The crystal structure of nizn3.r

Journal of the Less-Common Metals, 75 (1980) 51 - 63 @ Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands

THE CRYSTAL STRU~RE

51

OF NiZns.r

G. NOVER and K. SCHUBERT Max-Pianck-Znstitut fiir Metallforschung, 75, 7000 Stuttgart-i {F.R.G.)

Znstitut fiir Werkstoffwissenschaften,

(Received November 30,1979)

Summary The phase NiZna.r has an o~hor~ombic end-centred cell with the content 2(34Ni+104Zn) and iattice constants u1 = 33.326 A, rr2= 8.869 f\ andas = 12.499 A; the structure is closely related to the y-brass type. In contrast with the W-type substructure, there are 12 unoccupied sites in the cell and the atoms surrounding these are displaced towards the vacancy, causing further d~p~ernen~ of atoms that are not adjacent to a vacancy. The structure obeys the quasi-linear dependence of occupancy on vaIence electron concentration first found by Bradley in NiAI. This phenomenon may be interpreted by the two-correlations model which also gives arguments for the different deformation homeotypes and the extra vacancy formation at high valence electron concentrations.

1. Introduction In the brass-like phase NiAl a partial occupancy of the nickel positions that is qu~i-l~e~ly dependent on NdA - 1.5 has been observed for valence electron concentrations iVdA> 1.5 [l] . A similar morphotropy is known for the structural family of anion packings [ 2] where the anion (e.g. S2- in ZnS.r and Ga2S,) is in a close-packed array and the insertion of the cation into the array corresponds to completion of the anion octet. A unified explanation of both phenomena has been given by the two-correlations model [3]. Because of interaction, when the condensation of unoccupied sites in a brass-like phase is great enough, these sites become ordered, e.g. in CuciZn,, N&AI, and NisGad. The ordered distribution of vacancies in these structures gives information about the binding, since the binding causes differences in the energy of vacancy formation at different positions. From this point of view the study of low symmetry variants of the Cu,Zn, type was of interest to us. Cr,Al,.r is such a variant with a rhombohedr~y distorted C&Zn,-type structure and (Y< 90” for the quasi-cubic cell [4,5]. The typically brass-like Cu,Hgs [6] has been found to be of a very similar type with cr > 90”. Orthorhombically or monoclinically distorted variants of the Cu,Zn, struc-

52

ture at the valenceelectron-poor side of the y phases have been frequently observed (see, for example, refs. 7 and 8) and have recently been studied by electron diffraction [ 9 - 111; nevertheless, a structure analysis is still desirable. We therefore decided to investigate the structure of an orthorhombic variant of the CusZns type. The phase NiZns.r [12,13] was chosen because of the zero valence electron contribution of nickel, which facilitates partial occupancy (see Section 3). Many homologous isotypes exist, since it is well known that the valence electron concentration NJ* of some structures is invariant under change of the alloy system in brass-like alloys; they will be studied later. Several previous observations suggest that the structure of NiZns.r is related to a vacancy array. For the neighbouring cubic phase, which is homeotypic with CusZns and ranges from NizoZnso to Ni1sZns4, a linear increase of lattice constant Iail (i represents the vector indices, mostly dropped) depending on the zinc mole fraction NL$ is observed around the composition Ni,Znzl * Nils.sZnsss [8] (corresponding to the Westgren-Hume-Rothery rule [ 141 for the valence electron concentration N&* = 21/13). This increase is evidently caused by the greater atomic volume of zinc compared with that of nickel. However, at NY,, > 0.82 a non-linear decrease of the lattice constant has been detected by Schramm [ 121 and others [13] so that a maximum occurs at NLi = 0.84 [ 121 or 0.83 [ 131. Since NisZnP1 is a phase with Bradley partial occupancy [ 21 the vacancy concentration is expected to increase with increasing valence electron concentration; this does in fact occur [2,14,15]. Therefore the decrease of lal in the phase NiBZnzl must be caused by more than 2.9 vacancies in the cell of the NilsZnsa alloy [13] (extra vacancies; see Section 3). The lattice constant maximum within the mole fraction range of Ni,Znal indicates that the binding in the Cu,Zns structure is outstandingly good. There are even mixtures known in which a Cu,Zns structure, but no CuZn structure (CsCl type), is stable, e.g. NiCdM, CuHg, and FeZn, (M = undetermined mole number); this fact confirms the interpretation given later. The structure of Ni5Znzl has been worked out by Johansson et al. [13] (lying slightly off the for the composition NizZnll = NisZn& = Nia 154Zn0.&p6 homogeneous range) since the composition NisZn,, does not correspond to a structure with complete ordering of the components at the available sites. The fact that the isotypes or homeotypes of NiZns.r occur (like NiZns.r itself) at the valence-electron-poor side of the y phase indicates that the structure is caused by a smaller number N/N’ of unoccupied sites per atom site compared with the number valid for the cubic y phase. For Cu,Zns Ng = 2/54 = 0.037 but for NilsZn s2 [13] NAP= 3/54 = 0.055 and for NisCd, even N$ = 0.111 [ 161. Therefore the number of vacancies is not only a function of the valence electron concentration. An analogous phenomenon has been interpreted in the case of Pd,Pbs and PdisPbs [17] ; a similar explanation might be appropriate here. In any case it will be advisable to start from NE = 0.055 (for NiU,Znsz) and NE = 0 (for NiZn.h) and to expect Nf = 0.04 for NiZns. The planes with the smallest separations between

