a t u r e data. Subsequent to tes t ing, samples were
submitted for the determinat ion of hydrogen, oxygen, ni t rogen, and carbon
content.
C. DISCUSSION OF ERRORS
The major sources of e r r o r encountered in th is investigation were :
1) Nonisothermal specimen environment
2) Accuracy of t e m p e r a t u r e measu remen t
3) Accuracy of p r e s s u r e measu remen t
4) Gas permea t ion and leakage under p r e s s u r e and vacuum
5) Uncertainty in hydrogen concentrat ion of sample
6) Actual void volume of the "null-void" sys tem.
Regarding the f i rs t of these , nonisothermal specimen environment, this
effect was minimized through the use of a mass ive s ta in less steel heat sink
(see F igure 4b). Maximum t e m p e r a t u r e var ia t ion, as measu red in a mockup
specimen, was de termined to be < 0.5° C.
The prec i s ion of t e m p e r a t u r e measu remen t w^as '^ 1°C, as l imited by
thermocouple ca l ibra t ion. How^ever, the p rocedure employed in each run,
involving determinat ion of data at many t e m p e r a t u r e s and in two identical
i sochore appara tus , served to s ta t is t ical ly minimize t e m p e r a t u r e e r r o r .
Regarding p r e s s u r e measu remen t , the accuracy and prec i s ion of the
p r e s s u r e data, as m e a s u r e d with s t ra in-gage t r a n s d u c e r s and a p rec i s ion
potent iometer , was determined to be ±0.1 ps ia . This was s ta t is t ical ly
minimized by making many determinat ions on each sample .
In o rde r to de te rmine the extent to which gas pe rmea t ion and leakage,
under p r e s s u r e and under vacuum, would influence the data, p re l imina ry
runs were made, under vacuum and under p r e s s u r e , over the t e m p e r a t u r e
interval investigated. A s ta in less steel specimen was used, to maintain
s imi la r tes t conditions. The resu l t s of these de terminat ions a r e shown in
Figure 5. As may be seen from these cu rves , significant e r r o r may be
introduced, should the tes t extend over long per iods of t ime (1) at t e m p e r a t u r e s
above 700° C when under p r e s s u r e , and (2) above 600° C under conditions of
NAA-SR-9374 15
T I 1 INITIAL PRESSURE - 8 atm
LOSS OF HYDROGEN PRESSURE AS A FUNCTION OF TIME AT TEMPERATURES ABOVE 700°C
INITIAL PRESSURE - 5 atm
ELAPSED TIME (hr)
7635-4706
Figure 5. Retort Pe rmea t ion and Leakage Under P r e s s u r e and Under Vacuum
par t i a l vacuum. Based on these r e s u l t s , each individual t es t was planned so
as to minimize introduction of e r r o r due to these sources . Since e r r o r due to
these sources must introduce nonlineari ty in a plot of log p r e s s u r e vs rec ip roca l
t e m p e r a t u r e , we may conclude that it was essent ia l ly absent , since nonlineari ty
was not observed.
By far the g rea t e s t single source of e r r o r was due to the uncer ta inty in the
hydrogen concentrat ion of the individual samples . Because of the inadequacy
of hydrogen ana lys i s , by the vacuum fusion technique, in meeting the requ i red
degree of prec is ion (see Table 2), the weight gain of the hydrided specimens
was accepted as defining hydrogen composit ion. While c a r e was exerc i sed to
minimize contamination which would resu l t in e r roneous composi t ions , as
computed from weight gain data, a slight discolorat ion was apparent on the
surfaces of al l specimens after hydriding. The film could be in te rpre ted as
•Exclusive of deviation from linearity due to void volume considerat ions, a s will be d iscussed in a subsequent paragraph.
NAA-SR-9374 16
contamination of the sample with oxygen and /o r ni trogen as a surface film, and
possibly as dissolved in ters t i t ia l solid solut ions. While the apparent degree of
contamination was slight, in all ins tances , the re la t ive atomic w^eights of
oxygen and nitrogen, as compared to hydrogen, magnify the e r r o r significantly.
However, the influence on dissociat ion p r e s s u r e of the var ia t ion in in te rs t i t i a l
impuri ty concentrat ion between samples apparent ly lay within exper imenta l
e r r o r , since re la t ive displacement of the i sochores •was not in evidence. The
l e a s t - s q u a r e s computer p rog ram, used for final determinat ion of the i sochore
plot and the dissocia t ion p r e s s u r e equation, undoubtedly served to minimize the
effect of data sca t te r due to nonuniform concentrat ions of these impur i t i es in
individual samples .
