Effect of Oxide Additions on the Polymorphism of Tantalum Pentoxide

Abstract

The “low temperature structure type” of Ta₂O₅ has been found to occur in two distinct forms with the lowest temperature form having a unit cell 14 times the subcell and an intermediate temperature form with a unit cell 11 times the subcell. The two types form intermediate partially ordered mixtures which are apparently in thermal equilibrium at various temperatures between ~ 1000 and 1350 °C. The addition of MoO₃, WO₃, SiO₂, GeO₂, ZrO₂, TiO₂, B₂O₃ and Al₂O₃ each affect the multiplicity of the true unit cell in different ways. WO₃, SiO₂, GeO₂, B₂O₃, and Al₂O₃ form phases structurally similar to “low-Ta₂O₅” which are stable up to the solidus temperatures of the corresponding systems.

1. Introduction

The low-temperature form of Ta₂O₅ has an, as yet, unknown structure related to the low-temperature form of Nb₂O₅ as well as to α-U₃O₈ and α-UO₃. As Ta₂O₅ exhibits a reversible phase transition at about 1360 °C to a structurally dissimilar high-temperature form [1]¹ it is not possible to grow single crystals of the room temperature stable form by conventional high-temperature techniques such as the Verneuil and the Czochralski methods. Whereas impurities appear to enter into solid solution in the high-temperature form of Ta₂O₅ [2] they apparently form new discrete phases in the low-temperature form [2]. In a previous publication [2] the present authors suggested that at least two discrete phases related to the low temperature form of Ta₂O₅ (L-Ta₂O₅) were formed at about 2 and 12.5 mol percent TiO₂ in the Ta₂O₅ : TiO₂ system. However, these phases transform at even lower temperatures than does the low-temperature form of pure Ta₂O₅. Jahnberg and Andersson [3] concluded that a series of discrete compounds of a similar type exist in the system Ta₂O₅-TaO₂F. Although they were able to obtain small crystals by heating specimens in sealed Pt tubes between 800 and 1300 °C they did not report any crystallographic or phase equilibria data for these phases.

In the present study, oxides containing cations smaller than Ta⁺⁵ have been added to Ta₂O₅ in an effort to obtain compounds related to L-Ta₂O₅ which may be stable at the melting point of the compositions.

2. Materials, Specimen Preparation, and Test Methods

The general quantitative spectrochemical analyses for the Ta₂O₅ used in this study has been previously reported [2]. All other oxides used were of reagent grade or better as described in previous publications [4]. These other oxides were MoO₃, WO₃, SiO₂, GeO₂, B₂O₃, and Al₂O₃. Some of the results previously reported for ZrO₂ [5] are duplicated here for discussion. The specimen preparation and test methods were the same as reported in the previous paper [5].

3. Results and Discussion

The experimental data is shown in table 1 and interpreted diagramatically as phase equilibria data in figures 1–3. The table columns need no comment except for the next to last and last columns. The “C-line” represents the position of a characteristic and diagnostic peak in the x-ray powder diffraction patterns, first referred to by Moser [6].

Table 1.