53

with vacancies are ( llO)Nis&,,* If sets of atomic layers parallel to (llO)ni+,, different vacancy contents alternate with sets containing vacancies corresponding to the CuSZns structure, a superstructure is produced with a long axis al perpendicular to (llO)ni,zn,,; the long axis increases if the mole fraction NLfi approximates the value of the cubic y phase, Since lull is expected to be proportional to l/(0.055 - NAP), it should tend to infinity as IV& approaches the y range. Both expectations have been shown to be true by Morton in ref. 11 (p, 211). For brevity, in what follows the phases of the mixture NiZnM will be referred to according to their systematic designation [ 2] : Ni2n.h = C, NiZn.r = T, NiZns.r 3 Q, NisZnU = B, NisZnpz = N.

2. Results The alloys prepared by the amp&a method with heat treatment (12 h at 700 “C, 5 min at 950 “C, 4 d at 425 “C, water quenched) are represented in Fig. 1; the results of thermal analyses modifying some assertions of Schramm [ 123 are also noted. Instead of one transformation, two are found, a frequent occurrence in displacive transformations which split into different partial tr~~o~ations, Double effects have also been found [ 181 for compositions of approximately CugZns, Cu,Cd,, Ag,Zns and Ag,Cd,. High temperature powder photographs (Fig. 1) confirmed that the cell is also orthorhombic at temperatures above the transformation. This result corroborates a finding in the mixture PdZnM [19] in which the deformed 7 variant crystallizes from the liquid. It is also supported by powder photographs of quenched powders, which were all transformed after the usual quenching procedure. Polished sections confirmed the data in Fig. 1; the formation of martensite in Q was visible with a polarizing microscope; it corresponds to the tr~sfo~ations of Fig. 1. The Q translation group, ie. the indexing, allowed the determination of the lattice constant iall for the composition near NiZns from powder photographs, but the longlattice constant lail can also be determined independently of the index h for all compositions by measuring the 13angles of the dumb-bell reflections (640~&(540), (1~,2,0)&(10,2,0) in the Guinier photo~aphs (see Table 3). They give (with Ihi = 2 sinB/X) the equation IU~I =

simos-‘(k/ IU~llhJ) l&l -

lhzl

where h, is the reciprocal lattice vector of the nth dumb-bell reflection and k is the second Miller index of h,. From Ial I the number of layers parallel to (a,&az)o per cell can be derived. The results of Fig. 2 and Table 1 are in fair agreement with the results of Morton [9 - 111, It must be admitted that Morton’s measurement was more direct (although his concentration measurement may be more uncertain) but it is possible that the intensities of the Guinier lines are fairly dependent on composition so that in the powder

mole

fraction Zn/%

mole

traction N&/T4

Fig. 1. Part of the phase diagram for NiZnM. Fig. 2. The dependence of the long period of NiZn, on composition.

photographs the correspondence of one line with a zdumb-bell becomes more uncertain as the zinc mole fraction in the alloy increases. For the composition N&,Zn,s a 164ayer structure can be assumed with Ndc = 288 atom sites per centred cell. The insolation of the number A$’ of un~cupied sites per atom site between the C phase (A$’ = 0) and the B phase at NilsZnsz (A?&’= ” = 12 unoccupied sites per cell. The heat treatment and 0.055) leads to NN composition of the single crystal are noted in Table 2. An analysis of the (~,O,O)~ densities gave a d~t~bution of eight vacancies along the (a1 )o axis. The space group C:“, Ac2m allows a structure model which could be refined by alternate Fourier sections and least-squares refinements. Table 2 shows the unusually high proportion of 1 < 241) reflections resulting from the superstructure. The distribution of the nickel over the sites is not very reliable because of the similarity of the electron numbers of the components; it will be confirmed later by analysis of isotypic structures. In Table 3 the evaluation of a powder photograph which also showed many I < 241) reflections is reported. A drawing of the structure is shown in Fig. 3 which displays all the coordination details. It can be seen that a shear vector [ 21 (displacement vector) with a component; in the shear plane R = [ OlO]n/3 is contained in the structure and that R alternates with -R. Together with the shearing, a cluster layer parallel to (al&aa)o is also inverted, in agreement with Morton’s