Under ce r ta in conditions, the p resence of a void volume in the sample
chamber could introduce considerable e r r o r . How^ever, compensation for the
e r r o r involved can be made, if the void volume of the r e to r t is knoAvn accura te ly
at some t e m p e r a t u r e , and an express ion relat ing the change in this volume to
t e m p e r a t u r e has been determined. The void volume of both r e t o r t s used in this
exper iment was 15.6 cc at 22° C. The t empe ra tu r e -vo lume relat ionship was
de termined by: (1) loading a s ta in less steel sample in the r e t o r t s under identical
t es t conditions, (2) adding a kno^xni p r e s s u r e of hydrogen at the re ference
t e m p e r a t u r e (22° C), (3) heating the isolated r e to r t , and (4) recording r e to r t
p r e s s u r e as a function of t e m p e r a t u r e . Since initial p r e s s u r e , t e m p e r a t u r e ,
and volume a r e kno-wn, the molar hydrogen content of the r e to r t may be
calculated from the gas law:
^ O ^ O ^ ^ O ^ T Q . . . ( 3 )
P V 0^0 , .,
It then follows that, since the r e t o r t was isolated before heating ( i .e . , n .̂ =
constant = P„V^/RT-^), the volume may be de termined from the re la t ion
between specimen t e m p e r a t u r e and r e t o r t p r e s s u r e , at t e m p e r a t u r e t , as
follows:
^ t ^ t = ^ ^ T t • •••
Since
P V n = n^ = -^^=— = constant , • • • ^o;
P tV, = CT^ , . . . ( 7 )
o r
^ t V = C p i . . . . ( 8 ) ^ ^ t
It should be noted that V. i s not the t rue express ion for volume, but
r a the r that fiducial volume that would be applicable in the ideal gas law, were
the ent i re r e to r t volume at specimen t e m p e r a t u r e , r a the r than under a gradient
ranging from specimen t e m p e r a t u r e to room t e m p e r a t u r e . We shall t e r m this
fiducial volume the "equivalent volume" (V ). The change in equivalent volume
as a function of t e m p e r a t u r e , for the sys tems used in this exper iment , was
found to obey the equation
V ' = (2.97 + 0.042 T) x 10"^ , . . . ( 9 )
where (T) i s the specimen t e m p e r a t u r e , expres sed in deg rees Kelvin.
Correc t ion for dissocia t ion of hydrogen to the void can then be accompl ished
by applying the re la t ion given in Equation 9 to the following express ion:
2 P v ' ( H / Z r ) ^ = (H/Zr)Q - ^ . j N ^ ' • •• (10)
Zr
where :
( H / Z r ) „ = the a tom ra t io of hydrogen to z i rconium in the sample after dissociat ion of hydrogen to the void at t e m p e r a t u r e T
(H/Zr)„ = the hydrogen- to -z i rcon ium atom ra t io of the sample at the t e m p e r a t u r e T = 273°K(i.e., the "as -hydr ided" a tom ra t io of the sample)
P = the r e to r t p r e s s u r e (atm)
NAA-SR-9374 18
T = the specimen tempera ture (°K)
N_ = the number of g r a m a toms of z i rconium in the sample
R = the gas constant fo.08205 ^~^^"^ \ ^ V deg -mole /
Y ^ - the apparent volume at t e m p e r a t u r e T (i)
Analyzing this equation, the las t t e r m is a d i rec t m e a s u r e of the extent to
which hydrogen has d issocia ted to the void. This t e r m , when compared to the
magnitude of the a tom ra t io s , p e rmi t s evaluation of the re la t ive e r r o r
introduced through a zero void volume assumpt ion. Since the overa l l accuracy
of the exper iment might reasonably be approximated by an uncer ta inty of
±0.0025 in the a tom ra t io , the assumption of a ze ro void volume would introduce
significant e r r o r when the t e r m represent ing dissocia t ion to the void exceeds
0.005, or when
^ ^ ^ > 0.005 . . . .(11) R T N „ Zr
Since R and N „ a r e constants and V is a function of T (from Equation 9),
th is express ion may be rewr i t t en in the form
P ( 4 | ^ + 0.042) > 0.0225 . • • • (12)
Solution of th is express ion for the t empe ra tu r e l imi ts of the exper iment from
500 to 900° C shows that, for p r e s s u r e s in excess of '~ 0.5 a tm, significant e r r o r
may be introduced through assumpt ion of a ze ro void volume.
