Phase equilibria, crystal chemistry and polymorphism of

Zn7Sb2O12 doped with Cr and Ni

Richard Harrington, Gabrielle C. Miles, Anthony R. West 1

Department of Engineering Materials, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK

Received 6 March 2008; accepted 7 March 2008Available online 15 March 2008

Abstract

The binary phase diagram for Cr-doped Zn7Sb2O12 was determined and compared with that for Ni-doped

Zn7Sb2O12. The b! a transition temperature, 1225 8C for undoped Zn7Sb2O12, decreases extremely rapidly with

increasing Cr content; the solubility limit of Cr in b-Zn7Sb2O12 is <1% but 37.5% in a-Zn7Sb2O12. Bond valence

sum calculations for the tetrahedral site, which contains exclusively Zn, show it to be significantly underbonded in

undoped a-Zn7Sb2O12, but less underbonded with increased Ni2+ and especially Cr3+ content, thus providing an

explanation for the stabilisation of a-Zn7Sb2O12 to lower temperatures on doping with Ni and especially Cr. Sub-

solidus compatibility relations in the ternary system ZnO–Sb2O5–Cr2O3 were determined at 1100 8C for

compositions containing �50% Sb2O5.

# 2008 Elsevier Ltd. All rights reserved.

Keywords: A. Electronic materials; A. Oxides; C. Neutron scattering; D. Phase equilibria; D. Crystal structure

1. Introduction

Zn7Sb2O12 is a well-known secondary phase in ZnO ceramic varistors [1], which usually contain

transition metal dopants such as Ni, Co, Mn and Cr [2–5]. Undoped Zn7Sb2O12 is polymorphic; the

transition from the low temperature b-polymorph to the high temperature a-polymorph occurs at

1225 � 25 8C [6]. The a-polymorph has an inverse spinel structure; the b-polymorph adopts a more

complex orthorhombic structure [7]. The effect of the a-polymorph on ZnO ceramic varistors appears to

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Materials Research Bulletin 43 (2008) 1949–1956

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doi:10.1016/j.materresbull.2008.03.012

reduce the average grain size during processing of the final ceramic; this leads to an increased number of

Schottky barriers associated with grain–grain contacts and results in improved varistor action with a

higher a-coefficient. The coefficient a is associated with non-linearity in the current (I)–voltage (V)

characteristics, given by the following equation:

I ¼ V

C

� �a

(1)

where C is a constant [8,9].

Doping Zn7Sb2O12 with Cr is reported to stabilise the high temperature a-polymorph to lower

temperatures [10]; Cr, along with Mn, has the most dramatic stabilisation effect. From diffuse reflectance

spectra and Rietveld refinement of XRD data, Cr occupies only the octahedral site, with Zn exclusively

occupying the tetrahedral site [11].

The purpose of the present study was to investigate the phase relations in the ZnO–Cr2O3–Sb2O5

system and especially, details of the a! b phase transition with varying composition and

temperature.

2. Experimental

The reagents used were ZnO (99.99% pure, Aldrich), Sb2O3 (99.99%, Aldrich), Cr2O3 (99%,

Matthey). ZnO was dried at 600 8C, Sb2O3 and Cr2O3 at 200 8C. Starting materials were weighed

out to give 0.5–3 g totals, mixed in an agate mortar and pestle with acetone, dried and fired in Pt foil boats.

The powders were heated initially at 800 8C for 20 h, reground and reheated at 1100 8C for 20 h.

Subsequent heat treatments were often employed to determine whether any further changes in the

phase(s) present occurred.

It is assumed, for all samples, that oxidation of the Sb2O3 starting material occurs during reaction. All

the phases encountered were based on the known phases ZnSb2O6, CrSbO4 and Zn7Sb2O12 which all

contain Sb(V). There was no evidence for Sb loss during heat treatment, as shown by the synthesis of

phase-pure samples of ZnSb2O6, CrSbO4 and Zn7Sb2O12 solid solutions.

XRD data were collected with a Stoe Stadi P diffractometer, Cu Ka1 radiation, using either an

image plate detector for phase analysis or a small, linear position sensitive detector for accurate

lattice parameter measurement. Powder neutron diffraction, ND, data were recorded on the d2b

instrument at the ILL, Grenoble, France. Rietveld refinement was carried out using the graphical

user interface (GUI) [12] for the DOS-based programme General Structure Analysis System (GSAS)

[13].

Bond valence sums were calculated using the following equation [14]:

Vi ¼X

j

expr00 � ri j

B

� �(2)

where Vi = bond valence sum around an ion, r0 = empirical ideal bond length calculated from a range of

known compounds [14], rij = calculated bond length, B = constant [14]. Bond valence sums for the Ni-

doped system were calculated using previously published crystallographic data [5,15].

