CHAPTER VII

A. X-:-.ii:£~VESTIGATION OF Ni-Zr SYSTEJvi

B. THEHJVJAL EX£'At~S_Icm COEFFICIEN'r OB' I1\lTEf1-

JYIETALLIC PHASES IN Ni-Zr SYSTEr1;

VII A

X-RAY INVESTIGATION OF Ni-Zr SYSTEM

VII A. 1 INTRODUCTION

H.apidly cooled alloys ( upto 55 wt. % Zr) were

first investigated50 microscopically and based on these

findings a tentative phase diagram has been presented35 •

Phase diagram study on Zr-rich alloys was done by various

workers 1 • 56 •77. Examination of liquidus, for 0.55 atfoZr

shows75 the occurence of Ni4Zr and Ni3zr phases. Hayes

et a1. 36 , while investigating phase diagram (upto 50 at.

% Ni) reported intermediate phases, NiZr2 (24.34 wt.% Ni)

and NiZr (39.15 wt. % Ni) by microscopic work. The

eutectoid temperature was determined by DTA, and the

P-Zr field was outlined metallographically43, This

system has been investigated43 ,, (practically complete

range of composition) by X-ray, metallography and resis­

tometric measurements and liquidus and solidus were deter­

mined accurately (f!ig. VII A. 1) • The NiZr2-Zr portion

of the diagram is similar but the J3 -Zr · eutectoid was 36 found to be appreciably higher than that given earlier

and the existence of phases, Ni5Zr, Ni7Zr2 , Ni5zr2 ,

Ni10zr7 , NiZr, Ni11 zr9 and NiZr2 has been shown. Smith

and Guarct79 also reported phase diagram of partial

system Ni-Ni~fd~hich is very similar to that shown in .. : :~:~~- ;:~;;s .

Fig. VII A .1 ei:ee'pt ~at the peri tectically forming _,,.._~ -~-'

WEIGHT P'tFt C'ENT ZIRCONIUM

1900,.-..... 10-J.20_30"-_.40;;...._.;;.50;;_,.:.6.:.,0 _10.:.:..__;80;.:..,_.:i90~--;

tBOO

t700

1600

1500

1400 I .}J I f w 1300 130cr._ .. ~ I . / ~ 1200 17ff

~ ....... ...( 15 ·• ~ HOOf

..... 1000 t

900 f I I I

' I I

' ' I 10 20 30 40 50 60 10

~ATOMIC P&::R CENT Z'fRCONIUM

FIG. W ijittJ- Zr PHASE DIAGRAM , s-;t -· .. ~.~!'- ~· .

I I 1: I f I , • • I

t .. -' ' ·~ .

•.

152

Ni10zr7 and Ni11 zr9 were not separately distinguished

but. called Ni 5Zr4 • Electron beam microprobe analysis88

exhibited the presence of NiZr5 , NiZr2 , NiZr and

Ni10zr7 phases. Hayes et al.36 reported that solid

solubility of Ni inZr is very small, there being no

detectable change in lattice parameter in alloys anneale~

at 950 °C. The solubility of Zr in Ni was found1 •13 •75 .

Phase diagram and solid solubility data have been given

by Kubaschewski and Goldbeck53 also.

Kramer50 indicated homogeneity range of Ni5Zr

as 14.5 - 18.0 at.% Zr at 900 °C and reported AuBe5 type structure of this phase which was also confirmed by

a number of researchers14 •43,79. However, Kripyakevich

et a1. 51 assumed it to be Ni4Zr phase. At goo °C (21.0-

22.5 at.% Zr) a phase Ni7

Zr2 exists5°.Jcnr.\J was tentatively

assumed43 as orthorhombic, later on parameters of ortho­

rhombic lattice was also reported91 • However, another

group of workers 27 •30 treated it, as Ni7Ht2 type,

monoclinic structure. X-ray analysis show~·i~at structure of Ni3Zr is similar to Ni3Sn phase. Later on9

it was possible to isolate this phase, at room tempera­

ture. The phase decays by a peritectic reaction

Ni3

Zr --1- Ni7Zr2 + Ni5Zr2 at 940 °C. Earlier presented

phase diagram43 has been completed to show that .the ' •'~

homogeneity ~~e o£ this phase lies between 20-30 at.%1v-. :; ;-~'~ , . ..._, ',

153

The 1ntermetallic compound Ni5Zr2 , which forms

peritectically at 1180 °c, has pseudo-orthorhombic unit

ce1143 • The structure of Ni10zr7 phase, which is formed

peritectically at 1160 °C (at stoichiometric composition),

is base-centered orthorhombic43. Dilution with lr (41.1-

at.% Zr) causes distortion to primitive orthorhombic

cell . 45 of Ni 19~r15 phase Very recently, rapidly cooled

(melt spinning method) alloy Ni64zr36 has exhibited amor­

phous behaviour81 •82 • Using X-ray and microscopy techni­

que Bsenko13 has reported the phases: Ni 21 zr8 , formed

peritectically and stable down to 800 °C, Ni3

Zr is formed

in reaction between Ni 21 zr8 and Ni7Zr2 at 920 ! 10 °C

Peritectically formed (at 117 °C). Ni11 zr9

phase crystal­

lizes34•43 into body centered tetragonal structure with

2 molecules per unit cell. Orthorhombic structure of

NiZr compound has been confirmed44 •48 ,55,S9. Single

crystal X-ray analysis44 exhibits tetragonal unit cell

of NiZr2 phase, and confirms the earlier reportect63• 64

results. The alloy Ni24zr76 was found to show the glassy

nature17 •

Table VII A. 1 gives the details of crystallo­

graphic data of all the reported phases, along with the

present work.

15~

'fABLE VII A.1

Crystallographic data of binary phases in Ni-Zr system

-----------------------------------------------------o--------Phase Crystal Lattice parameters f3 Ref.

structure Ao or -- c/a a b c

--------------------------------------------------------------(Ni,Zr) Ni Cu 3.525- 1,13,

3.535 53,75.

Ni5Zr(t~Ni4Zr) AuBe5 6.708 - 14,43' 50,79.

Ni23zr6 Co23Ht6 11.532 - Present work,

Ni7Zr2(h) Ortho. 12.209 9.005 9.326 0.764 43,91,

Ni7Zr2(r) Mono. 4.691 8.225 12.192 95.59 27,30,

Ni3

Zr Ni3Sn(Do 19) 5.309 4.303 0.810 8,9, 13.

Ni5zr2 Pseudo 10.100 12.100 6.500 0.644 43.

-·Ortho,

Ni21 zr8 Ni21Ht8type 6.472 8.064 8.588 68.04 13.

Ni1 0zr7 Ortho. 12.386 9.156 9.211 0. 744 43' 44. +0.006 :!:0 • 008 ±0. 005

Ni11 zr5 Hex. 6.277 13.182 - present

work.

Ni13zr6 Tetrasonal 7-593 .9.527 1.255 . , Ni19Zr15 Ortho. 12.497 9.210 9.325 0.746 45.

Ni11 zr9 Tetragonal 9.900 6.620 0.669 34,43

N~11 zr9 Tetra. 10.299 6.936 0.673 Preseni ,. work ..

" NiZr Ortho. 3.268 9-937 4.101 1.255 43,44, •• 55 •

NiZr2 A1Cu2 6.477 5.241 0.809 43,44, 63,64.

--.-----------------------------------~-----------------------., . ,

155

VII A. 2 ~~TERIALS AND METHOD

The alloys were prepared from reacter grade

zirconium and nickel of 99,99% purity (Johnson Matthey

& Co. Ltd., London). The alloys were melted at Bhabha

Atomic kesearch Centre, Bombay, in a non consumable

electrode argon arc furnace. l"or homogeneous mixing

the alloys were inverted several times during melting.

The alloys were further homogenized in evacuated and

sealed quartz tubes. The change in weight after melting

was found to be less than 0.1% of the total weight of

the alloy. Therefore no chemical analysis of the alloys

were considered necessary.

Powder obtained after filing the ingot were

sieved through a 325 mesh screen and were sealed under

vacuum in silica tubes, for desired heat treatments.

The Debye-Scherrer photographs of these alloys

were taken with filtered CuK~ radiation. An exposure

of about 10 hrs. was found sufficient to bring out the

details of the X-ray patterns. Each X-ray photograph

was followed by duplicate runs to show the reproducibi-

11 ty of the data within the range of experimental error.

·:rp.e line positions were measured 2-3 times for achieving

better accuracy and the mean values have been considered

for the computation of lattice constants. -.\o\_.T, __

-:-~\~=-~~',

,

156

VII A. 3. RESULTS AND DISCUSSION

Many binary phases have been reported in this

system. For the present investigation, the composi­

tions of the alloys were selected in the range, 55 to

80 at.% nickel. The X-ray analysis shows the presence

of atleast three new phases viz., Ni13zr6, Ni23Zr6 and

Ni11 Lr5• The occurrence of these phases may be further

verified by using other standard techniques.