Experimental data

System	Composition	Heat treatment				X-ray diffraction analysesc	“C” line CuKα radiation 2θobs	m
		Initiala		Finalb
		Temp. °C	Time hr	Temp. °C	Time hr
Ta2O5		(as received)					26.75	14
				d 995	552	L-Ta2O3	26.65
				d 1220	264	L-Ta2O5	26.44
				d 1326	24	L-Ta2O5	26.40
				d 1327	312	L-Ta2O5	26.38	11
				d 1389	1.0	L-Ta2O5	26.35
				d 1402	2.0	L-Ta2O5	26.35
				d 1402	17	L-Ta2O5 + H-Ta2O5 (trace)	26.38
				d 1448	2	Htri-Ta2O5 + L-Ta2O5 (trace)
				d 1448	1	Htri-Ta2O5 + L-Ta2O5
				d 1450	0.5	Htri-Ta2O5 + L-Ta2O5
				d 1450	.25	L-Ta2O5	26.38
				d 1498	.08	Htri-Ta2O5
				d 1499	.03	L-Ta2O5	26.37
		e 1702	20			Htri-Ta2O5
				d 1224	425	L-Ta2O5	26.40
				1225	353	L-Ta2O5	26.44
		1350	336			L-Ta2O5	26.55
				d 1402	1.0	L-Ta2O5	26.45
				d 1404	5.0	L-Ta2O5	26.43
				d 1499	0.03	L-Ta2O5	26.35
		e 1405	2.5			L-Ta2O5	26.38
				d 995	552	L-Ta2O5	26.65
				d 1162	168	L-Ta2O5	26.58
Ta2O5–MoO3	95:5	500	10
		f 700	60			L-Ta2O5 phase(s)
				1185	19	L-Ta2O5 phase(s) + MoTa12O33	26.48
		f 1200	60			L-Ta2O5 phase(s) + MoTa12O33
				1323	71	L-Ta2O5 phase(s) + MoTa12O33	26.40
				1426	19	L-Ta2O5 phase(s) + MoTa12O33	26.34
				1599	4.5	Htri-Ta205 + Q-Liquid
	90:10	500	10
		f 700	60			L-Ta2O5 phase(s)
				1185	19	MoTa12O33 + L-Ta2O5 phase(s)
		f 1200	60			MoTa12O33 + L-Ta2O5 phase(s)
				1323	71	MoTa12O33 + L-Ta2O5 phase(s)	26.32
				1426	19	MoTa12O33 + L-Ta2O5 phase(s)	26.28
				1599	4.5	Htri-Ta2O5 + Q-Liquid
Ta2O5–MO3	95:5	1000	10	1326	19	L-Ta2O5 phase(s)	26.17
				1453	16	L-Ta2O5 phase(s)	26.15
				1603	100	L-Ta2O5 phase(s)	26.08	19
				1652	4	L-Ta2O5 phase(s) + H-Ta2O5 trace	25.98
		700	10
		f 1450	60			L-Ta2O5 phase(s)	26.20
	90:10	500	64
		1000	10
				1327	19	L-Ta2O5 phase(s)	25.90
				1449	19	L-Ta2O5 phase(s)	25.89
				1486	2.5	L-Ta2O5 phase(s)	25.86
				1649	4	L-Ta2O5 phase(s)	25.82
				1651	5	L-Ta2O5 phase(s)	25.85
				1652	4	L-Ta2O5 phase(s)	25.85
		f 1450	60			L-Ta2O5 phase(s)	25.90
	75:25	700	10
		f 1100	672			L-Ta2O5 phase(s) + WTa2O6	25.55
		700	10	1463	64	L-Ta2O5 phase(s)	25.22
				1659	4	L-Ta2O5 phase(s) + Q-Liquid	25.45
		f 1450	60			L-Ta2O5 phase(s)	25.24
				1602	1	L-Ta2O5 phase(s) + Q-Liquid	25.25
				1669	1	L-Ta2Or5 phase(s) + Q-Liquid	25.30
Ta2O5–SiO2	95:5	1000	10
				1325	65	L-Ta2O5 phase(s)	26.10	19
				1448	16	L-Ta2O5 phase(s)	26.00
				1597	4	Htri-Ta2O5ss + L-Ta2O5 phase(s) (trace)
	90:10			1325	65	L-Ta2O5 phase(s)	26.10
				1448	16	L-Ta2O5 phase(s) + cristobalite (trace)	25.95
				1595	4	Htri-Ta2O5 + L-Ta2O5 phase(s)
	75:25	1000	10
				1448	64	L-Ta2O5 phases + H-Ta2O5 + cristobaliteg	25.96