This uncer ta in ty above '^ 0.5 a tm was taken into considerat ion when
assigning significance to the data.
_ 10 •Since sample s ize was very nearly constant at 10 e, N ^ , = = 0.11. "̂ •̂ 91.22
NAA-SR-9374
19
OXYGEN ^ 1400 ppm NITROGEN :S ZOO ppm CARBON ~ 600 ppm
O
2 > I
cn
I
• 1 ^
O-Oll^-ji 4 5 0 500 550 600 650
TEMPERATURE {°C) 700 750 800 850 900 950
7635-4707
Figure 6. P r e s s u r e - T e m p e r a t u r e - C o m p o s i t i o n Data for Zirconium Hydride
III. RESULTS
The i sochores de termined in this study, relat ing dissociat ion p r e s s u r e ,
t e m p e r a t u r e , and composit ion of the 6 and € phases in the z i rconium-hydrogen
binary, a r e shown in F igure 6. These data a r e a lso tabulated in Table 3. An
isochore map, const ructed f rom resu l t s obtained from a l e a s t - s q u a r e s fit of
the data, is p resen ted in F igure 7.
NAA-SR-9374
21
TABLE 3
PRESSURE-TEMPERATURE-COMPOSITION DATA FOR DELTA-EPSILON ZIRCONIUM HYDRIDE
Sample
J - 1 4
J - 5 9
J - 6 4
J - 1 6
J -30
J - 4 2
J - 2 4
J - 6 0
J - 3 4
J - 4 8
J - 1 8
J - 4 9
J - 4 6
J - 3 5
J - 5 2
H / Z r
1.431
1.460
1.477
1.482
1.527
1.541
1.542
1.556
1.577
1.609
1.641
1.678
1.661
1.703
1.724
T e m p e r a t u r e (°C)
738 767 777 796 806 826 834
754 766
726
680 709 740
703
686
685 712 736 765 794
698 723
671 699
695
607 656 689
674 701
617
646
643
P r e s s u r e (atm)
0.045 0.087 0.113 0.170 0.207 0.325 0.381
0.0800 0.1046
0.0576
0.0210 0.0425 0.0820
0.0477
0.0373
0.043 0.077 0.126 0.224 0.392
0.0634 0.1017
0.0354 0.0660
0.0830
0.020 0.065 0.141
0.138 0.232
0.0400
0.115
0.133
T e m p e r a t u r e (°C)
856 864 883 893 941 952
780
749
766 882 904
713
698
827 850 882 912 940
725 755
727
725
720 746 778
728
645
671
670
P r e s s u r e (a tm)
0.600 T 0.711 1.054 1.260 3.030 3.780
0.1392
0.0902
0.146 1.060 1.590
0.0608
0.0496
0.689 1.019 1.68 2.58 3.69
0.1111 0.2055
0.1218
0.1628
0.260 0.439 0.730
0.296
0.0815
0.201
0.241
Sample
J - 3
J - 1 9
J - 3 3
J - 4 3
J - 3 2
J - 4
J - 3 7
J - 2
J - 3 8
J - 5
J - 5 7
J - 6 1
J - 3 9
H / Z r
1.710
1.734
1.751
1.781
1.804
1.810
1.845
1.860
1.868
1.890
1.903
1.908
1.915
T e m p e r a t u r e (°C)
608 j 617 630 653
586 616
615 646
607 616
595 616 643
523 550 575 577 589
550 611
540 545 570 584
557 588
569 581
511 534
491 553
479 492
P r e s s u r e (atm)
0.0604 0.0737 0.104 0.176
0.050 0 . U 2
0.124 0.257
0.137 0.170
0.171 0.289 0.547
0.0249 0.0589 0.121 0.127 0.169
0.0945 0.498
0.0778 0.0922 0.186 0.283
0.185 0.431
0.384 0.515
0.114 0.206
0.0705 0.436
0.0731 0.117
T e m p e r a t u r e
CO 654 677 687 699
643
671
653
644 674 676
596 603 614 640 641
647
588 601 613 613
598
595
550 568
556
508 534
P r e s s u r e (atm)
0.182 0.301 0.374 0.468
0.226
0.450
0.434
0.567 1.065 1.U5
0.219 0.252 0.351 0.636 0.651
1.081
0.311 0.449 0.608 0.602
0.555
0.718
0.328 0.526
0.490
0.190 0.396
• . , . , , , •
ez ^Z.e6-HS-VVN
(SOTttBJ: UIOt^'E
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096 006 0S8
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KM 1 i^imiiil^^ gr •̂i 1 -1 i!:
1 - •-
.'iM^mammf̂fl uff ^ fflM^^ M^ iff ^ Pf MMm Mf̂fltttifflPMfflMM^^ ™EMffl Mm^e
nil nil IIHILIfHI III i'tltill III IIJKIII m
-^i ::;:::i:: :::«•:::::