VII A. 3. 1. Alloy: Ni68~r32

The X-ray photograph of this alloy can be easily

indexed with a tetragonal unit cell. The following

Table VII A.2 gives the details of X-ray analysis.

In the vicinity of this composition, Nevitt65

ha5 shown the existence of Pd2Hf phase, which is MoSi2 type with a= 3.399 A0 and c = 8.658 A0

, having 6 atoms

per unit cell. In Pq-Ti system also a similar phase,

Pd2Ti exists50(a). As Pd and Ni belong to the T10

group of the Periodic ·rable, their alloying behaviour

with Ti, Hf and Zr is.expected to be similar. In

Table VII A.3 mean atomic volume (MAV) and the number

of atoms in unit cell of different binary phases, exist-

.· ing in this system haye been listed. From the curve drawn

~~Fig. VII A.2) between MAV and composition of different

phases, the corresponding point of this phase, shows the

presence of 38 atoms in unit cell, which in turn suggest .. the possible formula for this new phase as ~i13zr6 •

~------------------------------------~--~,z

0 • JZ StN

t.,~zEZtN ZJ\-'tH

IJzlt,' IN e z.~zstN

f s.~zu,N IJztltN .

t!.,~zOitN SIJZ6ltN 1Jzli1N

~

oL-~~o~--~oL---~~----oL---~o~.----~0~--~o~---o-'N u\ ... ..:. - .:.. .;. ... .;. -N -~r¥1 N ..- - - - -

...---. .,w· 3tfft1CM 3fW01Y NW'ilt .£

.i 0 -'· .,.,,

rr \ ' '

.. .

' .~ • f'"j .

;I I. ~ • -,·.· ... a "" -• I ...

'~· ... .. ... I ..

u i • 0 ... ~ 0 ...

0 _, q.

N

~

• . 0 -...

TABLE VII A.2

X-ray analysis of the new phase Ni 1~

Alloy composition:

Heat treatment:

Radiation:

Exposure:

Structure:

Lattice parameters:

Ni68Zr32

Powder annealed at 1150 °C for 20 minutes and quenched in water.

Filtered CuKI(, Debye-Scherrer camera.

10 hrs.

Tetragonal with 38 atoms/cell

a: 7.593 A0, c = 9.527 A0

•

----------------------------------------------------I obs. (hkl)

----------------------------------------------------1 2 3 4

M 58.71 58.92 (003)

M- 68.90 68.92 ( 103) -M 77.08 77.12 (212)

vs 82.35 82.45 (220)

M+ 104.17 104.75 (004)

s 109.58 109.62 (311) ',

vvs 146.10 146.08 (204)

vs 160.5.3 160.18 (322)

w- 170.52 171 .46 (401)

w- 174.38 175.22 (410) : - ~ ...

(411) F ·' "l'B2.15 181.77

vs 192.34 192.07 (311) •

----------------------------------------------------" ~ ',., ,, ...

157

158 TABLE VII A.2 continued ----------------------------------------------------1 2 3 2 ----------------------------------------------------

S(diff.) 216.05 215.21 (215)

F 258.91 257.67 (430)

VF 283.76 283.86 (432)

S(diff.) 298.81 298.90 (520)

M 320.45 320.80 (007)

M(diff.) 329.08 328.45 (306)

VS 357 .t31 357.83 (523)

vs 381.04 381.36 (610)

VS 422.82 422.89 (540)

w- 434.09 435.46 (444)

Mtdiff.) 521 .98 522.74 (633)

w+ ( di.ff.) 544.42 544.28 (641)

M 569.02 568.57 (634)

M 581.70 581.84 ( 219)

M(diff.) 654.88 654.91~ ~g6~U 654.71

M(diff,) 733.47 733.48 ~ ~654p 733.08 627 J VS(diff.) 778.10 778.86 (832)

w ( diff,) 844.51 843.72 (2111) -w- 901.25 901 .36 (609)

M(diff.) 949.63 949.53 (657)

----------------------------------------------------

159 TABLE VII A. 3

Mean atomic volume in Ni-Zr system

---------------------------------------------------------Phase Volume of the

unit cell A0 3 Atoms/ cell

Ref.

----------------------------------------------------------~-Ni

Ni5Zr

Ni23zr6

Ni7Zr2(r)

Ni3

L:r

Ni5zr2

Ni21Zr8

Ni11 zr5

Ni13zr6 Ni10zr7 Ni19Zr15

Ni11 zr9

NiZr

N1Zr2 o(. -Zr

f' -Zr

43.75

301.62

1506.04

466.56

105.03

794.36

416.83

449.79

549.31

1044.58

1073.28

648.82

133.17

219.86

46.60

47.20

4

24

116

36

8

56

29

32

.$8

68

68

40

8

12

2

2

10.93 9(a)

12.56 43

12.98 Present work

12.96 27' 30

13.13 a, 9

14.18 43

13 14.32

14.06 Present work

15.36 43

15.78 44

16.12 43

16.64 43

18.32 43

23.30 93

23.60 78

, '

~ .~ . . ;_ ....

VII A, 3.2 Alloy: Ni80zr20

The X-ray photograph ot this alloy shows the

lines of Ni-solid solution along with those of a new

intermetallic phase Ni23zr6 , which is stable at room

temperature also (as-cast X-ray_pattern also shows this

phase with a= 11·1!53 A0). It is a face centered cubic

phase, with 116 atomsper unit cell. All the lines could

be very well indexed with this structure. The· details

of the X-ray diffraction analysis 1i,.e given in the

following Table VII A.4.

TABLE VII A. 4

X-ray analysis.Ef the ne~hase Ni23zr6 in equilibrium

with nickel solid solution

Alloy composition

Heat treatment:

Radiation:

Exposure:

Structure:

Lattice parameter:

Powder annealed at 1220 °C for 30 minutes and quenched in water.

Filtered CuKI(. , DebyeSciherrer camera.

8 hrs.

Face.p::~Ul~eii ~ie, co23zr5 type

a= 11.532 A0

-------------------------------------------------------3 2 3 2 !obs,' 10 Sin eobs • 10 Sin 9cal. 'hkll -----------------------------------------------~--- ---1 2 3 4 -------------------------------------------------------

53.03 53.64 71.52 84.93

(222) (400)

(331)

161 TABLE VII A.4 continued

-------------------------------------------------------1 2 3 4 -------------------------------------------------------w+ s vvs s w­w­w+ M

F

M

liJ w s s F w-M-w-s w-F

W(diff.)

107.15 120.31 143.08 160.81 177.95 197.82 227.34 232.82 251 • 98 286.51 299.90 304.52 322.24 335.63 514.13 537.66 643.71 732.54 768.81 836.80 858.14 944.87

107.28 120.69 143.04 160.92 178.80 196.68 227.97 232.44 250.32 286.08 299.49 303.96 321.04 335.75 514.05 536.40 643.68 733.08 768.84 835.89 858.24 943.17

(422) (511) (440) (600) (620) (622) (711) (640) (642) (800) (733) (820) (822) (751) (953)

( 1 042) -(884) (886)

(1066) -(995) (888) (997)

-------------------------------------------------------Note: Nickel solid solution lines have been omitted,

------------------------------------~-------------------

182

In Co-Zr system Pechine et al.71 have shown the

existence of cubic phase, Co 23zr6 with a= 11.515 A0•

As cobalt and nickel both belong to group VIII of the

Periodic Table, their alloying behaviour with zirconium

will be very similar as discussed by Panda and Bhan67.

Hence, the new phase Ni23zr6 at the Ni80zr20 composition

seems to be isostructural with Co 23zr6 phase and comes

under the category of Mn23Th6 type of phases.

X-ray photograph of this alloy shows the exist­

ence of a new phase. The lines can be very well indexed

with a hexagonal structure (Table VII A.5).

The value of MAV from the MAV versus composition

graph (Fig. VII A. 3) and the atomic volume computed

according to the present finding of lattice parameters

of this phase, suggest that this phase contains 32 atoms

in unit cell. Therefore, the molecular formula of this

new intermetallic phase has been proposed as Ni11 Zr5 •

The Debye-Scherrer X-ray pattern of this alloy

at 1220 °C can be easily indexed as bet structure. The !

. following Table VII A.6 gives the details of X-ray data.

-..r:

''

TABLE VII A. 5

Alloy composition:

Heat treatment:

Radiation:

Exposure:

Structure:

Lattice parameters:

Ni70Zr30

Powder annealed at 1100°C for 40 minutes and quenched in water.

Filtered Cul\(_, Debye-Scherrer camera.

