Phase Equilibria as Related to Crystal Structure in the System Niobium Pentoxide-Tungsten Trioxide

Abstract

The phase equilibrium diagram for the binary system niobium pentoxide-tungsten trioxide has been constructed from results of x-ray diffraction studies on both single crystals and powders and from fusion characteristics. Twelve stable compounds have been found in the system. The exact composition of eight of these compounds has been established by single crystal analyses at the Nb₂O₅:WO₃ ratios of 6:1, 13:4, 7:3, 8:5, 9:8, 1:1, 4:9, and 2:7. The approximate compositions of the remaining four other phases are 30:1, 6:11, 1:11, and 1:15. The 6:1, “6:11”, 4:9, and 2:7 phases melt eongruently at 1476, 1378, 1380, and 1357 °C, respectively. The “30:1”, 7:3, 8:5, 9:8, “1:11”, and “1:15” phases melt incongruently at 1470, 1440, 1385, 1375, 1356, and 1358 °C, respectively; and the 13:4 and 1:1 phases decompose before melting at 1435 and 1115 °C, respectively. The 8:5, 9:8, “6:11”, 2:7, “1:11”, and “1:15” compounds are shown on the phase diagram as having minimum temperatures of stability. One metastable phase having a narrow range of composition near the 3:8 ratio was also encountered. Although Nb₂O₅ apparently exhibits no solid solution, WO₃ was found to accept a maximum of three mole percent niobia in solid solution enabling all the reported polymorphs of WO₃ to be obtained at room temperature.

1. Introduction

A complete study of the phase relationships in the binary system Nb₂O₅ − WO₃ has been conducted as part of a continuing program of fundamental phase equilibria studies of ceramic materials. This particular system was selected for study in order to further the knowledge of the crystal chemistry of niobates in view of the results obtained from previous structural studies of single crystals [1–4].¹

Due to the complex nature of the x-ray diffraction powder patterns in this system, conflicting interpretations of the data have been reported [5–11]. In a previous study of the Nb₂O₅–WO₃ system, Goldschmidt [5] concluded that Nb₂O₅ could accept more than 50 mole percent WO₃ in solid solution and reported the existence of a compound at approximately Nb₂O₅:3WO₃. He also found a limited solid solution of Nb₂O₅ in WO₃. Kovba and Trunov [6] reported that the 1:3 compound was tetragonal with a structure related to that of a tetragonal tungsten-bronze. Fiegel et al. [7], studied the phase equilibria in the system at 1200 °C and below. They reported only about 33 mole percent solid solution of WO₃ in Nb₂O₅ with a 3:2 compound occurring at 1200 °C and a 1:1 compound at 1100 °C and below. They found very little, if any, solid solution of Nb₂O₅ in WO₃ and confirmed the existence of a compound at about 1:3 with a limited solid solution for both Nb₂O₅ and WO₃. Later [8] they reported that the 1:3 composition gave single crystal x-ray diffraction patterns which showed superstructure differing from one crystal to the next. Kovba et al. [9], also attempted to determine the phases formed in this system at about 1200 °C. They concluded that compounds existed at the Nb₂O₅:WO₃ ratios of 4:1, 2:1, 4:7, and 1:3. They also, reported a phase with variable WO₃ content occurring at high WO₃ concentrations and observed a small amount of solid solution in both Nb₂O₅ and WO₃.

In a description of preliminary phase identification, Roth and Wadsley [1] on the basis of single crystal x-ray diffraction studies reported the existence of five compounds structurally related to Nb₂O₅ occurring at Nb₂O₅:WO, ratios of 15:1, 6:1, 7:3, 8:5, and 9:8. They also confirmed the 1:1 phase and noted the existence of at least three phases related to the tetragonal tungsten bronze-type structure. The crystal structures of 6:1, 7:3, 8:5, and 9:8, were reported [2, 3] and the “building block” principle was elaborated as the basis of the crystal-chemistry of niobate compounds [4].

Schäfer and Gruehn [10] and Felten [11] have indicated in private communications that their interpretations of x-ray diffraction powder data for the Nb₂O₅–WO₃ system differ in some respects from the previously mentioned published reports.

Because of the conflicting nature of the reported data, it was thought desirable to study completely the phase equilibria of the Nb₂O₅–WO₃ system. With the use of the unit cell dimensions derived from single crystal data the existence of the various phases in the powder patterns can now be established more readily. The exact compositions of phases can often be determined only by a solution of the crystal structure. The approximate composition and even the existence of a phase can sometimes be found only by a rather complete phase equilibria study. The two disciplines, crystal structure analysis and phase equilibria are therefore complimentary and no system can be considered to be well characterized unless both such studies have been made. Therefore, x-ray diffraction data together with the melting points of the compounds and solidus and liquidus temperatures at various compositions across the system have been obtained in order to construct an equilibrium diagram.

2. Sample Preparation and Test Methods

The following starting materials were employed for the preparation of the majority of the specimens:

• Nb₂O₅ – high purity niobium pentoxide. Spectrographic analysis indicated less than about 0.01 percent Si; 0.001 percent Ca and Mg with As, Cu, and Ta only questionably present.

• WO₃ – high purity tungsten anhydride. Spectrographic analysis indicated less than about 0.1 percent Si; 0.001 percent B, Ca, Cr, and Mg; 0.0001 percent Cu with Pb only questionably present.

A few specimens were prepared with less pure starting materials, in order to determine qualitatively the effect of impurities on the equilibrium products. The following is a typical example of the nature of the impurities present in two specimens of ND₂O₅:WO₃ ratio of 16:5. For the less pure specimen the first series transition elements, in general, are present in amounts of an order of magnitude greater than for the more pure specimen.

• Nb₂O₅:WO₃ (16:5) – higher purity end members. Spectrochemical analyses indicated less than about 0.01 percent Cr, Cu, and Si; 0.001 percent Al, B, Ca, Mg, and Ni; 0.0001 percent Mn with Pb only questionably present.

• Nb₂O₅:WO₃ (16:5) – less pure end members. Spectrochemical analyses indicated less than about 0.01 percent Al, Ca, Cr, Cu, Fe, Mg, Ni, and Si; 0.001 percent Mn; 0.0001 percent B with Pb only questionably present.

For the preparation of the specimens, the weight percentages were calculated to within ±0.01 percent, with no corrections made for percentage of purity of the starting materials except for loss on ignition.

For the higher purity specimens, the starting materials were weighed to the nearest ±0.1 mg, in sufficient quantities to yield 3 g batches. Each batch was mixed in a mechanical shaker for about 15 min and pressed into a disk in a ⅝-in. diam mold at 10,000 lb/in². The disks were placed on Pt foil and calcined by heating in air at 700 °C for 19 hrs, with heating and cooling rates of approximately 4 °C/min.

The less pure specimens were weighed out in approximately 1 g batches and mixed with an alumina mortar and pestle. In order to minimize any possible loss of WO₃ these specimens were not calcined after mixing.

Subsolidus, as well as melting point data, were obtained by the quenching technique on samples sealed in platinum tubes. An electrically heated vertical tube furnace wound with 80 percent Pt-20 percent Rh wire was used for the quenching experiments. The furnace was controlled by an a-c Wheat-stone bridge controller which was capable of holding the temperature to at least ±2 °C for an extended period of time. Temperatures were measured with a Pt versus Pt-10 percent Rh thermocouple which had been calibrated against the melting points of Au (1063 °C) and Pd (1552 °C) [12]. The thermocouple was recalibrated several times during the course of the work. Specimens were suspended in the furnace by fine Pt wire. In order to quench the wire was fused allowing the sealed tubes to drop out of the heating chamber into a beaker of water. When the tubes were opened the specimens were examined for physical appearances of melting. The first sign of glazing of the surface of the specimen was interpreted as the first experimental evidence for the solidus temperature. Acceptance of this appearance as evidence of melting was found justified in many specimens by an abrupt difference in the x-ray diffraction powder patterns of the specimens. The formation of a concave meniscus, without the formation of relatively large crystals, indicated the liquidus temperature. The overall reproducibility of the temperature measurements for the experimental data points was within ± 2 °C or better and the overall accuracy of the reported temperatures was within ± 5 °C or better.

Equilibrium was considered to have been obtained when the x-ray diffraction patterns of specimens successively heated for longer times and/or at higher temperatures showed no change. X-ray diffraction powder patterns were made using a high-angle recording Geiger counter diffractometer and nickel-filtered copper radiation, with the Geiger counter traversing the specimen at l/4°2θ/min and the intensity of the radiation being recorded on the chart at l°2θ/in. The unit cell dimensions reported can be considered accurate to about ±2 in the last decimal place listed.

3. Compounds in the Nb₂O₅-WO₃ System

3.1. Nb₂O₅

The stability relations of the various reported polymorphs of Nb₂O₅ have been summarized by several workers [13–17]. It has been concluded that the high-temperature monoclinic form of Nb₂O₅ is the only stable form at atmospheric pressure [14, 16, 17]. The crystal structure of the high-temperature modification of Nb₂O₅ has been described by Gatehouse and Wadsley [18]. They report this phase to be monoclinic, (space group P2) with 14 formula units in the unit cell and a = 21.16 Å, b = 3.822 Å, c= 19.35 Å, β = 119°50′. The x-ray diffraction powder pattern previously listed for Nb₂O₅ [19] can be more correctly indexed on the basis of the published single-crystal intensity data and is shown in table 1. This indexing leads to slightly revised values of the unit cell dimensions, as follows: a = 21.149 Å, b = 3.823 Å, c= 19.352 Å, β =119°48′, in excellent agreement with the lattice constants given by Gatehouse and Wadsley [18]. The melting point of the pure Nb₂O₅ used for this study was previously determined to be 1485 °C [20].

Table 1.

X-ray diffraction powder data for Nb₂O₃ (CuK_a radiation)

da	Ib	$\frac{1}{d^2}obs$	$\frac{1}{d^2}calc$	hklc
16.66	6	0.0036	0.0036	001
10.517	5	.0090	.0090	$20\overline{1}$
10.063	2	.0099	.0097	101
9.615	2	.0108	.0107	$10\overline{2}$
9.148	5	.0120	.0118	200
8.354	4	.0143	.0142	002
6.942	2	.0208	.0206	$30\overline{1}$
6.486	3	.0238	.0236	102
6.285	11	.0253	.0252	$10\overline{3}$
5.590	4	.0320	.0319	003
5.273	6	.0360	.0359	$40\overline{2}$
5.116	48	.0382	.0382	$40\overline{1}$
4.734	4	.0446	.0446	103
4.616	36	.0469	.0465	$10\overline{4}$
3.852	6	.0674	.0670	$30\overline{5}$
3.821	6	.0685	.0683	$20\overline{5}$
			.0684	010
3.737	100	.0716	.0714	110
			.0717	$11\overline{1}$
3.636	100	.0756	.0755	105
3.577	4	.0782	.0782	111
3.553	4	.0792	.0791	$11\overline{2}$
3.515	4	.0809	.0807	$60\overline{3}$
3.483	100	.0824	.0824	602
			.0826	012
3.406	4	.0862	.0859	$60\overline{4}$
3.383	4	.0877	.0877	303
3.351	28	.0891	.0886	005
			.0890	$31\overline{1}$
3.316	5	.0909	.0911	$60\overline{1}$
3.264	4	.0939 949	.0936	$11\overline{3}$
3.247	4	.0949	.0951	310
3.153	11	.1006	.1003	013
3.078	6	.1055	.1051	$50\overline{6}$
2.994	7	.1116	.1113	$10\overline{6}$
2.832	36	.1247	.1246	$51\overline{2}$
2.826	38	.1252	.1248	014
			.1262	$51\overline{3}$
2.771	31	.1303	.1301	$51\overline{1}$
2.701	34	.1303	.1367	$21\overline{5}$
			.1377	$70\overline{6}$
2.668	3	.1405	.1401	$41\overline{5}$
			.1405	$20\overline{7}$
2.644	4	.1431	.1426	510
			.1433	$80\overline{4}$
2.628	5	.1448	.1445	$80\overline{3}$
			.1452	$60\overline{7}$
2.543	36	0.1546	0.1526	$80\overline{2}$
			.1541	$10\overline{7}$
			.1543	$61\overline{4}$
2.523	5	.1571	.1571	015
2.491	26	.1612	.1612	$70\overline{7}$
2.478	8	.1629	.1623	511
			.1625	214
2.452	5	.1664	.1662	$41\overline{6}$
			.1672	$61\overline{5}$
2.314	29	.1865	.1865	413
			.1869	$61\overline{6}$
			.1872	$20\overline{8}$
2.114	4	.2244	.2239	414
2.076	38	.2321	.2321	$\text{10,}\text{0,}\overline{3}$
2.037	34	.2411	.2410	$\text{20}\overline{\text{9}}$
1.912	29	.2736	.2736	020
1.873	5	.2852	.2846	$\text{3,}\text{0,}\text{1}\overline{\text{0}}$
			.2847	$\text{11,}\text{0,}\overline{7}$
			.2847	$\text{11,}\text{0,}\overline{3}$
			.2855	220
1.856	3	.2903	.2904	208
1.819	20	.3020	.3020	$\text{2,}\text{0,}\text{1}\overline{\text{0}}$
			.3031	$\text{11,}\text{0,}\overline{8}$
1.789	16	.3124	.3115	407
			.3118	$\text{42}\overline{\text{1}}$
			.3127	902
1.765	5	.3211	.3201	$\text{12}\overline{\text{4}}$
			.3227	$\text{12,}\text{0,}\overline{5}$
			.3230	$\text{12,}\text{0,}\overline{6}$
			.3231	$\text{0,}\text{0,}\text{1}\overline{\text{1}}$
1.742	23	.3295	.3292	$\text{11}\overline{\text{9}}$
			.3296	$\text{12,}\text{0,}\overline{4}$
1.727	25	.3353	.3353	$\text{8,}\text{0,}\text{1}\overline{\text{1}}$
1.709	10	.3424	.3422	$\text{11,}\text{1,}\overline{4}$
			.3425	$\text{11,}\text{1,}\overline{6}$
1.692	20	.3493	.3491	$\text{12}\overline{\text{5}}$
1.683	51	.3529	.3530	$\text{3,}\text{1,}\text{1}\overline{\text{0}}$
			.3531	$\text{11,}\text{1,}\overline{3}$
1.627	8	.3776	.3776	408
1.592	27	.3945	.3946	$\text{7,}\text{1,}\overline{1}\overline{1}$
1.582	20	.3994	.3982	11,0,1
			.3995	318
1.579	18	.4012	.4011	10,1,1
1.556	22	.4130	.4133	$\text{12,}\text{1,}\overline{8}$

^aInterplaner spacing.