R. Harrington et al. / Materials Research Bulletin 43 (2008) 1949–19561950

3. Results and discussion

3.1. Zn7�4xSb2�2xCr6xO12 solid solutions

Since a-Zn7Sb2O12 and ZnCr2O4 [16,17] are both known spinel phases, it was initially assumed that a

partial or complete range of solid solutions might form between them. If so, Cr3+ would substitute

aliovalently for both Zn2+ and Sb5+ ions according to the mechanism:

2Zn2þ þ Sb5þ ! 3Cr3þ

Compositions with the general formula Zn7�4xSb2�2xCr6xO12, 0 � x � 1, were synthesised as

described above, with a final reaction temperature of 1100 8C for 1–2 days. Samples were removed

from the furnace and allowed to cool in air.

Compositions x = 0.01 and x = 0.025 yielded a mixture of a- and b-phases at 1100 8C; compositions

x = 0.05–0.35 yielded phase-pure a solid solution. Compositions x � 0.40 gave a two-phase mixture of a

solid solution and ZnCr2O4, showing the solid solution limit to be 0.375 � 0.025. Upon reheating,

composition x = 0.025 transformed to phase-pure a-polymorph at 1250 8C; all other compositions

remained unchanged.

From these data, the binary phase diagram, Fig. 1, was constructed. The b! a phase transition in the

undoped end-member occurs at 1225 � 25 8C [6]; this temperature decreases extremely rapidly with

increasing Cr concentration. For x � 0.05, no b-polymorph was observed at any temperature. At no

concentration investigated was phase-pure b-polymorph observed; although there must be a region of the

phase diagram within which the b-polymorph exists exclusively, the compositional extent of this region

is x < 0.01. The stabilisation of the a-polymorph with respect to the b-polymorph at increasingly lower

temperatures is consistent with literature reports on Cr- and Sb-doped ZnO varistors [4].

When compared to Ni-doped Zn7Sb2O12 [5], doping with Cr has a much more dramatic effect on the

stabilisation of the a-polymorph to lower temperatures. Table 1 compares the solid solution limits for the

R. Harrington et al. / Materials Research Bulletin 43 (2008) 1949–1956 1951

Fig. 1. Sub-solidus phase diagram for the binary join between Zn7Sb2O12 and ZnCr2O4. The doping of Zn7Sb2O12 can be represented by the

general formula Zn7�4xSb2�2xCr6xO12. (l) b s.s. + a s.s., (& ) a s.s. and (&) a s.s. + ZnCr2O4.

a- and b-polymorphs as a function of temperature for the Ni and Cr systems (for the Ni system the

formula is rewritten so that 0 � x � 1, rather than 0 � x � 7 used in Ref. [5]).

A plot of lattice parameter, a, versus composition is shown in Fig. 2; the plot is essentially linear,

obeying Vegard’s law [18] and shows a decrease in a with increasing Cr content:

a ¼ a0 þ bx (3)

where a0 is the value for x = 0; b = �0.04. The decrease in a is more dramatic for the Cr-doped system

than for the Ni-doped system (where b = �0.02) [5]. Both the decrease in a and the more rapid decrease

in a with Cr substitution, Fig. 2, may be rationalised in terms of the relative sizes of the atoms, with

octahedral radii: Zn2+, 0.88 A; Ni2+ 0.83 A; Sb5+, 0.74 A; Cr3+, 0.63 A [19]. Even though the substitution

mechanisms are different and Ni substitutes for only Zn whereas Cr substitutes for both Zn and Sb, Cr3+ is

the smallest of the various species and its substitution is associated with the more rapid decrease in a.

Rietveld refinement of neutron diffraction data was carried out for three a solid solution compositions,

Table 2. Refining a small amount of Cr on the tetrahedral site in each case returned a negative value for its

Uiso indicating that Cr is exclusively located on the octahedral sites. Fig. 3 shows how the tetrahedral and

octahedral bond lengths, which are dependent on both a and the oxygen atomic coordinate, vary with x.

Neither variations are linear; the tetrahedral bond length decreases rapidly at low values of x before

levelling off; the octahedral bond length follows a different trend, consistent with the oxygen parameter,

Table 2, which also remains almost constant between x = 0 and 0.1, but increases slightly at higher x

values. Thus, as Cr is incorporated, the oxygen coordinate changes and the lattice parameter decreases;

the net effect is that the tetrahedral and octahedral bond lengths change differently with composition.