55 TABLE 1 The long period of NiZnB as a function

Ni25Zn75 Ni24Zn76 Ni23Zn77 Ni22Zn78 NizlZn7g Ni2oZngg

71.727 71.561 71.432 71.322 71.146 70.969

67.390 67.431 67.493 67.605 67.781 68.027

of composition

33.6251 36.94*2 38.6922 40.98* 2 45.22+4 51.64rt4

87.862 87.709 87.564 87.410 87.268 87.127

85.840 85,819 85.807 85,787 85,792 85.801

Heat treatment: cast, 1 d at 950 “C, water quenched;regulus, quenched; powder, 6 d at 4 70 “C!,water quenched.

33.50 rl 36.88+3 39,26+3 42.02+3 45.72 k4 50.34 +4

6 d at 470 “C, water

findings. However, the layers between the B layers mean that NiZn, is not a shear structure ; its structure is more complex.

3, Discussion The structure of Qz like that of B, is a supersede of the W type. The commen~rab~i~ is aw(8,0,-3;0,3,0;8,0,3) and since a3 = a&3), the non-integer commensurability found; it follows that ho = (8/3,0,8/3;0,‘1,0;-l,O,l)h, where h are the Miller indices in a vertical array. Considering the strong superstructure line hB = (2,2,2), the morphotropy with Q results in the strong superstructure doublet h, = (10.66,2,0) = (l&2,0) and h, = (0,2,4). It must be concluded from this that the split of these lines is not the result of substructure strain alone but mainly the result of the a~p~x~ation 10.6 * 11. The line may therefore be called a moving line, ie. its position 8(11,2,0) > 0(0,2,4) depends strongly on the composition of the alloy, whereas for (0,2,4) this is not the case. The strong dependence of the split of these lines in the range of Q on composition shows that Q is composed of different superstructures with different al axes, as is usual with shear structures [2] . The designation of a layer parallel to or f, depending on whether it conta&s a vacancy pair or not, results in the stacking symbol (fvffvf) in the fllO)B direction for B, the true y-brass structure. Frum this we might expect 2(fvffffvf) for Q; however, since NisZneL contained statistically distributed vacancies we found 2(fvff ‘f’fvf) where f ‘f r together contain a vacancy pair. The stability of the layer set (fvffvf) is explained by the binding. The decisive role of vacancies also explains why the shear density can be temperature dependent [ 9 J ; the composition is not dependent on temperature as long as the alloys contain only one phase but the vacancy eoncentration always depends on temperature. The binding in phases of the & and r-brass types has been fuund for the example AuCd.r [26] as aAUaz = (H&IO5;5.‘797) z&= b&2;2;7/3) = cau(4;4;14/3). Here a, b and c are the cells of the crystal, of the valence electron aQ

=

aQ

=

asls/3,0,-1;0,1,0;8f3,0,1)

be

(11,2,0)Q

(a&a3)Q

as

v

Cm

56

correlation (VC) and of the core electron correlation (CC) (B indicates the b.c.c. lattice and H the hexagonal aspect [21] ). This binding has been found using the methods described in refs. 2,3 and 21. The excellent commensurability makes the assumption of the binding very reasonable. This binding must be considered as the fundamental property of all homeotypes of the Cu5Zne family; it should explain and interrelate all the structural features found in the family, and it does. The binding has the favourable factorial property ba = ca(2) and may therefore be called a BB2 binding. Since TABLE 2 Structure and single-crystal data for NiZn3.r Experiment:

Structure :

Caiculation:

Ni25Zn75 (granulated, 2 min at 880 C, cooled in 3 h to 770 “C, 1 d at 770 “C, cooled in 4 h to 470 “C, 5 d at 470 “C, cooled in 6 h to 380 “C, 7 d at 380 “C, cooled in 6 h to 200 “C, air quenched); crystal size, 0.06 mm X 0.03 mm; diffractometer measurement with MO Ka radiation up to 28 = 55” with a 1” scan width of 2428 F(kk1) in the w scan, resulting in 1678 independent F(hkl); refiections with Z < 20(Z) are. marked with an asterisk and were omitted from the R calculation but included in the refinement (I = net count, u = standard deviation). NiZna(Q34.104) AcZm, al = 33.326(8) & a2 = 8869(l) A, 03 = 12.499( 4) A, x1, x2, x3, 1oou = Zn.O263(3).518(3).0718(1)0.9(2) Ni.2846(3),194(3).0752(9)0.8(3) Zn.0416(3).219(3).0689(8)1.1(2) Ni .2812(5).372(4).25 0.6( 3) Ni.O307(4).350(3).25 Zn.336~3).702(3).0734~8~1.0(2) 0.7(3) Zn.O9~4(3).984(3).0627(8)1.1(2) Zn.3524(3).011( 3).0716~8)0.%( 2) Ni.3448(5).861(2).25 Zn.O944(3).410(3).1383(8)0.8(3) 0.6( 3) Zn.0957(4).157(3).25 Ni.4053(2).524(3).0730(9)0.5(4) 0.9( 2) Zn.4059(2).806(3).1378(8)1.0(2) Zn.1465(3).209(3).0723(8)1.0(2) Ni .4065(5).339(4).25 0.7(3) Zn.l635(2).515(3).0716(‘7)0,8(3) Zn.4603(3).002(3).0690(8)1.2(2) Zn.1730(4).076(3).25 0.9( 2) Zn.4703(3).390(3).1288(8)1.0(2) Zn.2175(3).312(3).1328(8)1.2(2) Zn.4786(4).151(3).25 1.1(2) Zn.2132(4).560(3).25 1.2( 2) Zn.2490(5).108(4~.25 Zn.2828~3).%04(3~.1339(8)0.9(2~ l*l( 2) Zn.2867(4).657(3).25 O.S( 2) Zn.O290(3).829(3~.3731(8)1.3(2) Zn.3435(3).369(4).1250(8~1.2(2) Zn.O198(4).068(3).25 1.3( 2) Zn.0569(4).621(3).25 Zn.3278(4).142(4).25 l.O( 2) 0.9( 2) Ni.0950(3).692(3).0762(9)0.8(3) Zn.3650(4).585(4).25 O.S( 2) Zn.4094(3).236(3).0620(9)1.4(2) Ni .0937(4).872(4).25 0.6( 3) Zn.1351(4).632(3).25 Zn.4047(4).058(4).25 O.S( 2) 0.9( 2) 1.0(2) Zn.1578(3).849(3).3758(8)1.2(2) Zn.4420(4).595(4).25 Ni .1572(5).355(3).25 Zn.4738(3).698(3).0738(8)1.0(2) 0.7(3) O&(4) Ni.2160(2).022(3).0724(8)0.6t3) Ni .4683(4).868(3).25 Zn.2270(2).729(3).0645(8)1.2~2) Ni .2190(5).844(4).25 O.%(2) Zn.2748(3).491(3).0650(8)1.2(2) X-Ray 72, /.tR = 0.6 - 1.2, absorption correction with $ scan program; R = 21 IF01- lFCl I/~lF,,I = 0.083 with isotropic temperature coefficients, R = 0.073 with anisotropic temperature coefficients, R = 0.489 for Z < 20(Z). Headings in the F table, h, F,, IFeI. (continued on facing page)

57 TABLE

2 (continued)

(continued overleaf)

58 TABLE 2 (continued)

i i. i IO

4,

::

e ‘: . 2a

,I

4”

8.

I

0 0 0 0 0 0 oo0 0 0 0 0 0 0 0 0 0 I 1 0 0 OO5 E 0 0 0 2 0 0 0 0 Z 0 c 9 b 9 0 0 0 0 ObSI 2P$I SE21 5191 EC91 226I LI6 CBS 1% WIZ bbOI FI61 0031 92Ii ESb 2002 LIE b291 CSt SETI 9JEI

P b 8197 0 0 0 0 0 0 0 0 0 0 0 0 ” 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 " 0 0 0 0 0 0 0 0 . ” Zb91

8131 0291 0291 CLBf b291 w.91 5291 OEQI IE91 2E9I x91 bC91 rt91 ewr 8b91 8f91 9591 6S91 1991 2991 9991 9991 0191 Of91 SL91 9191 LL9I 0891 1891 6891 1691 :;;;

IS8 ZPCI KLI OTPI 1102 CS2 bb6 ESI 0261 ES0 SlSi EESi 9EOI LIL ISL 228T 9EOI bb8 PIILl ElBI 0002 9021 LI9 Lb21 IS9 bZSI mtr 326 ISI 2061 bbL ;;;I

0 0 i

0

EEbI SE6 155 1161

0 0 0 2 0 b69T L6QI 8691 sot7

I

”

_ SOII

0 0 2 0 0 0

‘02~08

0 6011 iIL1 ; I iiiI ;: 8fLI 6T1I I OLLI OZLI 0 OELI 0 c211 1 6ZLI 62LI 0 ECLI CELI II B il SUI SELI 0 SELI bCL1 ; : lb11 0 lb11 2 bbii SbLI Lb11 ; 1 8blI 0 ISiI ;: CSfI bSL1 0 bSL1 6I IELi bSLI