8 hrs.

Hexagonal, own type

a= 6.277 A0, c = 13.182 A0

----------------------------------------------------------I

0b 103s1n2e b 103Sin2e 1 (hkl) s. o s. ca . --------------------------------------------------------

1 2 3 4 --------------------------------------------------------F 61 .02 60.33 (110)

w- 74.25 74.01 ( 112)

M 83.70 83.86 (201)

w- 86.15 85.50 (005)

F 93.83 94.16 (202)

M- 111.07 111.22 (203)

W(diff .) 114.89 115.05 (114)

M 123.13 123.12 (006)

w+ 134.96 135'.16 (204)

W(diff .) 139.92 140.77 ~. '

~ t~ifJII!1r'' >

.. ~!+ 1'i~· 21

----':'";_< ~;.

16~

TABLE VII A. 5 continued

--------------------------------------------------------1 2 3 4

--------------------------------------------------------M 145.94 145.83 ( 115)

F 155.90 154.45 (211)

F 168.71 167.58 (007)

F 172.48 171 • 55 ( 213)

F 180.90 180.99 (300)

w 219.14 218.88 (008)

VF 254.87 255.00 ( 222)

F 271.33 272.10 (223)

F 278.05 277.02 (009)

w 300.39 299.32 (208)

F 316.54 316.15 (315)

F 338.06 337.35 ( 119)

w+ 377.09 376.48 (404)

F 386.11 385.51 {321)

w+ 396.18 395.77 (322)

w 421.94 422.31 ~ ?410) ] 422.44 2010)

F 433.74 433.93 (101])

F 445.12 444.88 (406)

F 458.62 458.0'7 . (~Q~) .

F 495.63 494 • .26 (2011)

F 518.73 '·~~/.34 .· (229) :1~-:~~:·-- ·~ ~i·t;· . , ·._ ....

------------------------------------~·.;.;.~-";f.~--------------•

--~ • I>< ')•

"

165

TABLE VII.A.5 continued

--------------------------------------------------------1 2 3 4 --------------------------------------------------------W(diff .) 534.88 533.53 (503)

VF' 545.01 545.43 (416)

F 562.65 563.08 (420)

F 658.06 657.20 j (512) } 658.40 (2013)

W(diff .) 734.79 735.60 (40~)

VF 759.55 758.97 (3013)

W(diff.) 896.13 895.63 ~ ~1016) 1 895.51 611) j "

F 931.80 931.75 (3114) -W(diff .) 943.52 942.84 (608)

-------------------------------------------------------~

166

TABLE VII A. 6

X-ray powder data of Ni 11~9 phase

Alloy composition:

Heat treatment:

Radiation:

Exposure:

Structure:

Lattice parameters:

Powder annealed at 1220 °C for 30 minutes and quenched in watE

F'il tered CuKD(, De bye Scherrer pattern.

10 hrs.

Body centered tetragonal with :: 40 atoms per unit cell, ·"' Pt11 zr

9 type. ;~ •

a = 10.299 A0 and c = 6.936 A0

--------------------------------------------------------(hkl)

--------------------------------------------------------1 2 3 4 --------------------------------------------------------VF 4 r>•2" ... ~ ~ 40.36

F 46.41 44.82

VF 59.98 60.62

vs 62.24 62.77

vs 71.51 71 .82

w+ 90.12 . e9.63

w 95.52 94.23

s 100.56 100.84

VF 112.94 "'it 12.04 ,, ~- .

F 11 8 • 1 3 ;1 {6 '."it~' .~-, "-·;"' - . ' .

( 211)

(220)

( 112)

(301)

(202)

(400)

'(222)

~~\ ',- -:-,'-:?.t{h~'.J

(420)

( 1 03)' Jllllf' . . ' ~·· . '

. ' . --.-----------------------------~-------------------­.

'\,.

-~> -"f~·

16"/ TABLE VII A. 6 continued

--------------------------------------------------------1 2 3 4

--------------------------------------------------------M

F

vs

F

M

M

M

VF

\'/

M

M

F

F

w

F

w

F

w

VF

w ,;".F -~ ,~- .·

139,02

144.60

152.31

161 .05

175.12

178.57

183.92

190.66

207.13

220.43

228.01

237.90

252.27

254.20

267.99

275.44

287.90

298.40

324.72

344.99

375.54

~§§:64 ~ ~~6~~} 145.65 (510)

152.40 (501)

161.59 (303)

174.81 (521)

179.26 (440)

184.00 (323)

190.47 (530)

208.85 (114)

220.06 (204)

228.61 (442)

239.88 (532)

242.46 ) (224)) 242.03) (541)j

253.67 (314)

264.44 (631)

273.63 (523)

287.28 (404)

298.48 (~34)

. ;f$i~~f

. .., .... ·~- ( 514) ' ,~-,

TABLE VII A. 6 continued

-------------------------------------------------------' 1 2 3 4

-------------------------------------------------------· F 409.40 408.08 (723)

w 448.17 448.16 ~ ~~6gn 448.37

F 469.65 467.12 (206)

w 490.13 488.52 (921)

Vl" 502.80 500.73 (316)

F 537.19 538.41 (545)

w 563.78 564.94 (903)

F 581 .87 583.32 (705)

F 600.32 600.99 (664)

F 632.41 633.31 (217)

VF 699.49 700.53 (417)

w 761.93 762.59 (905)

VF 812.87 813.00 ~ ( 208~] 812~57 (617

1({ 825.73 825.64 (826)

F 847.06 848.05 ~ ~666~ I_ 846.61 318 J

VF 877.46 879.79 (707)

w 903.94 904.07 (916) . ~ '

-----------------------------------------------~1~~---

.. : i .;~~~ ···=' · ....

169

Kirkpatric and Larsen43 have shown the exi~tenc.e

of this phase as body centered

parameters, a = 9.90 + 0.02 A0

with 2 molecules per unit cell.

tetragonal with lattice 0 and c = 6.62 + 0.04 A

The mean atomic volume

calculated by these values of lattice.constants £its

nearly in the mean atomic volume (~~V) versus composi­

tion curve. The point on the curve corresponding to

the unit cell found by us, will lie slightly above the

curve, since this phase is related to b.c.c. structure

and such types of structures are known to have lattice

vacancies with correspondingly higher MAV. Such is also

the case with pure zirconium. Therefore, the correctness

of the structure has to be decided with the comparison

of the isostructural phase Pt11 Zr9 reported by Panda

arid Bhan68 (having 40 atoms per unit cell and is bet

with parametric values a = 10.259 A0 and c = 6.888 A0,

at 1200 °C), Gomparison of lattice constants and number

of atoms in the unit cell of Ni11 Zr9 with Pt11 Zr9 phase

indicates that both the phases are isostructural. This

is expected as Ni and Pt both are the members o£ the 10 T group with ground state electron configuration of

their free atoms as 3d84s 2 anq,_.5d86s 2 respectively and

'VII A. 4

••• -~~

... .. The investigation on Ni-Zz;ibinary system in the

composition range. 65 to · 80 at.% nickel reveals· the exist-'. ~.

170

-ence of at least three new intermetallic phases besides

the known phases. The alloy Ni80zr20 exhibits the

presence of nickel solid solution along with Ni23~r6 phase which seems to be isostructural with the phase

Co 23~r6 • The cubic lattice constant of this phase has

been found as, a= 11.532 A0• The phase Ni13zr6 (at

68 at.% nickel) crystallizes in tetragonal structure

with lattice parameters, a= 7.593 A0 and c = 9.527 A0•

In Ni70zr30 alloy a new phase Ni11 ~r5 (h) having hexa­

gonal structure with parametric values a = 6.277 Ao

and c = 13.182 A0 has been observed. The mean atomic

volume (MAV) values of these new phases also fit well

in the MAV versus composition curve. At 55 at.% nickel,

the phase Ni 11 Zr9 occurs. Comparison of crystal

structure of this phase with the phase Pt11 ~r9 in Pt-Zr

system shows that they are isomorphous.

VII B

THERMAL EXPANSION COEFFICIENT OF INTERMETALLIC PHASES

IN Ni - Zr SYSTEM

VII B.1. INTRODUCTION

In any crystal the atoms, that go in its consti- ,,,

tution are arranged in a regular pattern in three dimension

The lattice parameters of the crystals are determined by '

the spacing between these atoms{ or groups of atoms. Wi~ I

increasing temperature, as the amplitude of thermal

vibration • of the constituent atoms increases, the average,

interatomic distance also increases, giving rise to the

phenomenon of thermal expansion. Studies of the dimen­

sional changes that result from a given temperature cha~ge

can give some insight into the nature and directional , ·

character of the interatomic forces that hold the solid

together37 . Thermal expansion is considered to be a

measure of the anharrnonicity of the lattice vibrations.