^bIntensity relative to the strongest peak(s).

^cIndexed on the basis of a monoclinic unit cell (space group P₂) a = 21.149 Å, b = 3.823 Å, c = 19.352 A, β = 119°48′ and the previously reported observed structure factors from the single crystal data [18].

3.2. Compounds Structurally Related to Nb₂O₅

a. Compounds Belonging to the Homologous Series B_nm+1O_{3nm−(n+m)+4}

Roth and Wadsley [4] have shown that most of the phases formed by the addition to Nb₂O₅ of oxides with cations similar in size to Nb⁺⁵, regardless of valence, can be described by the homologous series notation B_nmp+1O_{3nmp−(n+m)p+4}. Structurally, these phases are made up of blocks of octahedra in a given plane n long and m wide with a variable number (p) of blocks connected by edge sharing of octahedra at the corners of the blocks. Similar block units occur at two levels in the unit cell, zero and one-half, in a plane perpendicular to one axis which always has a value of approximately 3.8 Å. This axis is the b-axis of a monoclinic cell or the c-axis of a tetragonal cell. The octahedra occurring at the two different levels are connected to each other by edge sharing except at the junction of four such blocks, two at each level, where they are bonded by a tetrahedrally coordinated cation. Those compounds in the Nb₂O₅−WO₃ system whose structures have been described all have p = l and the formula simplifies to B_nm+1O_{3nm−(n+m)+4}, where the tetrahedral position is always occupied by W⁺⁶ ions. In this arrangement when n = m, the unit cell is body-centered tetragonal as in PNb₉O₂₅ [21]. When n ≠ m the cell is C-centered monoclinic.

b. 6Nb₂O₅ · WO₃,WNb₁₂O₃₃)

The unit cell of this compound is C-centered monoclinic (probable space group C₂) having n = 3, m = 4[2]. The indexed x-ray diffraction powder pattern obtained in the present study is listed in table 2. The unit cell dimensions derived from this pattern are a=22.282 Å, b = 3.824 Å, c= 17.724 Å, β = 123°22′. WNb₁₂O₃₃ is apparently stable from room temperature to the congruent melting point at 1476 °C.

Table 2.

X-ray diffraction powder data for the compound WNb₁₂O₃₃ (CuK_a radiation)

da obs	Ib obs	$\frac{1}{d^2}obs$	$\frac{1}{d^2}calc$	hklc
14.77	19	0.0046	0.0046	001
11.08	23	.0081	.0081	$\text{20}\overline{\text{1}}$
7.42	16	.0182	.0183	002
6.43	8	.0242	.0241	201
5.54	18	.0326	.0325	$\text{40}\overline{\text{2}}$
5.35	6	.0349	.0348	$\text{40}\overline{\text{1}}$
5.04	48	.0394	.0394	$\text{40}\overline{\text{3}}$
4.937	12	.0410	.0411	003
4.674	58	.0458	.0458	202
3.743	76	.0714	.0713	110
3.729	96	.0719	.0718	$\text{11}\overline{\text{1}}$
3.702	40	.0730	.0730	004
3.697	40	.0732	.0732	$\text{60}\overline{\text{3}}$
3.670	20	.0742	.0742	$\text{60}\overline{\text{2}}$
3.616	284	.0765	.0766	203
3.535	43	.0800	.0798	111
3.510	300	.0812	.0811	$\text{60}\overline{\text{4}}$
3.437	13	.0847	.0846	$\text{60}\overline{\text{1}}$
3.415	15	.0857	.0857	$\text{20}\overline{\text{5}}$
3.358	29	.0887	.0887	$\text{31}\overline{\text{2}}$
3.203	27	.0974	.0975	112
2.930	16	.1165	.1165	204
2.901	5	.1189	.1189	$\text{51}\overline{\text{2}}$
2.866	58	.1217	.1218	$\text{51}\overline{\text{3}}$
2.836	37	.1243	.1243	113
2.799	7	.1277	.1279	$\text{20}\overline{\text{6}}$
2.735	41	.1337	.1337	$\text{51}\overline{\text{4}}$
2.706	31	.1365	.1366	312
2.682	17	.1390	.1392	$\text{80}\overline{\text{2}}$
			.1392	$\text{80}\overline{\text{5}}$
2.542	8	.1548	.1548	$\text{51}\overline{\text{5}}$
2.520	116	.1575	.1574	$\text{80}\overline{\text{1}}$
			.1580	$\text{40}\overline{\text{7}}$
2.499	10	.1602	.1599	$\text{60}\overline{\text{7}}$
			.1603	114
2.462	16	.1650	.1651	511
2.410	4	.1722	.1722	$\text{71}\overline{\text{2}}$
2.339	6	.1828	.1831	404
2.328	15	.1845	.1842	$\text{71}\overline{\text{5}}$
			.1848	800
2.316	29	.1864	.1865	$\text{71}\overline{\text{1}}$
			.1868	$\text{31}\overline{\text{6}}$
2.215	11	.2038	.2043	$\text{60}\overline{\text{8}}$
2.183	7	.2098	.2099	710
2.167	6	0.2130	0.2135	$\text{10,}\text{0,}\overline{6}$
2.128	5	.2209	.2213	801
			.2213	$\text{80}\overline{\text{8}}$
2.116	6	.2233	.2236	007
			.2237	206
2.112	6	.2242	.2244	$\text{51}\overline{\text{7}}$
2.072	67	.2325	.2328	$\text{10,}\text{0,}\overline{7}$
2.042	52	.2398	.2401	405
2.006	6	.2484	.2487	$\text{91}\overline{\text{2}}$
1.9375	9	.2664	.2669	802
			.2669	$\text{80}\overline{\text{9}}$
1.9324	8	.2678	.2683	315
1.9121	60	.2735	.2735	020
1.8729	4	.2851	.2851	220
1.8664	5	.2871	.2873	$\text{22}\overline{\text{2}}$
1.8560	15	.2899	.2903	$\text{12,}\text{0,}\overline{5}$
1.8524	29	.2914	.2910	207
			.2918	022
			.2920	008
1.8342	8	.2969	.2972	$\text{12,}\text{0,}\overline{4}$
1.8144	8	.3038	.3040	$\text{12,}\text{0,}\overline{7}$
1.8090	20	.3056	.3063	406
1.8007	8	.3084	.3093	$\text{20}\overline{\text{9}}$
1.7895	13	.3126	.3123	$\text{11,}\text{1,}\overline{5}$
1.7720	8	.3185	.3185	$\text{11,}\text{1,}\overline{6}$
1.7697	9	.3193	.3193	222
1.7640	22	.3214	.3217	$\text{8,}\text{0,}\text{1}\overline{\text{0}}$
1.7567	19	.3240	.3245	$\text{12,}\text{0,}\overline{8}$
1.7403	21	.3302	.3305	316
1.7329	19	.3330	.3332	10, 0, 1
1.7311	18	.3337	.3339	$\text{11,}\text{1,}\overline{7}$
1.6903	20	.3500	.3501	223
1.6805	42	.3541	.3545	515
			.3547	$\text{62}\overline{\text{4}}$
1.6709	26	.3582	.3585	$\text{11,}\text{1,}\overline{8}$
1.6088	21	.3864	.3869	10,0,2
1.6070	23	.3872	.3880	$\text{2,}\text{0,}\text{1}\overline{\text{0}}$
1.5975	16	.3918	.3924	912
1.5838	21	.3987	.3992	$\text{9,}\text{1,}\text{1}\overline{\text{0}}$
1.5801	20	.4005	.4006	$\text{14,}\text{0,}\overline{5}$
			.4017	$\text{10,}\text{0,}\overline{1}\overline{1}$
1.5734	21	.4039	.4049	119
1.5608	19	.4105	.4109	$\text{13,}\text{1,}\overline{5}$
1.5527	9	.4148	.4154	$\text{14,}\text{0,}\overline{4}$
1.5405	5	.4214	.4227	$\text{14,}\text{0,}\overline{1}\overline{1}$

^aInterplanar spacing.

^bObserved intensity.

^cIndexed on the basis of a monoclinic unit cell (space group C₂) a = 22.282 Å, b = 3.824 Å, c= 17.724 Å, β =123°22′ and the previously reported structure factors from the single crystal data [2].

c. 7Nb₂O₅ · 3WO₃ (W₃Nb₁₄O₄₄)

The unit cell of this compound is body-centered tetragonal, space group I4/m or $\text{I}\overline{4}(n=4,m=4[3|)$. The indexed x-ray diffraction powder pattern is listed in table 3 and the unit cell dimensions derived from this pattern are a = 21.002 Å, c = 3.820 Å.

Table 3.

X-ray diffraction powder data for the compound W₃Nb₁₄O₄₄ (CuK_a radiation)

da obs	db obs	$\frac{1}{d^2}obs$	$\frac{1}{d^2}calc$	hklc
14.87	25	0.0045	0.0045	110
10.52	5	.0090	.0091	200
7.42	33	.0181	.0181	220
6.65	8	.0226	.0227	310
4.951	23	.0408	.0408	330
4.694	82	.0454	.0453	420
4.118	5	.0590	.0589	510
3.757	142	.0708	.0708	101
3.712	37	.0726	.0725	440
3.598	480	.0772	.0771	530
3.539	52	.0798	.0799	211
3.321	20	.0907	.0907	620
3.195	42	.0980	.0980	321
2.968	8	.1135	.1134	710/550
2.912	22	.1179	.1179	640
2.826	80	.1252	.1253	501/431
2.756	21	.1317	.1315	730
2.649	105	.1344	.1343	521
2.623	4	.1453	.1451	800
2.560	22	0.1526	0.1524	611
2.546	122	.1543	.1542	820
2.488	10	.1616	.1615	541
2.441	7	.1679	.1678	750
2.421	16	.1706	.1705	631
2.358	9	.1799	.1796	701
2.347	8	.1814	.1815	840
2.319	13	.1860	.1859	910
2.302	41	.1887	.1887	721
2.215	2	.2037	.2040	930
2.152	9	.2159	.2159	811/741
2.121	3	.2222	.2222	770
2.100	11	.2268	.2267	10.0.0/860
2.067	18	.2341	.2340	831
2.039	130	.2405	.2403	950
1.9497	3	.2631	.2630	10,4,0
1.9102	40	.2741	.2743	002
1.9004	10	.2769	.2766	11,1,0
1.8797	5	.2830	.2831	202
1.8620	6	0.2884	0.2884	941
1.8564	15	.2902	.2902	880
1.8419	28	.2948	.2947	11,3,0/970
1.8367	15	.2964	.2967	312
1.8007	54	.3084	.3083	10,6,0
1.7694	16	.3194	.3194	422
1.7546	10	.3248	.3247	871
1.7499	40	.3266	.3265	12,0,0
1.7305	43	.3339	.3338	961
1.6874	65	.3512	.3511	532
1.6857	85	.3519	.3519	11,2,1/10,5,1
1.6612	4	.3624	.3627	12,4,0
1.6559	5	.3647	.3647	622
1.6396	5	.3720	.3718	10,8,0
1.6239	4	.3792	.3791	11,4,1
1.6103	35	.3856	.3854	13,1,0/11,7,0
1.5861	40	.3975	.3973	12,1,1/981
1.5686	62	.4064	.4063	10,7,1

^aInterplaner spacings.

^bObserved intensities.