0281 fib 9011 928 ISb !a9 Zbl.1 22LI I1C ODZI b09, 1% 5C8 Elf1 LIZ bZbI bbS 1% III LIO 921 IS, 0061 SIC1

!I 9SLI 9"::: EE, 0 8511 IEEl I 9911 4911 9001 0 19Ll PBb I O1LT OLLI 2bOI 0 2LlI S&L ; : SLLI 2081 WI bfE 0 S8LT 929 LI OPLT 68LI Obll C6LI OZLi I $611 II81 ;

~%I)

‘“I

‘4

-

‘(VI

yead

0 0 8611 bb?. cc SC 5081 SO81 2291 0 0 OO%;I ',:: OI II 6081 808I DbO 0 0 6081 b2EI 0 0 _ 1181 OOSI 91 LI bI81 D'I8I 92s 0 0 9181 906 0 0 618I Sl2I OO02x1 2% oo1281 EEZi CZ81 EI91 PF81 It*1 SEEI SE5 SE81 9T.b 9b81 ObOI IS"I 0081

ooIO OOoo* 0 OO-

‘(~PP,OI

ii

i

:

-

0 02 ST61 0 0 0 2 CS6I 0 956, ;: 0 0 c 9161 0 _ 0 986I 0 0 5667 : 0 0 F PI"2 [I lZD2 0 :, 0 E 9202 : 6902 0 E; 0 0 _ 0 0 00 1001 S802 00 1001 B CO 1001 be02 0 0 *

oo-

0

0010019802 O"inOlO6*2 0 0 0 0 0 0

0

-

1922

-

-

-

no1ouI~oIz 51 IL 8112 oo0 n

oo-

0 0 0 0 0 0 a 0 0 0 0 II oo0 0 0 0 0 0 0 0 0 II 0 0 0 0 OO? 0 I 1 0 0 0 0 0 0 0 0 0 0

0 00 I1 82 2X2

‘f@u!pv

ue se uoqs

‘(fvf~

9802 LROZ 06OZ 1602 E60Z 1602 to12 WlZ 0212 b2IZ Fbil ibI2 ISiZ bLi2 SLIZ 8iIE 8112 8612 cozz 8022 Ll22 2122 LIE2 6122 2222 SZ22 9c2z IS22 1922 E912 L92Z 2L22 ;a;

IEII 6F8 ZbO 22El 2051 OZb1 bZ6 OCS FICI IISI ObP SI‘ E&L Obi boll b28 If01 Ob2 2221 (119 cc9 OQI OPO OZEI OOSI 2Obl El21 PZL IlbI SIS EES IE6 :;;I ;;:; ::9" ZZtZ 2ZIi

0 0 bI 9

0

0 0 02 II

I 0 2

0

: : 0 0 0 0 0 0. Ll 91 "0 I I 0 0 0 0 0 0 0 0 PS 65 0 0 0 0 0 0 89 89 0 0 0 0 0 0 0 0 0 0 0 0 I 0 I

cccz ?SEZ iic t‘s12OZZI 9SE2 EEC Z9EZ Cl11 LQCZ TE8 2x2 2OFI 08EZ OObl I8FZ ST2

49EZ -

‘E T L = M

:,,2 z ES . 88t2 PO6 ^ cab2 Sil sot2 EEi 9002 SIO IIb2 CEO 61P2 9lb2 IIC, Zbb, b7b OSbZ 1s*2 2201 29bZ IEL 68tG WC Em EiOl _ OOSZ 008 205Z 1052 0211 SZSZ b22 PC52 202I LbS2 bZ1 tQ42 bSS2 020 SES2 TCQ ‘~952 ONI ‘852 226 E652 II2T 2192 bOL Zb92 [ES lb92 EI6 (932 bQ92 0201 02L2 IEb 92i.Z EZLZ to9

‘1 T g = MA

bOS ICZ 026 ITI 1co 2ZL boP 2001 t11 VOC 1101 OOIT 229

PO2 CO1 El9 bO0 225 206 021 E15 116 27.b 0001 EIP 22E 029 208 222 EIL

= tu

9EOE ILOE ITIE OLIC SZIE 6LIC 981s Sb2E 28ZC Q62C 8iCI CCEE 9EbE 6CbE 99bE 99bE PCSC IL%

‘c; T 91

yderfdo?oyd

. I”,flfYIdH ,-+_OIx LL’O = “I = 8 D ‘y (8)gzc’EE = h ‘GIZ~N

IJ~!M

c c

”

0 2 2

0

n

0 0

oo-

0 0

0

0

0 0

oo-

0

0

0 0

k 0 0 0 0 -

0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 II ii oo-

z 0 0 0 0 0 0 0

96SE 2ZI 219t 019t I18 EI9C 119E 220 8L9C Cl2 269C 025 COLE "06 LVLE El1 ILLE EIO LilLE EOL 516C 02t LLbE iIL

-

2;: ;;: 991b 008

E ",",i; * SObb II9 Ibbf :::", ;z !9Lb OOL -

-

sss

SE; k4 6941 111 rc21 Ii0 Iwa 0000 6011100c E9991002 9ZEsCoO!

