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Nuclear magnetic resonance studies of the glasses in the system K2OB2O3P2O5
Journal of Non-Crystalline Solids 30 (1978) 45 -60 © North-Holland Publishing Company
NUCLEAR MAGNETIC RESONANCE STUDIES OF THE GLASSES IN THE SYSTEM K 2 0 - B 2 0 3 - P ~ O s * Y.H. YUN ** and P.J. BRAY * Department o f Physics, Brown University, Providence, Rhode Island 02912, USA Received 21 April 1978 Revised manuscript received 18 Juli 1978
B11 NMR spectra have been used to study the structure of glasses in the system K 2 0 BzO3-P20 s . The results indicate that the glasses do not contain an appreciable number of boron atoms in BO3 units with one or two non-bridging oxygens. The fraction N 4 of boron atoms in BO4 units is measured and analyzed according to a structural model containing the following elements. (1) If the binary borophosphate system forms glasses, they consist of a borophosphate (BPO4) network and a borate network for K < 1, or a borophosphate (BPO4) network and a phosphate network for K > 1, where K = mol.% P2Os/mol.% B203. (2) The conversion rates of BO4 units (i.e. the rate of production or destruction by added oxygens) in the borate network and the borophosphate (BPO4) network are given as (+2) and (-0.38), respectively. (3)K+1 ions are proportionally shared between the two networks; (i.e. between the borate and borophosphate (BPO4) networks for K < 1, and between the phosphate and borophosphate (BPO4) networks for K > I).
1. Introduction Previous papers [ 1 - 1 6 ] from this laboratory have described the application of nuclear magnetic resonance (NMR) techniques to the studies of structure and chemical bonding of borate glasses. In particular, NMR has been used to determine the fraction (N4) of boron atoms in BO4 units, the fraction of BO3 units with all bridging oxygens and the fraction of BO3 units with one or two non-bridging oxygens. In binary alkali borate glass systems, the N4 data have been effectively analyzed [11] by plotting N4 as a function of R which is the ratio of the molar percentages of the alkali oxide and boron oxide in the glass. In more complex ternary borate systems, recent studies of glasses in the systems P b O - B 2 0 3 - S i O 2 [15] and N a 2 0 - B 2 0 3 -
* Research supported by the Materials Research Laboratory at Brown University funded through Grant No. DMR76-80560. Research also supported by National Science Foundation Grant No. DMR77-08600. ** Based on the work performed by Y.H. Yun in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Brown University. 45
46
Y.H. Yun, P.J. Bray/NMR studies of glasses
Si02 [16] have provided a clear picture of the variations of N4 as a function of R (= mol.% PbO or Na20/mol.% B203) by focussing on families of glasses for which K (= mol.% Si02/mol.% B203) is held constant. Similar studies of ternary alkali borophosphate glasses would be of particular interest because in this glass system, in addition to the structural units that are found in alkali borate or alkali phosphate glasses, a further type of structural unit, the BP04 unit, should be taken into consideration [17-23] when describing the structure of the glasses.The BP04 unit, which exists in the crystalline compound boron phosphate (BP04), consists of one B04 and one P04 unit, both units having four bridging oxygens. The excess of negative charge on the B04 unit is compensated by the excess of positive charge on the P04 unit. Thus the presence of BP04 units directly affects the N4 values of the glasses. Both B20a and P20s are water soluble glass network-forming oxides of low melting points, and yet their combination produces the chemically resistant and refractory compound boron phosphate (BP04). Kreidl and Weil [17], in a study of the durability of phosphate glasses containing boron oxide, were the first to assume that in these glasses BP04 units with a structure similar to that of crystalline BP04 were present. Since that time, additional evidence for the existence of BP04 units in borophosphate glasses has been reported. Takahasi [18] observed that the addition of boric acid to sodium phosphate glasses caused a rise in transformation temperature and increased their chemical durability. He attributed this to the formation of silica-type BP04 units. A detailed investigation [20] of an ESR spectrum of an irradiated lanthanum borophosphate glass has shown that there are two physically different B04 units differing from one another in the values of the g-factor and the hyperfine structure constant. The excess of negative charge on the B04 unit is compensated by the cation-modifier in one type of B04 unit, and by the excess of positive charge on the P04 units in the other type of BO4 unit. The formation of a borophosphate (BP04) network has also been suggested by Bogomolova et al. [21] in their ESR study of the Cs20-B203-P20s glass system and by Ushakov et al. [22] in their infrared study of the ZnO-B203-P20s glass system. In this paper, measured values of N4 for ternary potassium borophosphate glasses are reported and analyzed. A structural model is proposed to explain these data. K20 is chosen as the alkali oxide in order to check the N4 values recently measured [23] for the K20-B2Oa-P20s glass system by using Raman spectroscopy.