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;;;i ;:;::::: ;FM;;;f-..:M
#
IV. DISCUSSION
The dissociat ion p r e s s u r e equil ibria of the z i rconium-hydrogen binary in
the 6 and f regions , r ep resen ted by the i sochores of F igure 7, may be
expressed in t e r m s of t empe ra tu r e and composit ion by the relat ion
K X 10-̂ l o g P =K^ + - ^ . . .(13)
where:
K^ = -3.8415 + 38.6433 X - 34.2639 X^ + 9.2821 X̂ ^
K^ = -31.2982 + 23.5741 X - 6.0280 X^
P = pressure (atm)
T = t empe ra tu r e (°K)
X = hydrogen- to-z i rconium atom ra t io
This equation form w^as given preference to that involving separat ion of
Ki in t e r m s of A + BX, as expressed in Equation 2, since the heat of solution
coefficient (K-,) was determined to be concentrat ion dependent. That i s ,
since K^ = f (X), B would not define the slope of the i so therm, as d i scussed
previously (see page 9), and therefore apparent ly would not contribute
physical significance to the dissociat ion p r e s s u r e equation.
Considering f i rs t the coefficient K- of Equation 13, we may conclude that
the pa r t i a l molal heat of solution is not constant within the 6 and € regions of
the binary, but r a the r d e c r e a s e s continuously with increas ing hydrogen
concentrat ion, a c r o s s both the 5 and € regions . A plot of the heat of solution
coefficient as a function of hydrogen concentrat ion, as der ived from the
i sochore plot (Figure 7), is p resen ted as F igure 8. F r o m this plot, it may be
seen that the heat of solution of hydrogen in the hydrided phase d e c r e a s e s ,
with increas ing solute concentrat ion, but at a decreas ing r a t e , attaining a
limiting value of -^ 8.26 for a sa tura ted solution of limiting composit ion
H / Z r ::: 2.
In t e r m s of actual molal quanti t ies , obtained by multiplying K^ by the
na tura l log conversion and the gas constant, the pa r t i a l molal heat of
NAA-SR-9374 25
16 17 HYDROGEN-TO-ZIRCONIUM ATOM RATIO (X)
7635-4709
8. Heat of Solution Coefficient (K„) of Zi rconium Hydride as a Function of Hydrogen- to -Zi rcon ium Atom Ratio (X)
17 O
9 4
9 2
^ fe liJ O 9 0 l i . Li.
O
> t - 8 8 _) CD =) C/)
6 6
8 4
a o
1 1
_
-
-
^
1 1
1 1
/ _
1 1 15 16 17 18
HYDROGEN-TO-ZIRCONIUM ATOM RATIO (X)
7635-4710
Figure 9. Solubility Coefficient (Kj^) of Zirconium Hydride as a Function of Hydrogen- to-Zi rconium
Atom Ratio (X)
NAA-SR-9374
26
so lu t ion of h y d r o g e n in the h y d r i d e d e c r e a s e s f r o m -46 .3 k c a l / m o l e , in 6 of
c o m p o s i t i o n Z r H , . , to -37 .7 k c a l / m o l e , in € of c o m p o s i t i o n Z r H , „. Of
s i gn i f i c ance i s t h e fac t t h a t no d i s c o n t i n u i t y in t h e funct ion i s in e v i d e n c e
t h r o u g h o u t the e n t i r e 6 and € c o m p o s i t i o n r a n g e . T h i s i s not a s would be
e x p e c t e d if t h e 5-* C t r a n s f o r m a t i o n w e r e of f i r s t o r d e r , but i s e n t i r e l y connpat ib le
if t r a n s i t i o n f r o m f e e - 6 to fc t -e i n v o l v e s a c o n t i n u o u s a n i s o t r o p i c e x p a n s i o n 5
of t h e cub ic p h a s e , a s r e p o r t e d by Vaughan and B r i d g e .