SLO9 2909 IIE co19 201 GSZQ ZOO

?2g _ i -

: axqanqS

:uownv3

:?uaur!mdxg

3TiVb

.I03 l?lep UO!$XS33!p SapMOd

‘sn@Ja~ tpayauanb JaleM ‘pm) %IZ’%N

pue uoye!pt?.t x)x n3

u~wY3

ayl s! 4 ! 1 F 1 = MM

6061 901 6061 SE0 8161 Zbi ,161 ICC1 bi6I FISI IS61 909 IS61 SlOi ES61 bZ11 ES61 EEO, 9S61 ZP9 156I Ob8 0961 OOLI 9L.51 ZOQI 2861 bOEI 9tl61 OZS1 8861 2ZQI 8861 905 0661 Zb(1 8661 IEZI 2002 1IQ1 OIDE cm( ET02 ?I*1 8I"Z 516 ~ZCIL CC6 iZO2 9Ob IZOZ 2bb L202 b2OI mo2 9DE bSOT EbC 6502 ObY PLO2 2b2 9LOZ bO2I 6102 901 E80L 0091 1802 900 P802 SI8 9FOZ 201

papunor V,OT

[eura~u!

.Ia$eM ‘3, ()~p !)a p 9

pxepue?s fpaymanb

pm

*z a[qeJ; aas saleu!prooa ~03 :y (f7)ijfjfi’z~ = Et2‘y (5)fjgtyg

= WfJ ‘“I

*(ura$led uo!$sey3!p lapmod e 30 $qi$aq = P

ra$aEn ‘3, OLp la p gz ‘JapMod

‘b$!suar+u! f03 umr%oqaer33!p naptiod “( paqmanb

‘OZ~OP

6951 OL51 t141 SLSI YLSI 8151 WI SIG1 L8SI LESI LBSI 6851 0651 0651 F6SI IWI 1091 2091 0191 0191 b191 S191 4191 t191

b19I P SI91 -

.ta!u!nf)

kZ!N

E

60 Ni

82n.042.219.069

SZn.091.984.063 4tn.147.209.072 8Ni.216.022.072 BNi.285.195.075 8X11.352.011.072 8Ln.409.?36.062 ~2~.46~.~2.~9

82n.029.829.373 ~Ni.O95.692.~76 m.158.849.376 ah227.729.065 azn.283.905.134 am.337.703.073 8~~.4~6.8a?.~33 62~.4?4.6~9~~?4

Z,n

-a2

4fn.020.069.25 411.031.350.2542n.057.621.25 4Zn.096.158.25 4N1.094,873.25 42n.173.077.254Ni.157.356.25 4Zn.249.109.2542n.213.561.254Ni.219.844.25 4fn.328,142.25 4zn"405*059.26 4Zn.4f3.152.25

4Ni.281.373.25 42n.365.586.25 4Ni.406.339.25 42m.442.596.25

4zn.287.657.25 4tii.345.861.25 4N~.46~.869,25

aAuCder has a W subst~ctu~* an ideal axial ratio iasl/lql =: l/42 =L0.707 is expected for the sup~s~ctu~; the observed value of 0.715 is greater.This can be explained by the fact that the axial ratio 7+/3/l&/2 = 0,514 for undistorted b~d~g produces a small strainin the CE~ direction which is further increasedby the row shear 133. This smah straincauses the differences in the crangle of rhombohedrally deformed homeotypes of Cu5Zns. The BB2 binding also explainsthe Bradley partialoccupancy as follows: the factorial property of the binding is energetic~y so favoumbie that it is conserved during increase in N/e by the dropping out of atoms with smallvalence electron contribution; thisdoes nut markedlyinfluencethe CC sincethe core electronsarequasi-elastically bound to the atom, and the in~ueuc~on the VC is minor because of the smallervalence electron ~on~but~on. The simplestcase is found when the atom that drops out haidi a valence electron contribution of zero [l] but vacanciesmay also occur when this is not the case [22], Since the binding