	50:50	1000	10
				1442	17	L-Ta2O5 + H-Ta2O5ss + cristobaliteg	25.94
Ta2O5–GeO2	95:5	1000	10
				1325	16	L-Ta2O5 phase(s)	26.08
				1448	16	L-Ta2O5 phase(s)	25.97
				1536	5	H”30.1”-Ta2O5ss- Ta2OS phaseh
				1568	5	H”30.1”- Ta2O5ssh
				1592	4.5	Htri-Ta2Oi
				1614	3.5	H”30.1”-Ta2O5ss + Q-Liquid
	90:10	1000	10
				1322	16	L-Ta2O5 phase(s)	25.97
				1448	16	L-Ta2O5 phase(s)	25.92
				1536	4	L-Ta2O5 phase + L-Ta2Ori phase	25.05, 25.68
				1560	5	L-Ta2O5 phase(s)	25.90
				1597	4	H”30.1”-Ta2O5ss + Q-Liquidh
				1607	5	H”30.1”-Ta2O5ss + Q-Liquidh
	75:25	500	10
		700	10
				1445	16	L-Ta2O5 phase(s)	25.94	43
	50:50	500	10
		700	10
				1443	19	L-Ta2O5 phase(s)j	25.90
Ta2O5–ZrO2	95:5	1000	10
				1326	19	L-Ta2O5 phase(s)	26.60
	90:10	1000	10
		1225	168			L-Ta2O5 phase(s)	26.92
Ta2O5–B2O3	95:5	1000	10
				1325	65	L-Ta2O5 phase(s)	26.37
				1449	16	H-Ta2O5ss + L-Phase(s)
				1596	4.5	Htri-Ta2O5ss + L-Ta2O5 phases(s)
	90:10	1000	10	1326	16	L-Ta2O5 phase(s)	26.27
				1449	16	L-Ta2O5 phase(s) + H-Ta,O5ss
				1576	5.5	Htri-Ta205ss + L-Ta2O5 phase(s)
				1595	4	Htri-Ta205ss + L-Ta2O5 phase(s)
	75:25	500	10
		700	10
				1442	20	L-Ta2O5 phase(s)	25.85	43
Ta2O5–Al2O3	95:5	1000	10
				1322	65	L-Ta2O5 phase(s)	25.84
				1449	16	L-Ta2O5 phase(s)	25.76
				1576	5.5	L-Ta2O5 phase(s) + H-Ta2O5ss	25.63
	94:6	1200	6
				1611	4	L-Ta2O5 phase(s) + H-Ta2O5ss	25.63
	93:7	1250	168
		1450	60
				1504	20	L-Ta2Os phase(s)	25.65
				1534	336	L-Ta2O5 phase(s)	25.65
				1540	20	L-Ta2O5 phase(s)	25.65
				1558	139	L-Ta2O5 phase(s) + H-Ta2O5ss	25.65
				1592	142	L-Ta2O5 phase(s) + H-Ta2O5ss	25.65
		1200	6	1594	288	L-Ta2O5 phase(s)	25.63
				1598	4	L-Ta2O5 phase(s)	25.60	29
				1668	4	H-Ta2O5ss + Q-Liquid
				1674	16	H-Ta2O5ss + Q-Liquid
		1560	60
		1600	12			L-Ta2O5 phase(s) + AlTaO4-AlNbO4 type	25.92
				1411	20	L-Ta2O5 phase(s) + AlTaO4-AlNbO4 type	25.60, 25.75
				1606	3.5	L-Ta2O5 phase(s) + AlTaO4-AlNbO4 type	25.60, 25.95
				1622	4	L-Ta2O5 phase	25.60	29
				1645	4	L-Ta2O5 phase	25.60
				1653	4	H-Ta2O5ss + Q-Liquid
				1699	1	H-Ta2O5ss + Q-Liquid
				1707	1	H-Ta.O5ss + Q-Liquid
				1719	1	H-Ta.O5ss + Q-Liquid
				1750	1	H-Ta2O5ss + Q-Liquid
	92:8	1200	6
				1605	4	L-Ta2O5 phase(s) + AlTaO4-AlNbO4 type	25.60
	91:9	1200	6
				1618	4	L-Ta2O5 phase(s) + AlTaO4-AlNbO4 type	25.60
	90:10	1000	10
				1300	16	L-Ta2O3 phase(s) + AlTaO4-AlNbO4 type	25.85
				1444	64	L-Ta2O3 phase(s) + AlTaO4-AlNbO4 type	25.75
				1586	4	L-Ta2O5 phase(s) + AlTaO4-AlNbO4 type	25.60
				1640	4	L-Ta2O5 phase + Q-Liquid (rutile type)	25.60