Thermal expansion plaY1il an important role in .£:~,', ;,·~ '~- ' -" t,' -.· -

crystal physics, in view of ftill applications,, &'me of ·

'~~~-;, which are mentioned below: '.·, L_ '~--

(a). In case of crystals ti!4d.~r;g0i~g »hase tran~ltions, \ .. _'~-':,,.,.---, ··~-' 1t"·' '

;he .thermal expansion coffffiq·i=~~tt·"· varies anomal-

l:;.y near the transition tejii~t • : • .. • · .·

17 ~

(b) Several attempts31 ,54,60,76 have been made to

use thermal expansion data as means of investija-t'iYl~ tile

nature of defects in crystals.

(c)

on the

The thermal expansion data can be

theories of lattice dynamios5,6.

used as a check< ' ~.

,;} '

(d) It is useful in estimating the thermal conductiv~ty

of insulators26.

(e) Resistance to thermal spalling and thermal shoe~

and the design of casting moulds are all dependent on the

. h t . t. f th t . 1 16 expans~on c arac er~s ~cs o e rna er~a s •

(f) In the calculations of some of the physical prGper-

ties, viz., refractive index, the elastic and photoelastic

constant at different temperatures, the knowledge of thermal

expansion data is essential.

(g) The-knowledge of thermal expansion gives an indi­

cation of interatomic and intermolecular forces and their

variations with direction, temperature, impurity, vacant

sites, spin orientations, electronic transitions .. etc.

VII B. 2 THERNAL EXPANSION IN RELATION TO CRYSTAL

STRUCTURE AND OTHER PROPERTIES:

The ever increasing knowledge about the atomic .. ~

arrangements in cry?tals make it ~ossi'Q;La~~to obtain a ·<·. ,, ' •' II> ·'- ' • •

be'tter understanding of the s , e.:..expansi~ relation-

ships. Thus crystals could ed together according

to the general nature of es. In isosthenio

..

173

structures, where the atoms or ions are linked together

to their neighbours with bonds of the same strength, the

anisotropy of thermal expansion is small. In the laye.r

structures in which the atoms in the_layers are more

tightly bound than the atoms in the perpendicular directi,n

the coefficient of expansion perpendicular to the layers i•

is larger than that in the layers. In antilayer structures

the coefficient of expansion along the basal plane will be

more than that in the perpendicular direction as the at~s .,,,.,

in the basal planes are comparatively 'weakly bound than'

those in the perpendicular direction97 • A few more

structure-expansion relations.hips . which include·. the - 58

following facts. have been mentioned by Lonsdale •

1. ~xpansion is greater for crystals with small

molecules than for their larger homologues.

2. The expansion along the direction of H-bonds is

relatively small.

3. Expansion is relatively large when only Vander

Waal's forces are present or along directions where these

forces form the links between molecules.

4. Covalent bonds perm! t only a very small .• f/;Xpansion • ..

may

.. 6. The expansion of may be greater ._ ·

than that of either pure

17~

7. The thermal-expansion coefficient of an alioy

can not be predicted from its constitution.

Several attempts have been made in the past to

relate the thermal expansion to the lattice energy, the

melting point, the heat of formation, the, bond strength

and the index of refraction. For many f.c.c., b.c.c.

elements and binary compounds there is an empirical ''

relationship between the thermal expansion'coefficient

and the melting point18 •85 •95, The spacings and expans~Gl

coefficient are both, of course, seriously affected by

strain in a metal or alloy and near the melting point

a rise in the number of vacant sites may cause a change in 46 .

slope of the expansion coefficient curve. Klemm found

that for ionic crystals product of thermal expansion

coefficient and melting point is a constant quantity.,

The thermal expansion is found to be large for crystals of

low hardness. The value of expansion coefficient a~.lso

22 . 15 86 depends largely on texture , impur~ty ' and on second

order transformation94 within the crystals.

VII B. 3 BRIEF SUMMARY OF THE PAST WORK:

A comprehensive bibliography69 •83 on thetb.ermal

expansion data is available. The data on thermal expansion

of metals have been. compi:l~d ·~y·.P~~so~7<t- · The thermal

expansion data can also be 23 29 42 -66 sources ' ' •,... · • To .~.v'~"J"'

.;.:' :

~ -~~

the.major other

beautifully edited a

hand book series, consisting of.several volumes which

include thermal expansion data reported on elements,

intermetallic compounds and alloys.

17~

i 1 Survey of the literature shows that thermal expan• l.

sion coefficient of intermetallic phases in Ni-Zr system r has not been investigated in past. The aim of the present

study is an attempt in this direction.

VII B. 4 METHODS OF DETERMINING THERMAL EXPANSION

OF SOLIDS:

Many different methods for measuring the thermal

expansion of solids have been developed during the past

50 years. The choice of method may depend upon the material

to be measured, the quantity of material, the temperature

range of the measurement and the type of information

(accuracy, sensitivity and time factor etc.) required,

There are two main classes of experimental methods

of determining thermal expansion. They are (i) Macroscopic

methods and (ii) Lattice expansion method. The two methods · 38 D are not always in agreement · • isagreement have been

attributed to a difference between the lattice' expansion,

which measures correc.tly overCall expansion in single

crystals or in separate crystallites, and overall expansion - ·, . :< t ·•'·

of poly crystalline solids, may iiav1hve reorientation

G:J; crystal;Li tes: ·or other changes that affect the . . ··. ' ..

spacing 'betw.een, them~

A ~~·, ~escription ,, of .the macroscopic methods is

given below:

176

VII B. 4.1 MACROSCOPIC METHODS:

' VII B. 4.1.1 Push-rod dilatometer methods: The push-rod,

dilatometer method7• 20 •74 is experimentally simple, sensi~ tive, reliable and easy to automate. It is useful for J

i quality control measurements and for studying phase tran~ ,,

sitions. With this method the expansion of the specimen( ,,

is transferred to one of the heated zone to an extenso--­

meter by means of rods (or tubes) of some stable material.

VII B. 4.1 • 2 Twin-Telemicroscope method: This method33; is

most useful for measuring the absolute expansion of large

specimens at high temperatures. The best results are

obtained when the two telemicroscopes (microscopes with

a relay lens) are rigidly mounted to a bar of low expansion

material and the length change· is measured with filar

micrometer eyepieces. The sensitivity of this method

isrv 10-6 m.

VII B. 4. 1.3 Interferometric methods: These methods40

are based on the interference of monochromatic light

reflected from two surfaces that are separated by a speci­

men or by the combination of a specimen and a 'reference

material. 2 ....

The fizeau interferometer can be used to

measure either the absolute or relative expansion of a

specimen. When the optical f+~t$ '9f a F.~.wY-Perot inter­

fer,ter are mad~ ~hl~.:r~fe-~;ting the multiply reflected

''beam.S ~-cause a great i:ilcreaa_.,,,lf.sl:ilil.rpness of .the fringes

which in turn g~:<fes :h:igher sensitivity in the expansion

measurements.

A technique which utilizes the frequency shift

of a .to'abry-Perot interferometer has been developed by

Foster32 and by Jacobs39, The latter has used his system

to measure the low

with a sensitivity

expansion materials

of 10-9 m,

from 273 to

The polarizing interferometer28 is also a

600 K ~ ,,

sensi- i -:c

tive apparatus in which laser is used to emit polarised :

beam.

VII B. 4.1.4 High-sensitivity methods: At low tempera-

tures (< 30 K) expansivities are very small, and hence,·

high sensitivity (0J10-11 m) methods are used, In three

terminal capacitor technique49 •96 variation of either

capacitance or mutual inductance of the specimen in a

balancing bridge circuit is measured. In variable diffe­

rential transformer technique80 the relative displacement

between the primary and secondary windings of a tr~for­

mer is detected with a mutual inductance bridge. In

mechanical-optical system72 •73 the expansion of a 6 em.

specimen causes the rotation of a mirror which is attached

to the centre of a doubly twisted strip, The .;rptation of

the mirror is detected with a sensitive photo~lectric

device.

VII B. 4.1 .5 . c ' 19 Hig!l-sP:!el!i:· methads: . , . e~~1r,liyan has ....

described a· system in which t,Q..~.· elX:pansion of a specimen is

m'Msured by detecting 1}~ ~h·;t:tl•radiance from a

constan:t radiatillbn ·soi.u;~/;~':Cl'fi:bb.ange in radiance is '1/ ~· -~~: . .,. . ·:" ~' ,'·- <" '

c caused by the expansion .. pf the specimen which partially

blocks the radiation.