^cIndexed on the basis of a tetragonal unit cell (space group I4/m or $\text{I}\overline{4}$) a = 21.002 Å, c = 3.820 Å.

d. 8Nb₂O₅ 5WO₃ (W₅Nb₁₆O₅₅)

The unit cell of this phase is C-centered monoclinic space group C₂ (n = 4, m = 5, [2]). The indexed x-ray diffraction powder pattern is listed in table 4 and the unit cell dimensions derived from this pattern are a = 29.638 Å, b = 3.820 Å, c = 23.126 Å, β = 126°27′. Due to the very large monoclinic cell this powder pattern can only he indexed unambiguously with the aid of single crystal data. By utilizing the published F_obs values for W₅Nb₁₆O₅₅ [2] it was possible to assign indices to the observed peaks in the powder pattern with reasonable certainty up to about 60°2θ (Cu radiation). W₅Nb₁₆O₅₅ is probably not stable below about 1090 °C and melts incongruently at about 1385 °C.

Table 4.

X-ray diffraction powder data for the compound W₅Nb₁₆O₅₅ (CuKa radiation)

da	Ib	$\frac{1}{d^2}obs$	$\frac{1}{d^2}calc$	hklc
18.58	7	0.0029	0.0029	001
14.84	12	.0045	.0046	$\text{20}\overline{\text{1}}$
9.31	13	.0115	.0116	002
7.40	17	.0183	.0183	$\text{40}\overline{\text{2}}$
6.75	4	.0220	.0220	$\text{40}\overline{\text{3}}$
6.21	12	.0260	.0260	003
5.85	6	.0293	.0293	202
4.935	12	.0411	.0411	$\text{60}\overline{\text{3}}$
4.701	45	.0453	.0453	$\text{60}\overline{\text{4}}$
4.652	10	.0462	.0462	004
4.512	35	.0491	.0491	203
3.771	130	.0703	.0703	110
3.767	142	.0705	.0705	$\text{11}\overline{\text{1}}$
3.717	26	.0724	.0722	005
3.705	22	.0729	.0731	$\text{80}\overline{\text{4}}$
3.660	250	.0747	.0743	$\text{80}\overline{\text{3}}$
			.0747	204
3.630	40	.0759	.0759	111
3.587	222	.0777	.0777	$\text{80}\overline{\text{5}}$
3.539	25	.0798	.0799	$\text{31}\overline{\text{2}}$
3.506	8	.0813	.0813	$\text{80}\overline{\text{2}}$
3.406	8	.0862	.0863	403
3.386	10	.0872	.0872	112
3.252	6	.0946	.0947	$40\overline{7}$
3.188	16	.0984	.0984	$51\overline{3}$
3.095	12	.1044	.1044	113
3.072	10	.1060	.1061	205
2.980	7	.1126	.1126	800
2.897	8	.1192	.1192	$\text{10,}\text{0,}\overline{6}$
2.832	16	.1246	.1245	$71\overline{3}$
2.817	47	.1260	.1260	$71\overline{4}$
2.804	40	.1272	.1273	114
			.1274	$40\overline{8}$
2.775	5	.1299	.1300	$\text{10,}\text{0,}\overline{7}$
2.740	54	.1332	.1332	$71\overline{5}$
2.732	65	.1340	.1339	$\text{10,}\text{0,}\overline{2}$
2.727	71	.1345	.1345	313
2.615	8	.1462	.1463	$71\overline{6}$
2.574	16	.1509	.1509	512
2.562	84	.1524	.1520	$\text{10,}\text{0,}\overline{1}$
			.1528	$60\overline{9}$
2.549	22	.1539	.1538	$80\overline{9}$
			.1540	405
2.533	8	.1558	.1559	115
2.479	6	.1627	.1627	$91\overline{5}$
			.1628	314
2.425	11	.1701	.1699	$\text{12,}\text{0,}\overline{7}$
			.1704	$91\overline{6}$
2.397	4	0.1741	0.1744	$91\overline{2}$
2.382	8	.1763	.1764	711
2.350	4	.1811	.1811	$\text{12,}\text{0,}\overline{8}$
2.316	7	.1864	.1862	207
			.1873	$\text{8,}\text{0,}\overline{10}$
2.294	37	.1900	.1898	$91\overline{1}$
			.1903	$51\overline{8}$
2.254	6	.1969	.1968	315
			.1970	$\text{10,}\text{0,}\overline{10}$
2.177	6	.2111	.2111	910
2.104	8	.2260	.2260	$51\overline{9}$
2.067	8	.2340	.2340	$\text{11,}\text{1,}\overline{2}$
2.036	52	.2413	.2413	$\text{14,}\text{0,}\overline{9}$
2.021	36	.2448	.2448	407
1.9453	4	.2642	.2638	606
1.9099	37	.2742	.2742	020
1.8827	6	.2821	.2823	10,0,3
1.8783	6	.2835	.2837	$\text{12,}\text{0,}\overline{12}$
1.8602	17	.2890	.2890	0,0,10
1.8503	7	.2921	.2919	$\text{16,}\text{0,}\overline{7}$
1.8329	18	.2977	.2972	$\text{16,}\text{0,}\overline{6}$
			.2978	$\text{2,}\text{0,}\overline{1}\overline{1}$
1.8294	26	.2988	.2988	408
1.8007	12	.3084	.3083	$\text{16,}\text{0,}\overline{5}$
1.7944	18	.3106	.3107	$\text{16,}\text{0,}\overline{10}$
1.7800	4	.3156	.3153	$62\overline{3}$
			.3157	$\text{4,}\text{0,}\overline{12}$
1.7691	7	.3195	.3195	$62\overline{4}$
1.7580	25	.3236	.3233	223
			.3238	$\text{12,}\text{0,}\overline{13}$
1.7452	8	.3283	.3285	119
1.7421	14	.3295	.3292	12,0,2
1.7311	24	.3337	.3336	318
1.7229	12	.3369	.3368	$\text{15,}\text{1,}\overline{9}$
1.6943	28	.3484	.3479	517
			.3489	224
1.6862	57	.3517	.3515	$\text{15,}\text{1,}\overline{10}$
			.3518	$82\overline{5}$
1.6303	12	.3763	.3762	12,0,3
1.6284	13	.3771	.3772	$\text{4,}\text{0,}\overline{13}$
1.6101	10	.3857	.3861	$\text{14,}\text{0,}\overline{14}$
1.5888	12	.3962	.3958	11,1,3
1.5783	14	.4014	.4015	$\text{13,}\text{1,}\overline{3}$
		.4014	.4015	$42\overline{8}$
1.5732	26	.4041	.4041	3,1,12
1.5654	30	.4081	.4078	$\text{17,}\text{1,}\overline{6}$
			.4081	$\text{10,}\text{2,}\overline{2}$

^aInterplaner spacing.

^bObserved intensity.

^cIndexed on the basis of a monoclinic unit cell (space group C₂) a = 29.638 Å, b = 3.820 Å, c = 23.126 Å, β = 126°27′ and the previously reported observed structure factors from the single crystal data [2].

e. 9Nb₂O₅ · 8WO₃ (W₈Nb₁₈O₆₉)

The unit cell of the last compound observed in this structural series has n = 5, m = 5 [3] and is body-centered tetragonal with the most probable space group $\text{I}\overline{4}$. The indexed x-ray diffraction powder pattern is given in table 5 and the unit cell dimensions derived from this pattern are a = 26.270 Å, c = 3.814 Å. This compound is not stable below about 1265 °C and melts incongruently at about 1375 °C.

Table 5.

X-ray diffraction powder data for the compound W₈Nb₁₈O₆₉) (CuK_a radiation)

da	Ib	$\frac{1}{d^2}obs$	$\frac{1}{d^2}calc$	hklc
18.43	4	0.0029	0.0029	110
9.33	8	.0115	.0116	220
6.20	10	.0260	.0261	330
5.88	10	.0290	.0290	420
4.640	8	.0464	.0464	440
4.503	80	.0493	.0493	530
4.375	5	.0522	.0522	600
3.771	146	.0703	.0702	101
3.712	25	.0726	.0725	710/550
3.642	372	.0753	.0754	640
3.450	15	.0840	.0840	730
3.378	17	.0876	.0876	321
3.185	12	.0986	.0985	820
3.088	25	.1049	.1043	660
			.1050	501/431
3.054	15	.1072	.1072	750
2.901	5	.1189	.1188	910
2.793	82	.1282	.1282	541
2.769	26	.1304	.1304	930
2.731	119	0.1341	0.1340	631
2.626	12	.1450	.1449	10,0,0/860
2.622	18	.1455	.1456	721
2.575	96	.1508	.1507	10,2,0
2.522	11	.1573	.1572	651
2.477	15	.1630	.1629	811/741
2.458	7	.1744	.1745	831
2.378	9	.1769	.1768	11,1,0
2.304	6	.1885	.1884	11,3,0/970
2.283	38	.1918	.1919	921/761
2.253	11	.1970	.1971	10,6,0
2.248	7	.1978	.1977	851
2.242	6	.2086	.2087	12,0,0
2.156	9	.2151	.2145	12,2,0
			.2151	10,1,1
2.100	12	.2267	.2267	10,3,1
2.077	5	.2319	.2319	12,4,0
2.015	85	.2463	.2463	13,1,0/11,7,0
1.9584	5	.2607	.2608	12,6,0
1.9340	4	0.2674	0.2673	11,4,1
1.9068	40	.2750	.2750	002
1.8578	10	.2898	.2893	14,2,0/10,10,0
1.8482	12	.2928	.2927	11,9,0
1.8216	48	.3014	.3014	12,8,0
1.7791	12	.3160	.3159	13, 7, 0
1.7561	15	.3243	.3243	532
1.7474	26	.3275	.3275	15,1,0
1.7384	7	.3309	.3310	10,9,1
1.7235	28	.3366	.3362	14,6,0
			.3368	13,4,1/11,8,1
1.6943	57	.3484	.3484	12,7,1
1.6897	65	.3503	.3504	642
1.6614	5	.3623	.3624	15,5,0/13,9,0
1.6532	6	.3659	.3658	14,3,1/13,6,1
1.6292	22	.3768	.3768	16,2,0/14,8,0
1.5801	28	.4005	.4006	15,2,1
1.5688	48	.4063	.4064	13,8,1

^aInterplaner spacing.

^bObserved intensity.

^cIndexed on the basis of a tetragonal unit cell (space group $\text{I}\overline{4}$) a = 26.270 Å, c = 3.814 Å.

It should be noted that the binary equilibrium stability regions of this structural group of compounds tend to decrease with increasing W⁺⁶ content. This phenomenon is probably due to the increasing size of the basic “building block” unit, and therefore to the greater energy needed to maintain long range ordering.

f. Other Compounds Structurally Related to Nb₂O₅

In addition to the compounds with structures described by the homologous series formula B_mnp+1 O_{3nmp−(n+m)p+4}, the existence of several other phases has been reported, but their structures are, as yet, unknown. Notable among these is the NbO_2.482 (and (Ti,Nb)O_2.482) reported by Gruehn and Schäfer [22] which is apparently similar to the ‘X’ phase reported by Waring and Roth in the system vanadiumoxide-niobium oxide [23]. There are several stable phases in the Nb₂O₅−WO₃ system which fall in this category.

g. 13Nb₂O₅ · 4WO₃ (W₄Nb₂₆O₇₇)

Another phase, previously unreported, was found to occur between the known 6:1 and 7:3 compounds. The composition of this phase was deduced by Schäfer (private communication) to be 13:4 based on oxygen analyses. It was postulated that this compound might have an Nb₂O₅:WO₃ ratio of 16:5 and the structure would then be related to that of Nb₂O₅ by increasing the size of the basic “building blocks” from 3 × 4 and 3 × 5 (reported for Nb₂O₅ [18]) to 4 × 4 and 4 × 5. However, single crystals obtained from a 16:5 composition were found by A. D. Wadsley (private communication) to have a unit cell which is C-centered monoclinic a = 29.74 Å, b = 3.823 Å, c = 26.02 Å, β = 92°18′. These values are not in agreement with the primitive space group and approximate unit cell dimensions which can be derived for the postulated 16:5 structure. The partially indexed powder pattern is given in table 6. It cannot be fully indexed without the aid of single crystal intensity data due to the very large size of the unit cell. The structure of this phase, is actually a mixture of blocks of 3 × 4 and 4 × 4 occurring in alternate sequence to make an “ordered intergrowth” structure [24]. The composition can be arrived at by adding the homologous series twice (as for Nb₂O₅ [4]) n = 3, m = 4, p = l (B₁₃O₃₃) plus n = 4, m = 4, p = 1 (B₁₇O₄₄) = B₃₀O₇₇ (13Nb₂O₃ · 4WO₃). Although this compound does not form in short-time experiments (about 1 hr) it can be prepared readily by heating for several days at about 1400 °C. This phase was observed to decompose at about 1435 °C into 6Nb₂O₅ · WO₃ and 7Nb₂O₅ · 3WO₃.

Table 6.