^aInitial Heat Treatment – All specimens were calcined as pressed disks on Pt foil at the indicated heat treatment with heating and cooling rates of approximately 4 °C/min, unless otherwise specified.

^bFinal Heat Treatment – All specimens were quenched in sealed Pt tubes from the indicated temperature (unless otherwise specified).

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

^dPt tube not sealed.

^eQuenched from indicated temperature.

^fSpecimen was sealed in a large Pt tube to minimize possible loss of more volatile component.

^gPresence of three phases indicates non-equilibrium.

^hProbably due to change of specimen composition by the addition oxide reacting with Pt tube.

ⁱSpecimen tube leaked and all or most of addition oxide was lost by volatilization.

^jPetrographic examination shows considerable amounts of glass.

Figure 1. Ta₂O₅-rich regions of Ta₂O₅-MeO₃ systems, as deduced from limited quenching and x-ray diffraction data.

● – experimental data points

H-Ta₂O₅ – high temperature form of Ta₂O₅

L-Ta₂O₅ phase(s) – one or more phases with an x-ray powder diffraction pattern similar to the low temperature form of Ta₂O₅

( ) – numbers in parentheses indicate postulated multiplicity (m) of the unit cell for the indicated compositions.

Figure 3. Ta₂O₅-rich regions of Ta₂O₅-Me₂O₃ systems, as deduced from limited quenching and x-ray diffraction data.

● – experimental data points.

H-Ta₂O₅ – high temperature form of Ta₂O₅

ss – solid solution.

Figure 2. Ta₂O₅-rich regions of Ta₂O₅-MeO₂ systems, as deduced from limited quenching and x-ray diffraction data.

● – experimental data points

X – experimental data point – composition may have changed due to leak or reaction with Pt tube

H-Ta₂O₅ – high temperature form of Ta₂O₅

ss – solid solution.

Moser has pointed out that the exact nature of the x-ray diffraction powder pattern of low-Ta₂O₅ is dependent upon the heat treatment of the specimen. On the basis of the position of one characteristic peak (called the “C” line) he divided low-Ta₂O₅ into four different conditions (“Zustanden”) with the notation that one grades into the other with no perceptible boundaries. This “C”-line was also found in the present study to be very diagnostic of the amount of impurities added to Ta₂O₅, and its position is listed in table 1 for each specimen in which it could be observed.

Examination of single crystals [7] has shown that the “C-line” of the powder pattern is actually a 1k0 diffraction peak and is always the closest spot on the origin side of the 1k0 substructure reflection. The Low-Ta₂O₅ type phases in these systems always have only a b axis superstructure so that the “C-line” can be used directly to calculate the true unit cell. All of the superstructures in these systems are made up of ordered mixtures of phases having multiples of 3n + 5 (multiplicities, m) along the b axis [7]. Thus, if the structure happens to have a multiplicity of 5, 8, 11, 14, etc., the strong substructure line at about 28.3°2θ (CuKα radiation) will have the index (150), (180), (1,11,0), (1,14,0), etc., and the “C-line” will be (140), (170), (1,10,0), (1,13,0), etc. If, however, the true structure is a mixture of 3n + 5 multiplicities such as

$$5+8=13\mathrm{ or }5+8+8=21$$

etc., the substructure line will be (1,13,0), (1,21,0), etc., and the “C-line” will be (1,11,0), (1,18,0), etc. The “C-line,” therefore, has a k index equal to (m − x) where m equals the multiplicity and x equals the number of (3n + 5) phases involved in the ordered mixture. For m = 5, 13, 8, 19, 11, 25, and 14 the “C-line” has been observed to equal (24.14°)², 25.18°, 25.75°, 26.08°, 26.38°, 26.58° and 26.76°, 2θ (CuKα radiation), respectively. From the above information the real multiplicity and true unit cell (the b axis) can be calculated by trial and error and the powder pattern completely and uniquely indexed on this basis. The calculated multiplicity (m) is listed in table 1 for some of the appropriate specimens.

The Low Temperature Polymorph(s) of Ta₂O₅.

The various “conditions” of the low temperature form of Ta₂O₅ reported by Moser [6] can now be explained in terms of the multiplicities of their unit cells, as shown by the C-line (see figs. 15 and 16 and table 14 of ref. [6]). Moser used several different methods of preparing Ta₂O₅ and on the basis of the value of the C-line divided them into four different conditions: α₁, α₂, α₃, and α₄. His α₂ phase corresponds approximately to a multiplicity of 8 times the subcell and grades into α₁ which is about 8 + 13 = 21. These specimens were mostly from transport reactions or heat treatments above the phase transition. It can be concluded from the present work that these materials have been contaminated by the transport medium or during the heat treatment and do not represent pure Ta₂O₅. The α₄ phase apparently also is contaminated by impurities either from the transport reaction or from OH⁻ present in the amorphous or semiamorphous starting materials. The quoted value of the C-line makes α₄ intermediate in composition between the 8 and 11 multiplicities or about m = 19.