~

178

The use of stabilized lasers39, the use of

computer controlled data acquisition system to measure

a specimen during a rapid change20 and the use

diffraction method12 are the outcome of modern

of neutron ~­

technology o{

VII B. 4.2 X-RAY DIFfRACTION METHOD:

The macroscopic methods, have some inhe.rent dis-·

advantages. The specimens required for these methods are

of fairly large size and for non cubic crystals differen~

k

specimens, oriented in appropriate directions are necessary

to determine the thermal expansion along different crysta­

llographic axes. For the optical methods, crystals with

polished faces and fine finish are needed. Moreover,

hygroscopic and volatile substances can not be studied,

In the X-ray method, the changes in the lattice•

spacings produced by the thermal expansion cause shift-s

in the Bragg angles of X-ray reflections and these shifts 0.

in the angles, measured a:>,/unction of temperature, give

the lattice thermal expansion of crystal. The X-ray method

provides some unique advantages.in the measureiJ!eht of i(<

thermal expansion of solids. These advantages .:may be

roughly classified into~,two groups. ·~)~~

( 1) Technical advanta'gesl_ . • . . ... ~

(a) The posslbilj.':z of th~ _u,se . .:. . --~·.

spe'eime.ri. · . . """" · · ' - • > ~

:;·. ~-.·. '

-,"-::· of· a vecy.i. tiny

.. . ·, ,,,. _ _f....,. --~: . (b) All the linear lm,d"anj;ill~ar dimension (of the

! '\~~:;;,.

179. unit cell) of an anisotropic material are obtained simul­

taneously.

(c) The possibilities of using specimens of

irregular shape, without special surface preparation.

(d) Convenient examination of mechanically weak

specimens, such as molecular crystals.

(e) The possibility of studying hygroscopic and

volatile materials.

(f) The ability of studying conveniently substances

which condense or solidify only at cryogenic temperatures,.

2. Scientific advantages:

(a) There is unique possibility of determining

j

and relating the atomic structure of a crystal to the

thermal expansion57• 97 which in general is quite complieated

(b) Evidence on the extent and nature of crystal­

line perfection in solids can often be obtained simultane­

ously from the X-ray method.

(c) Information of intrinsic defect structure and

its possible contribution to thermal expansion can be

obtained25 •76 •84•

(d) In the case of simple structures, knowledge

of the precise values of the.lattice parameters provides

a direct measure oi inter nuclear distances. ' ' - ._ ' ', "~· 11': .

( e) Lattice parameters:· are .requi~ed: :for- the calcu-JIIIIIf .. . 411 lation of other physic~l prop,~'f!P:~~· ~uch. as couipressibili ty'

lattice energy, refractive index and photo elastic ;·, .t t 4,11,61 ,_ons an s .•

1~0

(f) For the construction of phase equilibrium

diagram the lattice parameter data are found to be nece­

ssary87.

VII B. 5 DETERMINATION OF LATTICE PARAMETERS:

For the calculations of thermal expansion coeffi­

cient, by X-ray method, knowledge of lattice parameters

at different known temperatures is essential. The

precision in the measurement of lattice parameters and

the specimen temperature are the important factors, which

affects the accuracy of thermal expansion measurement.

Excellent reviews on different methods of evaluating

accurate cell parameters are available3• 10 • 24 •47. The

two types of major sources of errors, the random errors

and the systematic errors, are to be considered in the

determination of accurate values of lattice constants.

By making careful and repeated experimental observations

on the same sample, the random errors of observations

can be minimi~ed. In the present work, extrapolation

method and least$quares method have been used for the

determination of accurate values of lattice coqstants,

which account for the corrections due to systematic errors.

Brief descriptions of these two methods are given below:

VII B. 9.1 Extrapo~tion metho4~,.;· '~, ~'{- ., .

~, ~ the Debye-Scherrer .. ~ay ph:Otographs the signi-

fic~f':$urces of systematic errors ar~ as follows:

181

1. Shrinkage of the film.

2. Lack of knowledge of the exact film radius.

3. Eccentricity of the specimen.

4. Absorption of X-rays by the specimen.

On id N 1 d R'l 6; cons ering the above errors,. e son an ~ e~

and Taylor and Sinclair9~ after rigorous analysis, proposE

the use of error function -

1 2 +

for getting the accurate values of cell parameters. The

systematic error approaches zero as e approaches 90°,

as can be seen from above expression. Precise values of

cell parameters can be obtained by plotting (large scale)

the calculated values of lattice parameters for different

(Cos 2e/Sin9 + reflections, against the

Cos2eje) values and then

corresponding

extrapolatingithe'lin~ar curve

to the zero value of the error functi0ri. for all practical

purposes lines at all anglesmay be employed in making the

extrapolation.

obtained, is as

better resu;L ts the foll0Wing ppin-ts should be.;i•~bserved in

practice:

(i) In

relativ~ly

18;

(ii) itEcdiation may

one good line in the

be cllosen so as to yield at least

far back-reflection re~:>ion (0) <30°)

in order to fix with highest accuracy, the point or intersection or the plot with the axis of ordinates.

(iii) Cnly lines between e = 30 and 90° should be used.

VII 3. 5.2 Least-sguares method:

The principle oi' this method is tllat, if the

angular dependence of the combined systematic errors is

expressible as a simple mathematical function, the effect

of these errors can be eliminated by Least-squares analy-

tical treatment of the data. The procedure suggested by

Cohen21

is in principle the analytical equivalent of a

graphical extrapolation, but it is superior to later

method in that it is applicable to noncubic crystals

also (if strong reflections (boo), (oko) and(ool) are

absent). However, the disadvantages of this method are

(i) labosrious calculations and (ii) assigning equal

weightage to all reflections, regardle_ss of 1rrhether they

can be measured with good or poor accuracy.

The method is as follows 1 ·

Square of the Bragg's equation gives

-~<,. ' ... -l:, "'f;,

-- (7.1)

183

- - (7 .2)

where ,6 Sin2e is the error in the observed Sin2e value

and ~d is the corresponding error in the 1 d 1 spacing.

If f(S) is the linear extrapolation function for

any camera, then the fractional error in the d-spacing

can be expressed by:

= D'f(e) -- (.7·3)

where D' is a constant of proportionality.

Combining equation (7.2) and (7.3) we have,

(7.4)

which can be written as

= -Db -- (7.5)

where D, is proportionality constant, called the drift

constant, which has the same value. for all the lines

recorded on one film and 6 is a t~igonometric expression

different for different lines recorded on a film •..

Equation (7 .5) indicaj:;e~ that t:[(Jlc·o values

of Sin2e will have/~ .error b;· ~ a~o~~ ' - Db,

and that this term has to be ~€ldeac tb:"~tJi?e quadratic ·-_,:;.. ' __ "

18~

A I C '( 0 C><.i + 0 i (7.6)

for a tetragonal crystal

.. 2 2 J_ 2 2 )\/4c

0 1 i =(h +k )i'

~ = [i and D bi = appropriate form of drift

error -

LlSin2ei

for a hexagonal crystal,

A0 = >f/3a~ , C0 =

and Y'1 = L/.

Equation (7 .6) is called the observational equation for

each line of the diffraction pattern and the number of'

such equations will be equal to the number of lines us~d

in evaluating the lattice parameters.

The effect of random errors, which is reduced by

the averaging procedure used, during measurements can be

J

minimized further by applying the principle

If such error do exist, the equation (7.6)

small residue in R.H.S., representing the

tional error. According to the principle

squaref

a

·observa-

the .. best value of the quanti ties A0

, ·t:0

and D are those . !~4:.~- ..... ~.

whi!~·afE! obtained by minimizing of the squares

observational

.filli!Uations o:! the ~ .,; ' ·-;/t"~· ; - . ,_ ~ -•

,.,~~·~·mbined to give a set e!

ines can be

equations.

185

These are as follows:

A f_J. 2 + co lii Y'i + D I)..i si --

=t/·fin2e1 0 i

Ao[_J.i Yi + coLYi2 + nLJ'd'"i = _LYisin2-ei (7.7).

Aof ~i~ + coi'{1ri +D,l-~L r- 2 =_oisin ei J

When these equations are solved simultaneously

for A0

, C0

and D, then, a0

and c0

are calculated from th• .·

2 '1.2 2 \2 relationships ao = " I 4Ao and co· = (I I 4C 0 for tetra-

gonal crystals or a0

2 = A213A0

and c0

2 = ~214C0 for

hexagonal crystals,

The precision of the results is greatly improved

by using a comparatively large number of lines. Again,

all the values of the observed Sin2e, are normalised to

a common wavelength, preferably to theJ~ wavelength. So

if a number of~ 1 ,(2 pairs are to be used, the Sin2e value

of theo( 2 reflections mus~be converted to the equivale

Sin2e values, corresponding to the o(1 wavelen

plying them with ( A.c1 / 'A .~, 2 ) 2 • The factor

for CuK~ radiation is 0.99503. It is a~so i1Portant to

observe that the value of b for -~ny ~iveh po;der line depen ~~~.,..... . ' ' ,·

_.upon the .{'bserved Bragg angle of th~t line and hence to ... . ' •- .

compute the c; value for.that'parj;icula flection, the ,'+. ' "' < •• ·~ ,: ""' ..,_ -

.obf'~v~d':;,a:i,;t~t··e·:~ -must "De used, and • ·' . "h,

value

af' ~. normalized to a d"iffe~~wa,y,elength. -.-.&.-. . ·<l:J.~.-'"1-"-~: •• -···

186

Orthorhombic crystals can be evaluated using the

Least-squares method . by a logical extension of the mathe­

matical theory given above. However, the opportunities

for successfully utilizing powder data from orthorhombic

crystals are rare and the calculations become very tedious:.