2. Experimental Thirty-seven glass samples were made spanning the glass-forming region reported by Imaoka [24]. The compositions were chosen so that the glasses were grouped into eight families, each family having the same K value (= mol.% P205/mol.% B203) but different R values (= mol.% K20/mol.% B203) as shown in fig. 1 and
Y.H. Yun, P.J. Bray/NMR studies of glasses
47
Table 1 Experimentally determined values of N4 [labelled N 4 (E) ] and calculated values of N 4 [labelled N4(C) ] were obtained from the model proposed in this paper. The N4(E) were measured by the "area method" except for the values in parenthesis which were measured by the "comparison method". Sample number
K
R
N4 (E)
N4 (C)
1
0.01
0
0.01
0.01
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
0.02 0.11 0.11 0.11 0.11 0.33 0.33 0.33 0.33 0.5 0.5 0.5 0.5 0.75 0.75 0.75 0.75 0.75 1 1 1 1 2 2 2 2 3 3 3 3 9 9 9 9
0 0.11 0.22 0.33 0.50 0.33 0.67 1 1.25 0.5 0.75 1 1.5 0.75 1 1.25 1.5 2 1 1.5 2 2.5 1.5 2 2.5 3 2 2.5 3 3.5 3 4 5 6
0.02 0.19 0.25 0.35 0.43 0.42 0.59 0.64 0.73 0.64 0,62 0.68 0.72 0.75 0.74 0.69 0.70 0.64 0.75 0.68 0.59 0.47
0.02 0.19 0.28 0.36 0.49 0.47 0.60 0.74 0.84 0.60 0.66 0.71 0.81 0.74 0.73 0.73 0.72 0.71 0.81 0.72 0.62 0.53 0.81 0.75 0.68 0.62 0.81 0.76 0.72 0.69 0.89 0.85 0.81 0.77
(0.78) (0.70) (0.55) (0.52) (0.85) (0.70) (0.71) (0.61) (0.78) (0.77) (0.61) (0.61) (0.79) (0.86) (0.71) (0.65)
table 1. In a d d i t i o n to those samples, t w o m o r e samples (no. 36 and no. 37) were prepared t o c h e c k the N4 values m e a s u r e d [23] b y R a m a n spectroscopy. The c o m positions are listed in table 2. Reagent grade potassium carbonate (K2 (303), orthoboric acid (H3BO3) and a m m o n i u m d i h y d r o g e n p h o s p h a t e (NH4H2PO4) were
48
Y.H. Yun, P.£ Bray/NMR studies of glasses K20
a,o,
'/9
2 3
9
P,O,
K~ Fig. 1. The glasses studied in the system K 2 0 - B 2 0 3 - P 2 0 s. The compositions are the batch
compositions. thoroughly mixed together. The mixtures were placed in procelain crucibles and fused at approximately. 800°C in an electric muffle furnace until all air bubbles had disappeared. The procelain crucibles do not react [23] significantly with the melt. The melts were agitated thoroughly to ensure homogeneity and then poured onto a metal plate and quickly covered with a brass block. Since the samples were hygroscopic, the quenching process was done in an atmosphere of dry nitrogen gas. Most samples were sealed in polystyrene vials, but some samples of extremely high hygroscopic character were vacuum-sealed in quartz tubes. The glasses were transparent and showed no sign of devitrification when checked by X-ray diffraction techniques. Varian Associates Wide-Line NMR Spectrometer (V-4200 B) was employed in
Table 2 Values of N4(E), N4(C) and the values of N4 [labelled N4(R)] measured by Raman spectroscopy (23). Sample number
K20 a)
B203 a)
P2Os a)
N4 (E)
N4 (C)
N4 (R)
11 15 25 36 37
25 30 40 23 16.7
50 40 20 54 66.7
25 30 40 23 16.7
0.64 0.75 0.70 0.56 0.43
0.60 0.74 0.75 0.55 0.38
0 0.08 0.26 0.03 0.52
a) Compositions are given by molar%.
Y.H. Yun, P.J. Bray/NMR studies o[glasses
49
connection with a Nicolet Signal Averager (Model 1072). The NMR spectra were obtained at a f~ed frequency of 16 MHz, by sweeping the magnetic field through the resonance condition. All measurements were made with the glass samples at room temperature.
3. Results and discussion The first derivative of the B 11 NMR absorption spectra for all the glasses studied consists of two lines. Examples of experimental spectra are shown in fig. 2. A narrow central line arises from boron atoms in oxygen tetrahedra (BO4 units) while boron atoms at the center of oxygen triangles (BO3 units) yield a broad resonance line due to a larger interaction between the B 11 nuclear quadrupole moment and the electric field gradient present at the boron site [3]. Particular attention was paid to those glasses having a high ratio of potassium oxide to boron oxide (samples no. 6, 10, 14, 19 and 23), since those glasses may contain BO3 units with one or two non-bridging oxygens (denoted as 'asymmetric BO3 units") such as those found in alkali borate glasses of high alkali oxide to boron oxide ratio [11]. Since one or two non-bridging oxygens in a BO3 unit cause the electric field gradient tensor at
glass No. 6 ~K20" I B2Os" ~P~051 glass No. lO -~K20. I B2Os.-~P~,05
'S'~
gless No. 14 }K20. 18203- ½P205 g,ass N o , 9
2K20" I B203'~P205 ' ' ' ' ~
~G"J/
glass No. 2:3 ,._,,,~ 2.5K20 • I B203. I P~05~ "~
~, ~ / '~.j~a ' 28.5 K i l l I
I
Fig. 2. B11 NMR (derivative) spectra at a resonance frequency vo of 16 MHz for samples No. 6, 10, 14, 19, and 23.