X-ray diffraction powder data for the compound W₄Nb₂₆O₇₇ (CuK_a radiation)

da	Ib	hklc
14.82	10	200
12.93	8	002
7.43	12	400
6.55	5
5.19	7
4.951	14	600
4.833	15	205
4.686	60	$60\overline{2}$
3.786	18	110
3.748	200	$11\overline{1}$
		111
3.711	40	007
		800
3.657	15	112
		$20\overline{7}$
3.610	250	$80\overline{2}$
3.564	190	207
3.542	50	802
		$31\overline{1}$
3.463	10	113
3.367	10
3.264	10	114
3.199	16
2.966	5
2.919	15
2.845	32
2.832	48
2.777	10
2.731	52
2.724	55
2.529	90
2.418	10
2.346	7
2.309	22
2.277	5
2.113	7
2.067	13
2.055	42
2.042	88
1.912	68	020
1.857	12
1.854	15
1.848	25
1.835	5
1.816	5
1.805	33
1.781	16
1.763	15
1.756	19
1.744	13
1.736	16
1.731	15
1.706	5
1.689	25
1.684	68
1.675	12
1.610	25
1.597	8
1.592	20
1.585	18
1.571	25
1.565	38

^aInterplaner spacing.

^bObserved intensity.

^cPartially indexed on the basis of a C-centered monoclinic unit cell with a = 29.74 Å, b = 3.823 Å, c = 26.02 Å, β = 92°18′ by comparison with the single crystal intensities observed from a film taken with a Weisingberg camera [A. D. Wadsley, private communication].

h. “30Nb₂O₅:WO₃^”2

Another phase was found to occur in the Nb₂O₅-WO₃ system at a ratio of approximately 3.5 mole percent WO₃. This phase is apparently the same as that previously reported to occur at about 15:1, the structure of which could not be verified [1]. The 30:1 ratio is that deduced by Schäfer (private communication). It is apparently composed of some complex packing of the “building blocks” previously described. One possible structure might be n = 3, m = 4, p = 2 (B₂₅O₆₂) plus two blocks of n = 3, m = 4, p = l (B₂₅O₆₆) = B₅₁O₁₂₈ (25Nb₂O₅ · WO₃). Another possibility might be n = 3, m = 4, p = 2 (B₂₅O₆₂) + n = 3, m = 5, p = l (B₁₆O₄₁) = B₄₁O₁₀₅ (20Nb₂O₅ · WO₃). The exact structure and composition remain to be proven because no good single crystal data is yet available. The “30:1” phase was found to melt incongruently at about 1470 °C. Its unindexed x-ray diffraction powder pattern is listed in table 7.

Table 7.

X-ray diffraction powder data for the composition 30Nb₂O₅:WO₃ (CuK_a radiation)

da	Ib
16.20	10
13.93	4
10.73	16
8.96	7
8.10	5
6.37	14
5.36	8
5.10	50
4.797	7
4.645	60
3.742	132
3.638	312
3.579	10
3.556	10
3.493	228
3.354	37
3.173	16
3.093	7
2.984	14
2.845	55
2.836	47
2.763	38
2.707	46
2.693	18
2.647	8
2.614	7
2.597	6
2.538	65
2.503	45
2.476	10
2.458	10
2.435	9
2.376	40
2.212	6
2.100	8
2.076	74
2.041	90
1.999	5
1.936	8
1.913	48
1.871	10
1.866	10
1.857	12
1.825	18
1.819	42
1.796	8
1.791	8
1.782	23
1.769	7
1.746	14
1.743	25
1.731	30
1.716	10
1.693	22
1.684	30
1.680	60
1.623	15
1.603	8
1.595	30
1.581	44
1.558	28
1.548	8

^aInterplaner spacing.

^bObserved intensity.

3.3. Compounds Containing Pentagonal Bipyramid (Sevenfold) Coordinated Cations

a. Nb₂O₅ · WO₃ (WNb₂O₈)

A phase isostructural with Nb₃O₇F [25] might be thought likely to occur in this system, but no such structure has ever been reported in pure oxide systems. Instead a new phase was found with unit cell dimensions related to the tetragonal tungsten bronze-type structures. Single crystals of the 1:1 compound were prepared by decomposing the 9:8 phase (made with the less pure end members) at about 1100 °C. Single crystal precession patterns of this phase made by A. Perloff of the National Bureau of Standards staff showed these crystals to be orthorhombic, probable space groups Pmab or P2₁ab. From these data the x-rav diffraction powder pattern given in table 8 was indexed with a = 16.615 Å, b = 17.616 Å, c = 3.955 Å. The compound Nb₂O5 · WO₃ could not be made as a single phase in the quenching experiments. X-ray diffraction powder patterns of these specimens always showed a trace of a metastable bronze-type phase plus some 7Nb₂O₅ · 3WO₃. However, high temperature x-ray powder patterns showed that the extra phases disappeared quickly above about 900 °C. The 1:1 compound was found to dissociate at about 1115 °C to 8Nb₂O₅ · 5WO₃ plus a bronze-like phase, probably 4Nb₂O₅ · 9WO₃.

Table 8.

X-ray diffraction powder data for the compound WNb₂O₈ (CuK_a radiation)

da	Ib	$\frac{1}{d^2}obs$	$\frac{1}{d^2}calc$	hklc
8.83	6	0.0128	0.0129	020
8.30	25	.0145	.0145	200
4.689	6	.0455	.0455	320
4.403	5	.0516	.0516	040
4.259	12	.0551	.0552	140
3.952	272	.0640	.0639	001
3.894	46	.0660	.0660	240
3.759	112	.0708	.0708	420
3.608	4	.0768	.0768	021
3.570	9	.0785	.0785	201
3.449	202	.0841	.0841	340
3.279	20	.0930	.0929	031
3.215	8	.0967	.0966	131
3.165	22	.0998	.0997	311
3.110	98	.1034	.1034	520
3.051	16	.1075	.1074	231
2.937	4	.1159	.1160	060
2.893	80	.1195	.1196	160
2.825	11	.1253	.1251	411
			.1255	331
2.771	78	.1303	.1303	600
			.1305	260
2.725	50	.1347	.1348	421
2.654	16	.1420	.1421	540
2.644	18	.1430	.1432	620
2.633	12	.1443	.1445	051
2.599	86	.1481	.1481	341
			.1481	151
2.573	8	.1511	.1509	431
2.518	8	.1577	.1577	511
2.510	8	.1587	.1590	251
2.445	44	.1673	.1673	521
2.398	7	.1739	.1739	460
2.375	8	.1773	.1771	351
2.334	40	.1835	.1834	531
			.1836	161
2.293	5	.1901	.1903	720
2.268	23	.1943	.1943	601
			.1944	261
2.250	8	.1976	.1975	611
2.223	8	.2023	.2024	451
2.203	19	. 2061	.2060	541
			.2062	080
2.198	19	.2070	.2072	621
2.117	4	.2232	.2233	631
2.091	8	.2288	.2290	740
2.078	14	.2316	.2317	800
2.050	6	.2381	.2379	461
2.023	18	.2443	.2445	711
			.2446	820
1.9774	50	.2558	.2557	002
1.9652	7	.2589	.2590	012
1.9473	18	.2637	.2642	480
1.9247	13	.2699	.2702	081
			.2702	202
			.2703	731
1.8797	16	.2830	.2831	222
			.2833	840
1.8743	15	.2847	.2846	281
			.2847	032
1.8521	18	.2915	.2915	312
1.8475	24	.2930	.2929	741
			.2934	760
1.8373	30	.2962	.2956	801
			.2968	580
1.8284	15	.2991	.2988	811
			.2992	232
1.8178	6	.3026	.3027	381
1.8081	6	.3059	.3061	920
1.8017	8	.3081	.3073	042
			.3085	821
1.7908	7	.3118	.3109	142
			.3123	571
1.7852	6	.3138	.3137	402
1.7762	9	.3170	.3169	412
1.7637	14	.3215	.3218	242
			.3219	751
			.3223	0,10,0
1.7546	16	.3248	.3246	831
			.3249	091
1.7496	20	.3267	.3266	422
1.7464	23	.3279	.3281	481
1.7247	15	.3362	.3363	052
			.3366	680
1.7154	16	.3398	.3394	291
			.3399	342
			.3399	152
1.6969	40	.3473	.3472	841
			.3477	860
1.6885	9	.3507	.3508	252
1.6740	7	.3569	.3573	761
1.6684	22	.3593	.3591	522
1.6662	28	.3602	.3604	911
1.6651	27	.3607	.3607	581
1.6625	26	.3618	.3620	10,0,0
1.6548	5	.3652	.3652	442
1.6434	4	.3703	.3701	921
1.6396	4	.3720	.3717	062
1.6326	12	.3752	.3749	10,2,0
			.3752	532
			.3754	162
1.6234	14	.3795	.3802	4,10,0
1.6096	13	.3860	.3861	602
			.3861	0.10,1
			.3862	931
			.3862	262
1.6029	9	.3892	.3893	612
			.3898	1,10,1
1.5928	6	.3942	.3942	452
1.5853	8	.3979	.3978	542
1.5826	8	.3993	.3990	622
			.3992	771
1.5808	10	.4002	.4005	681
			.4006	2,10,1
1.5640	14	.4088	.4087	941
			.4093	960
1.5592	26	.4114	.4116	861
1.5326	12	.4257	.4260	10,0,1

^aInterplaner spacing.

^bObserved intensity.

^cIndexed on the basis of an orthorhombic unit cell (space group Pmab or P2₁ab) a = 16.615 Å, b = 17.616 Å, c = 3.955 Å.

WNb₂O₈ is related to WTa₂O₈ (a = 16.701 Å, b = 8.864 Å, c = 3.877 Å) by a doubled b-axis. The crystal structure of LiNb₆O₁₅F which is apparently isostructural with WTa₂Os was found by S. Andersson and M. Lundberg [26] to be made up of octahedrally coordinated cations. These octahedra are corner shared to form a ring of five, octahedra. Within this ring is a cation in sevenfold coordination, in a pentagonal bipyramid configuration. These rings are connected by further corner sharing to form double chains. The doubled cell in WNb₂O₈ is probably due to an alternate puckering of the positions occupied by the sevenfold coordinated ions, but the proof of this must await a complete single crystal structure analysis.

b. 4Nb₂O₅ · 9WO₃ (Nb₈W₉O₄₇)

A compound having a general diffraction pattern similar to tetragonal potassium tungsten bronze (K_xWO₃) was reported by Roth and Wadsley [1] to occur at the composition 4Nb₂O₅ · 9WO₃. Sleight and Magneli [27] described the structure of this phase from a crystal obtained from a 1:3 composition which had been heated to a temperature of 1200–1400 °C. The structure of this crystal was found to be made up of three tetragonal-bronze-like unit cells with four out of the twelve possible five-fold rings being occupied by cations, with oxygens above and below forming pentagonal bipyramid coordination polyhedra. This structure represents the composition Nb₁₆W₁₈O₉₄ and has orthorhombic symmetry. The unit cell dimensions found in the present work are a = 36.692 Å, b = 12.191 Å, c = 3.945 Å, and were obtained from the indexed x-ray diffraction powder pattern given in table 9. This compound was found to be stable from at least 1150 °C to the congruent melting point of about 1380 °C.

Table 9.

X-ray diffraction powder data for the compound W₉Nb₈O₄₇ (CuK_a radiation)