' VII B. 6 STANDARD ERRORS IN THE VALUES OF LATTICE CONSTENTf

--------~~~~~~~~~~~~-=~~~~~~~~

Jette and E'oote41 have suggested a statistical m~ttho<

for the estimation of the errors in the cell parameters . f.

determined by Cohen's method21 from the data of an indivfdua:

film. Using this method, the limits of errors in the para­

met~ic values have been evaluated from the variance, s2

of Sin2e given by :

= L_L~-~~!!~~l~ N- W

(7 .8)

where ~Sin2e = Sin2eobs.- Sin

2ecal.

N = number of reflections employed and W = number

of constants to be determined (for a tetragonal crystal,

W = 3). In the case of a tetragonal system,

of the constants A ( = \2/4a 2) and B ( = 0 I' 0 0

the,.·variance 2

0 ) are

187

The standard errors in the lattice parameters

I a I 0

and 1 c 1 0

are then

aoSA -----2 A

0

given by 1

• - - (7.10)

VII B. 7 EVALUATION OF THERMAL EXPANSION COEFFICIENT:

The linear thermal expansion coefficient is defi~a

as the change

range of 1°C.

in length per unit length for a temperatur•

For a crystal, if at' bt and ct are the

lattice parameters 0 ~ at t C along the three crystallograp~c

'0~

axes and if their dependence with temperature is expressed 2 by a quadratic relation of type at = a

0 + a1t + a 2t or

by a linear relation of at = a0

+ a1

t type, then the t~.ermaJ ,;"

expansion coefficients along the three axes are given lily

the following relations.

=

and =

(1/a0

) (dat/dt)

(1/b0

) (dbt/dt)

(1/c0

) (dct/dt)

VII B. 8 EXPERIMENTAL:

.. .•. For the determination of

cient, . three binary alloys of ::j:;he

exact compositions Ni55_zr 45 ,, .~l.-,tl'"~.~:<::>llf"!

':,

(7.11) '

coeffi-

the

The detail1

1&8

employed have already been mentioned in chapter VII A.

The powders of alloys Ni55zr45 and Ni80Zr20 were

annealed at 660°C for 3 hours in pyrex glass capsules,

sealed under vacuum and coo.led within the furnace. These II I ' strain-free' powders were used-for the room temperature

X-ray photographs. However, for obtaining the as-cast

X-ray photograph of Ni75zr25 alloy; the method suggested

by Becle et a19 has been followed, ~; '

''·t-' s4eved powders sealed under vacuum in silica tubes

were heat treated at different temperatures (alloy Ni 55zr45 0 .

and Ni80zr20 , from 730 to 1220 C and alloy Ni75zr25 , from

380 to 820°C) and quenched rapidly in water. These pow~er

samples were utilized for obtaining Debye-Scherrer X-ray

photographs. It was observed that ail the X-ray patterns c

of a particular alloy were similar thereby showing thitno "i

phase transformation occurs withill the entire range fff

temperature, studied,

VII B. 9 RESULTS AND DISCUSSION

VII B-. 9. 1 THERMAL EXPANSION OF ALLOY:

All the X-ray photographs o!- :lthiil'

presenc.e_ of Ni11 zr9 phase having-b¢.t:' .

.._ of'_,~~~ X-~, diffraction;,;ata of ~.~r; alri,ady- given (chapter._V~~-~ ~l·-~

the

The detailE

189

Accurate unit cell dimensions of Ni11 zr9 phase at

each temperature were determined {Table VII B,1) using

Least-squares treatment21 • The standard errors in the

lattice parameters so obtained, were calculated by the

method suggested by Jette and Foote41 • The s.n. of the

lattice parameters for all the x-ray films taken at diffej" t rent temperatures were found to be of the same order of / ; ' magnitude (equal to : 0.0058 A0 and + 0.0042 A0 for 1a 1

and 'c' parameters respectivel~.

Refraction correction has not been computed, bec:~us1 ,,·

it has a very small value in comparison to experimental ··

errors. .'-'

Graphs between lattice parameters and temperatur'e

were drawn in a large scale. Figure VII B,ishows that the i lattice parameters vary linearly with temperature and~.the

dependence may be analytical11 expressed as

at = 9.9591(11) + 2.795(13) X 1o-4t ·-~,

--(7.12)

and ct = 6.6894(27) + 1.989(31) X

\!>lhere, the numerals within tb.e '

S.D. of the respective constant_s. ·The ;u.ne:

of · . .thermal expansion for both .the were

... calculated using relation ( 7.11) cl : •io:; . . ..• ' ' . .. ' ,·

~;;,iii.£ '. '~·e'~~~~~·,~ at ~:~ ~ :· ~~~t-v ·a c

have: oeen dete~i~ee.·-~~-\h'e u~~al method59. .-,;~~~:.:: ·tr;:. • • ''•~: • ·-~~~

values of

I0·34r-----------------... 7·04

1 . "<

IX UJ ... UJ ~

~ -~-

... . ·'

10·10

. ,, ....._.,. ·.·

!i" .,. '" FIG."fl!l..,$.1

~ • a· PARAMETER

e e •c' PARAMETER

8.7Z

••••

. . ,

'"t, ···._, TABLE VII B .1 '.t ~Lattice parameters and thermal expansion

~:· '

data of Ni11 zr9

phase at

~ltifferent temperatures ' '"

--~--~~~~--~-~--~---------------------------------------------------------------------------·. ·He~t :.fef:~~tme* .. and 1 a 1 parameter 1 c 1 parameter r:f. x106 /°C o( x106 f 0 c · water q~!9jlching A 0 A o a c

-------~-------------------------------------------------------------------------------------Temp. 0 c \ Time Observed Calculated Observed Calculated

_.. ·;. minutes -~ .,

--------~------------------------------------------------------------------------------------. . 11 1'-.::,.-"' : .:~Jtc '

'!5(1\,s..:;~ast)' - 9.9646(58) 9.9661

1'5~ ··.1 70 tlO .1626 (58) 10.1631

~ -~ 60 10.1892(58) 10.1883

)~o~~ ··· . 'd:·, '·'_so 10.225o(ss) 10.2246

:f<l20' ' .~ .''40 10.2558(58) 10.2442 ' l,l.\<~ 111. ~. 'f'

'< 1150 . 1.:~ ;;;.f,,~.~ ' ;. 10.2703 (58) 10.2805

1220 :'::'" ~:0. 2996 (58) • . . 10. 3001

---.--____ &_ .. _.-...

6.6940(42) 6.6944

6.8357(42) 6.8346

6.8538(42) 6.8525

6.8758(42) 6.8783

6.8950(42) 6.8923

6.9125(42) 6.9181

6.9359(42) 6.9320

28.05(1)

27.50(1)

27.43(1)

27.33(1)

27.25(1)

27.21(1)

27.14(1)

29.71(4)

29.10(4)

29.02(4)

28.93(4)

28.85(4)

28.77{4)

28.68(4)

,.._ = C)

191

standard deviations of thermal expansion coefficient at

different temperatures are found (Table VII B.1) to be

nearly same (equal to + 0.0122 for rJ. and + 0.044 ford ) • ~ - a - c 1

VII B. 9.2 THERMAL EXPANSION OF ALLOY: Ni80

Zr20 J The X-ray photographs of this alloy at different ,

"''' temperatures showed similar pattern, nickel solid soluti4:' ,,

lines along with a new intermetallic phase Ni23zr6 , which'' '

has a f.c.c. structure. The details of the X-ray analys~j ,,,,

of this new phase have been already given (chapter VII A ,,,,

page iC:O).

Values of lattice parameter were calculated f~m

the line positions of the intense reflections (640), (8Q,O),

(733), (822), (751), (884) and (1Q66). Using the meth~dJ,

suggested by Taylor and Sinclair9° and by Nelson and ~. ·. '""''

Riley62" 'the accurate value of lattice constant at ~ch L·'

temperature , was determined by extra]Hiillating the plft~ of · · 2 · :r2

lattice parameter values against ~2 (cos 9/sine + Ccis e/e)

function to 8 = 90°. One such plot, at 122o°C h~s been

shown in Fig. VII B.2.