50
Y.H. Yun, P.J. Bray/NMR studies of glasses
the boron site to lose axial symmetry, the resulting spectra show definite structure [25]. The present potassium borophosphate glasses do not show this "extra" structure in the broad resonance lines (see fig. 2); therefore, these glasses do not contain an appreciable number of asymmetric BO3 units. The narrow and broad resonance lines can be separated and analyzed [25-29] in order to obtain the quadrupole parameters (i.e. the quadrupole coupling constant and the asymmetry parameter) and the fraction N4 of boron atoms in BO4 units. B 11 quadrupole parameters for all the samples studied appear to be similar to those found for alkali borate [3,7] an alkaline earth borate [8,10] glasses. Further, these parameters are relatively insensitive to changes of glass composition. A new method [30,31 ] of determining N4, involving the use of a signal averager, was employed in this work for samples with K ~< 1. Since the modulation technique [32] was used in the present study, the recorded signals are the first derivative of the absorption curve. The modulation frequency was 80 Hz and the modulation amplitude was 1.03 G which is small enough to ensure that appreciable broadening from the modulation field does not occur. A built-in integrator in the Nicolet signal averager was used to produce the absorption signals shown in fig. 3. The central peak is from boron atoms in BO4 units, and it is easily separated from the broad line. A direct measurement of the area under the central peak with respect to the total area gives the fraction N4. Although this method, called the "area method," has several advantages over the conventional "comparison method" [3] as described elsewhere [30,31], it will not yield accurate results for N4 for large values of N4. Thus for samples having K/> 1, which showed very large N4 values, the conventional comparison method [3] has been employed. N4 values of the K = 1 family of
gloss No.6
gloss No.19 Fig. 3. B 11 NMR spectra (integrated) from samples no. 6 and No. 19, which are used for determination o f N 4 .
Y.H. Yun, P.Z Bray / NMR studies of glasses
51
the samples were measured by employing both methods. The two N4 values for a given sample agreed within experimental error. Since the N4 values depend on glass composition much more strongly than do values of the quadrupole parameters, the behavior of N4 as a function of composition will be discussed extensively. N4 values of binary alkali borate glasses have been analyzed [11] by plottingN4 as a function of R (= mol.% alkali oxide/mol.% B20a). For R < 0.5, the N4 values fall on the straight line N4 ---R whose slope is one half [11] of the rate of conversion of BOa units to B04 units due to the oxygens introduced by alkali oxides. Each oxygen added by an alkali oxide is capable of converting two boron atoms from BOa to B04 units, and N4 can be written as N, =½ aR
(1)
where a, the conversion rate, equals (+2) for R < 0.5. N4 values for the ternary glasses in the system K 2 0 - B 2 0 3 - P 2 0 5 are analyzed accordingly. The molar fractions of K20, B203, and P2Os are denoted byx, y, and z, respectively. R and K are thus defined as R = x/y,
(2)
K = z/y.
The measured values of N4 are listed in table 1 and plotted as a function of R for fixed K in fig. 4. The plots are separated into eight families, each corresponding to one K value. A least-square fit of the N 4 data yields K
N4
1
0.63R 0.32R O.09R -0.09R
!3 l2 3
+ 0.12 + 0.34 + 0.58 + 0.82
K
N4
1 2 3 9
-0.19R -0.14R -0.13R -O.06R
+ 0.96 + 1.06 + 1.06 + 1.01
(3)
The linearity between N4 and R suggests that N4 can be formulated as N4 = ~ aR +/3,
(4)
where ~a and/3 are constants depending upon the K value. Figure 5 shows a plot of/3 as a function of K. The value of/3, equivalent to N4 for binary borophosphate glasses, increases with K up to K = 1 and remains near/3 = 1 for K > 1. This might indicate that if the binary borophosphate system forms a glass, there exist BO4 units - presumably in the form of BPO4 units - which will form to the extent that equal amounts of B203 and P2Os are available. If this is the case, it can be reasonably assumed that a binary borophosphate glass having more B203 than P2Os consists o f a BPO4 network and B203, and also that a binary borophosphate glass having more P2Os than B20~ consists of a BPO4 network and P2Os. In other words, (vB203 + zP205) = (v - z) B203 + 2zBPO4 , = ( z - y ) P2Os + 2yBPO4,
for K ~< 1 forK~> 1 .
(5)
Y.H. }run, P.J. Bray/NMR studies of glasses
52 ,q.
z
/
O.e
/
0.6 0.4
K={
.t /
K={
Z
0.2
R
R
2
z [ K:{ ,q.
I
Ir
z
K=I
°"r"..-.-~.. ] --
°"f,
t
R
K--2
\:',~.. R
!