da	Ib	$\frac{1}{d^2}obs$	$\frac{1}{d^2}calc$	hklc
11.59	4	0.0074	0.0075	110
10.14	12	.0097	.0097	210
9.16	8	.0119	.0119	400
8.64	9	.0134	.0134	310
7.34	6	.0186	.0186	500
			.0186	410
6.12	6	.0267	.0267	600
6.09	11	.0269	.0269	020
5.46	57	.0335	.0335	610
5.08	5	.0388	.0388	420
4.314	22	.0537	.0537	620
4.081	6	.0601	.0602	900
4.064	10	.0605	.0606	030
4.044	10	.0612	.0613	130
3.945	212	.0643	.0643	001
3.867	176	.0669	.0669	910
3.858	195	.0672	.0672	330
3.754	6	.0710	.0709	301
			.0710	011
3.732	7	.0718	.0717	111
3.678	10	.0739	.0740	211
3.660	28	.0746	0.0743	10,0,0
			0.0746	820
3.587	4	.0777	.0777	311
3.559	14	.0790	.0791	530
3.474	6	.0829	.0828	501
			.0829	411
3.388	164	.0871	.0871	920
3.384	166	.0873	.0873	630
3.316	5	.0909	.0910	601
3.260	13	.0941	.0942	221
3.197	60	.0978	.0977	611
			.0979	321
3.145	7	.1011	.1012	10,2,0
3.115	4	.1030	.1031	421
3.058	20	.1070	.1070	12,0,0
3.048	25	.1076	.1077	040
3.019	6	.1097	.1098	521
2.964	146	.1138	.1137	12,1,0
2.958	158	.1143	.1143	340
2.912	17	.1180	.1179	621
2.878	50	.1208	.1207	930
2.835	5	.1244	0.1244	901
2.827	9	.1251	.1248	031
			.1256	131
2.799	7	.1277	.1276	721
			.1278	231
2.783	76	.1315	.1311	911
			.1315	331
2.732	80	.1340	.1339	12,2,0
2.727	78	.1344	.1344	640
2.684	12	.1388	.1387	821
2.643	7	.1432	.1434	531
2.569	77	.1515	.1514	921
			1.1516	631
2.490	6	.1613	.1612	731
2.442	5	.1677	.1675	12,3,0
			.1678	940
2.416	9	.1713	.1712	12,0,1
2.411	10	.1720	.1719	041
2.405	6	.1729	.1727	141
2.370	52	.1780	.1779	12,1,1
2.366	64	.1787	.1786	341
2.325	22	.1850	.1850	931
2.245	33	.1984	.1982	12,2,1
			.1987	641
2.158	4	.2147	.2146	12,4,0
2.095	10	.2278	.2277	15,3,0
2.091	14	.2286	.2284	950
2.078	10	.2316	.2314	15,0,1
			.2318	12,3,1
			.2321	941
2.072	10	.2330	.2325	051
			.2332	151
1.9725	54	.2570	.2570	002
1.9681	35	.2582	.2583	15,2,1
1.9644	12	.2591	.2592	651
1.9473	4	.2637	.2637	012
			.2637	302
1.9332	45	.2676	.2676	18,2,0
1.9278	48	.2691	.2690	660
1.9072	12	.2749	.2748	15,4,0
			.2752	12,5,0
1.8671	15	.2869	.2869	222
1.8553	34	.2905	.2905	612
			.2906	322
1.8503	20	.2921	.2919	15,3,1
			.2926	951
1.8219	34	.3013	.3012	18,3,0
1.8178	53	.3026	.3024	960
1.8040	6	.3073	.3072	161
1.7924	10	.3113	.3107	622
			.3116	18,1,1
1.7872	5	.3131	.3132	361
1.7749	8	.3174	.3172	902
			.3176	032
1.7568	22	.3240	.3239	912
			.3243	332
1.7397	12	.3303	.3304	170
1.7360	30	.3318	.3319	18,2,1
1.7305	60	.3339	.3332	661
			.3343	21,1,0
1.7269	80	.3353	.3353	15,5,0
1.7238	55	.3365	.3364	370
1.7172	20	.3391	.3390	15,4,1
			.3394	12,5,1
1.7045	20	.3442	.3441	922
			.3443	632
1.6808	6	.3540	.3545	21,2,0
1.6703	7	.3583	.3584	16,5,0
1.6540	32	.3655	.3655	18,3,1
1.6513	40	.3667	.3666	961
1.6417	24	.3710	.3707	12,1,2
			1.3714	342
1.6273	7	.3776	.3777	932
1.5991	12	.3911	.3909	12,2,2
			.3914	642
1.5921	9	.3946	.3947	171
1.5841	40	.3985	.3985	21,1,1
1.5818	46	.3997	.3996	15,5,1
1.5798	42	.4007	.4006	371
1.5635	10	.4091	.4089	18,5,0
			.4094	15,6,0

^aInterplaner spacing.

^bObserved intensity.

^cIndexed on the basis of an orthorhombic unit cell with a = 36.692 Å, b = 12.191 Å, c= 3.945 Å.

The presence of cations in the pentagonal holes of the tetragonal tungsten bronze structure suggests a possible homologous series which can be expressed as:

$$n{\text{B}}_{10}{\text{O}}_{30}+m\text{BO }or{\text{ B}}_{10n+m}{\text{O}}_{30n+m}$$

where n is the number of subcells of the tetragonal bronze type in the true unit cell and m is the number of pentagonal bipyramid polyhedra occupied by a cation. Each bronze-type subcell has only four pentagonal holes, therefore the maximum value of m must be equal to or less than 4n.

c. 2Nb₂O₅ · 7WO₃ (Nb₄W₇O₃₁)

One method of reducing the general formula B_10n+mO_30n+m to include the 4:9 compound and to predict a minimum number of other phases is to assume m = 4. This results in the formula B_10n+4O_30n+4. For the 4:9 compound n = 3. The composition of n = 2 is Nb₂O₅ · WO₃ and the composition of n = 4 would be 2Nb₂O_25:7WO₃. The 1:1 compound does not belong to the general homologous series but has a unique structure only vaguely related to the tetragonal tungsten bronze type, as previously described. The structure predicted for 2Nb₂O₅ · 7WO₃ would be either orthorhombic with one a-axis multiplied by four or tetragonal with both a-axes doubled. The latter structure, which exhibits a higher symmetry than the former, was found to occur for the 2:7 composition between a minimum temperature of about 1245 °C and the probable congruent melting point of 1357 °C. A crystal structure analysis of this compound is currently being conducted by N. Stephensen [28]. The unit cell dimensions of Nb₄W₇O₃₁ are a = 24.264 Å, c = 3.924 Å, and were obtained from the indexed x-ray diffraction powder pattern listed in table 10.

Table 10.

X-ray diffraction powder data for the compound W₇Nb₄O₃₁ (CuK_a radiation)

da	Ib	$\frac{1}{d^2}obs$	$\frac{1}{d^2}calc$	hklc
10.84	10	0.0085	0.0085	210
8.56	8	.0136	.0136	220
6.06	8	.0272	.0272	400
5.43	35	.0340	.0340	420
4.508	8	.0493	.0493	520
4.289	18	.0544	.0544	440
4.046	5	.0611	.0612	600
3.996	5	.0626	.0628	610
3.924	194	.0649	.0649	001
3.839	256	.0679	.0679	620
3.792	25	.0696	.0696	540
3.735	10	.0717	.0717	201
3.617	16	.0764	.0764	630
3.429	25	.0850	.0849	710/550
3.366	136	.0883	.0883	640
3.333	8	.0900	.0900	720
3.265	10	.0938	.0938	411
3.181	52	.0989	.0989	421
3.052	7	.1074	.1074	501/431
3.034	18	.1086	.1087	800
2.942	146	.1155	.1155	820
2.898	5	.1191	.1193	441
2.860	31	0.1223	0.1223	660
2.838	8	.1242	.1240	830
2.822	8	.1256	.1257	750
2.816	10	.1261	.1261	601
2.743	98	.1329	.1329	621
2.713	102	.1359	.1359	840
2.660	10	.1414	.1414	631
2.851	18	.1500	.1499	711/551
2.555	50	.1532	.1533	641
2.473	8	.1635	.1635	731
2.399	5	.1737	.1737	801
2.349	50	.1804	.1804	821
2.311	10	.1872	.1872	661
2.290	5	.1907	.1906	751
2.232	40	.2008	.2008	841
2.177	5	.2209	.2208	11,3,0/970
2.128	12	.2308	.2310	10,6,0
2.064	14	.2347	.2348	10,0,1/861
1.9620	42	.2598	.2598	002
1.9182	60	.2718	.2718	12,4,0
1.8967	7	.2780	.2773	11,2,1/10,5,1
			.2786	10,8,0
1.8664	9	0.2871	0.2869	402
1.8606	11	.2887	.2886	412
1.8447	24	.2939	.2937	422
1.8384	11	.2959	.2960	10,6,1
1.8189	12	.3023	.3022	502/432
1.8087	36	.3057	.3058	12,6,0
1.7878	7	.3129	.3129	11,5,1
1.7839	8	.3142	.3141	442
			.3142	13,4,0/11,8,0
1.7468	20	.3277	.3277	622
1.7232	50	.3368	.3367	12,4,1
1.7160	104	.3396	.3397	14,2,0/10,10,0
1.6949	15	.3481	.3481	642
1.6825	6	.3533	.3533	12,8,0
1.6480	7	.3682	.3685	802
1.6426	30	.3706	.3707	12,6,1
1.6326	15	.3752	.3753	822
1.6177	4	.3822	.3821	662
1.5896	12	.3958	.3957	842
1.5720	63	.4047	.4047	14,2,1/10,10,1
1.5535	7	.4144	.4145	12,10,0

^aInterplanar spacing

^bObserved intensity.

^cIndexed on the basis of a tetragonal unit cell with a = 24.264 Å, c = 3.924 Å.

d. “6Nb₂O₅ · 11WO₃” (Nb₁₂W₁₁O₆₃)

Roth and Wadsley [1] reported another compound in this system occurring at a ratio of about 13Nb₂O₅:24WO₃. Kovba and Trunov [9] described a phase to which they assigned the composition 4Nb₂O₅:7WO₃. The only logical ratio, near this composition, which could belong to the general formula B_10n+mO_30n+m is 6Nb₂O₅:11WO₃. In order to include this composition with the 4:9 and 2:7 compounds in one simplified formula, it is sufficient to postulate a series limited to the case m = n + 1. The new homologous series formula then becomes B_11n+1O_31n+1. In this case for the 2:7 compound, n = ∞ and for 4Nb₂O₅ · 9WO₃, n = 3. When n = 2 the composition is B₂₃O₆₃ and the predicted structure has two bronze-like subcells in the unit cell, with three filled pentagonal holes. Such a structure would have a very low symmetry and is apparently not formed in this system. Experimentally the compound “6Nb₂O₅ · 11WO₃” was found to be orthorhombic, probably with the a-axis of the tetragonal bronze subcell tripled. It is stable from about 1210 °C to the apparently congruent melting point of 1378 °C. The x-ray diffraction powder pattern listed in table 11 is indexed with a = 36.740 Å, b = 12.195 Å, c = 3.951 Å. It may be concluded from the size and symmetry of the unit cell, that the homologous series formula B_11n+1O_31n+1 is not correct for this compound. Therefore, “6Nb₂O₅ · 11WO₃” either has a defect structure or belongs to some other structural homologous series, as yet unknown. A single crystal structure analysis is currently under study by N. Stephenson [28].

Table 11.

X-ray diffraction powder data for the phase “6Nb₂O₅ · 11WO₃” (CuK_a radiation)

da	Ib	$\frac{1}{d^2}obs$	$\frac{1}{d^2}calc$	hklc
11.62	5	0.0074	0.0075	110
10.18	14	.0097	.0097	210
9.16	8	.0119	.0119	400
8.62	8	.0135	.0134	310
5.47	36	.0334	.0334	610
4.320	16	.0536	.0536	620
4.070	8	.0604	.0600	900
			.0605	030
3.952	236	.0640	.0641	001
3.865	140	.0669	.0667	910
			.0672	330
3.742	7	.0714	.0707	301
			.0708	011
			.0715	111
3.682	8	.0738	.0738	211
3.663	19	.0745	.0741	10,0,0
			.0743	820
3.596	6	.0774	.0775	311
3.562	10	.0788	.0790	530
3.388	156	.0871	.0869	920
			.0872	630
3.223	12	.0962	.0964	11,1,0
3.201	24	.0976	.0975	611
			.0976	321
3.061	14	.1067	.1067	12,0,0
3.049	22	.1076	.1076	040
2.968	100	.1135	.1134	12,10
2.959	106	0.1142	0.1143	340
2.917	10	.1175	.1176	621
2.880	33	.1205	.1205	930
2.803	5	.1273	.1273	721
2.763	76	.1310	.1308	911
			.1313	331
2.735	45	.1337	.1336	12,2,0
2.730	49	.1342	.1343	640
2.687	12	.1385	.1384	821
2.644	5	.1431	.1431	531
2.573	62	.1511	.1510	921
			.1513	631
2.492	5	.1610	.1609	731
2.421	6	.1706	.1708	12,0,1
2.414	7	.1716	.1717	041
2.373	49	.1776	.1775	12,1,1
2.368	59	.1783	.1783	341
2.328	15	.1846	.1846	931
2.248	25	.1978	.1977	12,2,1
2.246	22	.1983	.1983	641
2.097	7	.2273	.2272	15,3,0
2.095	8	.2282	.2281	950
2.072	6	.2330	.2329	151
1.9754	85	.2563	.2563	002
1.9355	22	.2669	.2669	18,2,0
1.9290	26	.2688	.2688	660
1.9087	8	.2745	.2743	15,4,0
			.2748	12,5,0
1.8696	7	.2861	.2861	222
1.8585	13	.2895	.2897	612
			.2898	322
1.8528	15	.2913	.2913	15,3,1
1.8496	11	.2923	.2922	951
1.8239	25	.3006	.3006	18,3,0
1.8195	32	.3021	.3021	960
1.7593	23	.3231	.3230	912
			.3235	332
1.7384	22	.3309	.3302	170
			.3310	18,2,1
1.7332	33	.3329	.3328	661
1.7317	35	.3335	.3334	21,1,0
1.7284	52	.3348	.3348	15,5,0
1.7244	51	.3363	.3362	370
1.7184	8	.3386	.3384	15,4,1
			.3389	12,5,1
1.7072	22	.3431	.3432	922
			.3435	631
1.6559	15	.3647	.3646	18,3,1
1.6524	25	.3663	.3662	961
1.6442	22	.3699	.3697	12,1,2
			.3705	342
1.6294	8	.3766	.3768	932
1.6012	12	.3901	.3899	12,2,2
			.3905	642
1.5926	5	.3943	.3943	171
1.5858	25	.3977	.3975	21,1,1
1.5833	32	.3989	.3989	15,5,1
1.5801	24	.4005	.4002	371
1.5654	5	.4081	.4081	18,5,0
1.5640	7	.4089	.4088	15,6,0

^aInterplanar spacing.