R e g a r d i n g t h e so lub i l i t y coef f ic ien t ( K , ) , a n a l y s i s of the funct ion shows
t h a t it o b e y s an e s s e n t i a l l y p a r a b o l i c r e l a t i o n , d e c r e a s i n g f r o m a va lue of
~-8.57 a t Z r H , , , a t t a i n i n g a m i n i m u m of '-^ 8.29 a t Z r H , ,-_, and t h e n
i n c r e a s i n g a t an i n c r e a s i n g r a t e to -^ 9.55 at Z r H , „. The funct ion i s shown
g r a p h i c a l l y in F i g u r e 9. T h i s b e h a v i o r i s not ev iden t f r o m the spac ing of the
i s o c h o r e s of F i g u r e 7, and would not be a n t i c i p a t e d f r o m a p lo t t h a t a p p a r e n t l y
i n v o l v e s c o n t i n u o u s l y i n c r e a s i n g s p a c i n g of {—) for equa l i n c r e m e n t s of
c o m p o s i t i o n (X).
One m a y s p e c u l a t e t h a t it i s m o r e t h a n m e r e c o i n c i d e n c e tha t the m i n i m u m
o c c u r s a t the c o m p o s i t i o n Z r H , ,-„, a p p r o x i m a t i n g the 6, 6 + e b o u n d a r y , 9 10 13
v a r i o u s l y r e p o r t e d a s Z r H , (-/ to Z r H , / i- ' ' Undoub ted ly , b e c a u s e of the
r e l a t e d n a t u r e of t h i s funct ion and a c t i v i t y , s i gn i f i c ance m u s t be a f fo rded the
fact t ha t t h i s i s a l s o t h e c o m p o s i t i o n a t which the m o s t t h e r m o d y n a m i c a l l y
s t a b l e h y d r i d e in the b i n a r y o c c u r s , a s c o m p u t e d f r o m a c t i v i t i e s by the 18
m e t h o d of S e a r c y and M e s c h i {See F i g u r e 10). While a d i s c o n t i n u i t y in t h e
p lo t of t h e a c t i v i t i e s of the m e t a l and the g a s d o e s not e x i s t at t h i s c o m p o s i t i o n ,
a s w^ould b e a n e c e s s a r y r e q u i s i t e for a f i r s t - o r d e r t r a n s f o r m a t i o n , we m i g h t
we l l a n t i c i p a t e o c c u r r e n c e of a h i g h e r - o r d e r t r a n s f o r m a t i o n , such a s an
o r d e r i n g r e a c t i o n o r d i f f u s i o n l e s s s h e a r m e c h a n i s m , in s o l u t i o n s m o r e c o n c e n -
t r a t e d t h a n Z r H , / ( i . e . , t h e 5 ~* C t r a n s f o r m a t i o n ) . M a x i m u m s o r i n f l e c t i ons
in the p r o p e r t i e s of h a r d n e s s , s t r e n g t h , and r e s i s t i v i t y have i ndeed b e e n 20 21 r e p o r t e d ' a t '~ 6 1 a t . % h y d r o g e n , the a p p r o x i m a t e c o m p o s i t i o n of t h i s ,
t he m o s t t h e r m o d y n a m i c a l l y s t ab l e h y d r i d e .
In v i e w of (a) t h e r e s u l t s of t h i s i n v e s t i g a t i o n , (b) the m a r t e n s i t e - l i k e
n a t u r e o f t h e 6 - e t r a n s f o r m a t i o n , (c) t he fact t h a t t h e two p h a s e s (6 a n d e ) have
not b e e n o b s e r v e d to c o e x i s t at h igh t e m p e r a t u r e s , and (d) the effect of
oxygen (and undoub ted ly t h e o t h e r i n t e r s t i t i a l i m p u r i t i e s , n i t r o g e n and c a r b o n )
on t h e ex ten t of the o b s e r v e d t w o - p h a s e f ie ld , it i s p r o p o s e d t h a t t h e 6 -*e
N A A - S R - 9 3 7 4 27
•
00 0! 02 03 04 05 06 07
XH
7635-4711
Figure 10. Activit ies of Hydrogen and Zi rconium in the Z r - H System at 600° C (Searcy and MeschilS)
t rans format ion should appear on the b inary phase d iagram as a dotted l ine,
denoting the C-transformation s t a r t , extending upward from the composit ion
Z r H , _„, and probably bending toward the ZrH^ axis at higher t e m p e r a t u r e s .