R i
2
2
Z
0.6
0.4
z
i Z
%,
,R
!
i !
3
.~
K:3
K:9
0.2
R
R
Fig. 4. The fraction N4 of boron atoms in BO4 units versus R. The values of N4 indicated by closed and open ckcles were measured by the area method and comparison method, respectively. Since a BP04 unit consists o f one B04 unit and one P04 unit,/3 is given by
= 2z/2y = K , =2y/2y =1,
for K ~< 1 , forK1>1.
(6)
Y.H. ]Tun,P.Z Bray/NMR studies of glasses
P
t
I.O
O.0
0.6
0.4
] ,,
53
]
l
0.2
i I I II I K I 2 3 9 Fig. 5. # versusK. The solid line indicates # = K for K ~ 1, # = 1 for K ~ 1.
These relationships are shown in fig. 5 by the solid lines. Comparison with the experimental values shows that the agreement is reasonably good to within experimental error. To confirm the above results, two binary borophosphate glasses were prepared and tested. Although most of the binary borophosphate system does not form a glass, it has been reported that clear glasses can be obtained with a P2Os concentration less than 5 weight % [33]. One and two molar% P2Os binary borophosphate glasses (samples no. 1 and 2) were carefully prepared by using platinum crucibles and vacuum-sealed in a quartz tube. Fig. 6A shows the first derivative of the B 11 NMR absorption spectra of the samples along with that of pure B2Os glass for comparison. Figure 6B shows the integration of fig. 6A, from which N4 values were obtained. The determination of the dotted lines in fig. 6B was guided by visual comparison with the absorption spectrum of the 100% B203 glass sample shown in fig. 6B. As listed in table 1, the N4 values of these two binary borophosphate glasses agree with the values predicted by eq. (6). According to fig. 4, the addition of K20 to borophosphate glasses increases or decreases the N4 values depending on the value of K. The slopes of the linear relationships between N4 and R in eqs. (3), S(K), are plotted in fig. 7 as a function of K. The values of the slope sharply decreases from +1 to -0.19 when K is increased from 0 to 1. As the K value is further increased the values of the slope increase slowly, but remain less than zero. It has been well-known [3,11] that in binary alkali borate glasses with up to 33~ mol.% alkali oxide content the N4 values are increased by adding alkali oxides and the conversion rate of BOa units to BO4 units is (+2). This has been explained by the structural model developed by Kroh-Moe [34] in which alkali borate glasses
[A]
[8]
glass 100% Bz03 glass 99Bz03. I PzOa
glass 98 B~33"2 PzOa
28.SKHz I
I
Fig. 6. (A) B 11 NMR (derivative) spectra at a resonance frequency v0 o f 16 KHz for binary b o r o p h o s p h a t e glasses. (B) B 11 NMR (integrated) spectra o f binary b o r o p h o s p h a t e glasses which are used for the determination o f N 4.
0
U)
2 0
Fig. 7. S(K) versus K. T h e solid line indicates that S(K) = (1 - 1.38K)/(1 + K ) , S(K) = - 0 . 3 8 / ( 1 + K ) ,
for K < 1 , for K ~ 1 .
3
9
K
Y.H. Yun, P.J. Bray / NMR studies of glasses
55
are viewed as a random mixture of boroxol units, tetraborate units, and diborate units which occur in crystalline alkali borate compounds. If the alkali content is over 33] mol.%, N4 decreases on addition of more alkali oxide. The decrease of N4 is always accompanied [11] by the creation of asymmetric BOa units. This has recently been explained [16] by the formation of metaborate units and loose BO4 units at the expense of diborate units on addition of alkali oxides. As a result, the conversion rate of BO4 units to asymmetric BO3 units equals (-0.5). The decrease of N4 in the ternary potassium borophosphate glass system, however, cannot be explained by this process because an appreciable number of asymmetric BO3 units has not been observed. A similar decrease of N4 without the formation of asymmetric BOa units has been observed in lead borate [4] and lead borosilicate [15] glasses. This has been explained [4] by assuming that at high lead content, some of the lead enter the glass as a covalent network former in the form of PbO4 pyramids. A Pb 2°7 NMR study of lead borosilicate glasses [15] has supported this explanation. However, this cannot be the case for the potassium borophosphate glasses because K20 is believed to be solely a network modifier due to its chemical characteristics, such as the single-bond energy or electronegativity, which serve as criteria [33] to determine whether or not a metal oxide will form a glass network. Thus, a completely different process must