^bObserved intensity.

^cIndexed on the basis of an orthorhornbic unit cell with a = 36.740 Å, b = 12.195 Å, c = 3.951 Å.

e. Metastable Tetragonal Bronze-Type Solid Solution (“3:8”)

In addition to the ordered bronze-like phases which have been found in the Nb₂O₅−WO₃ system, another, apparently disordered, phase has also been reported at about the Nb₂O₅:3WO₃ composition [5, 6, 7]. In the present study a tetragonal bronze-type phase without any indication of superstructure in the powder pattern was found to occur from about 72 to 74 mole percent WO₃ in a temperature range from about 1100 to 1250 °C. The unit cell dimensions of this phase were found to vary from about a =12.190 Å, c = 3.968 Å for the composition containing 72 mole percent WO₃ to a = 12.178 Å, c = 3.930 Å for the composition containing 75 mole percent WO₃. It must be concluded that the lower temperature phase is only metastable, because it decomposes at high temperatures into the two ordered compounds, 4Nb₂O₅ · 9WO₃ and 2Nb₂O₅ · 7WO₃.

3.4. Compounds Related to the ReO₃ Structure-Type. The Magneli “Shear Phases”

In the temperature interval from about 1270 to 1358 °C, at least two phases have been found to occur with x-ray diffraction powder patterns suggestive of the Magneli “shear phases” [29], which are structurally related to WO₃. These phases have been found to occur between about 91 and 94 mole percent WO₃. Due to the difficulty of obtaining equilibrium and the complex nature of the diffraction patterns, it is very difficult to decipher the exact composition of the phases by powder data alone. Although no single crystals have been examined, the best interpretation of the data suggests that there are two equilibrium phases having the Nb₂O₅:WO₃ ratios of 1:11 and 1:15. These compositions would correspond to the members n = 13 and n= 17 of the homologous series B_nO_3n−1. It is possible that other structurally related phases are formed in this compositional region which have very little or no thermal stability. Unindexed x-ray diffraction powder patterns for the “1:11” and “1:15” phases are given in tables 12 and 13, respectively.

Table 12.

X-ray diffraction powder data for the composition Nb₂O₅:11WO₃ (CuK_a radiation)

da	Ib
4.638	5
4.308	7
3.966	25
3.850	350
3.726	230
3.690	350
3.116B	15
2.764B	10
2.677	178
2.670	190
2.579	28
2.202	25
2.190	25
2.139	12
1.998B	10
1.927	90
1.910	30
1.865	58
1.845	90
1.812B	18
1.712	32
1.700	14
1.677	100
1.664	50
1.569	8
1.541	18
1.530	25
1.493B	10

B= broad.

^aInterplaner spacing.

^bObserved intensity.

Table 13.

X-ray diffraction powder data for the composition Nb₂O₃:15WO₃ (CuKa radiation)

da	Ib
3.931	25
3.839	284
3.760	116
3.682	336
3.134	10
3.089	23
2.763	7
2.676	140
2.647	96
2.584	18
2.214	14
2.181	30
2.152	12
2.006B	10
1.922	58
1.898	27
1.869	65
1.855	20
1.841	40
1.812B	15
1.799	25
1.711	23
1.695	20
1.671B	65
1.652	15
1.573	8
1.555	10
1.546	15
1.529	34
1.525	30

B= broad.

^a Interplaner spacing.

^b Observed intensity.

3.5. Polymorphs of WO₃ and WO₃ Solid Solutions

WO₃ has been reported to occur in many different polymorphs [30–32]. None of the various high- or low-temperature polymorphs have been previously reported to be quenchable to room temperature. However, many of these reported phases have been found at room temperature in the Nb₂O₅−WO₃ system.

a. Room Temperature Monoclinic Polymorph

A monoclinic polymorph of WO₃ was reported by Tanisaki [32] to have a monoclinic unit cell with a = 7.30 Å, b = 7.53 Å, c = 7.68 Å, β = 90°54′ at room temperature. However, the x-ray diffraction powder pattern can be completely indexed with the c-axis equal to one-half that of the true unit cell. The presence of superstructure requiring the doubled cell can apparently only be found with single crystal data. For this reason, the x-ray diffraction powder pattern listed in table 14 has been indexed on the basis of one-half the real c-axis value. The unit cell dimensions obtained from this pattern were found to be a = 7.299 Å, b = 7.535 Å, c = 7.688 (3.844) Å, β = 90°54′. With 1 mole percent solid solution of Nb₂O₅ in WO₃, the parameters are changed to a = 7.317 Å, b = 7.532 Å, c = 7.684 (3.842) Å, β = 90°55′. For pure WO₃ this monoclinic polymorph is apparently stable from about 17 °C [32] to about 310 °C.

Table 14.

X-ray diffraction powder data for the room temperature (monoclinic) form of WO₃ (CuK_a radiation)

da	Ib	$\frac{1}{d^2}obs$	$\frac{1}{d^2}calc$	hklc
3.840	154	0.0678	0.0677	001
3.761	160	.0707	.0705	020
3.646	268	.0752	.0751	200
3.419	5	.0856	.0853	011
3.344	65	.0894	.0892	120
3.114	70.	.1031	.1030	$11\overline{1}$
3.083	50	.1052	.1052	111
2.689	132	.1383	.1382	021
2.667	72	.1407	.1406	210
2.629	54	.1447	.1450	$20\overline{1}$
2.620	152	.1457	.1455	220
2.533	22	.1559	.1558	$12\overline{1}$
2.514	27	.1582	.1580	121
2.176	38	.2112	.2110	$22\overline{1}$
2.154	36	.2156	.2155	221
2.103	6	.2262	.2262	031
2.043	17	.2395	.2394	320
2.025	12	.2438	.2439	$13\overline{1}$
2.016	14	.2461	.2461	131
1.9955	20	.2511	.2509	$31\overline{1}$
1.9709	12	.2574	.2576	311
1.9216	44	.2708	.2708	002
1.8838	60	.2818	.2818	040
1.8246	133	.3004	.3004	400
			.3006	140
1.8111	45	0.3049	0.3050	$11\overline{2}$
1.7977	42	.3094	.3094	112
1.7116	48	.3414	.3413	022
			1.3414	$20\overline{2}$
1.6914	40	.3495	.3495	041
1.6894	32	.3504	.3504	202
1.6740	35	.3569	.3569	240
1.6581	34	.3637	.3636	$40\overline{1}$
1.6504	24	.3671	.3672	$14\overline{1}$
1.6455	42	.3693	.3694	141
1.6423	80	.3708	.3708	420
1.6385	50	.3725	.3725	401
1.6231	5	.3919	.3918	$33\overline{1}$
1.5843	5	.3984	.3985	331
1.5584	30	.4117	.4119	$22\overline{2}$
1.5419	32	.4206	.4208	222
1.5384	27	.4225	.4224	$24\overline{1}$
1.5312	10	.4265	.4268	241
1.5179	15	.4341	.4341	$42\overline{1}$
1.5029	20	.4427	.4430	421
1.4981	22	.4456	.4459	$13\overline{2}$
1.4899	42	.4505	.4503	132
			.4507	$31\overline{2}$
			1.4508	340
1.4679	14	.4641	.4641	312

^aInterplaner spacing.

^bObserved intensity.

^cIndexed on the basis of a monoclinic unit cell with a = 7.299 Å. b = 7.535 Å. c = 3.844 Å (1/2 × 7.688 Å). β = 90°54′.

b. Low-Temperature Triclinic Polymorph

According to Tanisaki [32] the room temperature polymorph of WO₃ transforms to a triclinic form at about 17 °C, on cooling. However, on reheating there is still some of the triclinic form remaining at room temperature, indicating some hysteresis in the phase transition. It was found in the present study, that the room temperature monoclinic polymorph could be partially transformed to the triclinic modification by grinding the specimen in a mortar and pestle, without lowering the temperature. The unit cell dimensions of the triclinic form were reported [32] as a = 7.30 Å, b = 7.52 Å, c = 7.69 Å, α = 88°50′, β = 90°55′ γ = 90°56′. The indexed x-ray diffraction powder pattern of the triclinic polymorph obtained at room temperature from a specimen which had been removed from liquid nitrogen, is listed in table 15. The value of the c-axis was again halved, as the larger value is not necessary to index the powder pattern. According to Tanisaki, this phase is stable from about − 40 °C to about 17 °C. The triclinic polymorph was never observed in any of the Nb₂O₅−WO₃ solid solutions.

Table 15.

X-ray diffraction powder data for the triclinic form of WO₃ (CuK_a radiation)

da	Ib	$\frac{1}{d^2}obs$	$\frac{1}{d^2}calc$	hklc
3.840	284	0.0678	0.0677	001
3.760	224	.0707	.0707	020
3.652	350	.0750	.0749	200
3.362	20	.0885	.0885	$\overline{1}20$
3.322	25	.0906	.0906	120
3.143	42	.1012	.1013	$\overline{1}\overline{1}\overline{1}$
3.099	20	.1041	.1042	$\overline{1}11$
3.085	65	.1051	.1051	$1\overline{1}1$
3.070	42	.1061	.1059	$11\overline{1}$
2.714	55	.1359	.1358	$02\overline{1}$
2.667	108	.1407	.1407	$20\overline{1}$
2.660	102	.1413	.1413	021
2.640	80	.1435	.1435	$\overline{\text{2}}\text{20}$
2.632	93	.1443	.1443	201
2.600	58	.1480	.1477	220
2.562	13	.1524	.1524	$\overline{1}\overline{2}\overline{1}$
2.527	11	.1567	.1564	$\overline{\text{1}}\text{21}$
2.501	15	.1598	.1598	$\text{12}\overline{\text{1}}$
2.500	17	.1600	.1600	$\text{1}\overline{\text{2}}\text{1}$
2.202	20	.2063	.2066	$\overline{2}\overline{2}\overline{1}$
2.159	20	0.2145	0.2145	$\overline{\text{2}}\text{21}$
2.154	53	.2155	.2158	$\text{22}\overline{\text{1}}$
2.150	51	.2163	.2163	$\text{2}\overline{\text{2}}\text{1}$
2.120	3	.2224	.2227	$\text{03}\overline{\text{1}}$
2.082	5	.2306	.2310	031
2.059	4	.2358	.2360	$\overline{\text{3}}\text{20}$
2.046	8	.2388	.2389	$\overline{1}\overline{3}\overline{1}$
2.032	5	.2422	.2423	320
2.025	10	.2439	.2439	$\overline{\text{1}}\text{31}$
2.011	9	.2474	.2481	$\overline{3}\overline{1}\overline{1}$
2.005	12	.2487	.2490	$\text{13}\overline{\text{1}}$
1.9985	10	.2504	.2503	$\text{1}\overline{\text{3}}\text{1}$
1.9844	9	.2540	.2540	$\text{3}\overline{\text{1}}\text{1}$
1.9746	12	.2565	.2564	$\text{31}\overline{\text{1}}$
1.9713	14	.2573	.2568	$\overline{\text{3}}\text{11}$
1.9216	48	.2708	.2708	002
1.8801	52	.2829	.2829	040
1.8273	148	.2995	.2995	400
			.2995	$\overline{\text{1}}\text{40}$
1.8198	44	.3020	.3021	$\overline{1}\overline{1}\overline{2}$
1.8040	26	0.3073	0.3068	$\overline{1}12$
1.8007	43	.3084	.3086	$1\overline{1}2$
1.7931	26	.3110	.3113	$11\overline{2}$
1.7244	17	.3363	.3360	$02\overline{2}$
1.7113	24	.3415	.3420	$20\overline{2}$
1.7013	23	.3455	.3451	$04\overline{1}$
			.3457	202
1.6975	22	.3470	.3470	022
1.6897	17	.3503	.3506	041
1.6825	13	.3533	.3536	$\overline{2}40$
1.6653	16	.3606	.3608	$\overline{1}\overline{4}\overline{1}$
1.6612	52	.3624	.3620	240
1.6570	31	.3642	.3635	$40\overline{1}$
1.6537	28	.3657	.3660	$\overline{4}20$
1.6502	33	.3672	.3669	$\overline{1}41$
			.3672	401 141
1.6358	30	.3738	.3736	$14\overline{1}$
1.6337	35	.3747	.3744	420
1.6303	18	.3763	.3760	$1\overline{4}1$

^aInterplaner sparing.

^bObserved intensity.