R. Harrington et al. / Materials Research Bulletin 43 (2008) 1949–19561952

Table 1

Comparison of solid solution ranges for Ni- and Cr-doped a- and b-Zn7Sb2O12 of general formulae Zn7�4xSb2�2xCr6xO12 and Zn7�7xNi7xSb2O12

Cr-doped Zn7Sb2O12 Ni-doped Zn7Sb2O12

b-Range (1100 8C) xmax < 0.01 0 � x � 0.07

b-Range (900 8C) xmax < 0.01 0 � x � 0.10

a-Range (1100 8C) 0.04 � x � 0.375 0.15 � x � 0.57

a-Range (900 8C) 0.04 � x � 0.375 0.22 � x � 0.57

Fig. 2. Comparison of lattice parameter, a, vs. x plots for the a solid solutions of Cr- and Ni-doped Zn7Sb2O12; formulae as in Table 1.

In both Cr and Ni systems [5], only Zn is present on the tetrahedral site. Bond valence sums (BVS)

calculated using Eq. (2) for the tetrahedral site, Fig. 4, show an increase as the concentration of the dopant

ion increases. At x = 0, the BVS of the tetrahedral site is significantly lower than the expected value of

2 (the oxidation state of Zn); this may be the reason why the a-polymorph is unstable relative to the

R. Harrington et al. / Materials Research Bulletin 43 (2008) 1949–1956 1953

Table 2

Refined parameters for samples x = 0.1, 0.25 and 0.35 in Zn7�4xSb2�2xCr6xO12

x

0a 0.1 0.25 0.35

Oxygen coordinate 0.2591(8) 0.25902(6) 0.25957(6) 0.25973(7)

doct�O (A´

) 2.072(5) 2.0686(5) 2.0531(5) 2.0465(5)

dtet�O (A´

) 2.015(8) 1.9899(9) 1.9872(10) 1.9844(10)

100 � Uoct (A´

)2 1.33(6) 0.789(27) 1.009(32) 0.924(32)

100 � Utet (A´

)2 1.29(10) 0.765(35) 1.019(40) 1.139(42)

100 � UO (A´

)2 1.64(22) 0.868(19) 1.108(23) 1.075(23)

wRp 6.76 7.97 8.91 8.39

Rp 8.23 9.52 6.45 6.51

a Taken from the literature [6].

Fig. 3. Octahedral and tetrahedral bond lengths in Cr-doped Zn7Sb2O12. The lines are present as a guide to the eye.

Fig. 4. Comparison of the bond valence sums for the tetrahedral site (which contains Zn exclusively) in Cr- and Ni-doped Zn7Sb2O12.

b-polymorph, except at high temperature, where it is entropically stabilised. Bond valence sums

represent an extension to more complex structures of the original electrostatic valence rule of Pauling

which essentially required local electroneutrality to be preserved in order for a structure to be stable.

Significant deviation of BVS values from expected values represent departure from local electroneu-

trality and potential instability in the structure leading to a reduction in lattice energy. This destabilisation

could, however, be offset by an increase in entropy associated with structural disorder, resulting in

stabilisation of the structure above a certain temperature, as found here for the a-polymorph. Any return

towards expected BVS values by means of doping would effectively reduce the extent of departure from

electroneutrality, increase the lattice energy and reduce the temperature at which entropic stabilisation

was required: hence the observed stabilisation of the a-polymorph to lower temperature by doping with

both Ni and Cr.

In Ni-doped Zn7Sb2O12, the BVS of the tetrahedral site increases steadily, Fig. 4; a is the

stable polymorph at all temperatures for x � 0.28 and for these compositions, the BVS has

increased significantly. For Cr-doped Zn7Sb2O12, the BVS of the tetrahedral site increases rapidly

with x initially because of the rapid reduction in Zn–O bond length, Fig. 3. Thus, the BVS value for

x = 0.1 with Cr is roughly equal to that of Ni at x = 0.42, Fig. 4. As the Cr concentration is increased

further, the BVS of the tetrahedral site increases very gradually, following the trend in the tetrahedral

bond length, Fig. 3.

Interpretation of the results of BVS calculations for the octahedral site are subject to uncertainty. For

the Cr-doped system, the octahedral site is occupied by three different cations, each with a different

charge and ionic radius. Diffraction techniques give only a single, average bond length of the site;

however, we do not know whether locally, there is a distribution of bond lengths and if so, whether this is

due to positional disorder of either the cations or the oxygens. Using the average bond length, the BVS

gives, as a first approximation, that for the octahedral site, Zn is overbonded, while Cr and Sb are

underbonded.