be taken into account in order to explain the decrease o f N 4 in this ternary system. Particular attention has been paid to the K = 1 family of K:O-B203-P2Os glasses since from the analysis of 13, it appears that the hypothetical glass of composition B203 • P2Os consists mainly of BPO4 units. The decrease of N4 in the K = 1 family might be attributed to the destruction of BPO4 units by addition of K20 in order to form other structural units. It would be of substantial interest and value to determine the kinds of structural units which are formed a t t h e expense of BPO4 units by added K20. However, it was not possible to secure that information in the present investigation because the B 11 and p31 NMR spectra employed in this work were not able to identify each structural unit that exists in the glasses. It has been known [28] for some time that B al NMR spectra are not sufficiently senstive to distinguish each kind of structural unit in the alkali borate glasses because the dipole-dipole interaction and the distributions [28,35,36] of quadrupole parameters smear out the details of the spectrum which might be characteristic of each structural unit. p31 NMR spectra for the K 2 0 - B 2 0 3 - P 2 O s glasses were obtained at 16 MHz in the hope that they might be used to distinguish the alkali phosphate units which exist in alkali phosphate compounds. Since p31 has a nuclear spin ~, it has no electric quadrupole moment, but there are chemical shift interactions [6,7,37] which are available to probe, the bonding and structure. Slightly different p31 NMR spectra have been reported by Bray [38] from two crystalline alkali phosphate compounds. However, all of the p3~ NMR spectra obtained from potassium borophosphate glasses were structureless and quite symmetric, and the line widths were between one and two gauss. Although it is not possible at this time to describe the destruction process of
56
Y.H. Yun, P.J. Bray/NMR studies of glasses
BPO4 units by the addition of K20, the conversion rate of BO4 units into other units due to the destruction of BPO4 units can be experimentally determined from eq. (5) by considering the K =1 family. From eq. (3) with K = 1, and eq. (4), the destruction rate of BO4 units in the borophosphate (BPO4) network is given by (-0.38); that is, each oxygen added as K20 destroys 0.38 BO4 units. The production rate of BO4 units in a borate network has already been given [ 11 ] as (+2). Since for ternary glasses having K < 1 there are two kinds of networks [i.e. the borate network and a borophosphate (BPO4) network], there might be a sharing of K+1 ions between the two networks. Proportional sharing of cations between two networks has been observed in the glass systems PbO-B203-SiO2 [ 15] and N a 2 0 B203-SIO2 [16]. If it is assumed that the K+1 ions are proportionally shared between the borate network and the borophosphate (BPO4) network, then the number of oxygens which can modify each network would be reduced by the factor O'
-
z)/[(y
- z ) + 2z] = (1 - K ) / ( 1 + K )
for the borate network and 2z/[(y - z) + 2z] = 2K/(1 +K)
for the borophosphate (BPO4) network [see eq. (5)]. Thus, the conversion rate a(K) of BO4 units for the K ~< 1 families is given by a(K) = 2[(1 - K ) / ( 1
+K)] + (-0.38)[2K/(1
= (2 - 2.76K)/(1 + K ) ,
+K)I (7)
for K ~< 1 .
If it also assumed that for K > 1 families the K+l ions are shared between the borophosphate (BPO4) network and phosphate network, then the number of oxygens which can modify the borophosphate (BPO4) network would be reduced by the factor 2y/[2y + (z - y ) ] = 2/(1 +K)
[see eq. (5)]. Thus the conversion rate a(K) of BO4 units for the K > 1 families is given by o~(K) = (-0.38)[2/(1 +K)] =-0.76/(1 + K ) ,
forK~> 1 .
(8)
From eqs. (7) and (8), the slope S(K), which is one half of a(K), is given by S(K) = (1 - 1.38K)/(1 + K ) , = -0.38/(1 + K ) ,
for K ~< 1
(9)
for K I> 1.
Plots of the two parts of eq. (9) are shown as the solid lines in fig. 7 and compared with the experimental values. The agreement is reasonably good within experimental error and considering the additional uncertainties involved in the simplified
Y.H. Yun, P.J. Bray/NMR studiesof glasses
57
model, which will be discussed later. Thus, from eqs. (6) and (9) N4 can be formulated as a function of K and'R according to the structural model proposed in this paper; N4 = [(1 - 1.38K)/(1 + K)] R + K , = [(-0.38)/(1 + K)] R + 1 ,
for K ~< 1 for K >t 1 .