^cIndexed on the basis of a triclinic unit cell with a = 7.30 Å. b = 7.52 Å, c = 3.845 Å (1/2 × 7.69 Å), a = 88°50′, β = 90°55′, γ = 90°56′.

c. Lowest Temperature Polymorph (Monoclinic)

From about − 40 °C to below liquid nitrogen temperature, another monoclinic polymorph occurs in pure WO₃ which was reported by Tanisaki [32] to have a = 5.27 Å, b = 5.16 Å, c = 7.67 Å, β = 91°43′. This polymorph can be obtained essentially single phase at room temperature by quenching a solid solution of 2Nb₂O₅:98WO₃ from the temperature interval 1230 °C to about 1385 °C, the solidus temperature. This polymorph also occurs as a mixture with other polymorphs in specimens containing 1 and 3 mole percent Nb₂O₅. The unit cell dimensions obtained from the powder pattern for the 2 mole percent Nb₂O₅ specimen are a = 5.305 Å, b = 5.192 Å, c = 7.671 Å, β = 91°33′. The indexed x-ray diffraction powder pattern is given in table 16, utilizing the 7.671 Å value for c as several peaks necessitating this doubled value are observed in the powder pattern. High-temperature x-ray patterns show this phase to be apparently stable in the 2 mole percent Nb₂O₅ composition up to a temperature of about 735 °C, at which temperature it transforms to a tetragonal polymorph. If the temperature is not raised above about 750 °C, this transition is reversible. However, if the temperature is raised to 900 °C the low-temperature monoclinic polymorph is not recovered and the tetragonal phase transforms lo the orthorhombic polymorph.

Table 16.

X-ray diffraction powder data for the low-temperature monoclinic form of WO₃ taken from 2Nb₂O₅:98WO₃ solid solution (CuK_a radiation)

da	Ib	$\frac{1}{d^2}obs$	$\frac{1}{d^2}calc$	hklc
3.834	400	0.0680	0.0680	002
3.703	380	.0729	.0729	110
3.145	25	.1011	.1011	$10\overline{2}$
3.083	50	.1052	.1051	012
3.067	32	.1063	.1064	102
2.691	138	.1381	.1382	112
2.641	144	.1381	.1432	200
			.1435	112
2.594	40	.1486	.1484	020
2.458	6	.1655	.1654	021
2.294	10	.1900	.1900	013
2.236	5	.2000	.1998	121
			.1999	211
2.206	22	.2056	.2058	$20\overline{2}$
2.148	70	.2167	.2163	022
			.2165	202
2.120	12	.2429	.2429	$21\overline{2}$
2.002	14	.2496	.2495	$12\overline{2}$
1.9860	17	.2535	.2536	212
1.9815	18	.2547	.2548	122
1.9178	68	.2719	.2719	004
1.8521	100	.2915	.2915	220
1.8192	27	.3022	.3023	$10\overline{4}$
1.7990	54	0.3090	0.3090	014
1.7875	28	.3130	.3130	104
1.7163	37	.3395	.3394	$11\overline{4}$
1.6900	25	.3501	.3501	114
1.6805	37	.3541	.3542	$22\overline{2}$
1.6692	41	.3589	.3592	310
1.6557	28	.3648	.3648	222
1.6448	26	.3697	.3696	130
1.6179	4	.3820	.3821	$30\overline{2}$
1.5851	4	.3980	.3981	302
1.5776	5	.4018	.4018	032
1.5729	10	.4042	.4044	$20\overline{4}$
1.5464	18	.4195	.4192	$31\overline{2}$
1.5422	21	.4205	.4202	024
1.5326	6	.4257	.4257	204
1.5161	28	.4351	.4349	$13\overline{2}$
			.4352	312
1.5056	26	.4412	.4402	132
			.4415	$21\overline{4}$
1.4895	13	.4508	.4507	$12\overline{4}$
1.4700	24	.4621	.4614	124
			.4628	214

^aInterplaner spacing.

^bObserved intensity.

^cIndexed on the basis of a monoclinic unit cell with a = 5.305 Å. b = 5.192 Å. c = 7.671 Å, β = 91°33′.

Tungsten trioxide has been reported to be ferroelectric below about − 40 °C [33]. Specimens of sintered WO₃ containing 2 to 4 mole percent Ta₂O₅ were reported to exhibit ferroelectric behavior at room temperature [34]. The low-temperature monoclinic polymorph formed by quenching a specimen containing 2 mole percent Nb₂O₅ was examined for evidence of ferroelectricity [35]. However, no conclusive ferroelectric properties could be found.

d. High-Temperature Orthorhombic Polymorph

Although no thermal effect was indicated with DTA, the room-temperature monoclinic polymorph of pure WO₃ is observed in the high temperature x-ray furnace to transform reversibly at 310 °C to an orthorhombic phase in agreement with Wyart and Foex [31]. This orthorhombic form is observed at room temperature in the solid solutions whenever the low-temperature monoclinic polymorph is heated to about 900 °C and cooled by removing from the furnace. The indexed x-ray diffraction powder pattern of a specimen of this polymorph containing 2 mole percent Nb₂O₅ is listed in table 17. It shows no indication of a doubled c-axis and is indexed on the basis of the smaller orthorhombic cell. The unit cell dimensions obtained for this composition, at room temperature, are a = 7.384 Å, b = 7.512 Å, c= 7.692 (3.846) Å. The orthorhombic phase is observed in this composition to transform to tetragonal in the high temperature x-ray furnace at 510 °C and the reverse transition was observed to take place at 440 °C.

Table 17.

X-ray diffraction powder data for the orthorhombic form of WO₃ taken from 2Nb₂O₅:98WO₃ solid solution (CuK_a radiation)

da	Ib	$\frac{1}{d^2}obs$	$\frac{1}{d^2}calc$	hklc
3.845	248	0.0676	0.0676	001
3.754	156	.0710	.0709	020
3.691	232	.0734	.0734	200
3.427	5	.0852	.0853	011
3.346	18	.0893	.0892	120
3.104	60	.1038	.1037	111
2.686	85	.1386	.1385	021
2.662	80	.1411	.1409	201
2.633	126	.1443	.1442	220
2.525	10	.1568	.1568	121
2.173	42	.2119	.2118	221
2.099	5	.2270	.2271	031
2.056	5	.2365	.2359	320
2.018	20	.2455	.2454	131
1.9976	14	.2506	.2504	311
1.9232	48	.2704	.2704	002
1.8779	33	.2836	.2836	040
1.8461	46	.2934	.2934	400
1.8198	21	.3020	.3019	140
1.8064	37	.3065	.3064	112
1.7119	24	.3412	.3413	022
1.7057	25	.3437	.3437	202
1.6879	35	.3510	.3512	041
1.6740	26	.3569	.3569	240
1.6645	32	.3609	.3610	401
1.6568	34	.3643	.3643	420
1.6453	14	.3694	.3695	141
1.5968	5	.3922	.3922	331
1.5530	10	.4147	.4146	222
1.5349	17	.4244	.4245	241
1.5217	20	.4319	.4319	421
1.4933	16	.4484	.4482	132
			.4486	340
1.4858	13	.4530	.4531	312

^aInterplaner spacing.

^bObserved intensity.

^cIndexed on the basis of an orthorhombic unit cell with a = 7.384 Å, b = 7.512 Å, c = 3.846 Å (1/2 × 7.692 Å).

e. Tetragonal High-Temperature Polymorph(s)

In pure WO₃ the orthorhombic polymorph was found to undergo a transition to the tetragonal form at about 750 °C in the high-temperature x-ray furnace. The DTA data indicated that the phase transition occurred at a temperature of 740 °C on heating and 730 °C on cooling. These results are in reasonable agreement with those of previous workers [7, 31]. The tetragonal polymorph is found as a single phase as low as 440 °C in the specimen containing 2 mole percent Nb₂O₅. However, in the 3 mole percent Nb₂O₅ specimen, the low-temperature monoclinic polymorph transforms after heating at about 900 °C into a mixture consisting predominantly of a tetragonal modification with only a trace of the orthorhombic form. The unit cell dimensions obtained at room temperature from this composition are a = 5.265 Å, c = 3.846 Å, and the x-ray diffraction powder pattern from which the data were obtained, indexed on the basis of the smaller cell, is listed in table 18.

Table 18.

X-ray diffraction powder data for the tetragonal form of WO₃ taken from 3Nb₂O₅:97WO₃ solid solution (CuK_a radiation)

da	Ib	$\frac{1}{d^2}obs$	$\frac{1}{d^2}calc$	hklc
3.847	280	0.0676	0.0676	001
3.725	252	.0721	.0722	110
3.106	58	.1037	.1037	101
2.674	116	.1398	.1398	111
2.638	96	.1438	.1443	200
2.173	40	.2118	.2119	201
2.008	25	.2481	.2480	211
1.923	45	.2705	.2705	002
1.861	48	.2886	.2886	220
1.806	42	.3067	.3066	102
1.707	26	.3430	.3426	112
1.675	40	.3566	.3563	201
1.665	48	.3606	.3608	310
1.597	5	.3922	.3923	301
1.552	8	.4150	.4148	202
1.528	28	.4284	.4284	311
1.489	15	.4510	.4509	212

^aInterplanar spacing.

^bObserved intensity.

^cIndexed on the basis of a tetragonal unit cell with a = 5.265 Å, c = 3.846 Å.

In addition to the transformation at 730–740 °C, another transition is observed at about 900 °C in pure WO₃, as indicated by a very small peak in the DTA pattern. High-temperature x-ray diffraction powder patterns indicate that WO₃ is tetragonal both above and below this minor thermal discontinuity. It is possible that the unit cell has a doubled c-axes below 900 °C and only above this temperature does the powder pattern yield the correct unit cell. However, this hypothesis cannot be verified without single crystal data.

Although WO₃ might be expected to have a cubic polymorph of the ReO₃-type, there is no evidence in either the present work or previously reported studies that such a polymorph exists.

4. Discussion of Phase Equilibria

The postulated phase equilibrium diagram of the binary system Nb₂O₅−WO₃ is shown in figure 1. The experimental data from which this diagram was constructed are given in table 19. The system contains four compounds which are shown as melting congruently, 6Nb₂O₅ · WO₃ “6Nb₂O₅ · 11WO₃,” 4Nb₂O₅ · 9WO₃ and 2Nb₂O₅ · 7WO₃. Six compounds melt incongruently “30Nb₂O₅ · WO₃,” 7Nb₂O₅ · 3WO₃, 8Nb₂O₅ · 5WO₃, 9Nb₂O₅ · 8WO₃, and the two Magneli phases estimated to be “Nb₂O₅ · 11WO₃” and “Nb₂O₅ · 15WO₃.” In addition, two stable phases, 13Nb₂O₅ · 4WO₃ and Nb₂O₅ · WO₃ dissociate before melting as does the apparently metastable disordered bronze type solid solution labeled “3:8” in the phase diagram. Six of the compounds (8:5, 9:8, “6:11”, 2:7, “1:11,” and “1:15”) are shown on the phase diagram as having minimum stability temperatures. In many of these cases, it is impossible to determine whether or not the minimum temperature represents a stable transition. The existence of solid solution could neither be definitely established in any of the compounds nor in Nb₂O₅. However, WO₃ accepts a maximum of about 3 mole percent Nb₂O₅ in solid solution.

Figure 1. Postulated phase equilibrium diagram of the binary system Nb₂O₅-WO₃.

Heavy lines represent well-established portions of the system and dashed lines represent not as well-established portions. Dotted lines represent persistent metastable equilibrium.

● – not melted.

◒ – partially melted.

O – completely melted.

× – experimental data obtained from “less-pure” materials.

Δ – high-temperature x-ray data.

Table 19.

Experimental data for compositions in the binary system Nb₂O₅−WO₃. Part I

^aAll specimens were initially calcined at 700 °C for 19 hr with heating and cooling rates of approximately 4 °C/min. Small portions of this calcine were then reheated lot the designated time at one or more designated higher temperatures and generally quenched in sealed Pt tubes.

^bAfter the initial heat treatments) all specimens were reheated at the indicated temperature and quenched in sealed Pt tubes, unless otherwise specified.

^cThe phases identified are given in the order of amount present at room temperature. The phases are not necessarily those present at the temperature to which the specimen was heated.

(?) = interpretation is not certain.

ss = solid solution.

(tr) = trace just barely discernible in x-ray pattern.

“30:1” = a phase of unknown structure occurring at a mole ratio of approximately 30:1 Nb₂O₅:WO₃.

(unknown) = extra peaks in the x-ray pattern which cannot be assigned to any recognized phase.

6:1 = 6Nb₂O₅ · WO₃ (WNb₁₂O₃₃).

low Nb₂O₅ = nonequilibrium phase (similar to the low temperature form of Nb₂O₅), when quenched from above the liquidus and examined at room temperature.

7:3 = 7Nb₂O₅ · 3WO₃ (W₃Nb₁₄O₄₄).

13:4 = 13Nb₂O₅ · 4WO₃ (W₄Nb₂₆O₇₇).

“bronze” = a metastable disordered phase having a variable composition and an undistorted tetragonal-tungsten-bronze type x-ray pattern (designated as “3:8” on the phase diagram).

8:5 = 8Nb₂O₅ · 5WO₃ (W₅Nb₁₆O₅₅).

9:8 = 9Nb₂O₅ · 8WO₃ (W₈Nb₁₈O₆₉).

l:l = Nb₂O₅ · WO₃ (WNb₂O₈).

“6:11” = a tungsten bronze type phase of orthorhombic symmetry and with superstructure lines indicative of the unit cell being tripled in the a and b directions.

Q – liq = metastable phase or phases which form only from the quenched liquid and give very poorly defined x-ray powder patterns, having the general appearance of the ReO₃ subcell characteristic of most of the compounds in this system.