61

introduces a stress which is periodic in the lattice, an ordered distribution of vacancies will be preferred which relieves the stress, i.e. which causes a further decrease in energy. Figure 4 shows that the BB2 binding with the commensurability of AuCd.r just favours the CuBZns structure if the binding is twinned in such a manner that its unique axis points statistically in ah four [ lll]z directions of the CusZns cell. If the unique axis of the binding, as a result of the particular commensurability to the crystal, points statistically in only three [ 11 l] a directions a rhombohedral cell with Q > 90” is expected, as found in Cu,Hgs [6]. (In this phase the anomalous valence electron contribution of 2.2 for mercury parallels the contribution from gold of 1.15 [ 21.) If the unique axis of the BB2 binding points in only two [lll]z directions of the CusZns cell, a monoclinic [9] or orthorhombic cell should be stabilized, as found in NiZn+r. The monoclinic or orthorhombic symmetry depends on the sequence of R and -R shears. The detwinning of the binding of CuSZn, is promoted by the lack of vacancies caused by the less than ideal N&* in NisZn.r. Since the tri-BB2 binding of Cu,Hgs is intermediate between the di-BB2 binding of NiZna.r and the tetra-BB2 binding of Cu5Zns, it is possible that it corresponds also to the triangular domain structure detected by Morton [ 9 - 1 l] According to Morton [lo] ,_in the triangular domain strucin Cu41.9Zn68.1. ture the shear planes are (112)x and R = [110],/3, i.e. normal to (112), and this is compatible with the assumption of a decrease in the vacancy density compared with that of CusZns, i.e. it is compatible with the fihing of vacancies by atoms. Finally it is conceivable that the unique axis of the BB2 binding points in only one direction. This case is evidently realized in Cu,,,Sns.m [ 23,241, which has NN ” = 1 unoccupied site per ceII and also displays row shear [ 31. From the morphotropic commensurability u~,,-~, = (H7.33;7.87) A = a,.n(l,l,O;-1,2,0;0,0,3), where aw.n is the W ceII in the hexagonal aspect,

Fig. 4. The relation between the CugZnS, AuCd.r and Cu&ns.m structures. Vacant sites ( q) in the ‘y-brass structure () and the basal plane of the AuCd.r structure (-) are related; vacant sites of CqOSn3.m (0) are also related to the basal plane of the AuCd.r structure. It should be noted that the AuCd.r submeshes are drawn.

62

it follows that the ideal axial ratio la,l/la,l is 1.061 but the observed ratio is 1.074. The binding acu,,sn, = bBH(2;2;10.6/3)_=‘cBn(4;4;21/3) gives I~al~lall= 1.072 for an ideal geometry. It can be conclude that a BB2 binding dominates in Cu,,Sns.m. It must be admitted that from the composition CuloSns the number A$’ of valence electrons per cell should be 44 while the number N$” of valence electron sites per ceII should be 42; in fact the homogeneous alloy was ~78.2Sn21.s 1231, giving NV” = 43. Since the number of statisticaIIy distributed vacancies is not known the fit of the numbers must be considered as satisfactory. An example of untwinned BB2 binding without vacancies is Ag,Zn.r (H6.3,SR15.120) with the morphotropic relation a = (H7.6362.820) A = CIW,~( l,l,O;-1,2,0;0,0,1) giving an ideal ratio l~sl/lu~l of 0.354 and an observed ratio lasl/ Ial I of 0.369, whereas the binding a = &,,(2;2;3.5/3) = can(4;4;7/3) gives lasl/ Iall = 0.357. It can be seen that the row shear produced by the binding causes additional anisotropy, which interacts with the binding. A structure analysis of Pd,ZnsGa, [ 251 has shown that superstructures other than AgsZn.r are a.Isopossible. A satisfactory BB2 binding for Pd,ZnsGad has since been found [ 26). Does the f’f’ content of the structure decrease with increasing Nr, while NC increases? Evidently there is a further (more or less statistical) po~ib~ity of locating vacancies in Ni2Znu, This problem wiII be further studied in the future. How is the strong additional (extra) vacancy formation in NisCdm [16 3 to be understood? The phase NisCda = NiCds with A$* = 1.67 is in thermodynamic equilibrium with NizCds showing the low value NC* = 1.43. A CsCl structure is impossible for Ni&!ds because of its composition but a BB2 binding remains possible. To check this we can consider the hexagonal ceII of NizCds(SR19.80) (an = (H13.683;8.379) A) which presumably has Nhc = 111 valence electrons and 780 core electrons. This yields oH = c&6,1,0; ‘9 = 107 if BB2 binding is proposed. The -1,7,020/3) giving A$9 = 860 and iVp commensurability is a neighbouring commensurability [3] of the usuaI an = b&2,2,0;-2,4,0;10.3/3) = canK’(2) givingNd9 = 123 and A$$= 960. Since at the composition NiCds the normal y structure requires A$’ = 78 X 1.67 = 131, approximately four cadmium atoms must faI.Iout of the structure. Therefore if the composition of the y structure is shifted to NiCds, cadmium atoms must fall out of the cell. Probably this also explains the lattice constant anomaly of NifiZnzl. Problems of atomic positions in y brasses have been considered by Pearson et al. 1271 and wiII not be discussed here. A band model ~~~~tation has been successful only in some of the phenomena [ 281 whereas the two-correlations model immediately proposes the occurrence of phases with mono-, di-, tri- and t&a-BB2 binding. The anomaIous diamagnetism 1291 of the B phase must be connected with the fact that the alloys of the zinc-rich part of the B phase are at the valenceelectron-rich end of the BB2 binding.