(10)
The treatment of N4 given above is based on a simplified model. The real glasses are not as simple in several respects. First, asymmetric BO3 units are completely ignored in the analysis on the basis of characteristics of the B 1~ NMR spectra for the three-coordinated borons. Since small concentrations of asymmetric BO3 units (involving less than perhaps 5% of the total borons) are not easily detectable in B 1 NMR spectra, the glasses may contain small quantities of asymmetric BO3 units. Second, the proportional sharing of IC l ions between the two networks may not be exactly according to eqs. (7) and (8). As shown in fig. 7, the experimental values of S(K) are generally a bit lower than the values predicted by eq. (9). This might indicate that some preferential association of K*~ ions with the borophosphate (BPO4) network rather than the borate network or phosphate network occurs. Similar preferential association of metal ions with one of the two networks in borosilicate glass systems has been reported [ 15,16]. Third, the conversion rate (-0.38) of BO4 units to other units in the borophosphate (BPO4) network has an experimental uncertainty (+0.10). Careful studies of these K20-B203-P2Os glasses by means of B 1° NMR and Raman spectroscopy are desirable to obtain more precise information concerning both the destruction process of BPO4 units and the conversion rate of BO4 units to other units due to the destruction of BPO4 units. All of the approximations noted above introduce some additional uncertainties into the calculated values of N,. Nevertheless, the simplified model proposed here permits a useful determination of the N4 values in ternary potassium borophosphate glasses from a knowledge of glass composition (i.e. from K and R). Table 1 lists the experimental values of N4 and the calculated values of N4 obtained from the model presented above. In fig. 8, all of the experimentalN4 data in table 1 are shown and compared with the calculated values. The agreement is good within the experimental error and the additional uncertainties involved in the simplified model. Raman spectroscopy has recently been employed [23] to extract quantitative values of N4 for this ternary glass system. The Raman technique has proved to be extremely useful in helping to identify structural units in glasses by means of band frequencies, but evaluation of N4 depends on a determination of band intensities which are sometimes uncertain, particularly in cases of overlap and fluorescence. Five glasses in table 2 have the same compositions as those studied by Raman techniques [23]. The results of N4 measurements for those samples using B 11 NMR are shown in table 2, along with the N4 values from Raman studies [23] and also with the calculated values of N4 from their corresponding compositions according to the
Y.H. ]run, P.J. Bray /NMR studies of glasses
58
/," ,/
%,
O
•
*
I
// /t / m
6 //
/
./
,~'"
,/ :.'"
I
I o.2
I
I o 4
I
I. o a
I
I o.a
t
| Lo
N4(E)
Fig. 8. Experimental values of N4(E ) versus the values of N4(c) calculated from their corresponding compositions according to the model proposed in this paper. The solid line indicates N4 (E) = N4 (C).
model proposed in this paper. The differences between the N4 values of the same sample as measured by NMR and Raman spectroscopy are obvious.
4. Summary The B 11 NMR spectra obtained from glasses in the system K20-B203-P2Os consists of a broad resonance line and narrow resonance line which indicate that these glasses contain both BO3 and BO4 units, but no appreciable numbers of BO3 units with one or two non-bridging oxygens are present. The values of N4 were measured by the area method, which involves the use of a signal averager, for samples with K < 1. For samples having K i> 1, the conventional comparison method was employed to measure N4 (K = mol.% P2Os/mol.% B2Oa). Equations which predict the behavior of N4 as a function of composition are formulated according to a simplified model containing the following elements. (1) If the binary borophosphate system forms glasses, they consist of a borophosphate (BPO4) network and a borate network for K < 1, or a borophosphate (BPO4) network and a phosphate network for K > 1. (2) The conversion rates of BO4 units in the borate network and the borophosphate (BPO4) network are given as (+2) and ( - 0 . 3 8 ) , respectively. (3) K"~1 ions are propo~ionally shared between the two net-
Y.H. Yun, P.J. Bray/NMR studies of glasses
59