4:9 = 4Nb₂O₅ · 9WO₃ (Nb₈W₉O₄₇).

L-MonWO_3ss = the monoclinic polymorph of WO₃ reported [30] to occur below −40 °C “stabilized” by a small amount of solid solution of Nb₂O₅ in WO₃.

2:7 = 2Nb₂O₅ · 7WO₃ (W₇Nb₄O₃₁).

“1:1l” = Magneli “shear” phase having the approximate composition lNb₂O₅:l1WO₃.

“l:15” = Magneli “shear” phase having the approximate composition lNb₂O₅:15WO₃.

Tet WO_3ss = the high temperature polymorph of WO₃ stabilized by solid solution of Nb₂O₅ in WO₃.

Orth WO_3ss = the orthorhombic polymorph of WO₃ ordinarily stable between about 320 °C and ~745 °C, “stabilized” by addition of Nb₂O₅ in solid solution.

Tri WO₃ = the polymorph of WO₃ which is stable just below room temperature and occurs at room temperature when pure WO₃ is ground in a mortar and pestle for a short time.

^dSpecimen heated and cooled at about 4 °C/min rather than quenched.

^eNonequilibrium, probably due to incomplete reaction.

^fNonbinary equilibrium, postulated as being due to reduction.

^gMetastable melting.

^hPt tube not sealed.

ⁱDid not receive preliminary 700° heat treatment.

The solidus temperature between the “30:1” phase and 6Nb₂O₅ · WO₃ has been found to be about 1464 °C. The exact eutectic composition has not been determined but probably exists between about 7 and 10 mole percent WO₃. The peritectic corresponding to the incongruent melting point of 7Nb₂O₅ · 3WO₃ occurs at 1440 °C and about 40 mole percent WO₃. However, the composition of the two peritectics at 1385 and 1375 °C and of the eutectic at 1364 °C, were not determined exactly. They probably occur between about 60 and 63 mole percent WO₃.

Both the 8:5 and 9:8 compounds apparently have minimum temperatures of stability. However, all efforts to locate accurately the temperature of these minimums proved inconclusive (table 19). For both compounds, the experimental temperature at which the phase begins to form on heating and the temperature at which it begins to dissociate on cooling had a wide range of overlap. Furthermore, the actual temperature of the minimum stability seemed to be strongly dependent on the purity content (table 19, parts I and II). For these reasons the minimum stability temperatures of the 8:5 and 9:8 are indicated on the phase diagram by dashed lines and the temperatures assigned to each, ~ 1090 and ~ 1265 °C, respectively, represent the best compromise between the inconsistencies in the experimental data.

None of the ordered bronze-type phases can be prepared in reasonable laboratory time at 1100 °C. The “6:11” phase was not found to be well crystallized below about 1210 °C. The minimum line at this temperature is dashed to indicate uncertainty in both the temperature value and the stability relation. The same discussion also is relative for the minimum value of the 2:7. In this case, however, the superstructure lines characteristic of this phase do not begin to appear below about 1245 °C. The three ordered bronze-type phases, “6:11”, 4:9, and 2:7, all appear to melt congruently at 1378, 1380 and 1357 °C, respectively. The solidus temperatures between these phases at 1365 and 1335°C appear to be measurably lower than the observed melting temperature of the compounds. However, no eutectic compositions could be experimentally determined, possibly due to reduction and, therefore, the liquidus curves are necessarily dashed (see discussion on reduction in sec. 5).

The ability to distinguish a two-phase region between the two bronze-type phases 4Nb₂O₅ · 9WO₃, and 2Nb₂O₅ · 7WO₃ was greatly increased by a separation of those phases in the experiments of long-time duration. The top of the specimens within the two-phase region showed only 4:9 in the x-ray diffraction pattern while the bottom of the specimen showed mostly 2:7. This apparent gravity separation is probably enhanced by an appreciable vapor phase in the sealed Pt tube and is considered to be due mainly to vapor transport. A similar gravity separation takes place throughout most of the system and adds more evidence to the probability of a two-phase region between “6Nb₂O₅ · 11 WO₃” and 4Nb₂O₅ · 9WO₃. This two-phase region is based mostly on the different morphology and color of these phases, as well as the slight differences in the superstructure exhibited by single crystal patterns. Almost all of the high-temperature phases in the Nb₂O₅-WO₃ system are needle formers. Most of those which contain appreciable WO₃ are yellow-green or blue-green in color. However, the “6:11” phase is white and forms tabular crystals rather than needles.

A eutectic exists between the 2:7 compound and the Magneli “shear” phases at about 1340 °C and 83 mole percent WO₃. However, the exact compositions of the peritectics at 1356 and 1358 °C, corresponding to the decomposition temperatures have not been determined.

Tungsten trioxide has been found to accept a maximum of about 3 mole percent Nb₂O₅ in solid solution at the solidus temperature of 1358 °C. The amount of solid solution decreases with decreasing temperature to about 2 mole percent at 1230 °C and less than 1 mole percent at 1100 °C. The melting point of WO₃ was found, in the present study, to be 1435 °C. This value was independently confirmed by E. M. Levin [36] and is in disagreement with the previously published value of 1472 °C (Jaeger and Germs) [37]. In a discussion of the 1472 °C value for the melting point of WO₃, Phillips and Chang [38] concluded that this temperature was probably too low and might actually represent the eutectic between WO₃ and W₂₀O₅₈. However, they did not attempt to experimentally determine the melting points of the compounds WO₃ and W₂₀O₅₈ or the solidus temperature between them. The 1435 °C value for the melting point of WO₃ is internally consistent with the experimental phase diagram of both the Nb₂O₅-WO₃ and WO₃-B₂O₃ systems [36]. This value apparently represents the practical melting point for the experimental conditions utilized: sealed Pt tube, heated for very short intervals of time (≦ 5 min). This method is preferable to that of Jaeger and Germs [37] who utilized an open Pt crucible and much longer heating time. However, the true melting point of WO₃ can probably only be established by utilizing an oxygen pressure furnace and extrapolating to one atmosphere pressure.

5. Reduction

As has been previously mentioned there is some tendency for WO₃ to reduce on heating to high temperatures, even in the sealed Pt tubes. This tendency is greatly enhanced by subjecting the specimens to high temperatures for extended periods of time. The problem of reduction of WO₃ is apparently carried into the Nb₂O₅-WO₃ system to such an extent that the system may not be completely binary at high temperatures.

The experimental data indicate that the system probably remains essentially binary as long as no melting occurs. However, above the solidus, reduction very likely takes place and the measured liquidus values may not represent binary equilibrium. The melting relations around the ordered bronze-type phases, from about 60 to 80 mole percent WO₃, were particularly difficult to obtain experimentally. The three compounds at “6:11”, 4:9 and 2:7 all appeared to melt congruently with binary solidus relations between them. However, the liquidus values appear to form smooth curves between these congruent melting points without any indication of a change in slope toward a eutectic composition. The phenomena is characteristic of a nonbinary system. For the sake of simplicity, the phase diagram has been drawn to indicate the most likely binary relationships and liquidus curves have been dashed to illustrate the uncertainty in values.

Another indication of reduction occurs in the melting relations of the B_nm+1O_{3nm−(n+m)+4} homologous series compounds. The phases W₃Nb₁₄O₄₄, W₅Nb₁₆O₅₅, and W₈Nb₁₈O₆₉ were all observed to melt incongruently. Experimentally these compound compositions were observed to begin to form a second phase at about 1440°, 1385°, and 1375°, respectively. However, compositions in two-phase regions between these compounds did not begin to form the new phase until considerably higher temperatures, even though the specimen may have shown an appearance of partial melting. This apparent increase in the stability temperature of the phases is dependent on the amount of time the specimen is held at temperature, and binary melting relationships can be approximated by only holding the experimental specimens for relatively short periods of time. It may therefore be concluded that reduction takes place in these specimens, when held above the solidus temperatures. However, it has previously been concluded [1–4] that the crystal structure of these compounds precludes any appreciable nonstoichiometry. Therefore, it appears likely that, as the W⁺⁶ ion is reduced, the Nb/W ratio of these phases shifts towards higher tungsten content, maintaining an essentially constant cation: anion ratio.

In addition to the relatively large amount of reduction which apparently takes place above melting, there is possibly some tendency towards reduction at lower temperatures. The amount of reduction which can take place experimentally below melting is probably several orders of magnitude less than that which occurs above melting because it seems in no way to affect the equilibrium relationships. The only indication of this minor reduction is in a tendency for discoloration of the specimens. Almost any composition in the system, held for long periods of time in a sealed Pt tube will show a much darker green or blue color than does the same composition either held for shorter periods or not sealed. This darker color can always be lightened by annealing the specimen in an open Pt tube, at about 1000 °C.

It is intriguing to postulate that the Nb₂O₅-WO₃ system might more closely approach binary conditions if the experiments were performed under conditions of high oxygen pressure, such as that utilized by Van Hook [39]. Such studies will probably become more common in the near future.

6. Metastable Phases and Nonequilibrium

6.1. Metastable Melting

It can be seen from table 19, that all compositions containing more than about 72 mole percent WO₃ were calcined for about 2 hr at 1200 °C prior to attempting to obtain equilibrium data. This was because the few preliminary heat treatments, performed at temperatures above 1250 °C, without the 1200 °C calcine, exhibited some indication of melting, whereas those with a prior 1200 °C calcine did not show melting until much higher temperatures.

The metastable melting apparently is due to a eutectic type reaction between the metastable bronze-type solid solution (labeled “3:8” on fig. 1) and pure WO₃. It must be emphasized that in order to obtain equilibrium products in the region 72 to 100 mole percent WO₃, this preliminary calcine at 1200 °C is imperative. Without such preliminary heat treatment, neither the 2:7 compound nor the “Magnelishear” structures can be prepared as single phases.

6.2. Metastable Phases

The bronze-type solid solution previously mentioned (“3:8” of fig. 1) has been interpreted as a metastable phase for several reasons. It appears to be responsible for very low temperature metastable melting which takes place between about 72 and 100 mole percent WO₃. The x-ray powder pattern of the bronze-type solid solution shows no superstructure and the phase must contain disordered pentagonal bypyramid polyhedra. It must be concluded that the disordered phase is metastable because it dissociates on heating to two ordered phases. All compositions between about the 6:11 and 2:7 ratios, when quenched from above the liquidus exhibit the tetragonal bronze-type “disordered” phase with no indication of any superstructure peaks in the x-ray diffraction powder pattern. In addition, many specimens also show a small amount of a quenched liquid phase which exhibits a poorly defined x-ray pattern characteristic of a disordered ReO₃ structure, the basic building unit of all the compounds in the system.

From about 5 mole percent WO₃ to at least 15 mole percent WO₃ another metastable phase is formed from the quenched liquid. This phase has an x-ray pattern, characteristic of the orthorhombic low-temperature form of Nb₂O₅. The diffraction pattern shows diffuse peaks and little or no superstructure lines. This phase never appears below the melting point and only forms as a single phase if the quenching temperature is considerably above the liquidus. The ability of a specimen to be quenched as a phase with a powder pattern similar to the low-temperature form of Nb₂O₅ seems to be dependent on cooling rate and composition. This phenomena has been previously reported for other niobate systems [23, 40].

As shown in table 19, another unknown phase has been found occasionally in nonequilibrium mixtures between about 7 and 25 mole percent Nb₂O₅. All efforts to establish an equilibrium region for this phase have proved negative. It is possible that the unknown compound may represent a complex structure involving a mixture of 3 × 3 blocks along with the 3 × 4 and/or 4 × 4 blocks normally found in other compounds occurring in this composition range. Such a structure would contain a considerable number of Nb⁺⁵ ions in tetrahedral coordination and would not be expected to form a stable assemblage.

It has been previously mentioned [1] that WNb₁₂O₃₃ appears to have a small region of homogeneity, in that the 8:1 composition showed only a single phase. However, no change in lattice parameters could be detected. This apparent region of solid solution is most likely due to the very similar powder patterns of the 6:1 compound and the “30:1” phase. A solid solution structure containing either a considerable number of oxygen vacancies or cation interstitials (in either the tetrahedral or octahedral position) would be expected to cause some measurable change in the lattice parameters. One other possible mechanism which has been suggested for solid solution [41] is again raised by the appearance of the “ordered intergrowth” structure of the 13:4 compound, and the suggested possible structure of a 25:1 or 20:1 compound. It is possible that a “disordered intergrowth” of double 3 × 4 blocks might occur in association with the isolated 3 × 4 blocks of the WNb₁₂O₃₃ compound [24]. Such a disordered structure or “compositional stacking fault” would cause only a slight broadening of some of the lines of an x-ray diffraction powder pattern, as would a mixture of a small amount of the ordered second phase. It is problematical as to whether such a picture of solid solution would represent a stable or only a metastable condition. Nevertheless, proof of such a postulated disorder would necessarily depend upon other data, outside the scope of this project. A careful electron diffraction and/or electron microscope study might prove of value in deciphering the nature of any possible disorder of this type.