The standard error of so

obtained, have been calculate<Ltl.Qi·: ·, :·~·.;_/.

·of the

'

··'-<·-·.;· ' ...•

'

-~

"' I ' ... • :-_ ~ " -

0 ,.l· ~ ;.(

. '

l 19 -.........

o.1JG ~ v

~ o.,.

"' 1')1 0

·<-

+ .. ·r 'jc .u ·;

........ . _,,.,.

• • 'I

I

·~ II! c -... ~ ;::1 II.

Cl: 0 Cl: a: Lll . • > Cl: LiJ ...

. W

·~ .a: ·~ ·a.;

Lll u

t: • _, .u 0 N N

N

CD

192

TABLE VII B. 2

Lattice constant and thermal expansion data of Ni2~

phase. I

1 ------------------------------------------------------------! Heat treatment

and water quenching

Temp. °C Time minutes

'a' parameter Ao

Observed Calculated

----------------------------------------------------------f/;i.-•.1} ', ,.

25(As-..cast) - 11.3534(37) 11.3547 13.03(1)

730 70 11.4603(37) 11.4590 12 .900)

820 60 11.4702(37) 11.4723 'k

12.89(~) /

950 50 11.4910(37) 11.4915 12.87(~)

1020 40 11.5027(37) ;\

11.5018 12 .86(:¥1) 1':

1150 60 11.5201(37) 11 .5211 ~:l:~~ 1220 30 11.5324(37) 11.5314 t~·--

-l.: ~:.h

----------------------------------------------------~-------

A graph between lattice parameter

was drawn preferably .with a large ~Q~J:;~,. :.

represents a .linear variation of

temperature.

• 1.479(12) xto-4t

B. 3

-- .. "(7.13) ~

I a""'"' the S.D. of the

of linear

u.ss , _______ .-.. _______ _,

u.s,

I f.49

1 11.47

•.c ex 11.45 w .... w ::E .( ex n-43 ~ • " •

. "·" ,,··.,

' ',,t/

. '.

11.39

11-31

WIT I

193 The thermal expansion coefficients at each temper­

ature were evaluated using equation (7.11) along with their

S.D. values. The numerals within the brackets o£ columns :~

3 and 5 of Table VII B. 2 represent S,D. values of lattice -; {~

parameter and thermal expansion coefficient respectively. ~·

VII B. 9.3 THERMAL EXPANSION OF ALLOY: Ni75zr25 Jr.,· ~;~~' ~

All the high temperatures as well as as-cast X-rfY' •

photograph exhibited similar pattern. ·The hexagonal unit

cell

ment

parameters of Ni3

Zr phase were

with the reported values8•9.

t found to be in agre1:

i'~

Accurate cell parameters of this phase at each .. -:· . "'''' / "~ . 21 W·

temperature were computed by Least-squares method • Jhe , ..

standard errors of the parametric values were calculat~d 41 ;·

using the procedure suggested by Jette and Foote • ~e

accuracy in the lattice parameter measurements were

as ± 0.0006 A0 and + 0.0004 A0 for 'a' and· 'c'

respect! vely. ~- -·~ '

The observed values of lattice

listed in Table VII B. 3 and the n.ature

temperature is shown in Fig •. VII~&"':'*''

analysis of the experimental . : ' '

analytical expressions .• · "' .~.-· . . :~' . . ... i,, ~-··-. V.iP

.. are

ers

-~ "' 0

3 0

·~· "" "' 31 ..; • .,

I ~'I , ,

r i! J

I l i ·"' 1:.

-~ .., ; ~'ii! ~ ·,~ In o:r 0: w

~·-a l i' ... • 0: • I "" w .... ... ·:· ·, -·~ '- " _, ·w I . : ~· ~-·. 2 , w ~ I

'·:,., u I= t. '!('

3 IlL

• • • u . • 1&. 0

I 1 z 0 I= ·.t

:! a: J ,., .,

~ ,•,. • ·" ID ""

, , -· ,::i: •!._ ,, .;. .;. !'!" , ' ·.~

':·· ,'f -

•"

.~ ' \

':t:. ,, .

' ~~-, . , . '

~

TABLE VII B. 3

.,Lattic-e parameters and thermal expansion coefficients at various temperatures of the compound Ni

3Zr

'a' parameter 'c' parameter

Observed Calculated Observed Calculated from least- from least-squares squares analysis analysis

Ao Ao Ao Ao

5.2529 4.2454

Coefficient of thermal expansion

tXa ~

x106/°C x106/°C

44.58 34.35 as t) .. :-. . .... ~'"~~~

5.2530(6) 4.2452(4)

5.3186(6) 5. 31.89 .:;3'61 ( 6) 5.3290

352(6) 5.3356 .3416(6) 5.3426 ,,

.3482(6). 5.34~0, ' -· ' ~

) 5.3517 5.3534

------',.-,,._~!.!,.

4.2885(4) 4.2882 4.2961(4) 4.2953 4.3002(4) 4.3003 4.3053(4) 4.3057 4.3100(4) 4.3103 4.31-41(4) 4.3142 4.3163(4) 4.3164

26.30 22.16 19.08 14.96 10.82

6.71 3.62

22.47 19.80 17.80 15.13 12.45 9.78 7.78

..... ~ ...-..

195

It may be seen from the Fig, VII B. 4 that the

lattice parameters increase in a non-linear manner over the

whole range of temperature considered which is also impli

from the above analytical expressions. The non-linearity

with the increase of temperature is the manifestation of

the anharmonic contribution and the vacancy concentrati

It is, however, interesting to see that, linear thermal

expansion coefficient values decrease. with increasing

temperature. This suggests that although there is uni

cell expansion with the increase in temperature, the

of change of this expansion with the rate of change

temperature is not influenced accordingly. This

in a net decrease in the value of the expansion coeff

This behaviour can only be predicted f~Qm the nature

binding forces between the constituent

temperature variation of the Grl:l!De:is~ paJ•ameter,

which is a weighted average of th~ G~ef'sen nmram

of various lattice vibrational I~oetes.

of thermal expansion coefficient, vri th,

1 a' parameter is noted to be l~rg~,, 'c' parameter, showing that at()m$

loosely bou:ii,§ than those in i;h~: ·

the

1G8 REl<,ERENCES

1 •

2,

3.

4.

5.

6.

7.

B.

9.

9(a)

10.

11 •

12.

14.

Anderson, c.T. et al. (1950), u.s. Bur. Mines Rept. Invest. 4658.

ASTM standards (1974), Part-41,

Azaroff, L.V, and Buerger, M.J, (1958)~ "The Powder Method in X-ray Crystallography , Mc-Graw Hill Co., N.Y. .

Bansigir, K.G. and Iyengar, K.S. (1961), Acta Cryst., .1!!_, 727.

Barron, T.H.K. et al. (1964), Proc. Roy. Soc., A279, 62.

Eerron, T.H.K. and Munn, R.W. (1967), Phil. 15. 85.

Baudran, A. (1955), Bull. S.F.C., 27, 13. ' ---

Becle,. r;. et al. (1975), C,R, Hebd. Seances. Sci. ~1$60(3L, 44. .

Becle, c. et al. (1979), J .Less-Cemmon Metals, 66(1), 59. ,:!;!,;y; '. Betchleder, F.W. and Raenchlejc)~~.F. (1954), Acta Cryst., 7, 464. · · ·

Beu, K.E. ( 1967), "Hand BoGk of x.:..rays" Edi Kaelble, E .F., Mc-Gra\'f Hi=\.1 Co., N. Y, ,

Born, M. and Haung, K; (1954), "Dynamical. of Crystal Lattices", _(;!1arenden Press

Bowman, A.L. (1972); AIP'Conf· American Institute of

Bsenko, L. ~1979), 63(2), 171 •..

Burkhardt, W. and Schub z . lk • • 50' 442 • .

, ... ,....~ ..... ~.

•

17.

18.

19.

20.

21 •

22.

23.

24.

25.

Carti(r~ E, and Heinricb, F~ (1981), Phys. Lett.,· A. 81 7 • 393. I ? . . . . .

Cartz, L. ( 1955) , Proc ,:. Phys. :soc,, B68, 957·,

Cezairliyan, A, (1971), Rev: :S:cL Inst., 42, 540.

Clusener, G.R. (1972), kiP C'onf~ Proc. No. 3, American Institute of Physics 1 N .• Y, 51.

Cohen, M.U. (1935), Rev. SoL Instr., ,, 6, 68: (1936), 1· 155 •.. ··.· .·.