works; (i.e. between the borate and borophosphate (BPO4) networks for K < 1, and between the phosphate and bo'rophosphate (BPO4) networks for K > 1).
Acknowledgments The authors express their appreciation to Mr. R. Kershaw for taking X-ray diffraction patterns of the samples, and also to S.A. Feller and F. Bucholtz for assistance in preparing the manuscript.
References [1] A.H. Silver and O.J. Bray, J. Chem. Phys. 29 (1958) 984. [2] P.J. Bray and A.H. Silver, Modem Aspects of the Vitreous State (Butterworth, London, 1960) Vol. 1. [3] P.J. Bray and J.G. O'Keefe, Phys. Chem. Glasses 4 (1963) 37. [4] P.J. Bray, M. Leventhal and M.O. Hooper, Phys. Chem. Glasses 4 (1963) 47. [5] M. Leventhal and P.J. Bray, Phys. Chem. Glasses 6 (1965) 113. [6] J.F. Bangher and P.J. Bray, Phys. Chem. Glasses 10 (1969) 77. [7] C. Rhee and P.J. Bray, Phys. Chem. Glasses 12 (1971) 165. [8] M.J. Park and P.J. Bray, Phys. Chem. Glasses 13 (1972) 50. [9] K.S. Kim and P.J. Bray, J. Nonmetals 2 (1974) 95. [10] S. Greenblatt and P.J. Bray, Phys. Chem. Glasses 8 (1967) 190. [ 11 ] S. Greenblatt and P.J. Bray, Phys. Chem. Glasses 8 (1967) 213. [12] S.G. Bishop and P.J. Bray, Phys. Chem. Glasses 7 (1966) 73. [13] D. Kline and P.J. Bray, Phys. Chem. Glasses 7 (1966) 41. [14] K.S. Kim and P.J. Bray, Phys. Chem. Glasses 15 (1974) 47. [15] K.S. Kim, P.J. Bray and S. Merrin, J. Chem. Phys. 64 (1976) 4459. [16] Y.H. Yun and P.J. Bray, J. Non-Crystalline Solids 27 (1978) 363. [17] N.K. Kreidl and W.A. Weyl, J. Am. Ceram See. 24 (1941) 372. [18] K. Takahashi, Advances in Glass Technology, Prec. 6th Int. Cong. on Glass, Washington DC, 1962 (Plenum Press, New York, 1962) p. 366. [19] P. Bcekenkamp and C.E.G. Hardeman, Verres et R6fr. 20 (1966) 419. [20] L.V. Bershov, E.S. Kutukova, V.O. Martirosyan and Z;M; Syritskaya, Inorg. Mater. Consultants Bur. Transl. 8 (1972) 476. [21] L.D. Bogomolova, V.A. Zhachkin, V.N. Lazukin, N.F. Shapovalova and V.A. Shmukler, Soy. Phys. Dokl. 16 (1972) 967. [22] D.F. Ushakov, N.F. Baskova and Yu.P. Tarlakov, Fizika i Khimiya Stekla 1 (1975) 151. [23] N.H. Ray, Phys. Chem. Glasses 16 (1975) 75. [24] M. Imaoka, Advances in Glass Technology (Plenum Press, New York, 1962) Part I, p. 149. [25] H.M. Kriz, S.G. Bishop and P.J. Bray, J. Chem. Phys. 49 (1968) 557. [26] P.C. Taylor and P.J. Bray, Lineshape Program Manual, Brown University (1969) (unpubtished). [27] P.C. Taylor and P.J. Bray, J. Mag. Reson. 2 (1970) 305. [28] H.M. Kriz and P.J. Bray, J. Mag. Rosen. 4 (1971) 76. [29] J.F. Baugher, H.M. Kriz, P.C. Taylor and PJ. Bray, J. Mag. Reson. 3 (1970) 415. [30] W. MiiUer-Warmuth,W. Pooh and G. Sieloff, Glasteeh Ber. 43 (1970) 5.
60
Y.H. Yun, P.J. Bray/NMR studies of glasses
[31] M.E. Milberg, J.G. O'Keefe, R.A. Verhelst and H.O. Hooper, Phys. Chem. Glasses 13 (1972) 79. [32] E.R. Andrew, Phys. Rev. 91 (1953) 425. [33] H. Rawson, Inorganic Glass-Forming Systems (Academic Press, London, 1967) p. 23. [34] J. Krogh-Moe, Phys. Chem. Glasses 6 (1965) 46. [35] H.M. Kriz, M.J. Park and P.J. Bray, Phys. Chem. Glasses 12 (1971) 45. [36] G.E. Jellison and P.J. Bray, Solid St. Commun. 19 (1976) 517. [37] N.F. Ramsey, Phys. Rev. 86 (1952) 243. [38] P.J. Bray, Interaction of Radiation with Solids (Plenum Press, New York, 1967) p. 25.
NUCLEAR MAGNETIC RESONANCE STUDIES OF THE GLASSES IN THE SYSTEM K 2 0 - B 2 0 3 - P ~ O s * Y.H. YUN ** and P.J. BRAY * Department o f Physics, Brown University, Providence, Rhode Island 02912, USA Received 21 April 1978 Revised manuscript received 18 Juli 1978
B11 NMR spectra have been used to study the structure of glasses in the system K 2 0 BzO3-P20 s . The results indicate that the glasses do not contain an appreciable number of boron atoms in BO3 units with one or two non-bridging oxygens. The fraction N 4 of boron atoms in BO4 units is measured and analyzed according to a structural model containing the following elements. (1) If the binary borophosphate system forms glasses, they consist of a borophosphate (BPO4) network and a borate network for K < 1, or a borophosphate (BPO4) network and a phosphate network for K > 1, where K = mol.% P2Os/mol.% B203. (2) The conversion rates of BO4 units (i.e. the rate of production or destruction by added oxygens) in the borate network and the borophosphate (BPO4) network are given as (+2) and (-0.38), respectively. (3)K+1 ions are proportionally shared between the two networks; (i.e. between the borate and borophosphate (BPO4) networks for K < 1, and between the phosphate and borophosphate (BPO4) networks for K > I).