The α₃ phase of Moser therefore is probably the only condition which represents pure Ta₂O₅. This condition still is not very satisfactory as the C-line varies with temperature of heat treatment from about 26.75°2θ to 26.35°2θ (table 1). Furthermore, the position of the C-line versus temperature apparently represents an equilibrium condition as it can be made to occur at the same value when approached from higher temperatures as when approached from low temperatures. This condition is reversible (table 1).

The as-received materials from several different sources all contain a C-line at about 26.75°2θ and represents the largest value (smallest d value) which can be observed for pure Ta₂O₅. This value corresponds approximately to a multiplicity of 14 times the subcell. Upon heating above 1000 °C the C-line changes gradually with temperature to a value of 26.38°2θ at the phase transition temperature ~1360 °C. Unlike Moser’s report, heating above this temperature did not cause a significant further shift in the value of the C-line. This last position corresponds to a multiplicity of about 11. Small single crystals of pure Ta₂O₅ with m = 11 can be obtained by inverting the high temperature form and holding the specimen for many weeks just below the phase transition. These crystals have been used to study the crystal structure of low Ta₂O₅ (m = 11) and the results of this study have been reported elsewhere (Stephenson and Roth [8]).

It may be concluded therefore that pure Ta₂O₅ exists in two low temperature polymorphic types: the lowest temperature form (~ 1000 °C and below) with m = 14 (Ta₂₈O₇₀) and a higher temperature form (~ 1350 °C) with m = 11 (Ta₂₂O₅₅). At intermediate temperatures ordered (or partially ordered) mixtures of the two phases occur in equilibrium with each other. The crystal structures of the two types must be very similar, and one can grade into the other by a small movement of only a few of the atoms (Stephenson and Roth [8]).

The Effect of other Ions on the Low Temperature Polymorph(s).

It can be seen from table 1 and figures 1–3 that WO₃, SiO₂, GeO₂, B₂O₃, and Al₂O₃ when added to Ta₂O₅, all form phases structurally similar to low-Ta₂O₅ which are stable up to the solidus temperatures of the corresponding systems. These oxides all contain small cations which are often found in tetrahedral coordination. It may be inferred that the stabilizing influence of these oxides on the L-Ta₂O₅ structure-type is due to the cations entering into the structure interstitially in tetrahedral coordination, or else lowering the average cation radius by substituting for Ta⁺⁵ in the lattice. MoO₃, although even more likely than WO₃ to go into tetrahedral coordination does not form these stable phases at high temperatures. Instead a new compound isostructural with WNb₁₂O₃₃ is formed with the Mo⁺⁶ ion in tetrahedral coordination and all the Ta⁺⁵ ions in octahedral coordination. GeO₂ apparently reacts with the Pt tubes when held at high temperatures for long periods of time (table 1), thus, making determination of the true equilibrium diagram very difficult. The Ta₂O₅-B₂O₃ and Ta₂O₅-SiO₂ systems show some promise in terms of determining the true phase diagrams. However, the Ta₂O₅-Al₂O₃ and Ta₂O₅-WO₃ systems appear to offer the most promise for determining the nature of the low-Ta₂O₅ type phases, as the characteristic “C”-line shows the most displacement for these systems.

The data for the system Ta₂O₅-ZrO₂ is reproduced in table 1 (from ref. [5]) as this is the only system yet found in which the “C”-line is displaced (from pure Ta₂O₅) toward higher 2θ (smaller d). It can be assumed that HfO₂ will also cause this type of displacement. These phases are not stable at high temperatures, since both Zr⁺⁴ and Hf⁺⁴ are larger than Ta⁺⁵ and would increase the average radius of the cations.