63

Acknowledgments This work was supported by Professor H. G. von Schnering and Dr. K. Peters with diffractometer measurements, by the Deutsche Forschungsgemeinschaft with financial aid and by Frau A. Komau and Herr W. Furmanski with technical help. We wish to express our thanks for this assistance. References 1 2 3 4 5 6 7 8 9 10 11 12 13

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

A. J. Bradley and A. Taylor, Proc. R. Sot. London, Ser. A, 159 (1937) 56 - 72. K. Schubert, KristaJJstrukturen Zweikomponentiger Phasen, Springer, Berlin, 1964. K. Schubert, Struct. Bonding (Berlin), 33 (1977) 139 - 177. A. J. Bradley and S. S. Lu, J. Inst. Met., 60 (1937) 319 - 337. J. J. Brandon, W. B. Pearson, P. W. Riley, C. Chieh and R. Stokhuysen, Acta CrystaJJogr., Sect. B, 33 (1977) 1088 - 1095 (SR43.8). T. Lindahl and S. Westman,Acta Chem. Stand., 23 (1969) 1181 - 1190 (SR34.77). A. Westgren and G. PhragmBn, PhiJos. Mug., 50 (1925) 311 - 341; Trans. AZME, 93 (1931)20-21. W. Ekman, 2. Phys. Chem., Abt. B, 12 (1931) 57 - 78. A. J. Morton, Phys. Status SoJidi A, 23 (1974) 275 - 289. A. J. Morton, Phys. Status SoJidi A, 31 (1975) 661 - 674. A. J. Morton, Phys. Status SoJidi A, 44 (1977) 205 - 214. J. Schramm, 2. MetaJJkd., 30 (1938) 122 - 130. A. Johansson, H. Ljung and S. Westman, Acta Chem. Stand., 22 (1968) 2743 - 2753 (SR33.108). W. Hume-Rothery, J. 0. Betterton and J. Reinolds, J. Inst. Met., 80 (1951) 609 - 616. A. Westgren and G. PhragmBn, Metallwirtsch., Metallwiss., MetaJJtech., 7 (1928) 700 703. K. Schubert, 2. MetaJJkd., 39 (1948) 88 - 96. H. Ljung and S. Westman, Acta Chem. Stand., 24 (1970) 611- 617. H. W. Mayer and K. Schubert, J. Less-Common Met., 71 (2) (1980) P29 - P38. F. Wallbrecht, F. Balk, R. Blachnik and K. C. Mills, Ser. Metoll., IO (1976) 579 - 584. H. Nowotny, E. Bauer and A. Stempfl, Monntsh. Chem., 82 (1951) 1086 - 1093. K. M. Alasafi and K. Schubert, J. Less-Common Met., 55 (1977) 1 - 8. K. Schubert, J. Less-Common Met., 70 (2) (1980) 167. M. S. Wechsler, Acta Metall., 5 (1957) 150 - 158. J. Lenz and K. Schubert, Monatsh. Chem., 102 (1971) 1689 - 1698 (SR39.54). J. K. Brandon, W. B. Pearson and D. J. N. Tozer, Acta Crystallogr., Sect. B, 31 (1975) 774 - 779 (SR41.62). A. V. Subrahmanyam and K. Schubert, J. Less-Common Met., 32 (1973) 199 - 206. M. Publj and K. Schubert, J. Less-Common Met., 41 (1975) 33 - 44. W. B. Pearson, J. K. Brandon and R. Y. Brizard, 2. KristaJJogr., 143 (1976) 387 - 416. W. Lomer, in P. S. Rudman (ed.), Phase Stability in Metals and AJJoys, McGraw-Hill, New York, 1967. J. Schramm, 2. Metallkd., 30 (1938) 327 - 334.