The proposed 6 -*€ boundary is likened to the M line in an a thermal ly act ivated
mar tens i t e t ransformat ion , t he rma l fluctuations and excess ive solute concen-
t ra t ion serving as the driving force in the instance of " i so the rma l " t r a n s f o r m a -
tion. The hydrogen- r ich end of the b inary phase d iagram, including the
proposed € - s t a r t boundary, is shown in F igure 11. Curva ture has been
const ructed in accordance with available data on the extent of the two-phase
6 ~* 6 + C boundary.
Based on this study, we may conclude that i sochores of the 6-6 regions of
the z i rconium-hydrogen sys tem must exhibit a p rogress ive ly increas ing change
in spacing with increas ing hydrogen concentrat ion. Any deviation from this
type of p rogres s ion can be at t r ibuted to significant contamination of the b inary
w^ith oxygen, ni trogen, e tc . , to form a t e r n a r y or h ighe r -o rde r alloy sys tem.
a
-
...
/
1
— £ _ ^
^ — V
1 1 1
r
"H
1
/
1 1 '
NAA-SR-9374 28
2 I-
a + 8
02 04 06 08 LO 12 14
HYDROGEN CONTENT (H/Zr)
18 20
7635-4712
Figure 11. P roposed Phase Diagram of the Zirconium-Hydrogen System
NAA-SR-9374 29
V. CONCLUSIONS
E q u i l i b r i u m d i s s o c i a t i o n p r e s s u r e s of the 6 - and € - p h a s e r e g i o n s in the
z i r c o n i u m - h y d r o g e n b i n a r y c a n be e x p r e s s e d by a s ing le equa t ion involv ing
p r e s s u r e , t e m p e r a t u r e , and h y d r o g e n - t o - z i r c o n i u m a t o m r a t i o . E x a m i n a t i o n
of t h i s e x p r e s s i o n p e r m i t s the fol lowing c o n c l u s i o n s :
a) E q u i l i b r i u m d i s s o c i a t i o n p r e s s u r e of t h e 6 and € p h a s e s i s a
con t inuous funct ion of h y d r o g e n c o n c e n t r a t i o n , exh ib i t ing no
p r e s s u r e d i s c o n t i n u i t i e s o r a n o m a l o u s i s o c h o r e spac ing o v e r t h e
H / Z r c o m p o s i t i o n r a n g e of ~- 1.4 t h r o u g h 1.9.
b) The p a r t i a l m o l a l h e a t of so lu t ion of h y d r o g e n in t h e 6 and €
h y d r i d e p h a s e s d e c r e a s e s c o n t i n u o u s l y wi th i n c r e a s i n g so lu te
c o n c e n t r a t i o n a t a d e c r e a s i n g r a t e , exhib i t ing no b r e a k o r
d i s c o n t i n u i t y a t t h e 6 " " € t r a n s f o r m a t i o n c o m p o s i t i o n . The quan t i t y
v a r i e s f r o m - 4 6 . 3 k c a l / m o l e , for 6 of c o m p o s i t i o n H / Z r = 1.4, to
-37 .7 k c a l / m o l e , for € of c o m p o s i t i o n H / Z r = 1.9.
B a s e d on the r e s u l t s of t h i s i n v e s t i g a t i o n , t o g e t h e r wi th p r i o r knowledge of
t h e s y s t e m ( i . e . , m a r t e n s i t i c n a t u r e of the 6-*€ t r a n s f o r m a t i o n , a b s e n c e of t h e
t w o - p h a s e r e g i o n a t h i g h e r t e m p e r a t u r e s , effect of i n t e r s t i t i a l i m p u r i t i e s on
the ex t en t of the t w o - p h a s e r e g i o n , e t c . ), t h e p h a s e d i a g r a m p r e s e n t e d in
F i g u r e 11 i s p o s t u l a t e d . The do t t ed l i n e , ex tending u p w a r d f r o m t h e
c o m p o s i t i o n Z r H , .̂Q and bend ing t o w a r d the Z r H ^ a x i s wi th i n c r e a s i n g
t e m p e r a t u r e , r e p r e s e n t s the " e - s t a r t " b o u n d a r y ( i . e . , t he beg inn ing of the
cub ic to t e t r a g o n a l t r a n s f o r m a t i o n ) . The ex ten t and exac t c u r v a t u r e of the
b o u n d a r y , whi le p r i m a r i l y s p e c u l a t i v e , h a s b e e n c o n s t r u c t e d in a c c o r d a n c e
wi th r e p o r t e d 6-€ c o - e x i s t e n c e .
N A A - S R - 9 3 7 4
30
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