The exact compositions at which each multiplicity is postulated to occur in the systems studied is shown in tables 2a and 2b. The addition ion is believed to occur substitutionally in the Ta₂O₅ structure in the systems involving WO₃, TiO₂, ZrO₂, and Al₂O₃ but interstitually, in tetrahedral coordination, for the systems involving MoO₃, SiO₂, GeO₂, and B₂O₃. All values of multiplicity equal to, or less than, 50 are shown dia-grammatically on the postulated diagrams (fig. 1–3). Several larger values are shown in the system Ta₂O₅-TiO₂ for illustrative purposes. It has now been found that the compound 7:1, originally described in the Ta₂O₅-TiO₂ system [2] has a multiplicity of 30. However, the compound originally described as occurring around 2 mol percent Ta₂O₅ has been found to be a manifestation of equilibrium obtained in the Ta₂O₅ by the impurities added. This phase has a multiplicity of exactly 11, which can not be achieved by pure Ta₂O₅ at the same temperatures.

Table 2a.

Postulated compositions of phases in the systems involving Ta₂O₅ and oxides of other small cations

System and mol ratio	m a	x1b (m=13)	x2 (m=8)	x 2 (m=11)	Formula per unit cell
Ta2O3	11			1	Ta22O55
Ta2O5:WO3		(Ta22W4O67)	(Ta15WO40.5)	(Ta22O55)
81:2	41		1	3	Ta81WO205.5
59:2	30		1	2	Ta59WO150.5
37:2	19		1	1	Ta37WO95.5
13:1	27		2	1	Ta52W2O136
67:6	35		3	1	Ta67W3O176.5
41:4	13		4	1	Ta82W4O217
15:2	8		1		Ta15WO40.5
41:8	45	1	4		Ta82W8O229
67:14	37	1	3		Ta67W7O188.5
13:3	29	1	2		Ta52W5O148
89:22	50	2	3		Ta89W11O255.5
37:10	21	1	1		Ta37W5O107.5
59:18	34	2	1		Ta59W9O174.5
81:26	47	3	1		Ta81W13O241.5
11:4	13	1			Ta22W4O67
Ta2O5: SiO2			(Si2Ta16O44)	(Ta22O55)
41:2	41		1	3	Si2Ta82O209
15:1	30		1	2	Si2Ta60O154
19:2	19		1	1	Si2Ta38O99
27:4	27		2	1	Si4Ta54O143
35:6	35		3	1	Si6Ta70O187
43:8	43		4	1	Si8Ta86O231
4:1	8		1		Si2Ta16O44
Ta2O5:TiO2			(Ta12Ti4O38)	(Ta22O55)
18:1	74		1	6	Ta144Ti4O368
61:4	63		1	5	Ta122Ti4O313
25:2	52		1	4	Ta100Ti4O258
39:4	41		1	3	Ta58Ti4O203
7:1	30		1	2	Ta56Ti4O148
Ta205:B2O3			(B4Ta,6O«)	(Ta22Os5)
41:2	41		1	3	B4Ta82O211
15:1	30		1	2	B4Ta60O156
19:2	19		1	1	B4Ta38O101
27:4	27		2	1	B4Ta54O147
35:6	35		3	1	B12Ta70O193
43:8	43		4	1	B16Ta86O239
4:1	8		1		B4Ta16O46
Ta2O5:Al2O3		(Ta24Al2O63)	(Ta15AlO39)	(Ta22O55)
81:1	41		1	3	Ta81AlO204
59:1	30		1	2	Ta59AlO149
37:1	19		1	1	Ta37AlO94
26:1	27		2	1	Ta52Al2O133
67:3	35		3	1	Ta67Al3O172
41:2	43		4	1	Ta82Al4O211
15:1	8		1		Ta15AlO39
42:3	45	1	4		Ta84Al6O219
69:5	37	1	3		Ta69Al5O180
27:2	29	1	2		Ta54Al4O141

^am = Multiplicity of the b axis.

^bThe phase with m = 13 is really (m = 5) + (m = 8), therefore x = 2 so in order to find the real k index of the “C”-line for the Ta₂O₅-WO₃ phases one must add 2×₁ + x₂ + x₃ to find the value of x in the equation k = (m − x)[k = m − (2×₁ + x₂+x₃)].

Table 2b.

Postulated compositions of phases in the systems involving Ta₂O₅ and oxides of other small cations

System and mol ratio	m a	x 3 b (m=13)	x 4 (m=14)	x 5 (m=17)	Formula per unit cell
Ta2O5ZrO2		(Ta22O55)	(Ta27Zr069.5)	(Ta32Zr2O84)
49:2	25	1	1		Ta49ZrO124.5
19:1	39	1	2		Ta76Zr2O194
27:2	14		1		Ta27ZrO69.5
59:6	31		1	1	Ta59Zr3O153.5

^am = Multiplicity of the b axis.