The isotropic thermal parameters for all three sites (tetrahedral, octahedral and oxygen) are

significantly lower for the three Cr-doped samples than for the undoped sample, Table 2. At room

temperature, a is the stable polymorph for all the Cr-doped samples, but metastable for the undoped

sample which was prepared by quenching from high temperature. The high Uiso values for x = 0 could be

indicative either of greater thermal motion or positional disorder in the quenched sample. However, the

values for x = 0 were calculated using XRD on a quenched sample [6], while those for the doped system

were calculated using neutron diffraction data on air-cooled samples and there is therefore some

uncertainty in attempting to draw quantitative conclusions by comparing results obtained from different

techniques. Nevertheless, we suggest that the high Uiso values for x = 0 may indicate structural instability

and disorder in the atomic positions which could reflect a combination of the high synthesis temperature

followed by rapid quenching of the sample, together with significant departures from local electro-

neutrality, as shown by the anomalously low BVS value for the Zn site.

3.2. The ternary phase diagram ZnO–Sb2O5–Cr2O3

The sub-solidus compatibility relations in the ternary system ZnO–Sb2O5–Cr2O3 were determined

following heat treatments on 19 compositions, Table 3 and Fig. 5. All samples were given a final heat

treatment of 1100 8C as lower temperatures often did not yield complete reaction. Generally, heating at

1100 8C for 20 h was sufficient to yield complete reaction, although for some compositions, longer

R. Harrington et al. / Materials Research Bulletin 43 (2008) 1949–19561954

heating times were employed to ensure that equilibrium was achieved. The phase diagram consists of one

solid solution series based upon Zn7Sb2O12, as discussed previously. Although there has been some

suggestion in the literature of Zn doping into ZnCr2O4 [20], no evidence of this was found here. The

remainder of the phase diagram is divided into a number of two-phase and three-phase compatibility

R. Harrington et al. / Materials Research Bulletin 43 (2008) 1949–1956 1955

Table 3

Phases present at different compositions of ZnO, Cr2O3 and Sb2O5

%ZnO: %Cr2O3: %Sb2O5 Phase(s) present at 1100 8C Time heated at 1100 8C/h

12: 38: 50 CrSbO4 + ZnSb2O6 20

25: 25: 50 CrSbO4 + ZnSb2O6 20

38: 12: 50 CrSbO4 + ZnSb2O6 20

9: 52: 39 CrSbO4 + ZnSb2O6 20

75: 6: 19 a-s.s. + ZnSb2O6 20

56: 10: 34 a-s.s. + ZnCr2O4 + ZnSb2O6 20

56: 20: 24 a-s.s. + ZnCr2O4 + ZnSb2O6 20

45: 50: 5 ZnCr2O4 + CrSbO4 20

5: 50: 45 ZnCr2O4 + CrSbO4 20

30: 44: 26 ZnCr2O4 + ZnSb2O6 + CrSbO4 20

6: 62: 32 ZnCr2O4 + CrSbO4 + Cr2O3 20

16: 75: 9 ZnCr2O4 + CrSbO4 + Cr2O3 20

86: 1: 12 a-s.s. + b-s.s. 20

77: 14: 9 a-s.s. 20

75: 17: 8 a-s.s. + ZnCr2O4 40

62: 34: 4 a-s.s. + ZnCr2O4 40

88: 6: 6 a-s.s. + ZnO 20

75: 22: 3 a-s.s. + ZnO + ZnCr2O4 20

70: 30: 0 ZnO + ZnCr2O4 20

60: 40: 0 ZnO + ZnCr2O4 20

55: 45: 0 ZnO + ZnCr2O4 20

10: 90: 0 ZnCr2O4 + Cr2O3 20

Key: a-s.s. = a-Zn7�4xSb2�2xCr6xO12, b-s.s. = b-Zn7�4xSb2�2xCr6xO12.

Fig. 5. Sub-solidus compatibility relations at 1100 8C for the ZnO–Sb2O5–Cr2O3 system. Closed (& ), half closed (l) and open squares (&)

refer, respectively, to 1-, 2- and 3-phase products.

regions: there are no previous reports in the literature on the sub-solidus phase diagram. No attempt was

made to study compositions containing >50% Sb2O5.

4. Conclusions

On substitution of Cr3+ into Zn7Sb2O12, the b! a phase transition temperature decreases extremely

rapidly; the decrease is much more dramatic for Cr- than for Ni-doped Zn7Sb2O12. From BVS

calculations, the tetrahedral site, which contains Zn exclusively, is significantly underbonded in a-

Zn7Sb2O12, which may explain why a-Zn7Sb2O12 is stable only at high temperatures, �1225 8C, where

positional disorder in the structure is entropically stabilised. Substitution of Ni2+ and especially Cr3+ into

Zn7Sb2O12 reduces the underbonding of the Zn site leading to stabilisation of the a-polymorph to lower

temperatures.

Acknowledgements

We thank Dr. Peter Slater for helpful discussions, Dr. Emmanuell Suard (ILL) and Dr. Emma McCabe

for their help in collecting ND data and EPSRC for funding.

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