Connell, L.F. Jr. and ~~rtin,. H.C, Jr. (1951), · Acta Cryst., 4, 75. · · · ·

Corruccini, R.J, and Glkewick 1 J,J, (1961), J{, "Thermal Expansion of T. echnieal Solids at Low . ·• Temperatures", N.B.S. fljo;nograph, 29, 22. /

Culli ty, B.D. ( 1967), ·~Ete~~nts ('};!! .X-ray Diffract-ion", Addison-"Weisly P't;l.b. Co. Inc. Massachus ·

' ' '' -". "' -" _·, ', ' '

Deshpande, V.T. and Mu~;pl;~~~.·';V>M. (1960), Acta Cryst., 13, 483. · · >:{·.'· 1 • ..

26. Dugdale, J .s. and 1'1"''""-''"'"''"'"''"'

27.

28.

29.

31;

Rev., 98, 1751.

Dutta Gupta, J .K. and ·scl1ul:1er' z. Metallk., 64, 789. ..,":.

Dyson, J. ( 1970), "Int~t'f~o'in,&tty j.&_:~a · Tool", Hunt, Burnard t:rinti:Q:!l;, Ltd., · ..

" ', >~:; ' ",~ '!_ • ,,.

Ebert, H. (1967!:·~h~lr~~~~~~i1i!~ii Und Funktiohen aus Geophysik·und T Springer Verlag,

E~lifl!lzilw~ I'•· ·a-nd· .Acta Cryst., B28(5),

Fischnit.i:ste!r

49.

35.

36.

37.

38.

39.

40.

41.

42.

~4.

~5.

!j.6,

Hansen, M, (1936lj Der Au!bau der Zweistofflegieru­ngen, p. 969, Spr1nger-Veflag OHG, Berlin.

Hayes, E.T. et al. (1953), Trans. ASM, 45, 893.

Helser, W ,T. (1956), z. KristallQgr., .1.QZ, 155. i Hume Rothery, W. ( 1945), Pro~. Phy. Soc., (London) •l 57, 209. . '

Jacobs, s.F. et al. (1972), AIP Conf. Proc. No. 3y, American Institute of Physics, N.Y., 1. f$'

' Jenkins, F.A. and White, H.E. (1957), "li'undament~s of Optics 11

, Me Graw Hill, N.Y. , 637. '.:.•

Jette, E.R. and Foote, F. (1935), J. Chern. Phys.,l 3' 605. t~.

:•;,'_

Kirby, R.K. et al. (1972), American Institute of Physics Handbook (Ed. Gray, D,li.,), Me Graw Hill,· N.Y., 119. ./ ,,

Kirkpatrick, M.E. and Larsen, W .L. (1961), ASM,_24, 580.

Kirkpatrick, M.E. et al. (1962)' Acta Cryst., 15, 252.

Kirkpatrick, M.E. et al. (1962). Acta cryst. 1 5. 894.

Klemm, w. ( 1928)' z. Elekt.:· cl!l:em .• ,

•

47. Klug, P.H. and Alexender, L.ll!·. (1 Diffraction Procedures for. "n'~"''+~ Amorphous l"laterials", John

48; Kerst, W .L. (1962), J. Phys.

49. Kos, J,F. al!i.d Lamarche, 47' 2590. . ' .

50. (1959},

J. Phys.

.. ' Physics" ..

t ·•

' '.

199

53. Kubaschewski, o. and Goldbeck, K.V. (1976), -Zirconium, Atomic Energy Review, .{§1, 67.

54. Lawson, A.W. (1950), Phys. Rev., 78, 185.

55.

56.

57.

58.

59.

60.

61.

62.

64.

65.

66.

Libowitz, G.G. et al. (1958), J. Phys. Chem., 62, 76.

Litton, F.B. (1951), Iron Age, 167(15), 112.

Lonsdale, K. (1959), z. Kristallogr., 112, 188.

Lonsdale, K. (1968), "International Tables for X-ray Crystallography", Vol. III, Kynoch Press, England, 125.

Margenau, H. and Murphy, G.M. (1971), "The matics of Physics and Chemistry", Affiliated West Press Pvt. Ltd., New Delhi.

Merriam, M.F. et al. (1962), Phys. Rev., 125,

Mott. N.F. and Gurney,'R.W. {1940), 11

Process in Ionic Crystals", Clarendon Press, Oxford.

Nelson, J .B. and Riley, D.P~ (1945), Proc. Soc. (London), 57, 160.

,s ', ' Nevitt, M.V~ (1960), U •• Atmoic Energy ANL-6330, 164. •··. C;,," .

Nevitt, M. V., et al. ( 1961), Trat:l's. AIJI1E, 221' 1014.

Nevitt!.. M.V. (1963).~, "Electronic. Alloy L;hemistry of Transi · El . · Paul, A. Beck., P.P• 101-61

Papadakis, E .P. ( 1 -·i~-

67. · Panda, S.C. and ' .,. .... 64.' 793 .

e

71 •

72.

73.

74.

75.

76.

77.

78.

79.

80.

81.

82.

83.

200

PE-chin, W.H. et al. (1964), Trans. QCtly. Amer •. Soc. Met., .21• 464. ·

Pereira, F.N.D.D., Barnes, C,H• and Graham, G.M. (1970), J, App. Phys., 41, 5050.

Pereira, F.N.D.D. and Graham, G.M. (1972), AIP I Conf. Proc. No.- ;3, American Ihstitute of Physics, J N.Y., 65. . .

Plummer, W.A. (1974), AIP Conf. Proc. No.-17, American Inst. of Physics, N.Y., 129.

Pogodin, S.A. and Skorobogatova, V.I. (1954), Izv. Sektora Fiz. Khim. Analiza, Inst. Obshch. Neorgan. Khim. Akad. Nauk. SSSR, 25, 70.

Simons, R.o. and Balluffi, R.W. (1960), Phys. Rev., 117, 52.

Shelton, S.H. (1949), U.S. Atomic Energy Comrn., Publ. A .F'. - TR - 5932, ;,

Skinner, G.B. and Johnson, H.I. {1973), J. Ch' Phys • , 21 , 1383 • . fi:

. . <' .. Smith, E. and Gaurd, R.W. (1957), Trans. AIME 209, 1189.

Sparks, P.W. and Swenzson, C.A. (1967), 163' 779.

Spit, F.H.M., et al. l1980), J, Phys. 41 ( c-8), c8/890. Fourth International Liquid and Amorphous Metals, Grenoble,

Spit, F.H.!Vl •. et al. (1980), Scr •. 14(10), 1071.

1Sriniwasan,. R. and ~~;;~:~~.: 1 Progress in!i.Crystal . , Madr

84. Straumanis, M .E. ( 1 . -... ' - -·

( 1969)-~ ·'<.!

88, Sweeney, W,E, and Batt, A.P. (1964), J, Nucl. Mater,, .12.• 87,

89. Tannenbaum, I.R. et al, (1962), U.S. Atomic Energy Comm. NAA-SR-7132, 14.

201

90. Taylor, A. and Sinclair, H. (1945), Proc. Phys. Soc, (London), 57, 126,

91. Thompson, E,R. and Lemkey, F,D. (1969), Trans. Am. Soc. Metals, 62, 140,

92. 1'oloukian, Y.S. (Editor), (1975), 11 Thermo Physic Properties of Matter", TPRC Data Series, Vol. 1 Plenum Pub. Corp., N.Y.

93. Treco, R.M, (1953), J. Metals, 5, 344.

94. Ubbelohde, A,R, and Woodward, I. (1946), Proc. Roy. Soc., A 185, 448. ·

95. Vander Heyden, D. (1951), J, App. Phys., 22,

96. White, G.K. (1961), Cryog~;nics, .1• 151.

97. Wooster, W .A, (1949), 11A Text B0ok of Crystal Physics 11

, Cambridge Uni v, Preso11 ~ . ·

APPENDIX

List of Published Work of the Author

1. X-ray Studies of Phase Transitions in Ni-Zr Alloys,

XI National Conference on Crystallography, -~adavpur, Calcutta (17-19 January 1980), c4-4

2, Crystal Structure of Two New Intermetallic Compounds: Pt-Zr System,

XII National Conference on Crystallography, Hyderabad (25-28 Pebruary 1981), 8.

3. New Intermetallic Phases in Ni-Zr System.

XIII National Seminar on Crystallography, Nagpur (15-18 March 1982), 169.

4. Structure of the Ni11 zr9 Phase and its Thermal Expansion-Coefficient.

(accepted for publication in Acta Cryst. B).

5. Thermal-Expansion-Coefficient of Ni3Zr PhasE

(Communi __ ..__,.,,

6. Studies on Ni-Sn-In Binary Systems. . . i,

",;~ ;,­

and Ni-Sn""'Sb Quas