^bTo find the value of x in the equation k = (m − x) expand into k = m − (x₃+x₄ +x₅).

It can be seen from table 2a that compositions having equivalent multiplicities in different systems have different cation/anion ratios. Each system has to be calculated on the basis of a different formula. In table 2a the formula k = (m − x) is expanded into

$$k=m-\left(2x_1+x_2+x_3\right)$$

where x₁, x₂, and x₃ are the number of (3n + 5) phases in the compositions with multiplicities of 13, 8, and 11 respectively. The only two systems which are alike are SiO₂ and GeO₂. The composition of the end member Ta₂O₅, of course, is the same in each case 11Ta₂O₅ (Ta₂₂O₅₅). Theoretically this structure might possibly accommodate three more oxygen ions [7,8]. For a phase with m = 8 the ideal composition is Me₁₆O₄₂. In the Ta₂O₅-WO₃ system this phase has been found to contain only 40.5 oxygen atoms per 8 subcells and has a composition of Ta₁₅WO_40.5. The phase with m = 13 having an ideal composition of Me₂₆O₆₈ has been found to have only 67 oxygen atoms and occurs at the composition Ta₂₂W₄O₆₇ [7,8]. All other multiplicities in this system can be calculated on the basis of these observations. In the Ta₂O₅-Al₂O₃ system the phase with m = 8 occurs at the 15:1 ratio and has the composition Ta₁₅AlO₃₉. Again, all other multiplicities have been calculated on this basis, also assuming the hypothetical phase with m = 13 (not actually observed in this system) having only 63 oxygens. In the Ta₂O₅-TiO₂ system however, the m = 30 phase has been found at the 7:1 ratio and the hypothetical m = 8 phase (not found) could therefore have only 38 oxygens as compared to 39 in Ta₂O₅-Al₂O₃, 40.5 in Ta₂O₅-WO₃ and 42 in the ideal structure. The larger Zr⁺⁴ ion causes the Ta₂O₅-ZrO₂ system to exhibit multiplicities in opposite direction from all the other systems. The data seem to indicate that the phase with m = 14 occurs at Ta₂₇ZrO_69.5 as compared to the ideal value of Me₂₈O₇₄ and compositions of the various phases have been calculated on this basis.

For the other systems, it has been concluded from the limited data that the addition ion enters into tetrahedral interstitual positions with one extra oxygen ion lying above each tetrahedral ion. The SiO₂ and GeO₂ systems have been calculated assuming that the hypothetical phase with m = 8 (not observed in either system) has the composition ${\text{Me}}_2^{+4}$ O₂Ta₁₆O₂

$$\left({\text{Me}}_2{\text{Ta}}_{16}{\text{O}}_{44}=8{\text{Ta}}_2{\text{O}}_5:2{\text{MeO}}_2\right).$$

However, the Ta₂O₅-B₂O₃ system seems to contain twice as many tetrahedral ions as are found in the SiO₂ and GeO₂ systems. The compositions have, therefore, been calculated on the basis of a formula for the hypothetical m = 8 phase (not found) of B₄O₄Ta₁₆O₄₂ (B₄Ta₁₆O₄₆ = 8Ta₂O₅:2B₂O₃). Due to the extreme volatility of MoO₃ at high temperatures as well as its tendency to reduce at these temperatures, no statement can be made as to the phases which might form in these systems on the basis of the reported experiments (table 1).

It should be noticed (table 1) that the “C”-line moves the same way for a W⁺⁶ cation as it does for an Al⁺³ cation or for any of the small ions regardless of valence. It is apparent that the position of the “C”-line is more dependent upon the amount and size of the cation than it is upon the valance. This leads to the conclusion that the size of the unit cell superstructure is more dependent upon the number of smaller cations which are included in the composition than upon the total number of oxygen ions. Before a final answer can be offered for this problem, single crystal structure determinations must be made for some of these compositions.

The system Ta₂O₅-WO₃ was, therefore, selected for further study in order to determine the number of phases of the low-Ta₂O₅ type which can be formed and to grow small single crystals for structural analyses. The results of this study will be reported elsewhere [9].