1. Introduction Previous papers [ 1 - 1 6 ] from this laboratory have described the application of nuclear magnetic resonance (NMR) techniques to the studies of structure and chemical bonding of borate glasses. In particular, NMR has been used to determine the fraction (N4) of boron atoms in BO4 units, the fraction of BO3 units with all bridging oxygens and the fraction of BO3 units with one or two non-bridging oxygens. In binary alkali borate glass systems, the N4 data have been effectively analyzed [11] by plotting N4 as a function of R which is the ratio of the molar percentages of the alkali oxide and boron oxide in the glass. In more complex ternary borate systems, recent studies of glasses in the systems P b O - B 2 0 3 - S i O 2 [15] and N a 2 0 - B 2 0 3 -
* Research supported by the Materials Research Laboratory at Brown University funded through Grant No. DMR76-80560. Research also supported by National Science Foundation Grant No. DMR77-08600. ** Based on the work performed by Y.H. Yun in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Brown University. 45
46
Y.H. Yun, P.J. Bray/NMR studies of glasses
Si02 [16] have provided a clear picture of the variations of N4 as a function of R (= mol.% PbO or Na20/mol.% B203) by focussing on families of glasses for which K (= mol.% Si02/mol.% B203) is held constant. Similar studies of ternary alkali borophosphate glasses would be of particular interest because in this glass system, in addition to the structural units that are found in alkali borate or alkali phosphate glasses, a further type of structural unit, the BP04 unit, should be taken into consideration [17-23] when describing the structure of the glasses.The BP04 unit, which exists in the crystalline compound boron phosphate (BP04), consists of one B04 and one P04 unit, both units having four bridging oxygens. The excess of negative charge on the B04 unit is compensated by the excess of positive charge on the P04 unit. Thus the presence of BP04 units directly affects the N4 values of the glasses. Both B20a and P20s are water soluble glass network-forming oxides of low melting points, and yet their combination produces the chemically resistant and refractory compound boron phosphate (BP04). Kreidl and Weil [17], in a study of the durability of phosphate glasses containing boron oxide, were the first to assume that in these glasses BP04 units with a structure similar to that of crystalline BP04 were present. Since that time, additional evidence for the existence of BP04 units in borophosphate glasses has been reported. Takahasi [18] observed that the addition of boric acid to sodium phosphate glasses caused a rise in transformation temperature and increased their chemical durability. He attributed this to the formation of silica-type BP04 units. A detailed investigation [20] of an ESR spectrum of an irradiated lanthanum borophosphate glass has shown that there are two physically different B04 units differing from one another in the values of the g-factor and the hyperfine structure constant. The excess of negative charge on the B04 unit is compensated by the cation-modifier in one type of B04 unit, and by the excess of positive charge on the P04 units in the other type of BO4 unit. The formation of a borophosphate (BP04) network has also been suggested by Bogomolova et al. [21] in their ESR study of the Cs20-B203-P20s glass system and by Ushakov et al. [22] in their infrared study of the ZnO-B203-P20s glass system. In this paper, measured values of N4 for ternary potassium borophosphate glasses are reported and analyzed. A structural model is proposed to explain these data. K20 is chosen as the alkali oxide in order to check the N4 values recently measured [23] for the K20-B2Oa-P20s glass system by using Raman spectroscopy.
2. Experimental Thirty-seven glass samples were made spanning the glass-forming region reported by Imaoka [24]. The compositions were chosen so that the glasses were grouped into eight families, each family having the same K value (= mol.% P205/mol.% B203) but different R values (= mol.% K20/mol.% B203) as shown in fig. 1 and
Y.H. Yun, P.J. Bray/NMR studies of glasses
47
Table 1 Experimentally determined values of N4 [labelled N 4 (E) ] and calculated values of N 4 [labelled N4(C) ] were obtained from the model proposed in this paper. The N4(E) were measured by the "area method" except for the values in parenthesis which were measured by the "comparison method". Sample number
K
R
N4 (E)
N4 (C)
1
0.01
0
0.01
0.01
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
0.02 0.11 0.11 0.11 0.11 0.33 0.33 0.33 0.33 0.5 0.5 0.5 0.5 0.75 0.75 0.75 0.75 0.75 1 1 1 1 2 2 2 2 3 3 3 3 9 9 9 9
0 0.11 0.22 0.33 0.50 0.33 0.67 1 1.25 0.5 0.75 1 1.5 0.75 1 1.25 1.5 2 1 1.5 2 2.5 1.5 2 2.5 3 2 2.5 3 3.5 3 4 5 6
0.02 0.19 0.25 0.35 0.43 0.42 0.59 0.64 0.73 0.64 0,62 0.68 0.72 0.75 0.74 0.69 0.70 0.64 0.75 0.68 0.59 0.47
0.02 0.19 0.28 0.36 0.49 0.47 0.60 0.74 0.84 0.60 0.66 0.71 0.81 0.74 0.73 0.73 0.72 0.71 0.81 0.72 0.62 0.53 0.81 0.75 0.68 0.62 0.81 0.76 0.72 0.69 0.89 0.85 0.81 0.77
(0.78) (0.70) (0.55) (0.52) (0.85) (0.70) (0.71) (0.61) (0.78) (0.77) (0.61) (0.61) (0.79) (0.86) (0.71) (0.65)
table 1. In a d d i t i o n to those samples, t w o m o r e samples (no. 36 and no. 37) were prepared t o c h e c k the N4 values m e a s u r e d [23] b y R a m a n spectroscopy. The c o m positions are listed in table 2. Reagent grade potassium carbonate (K2 (303), orthoboric acid (H3BO3) and a m m o n i u m d i h y d r o g e n p h o s p h a t e (NH4H2PO4) were
48
Y.H. Yun, P.£ Bray/NMR studies of glasses K20
a,o,
'/9
2 3
9
P,O,
K~ Fig. 1. The glasses studied in the system K 2 0 - B 2 0 3 - P 2 0 s. The compositions are the batch
compositions. thoroughly mixed together. The mixtures were placed in procelain crucibles and fused at approximately. 800°C in an electric muffle furnace until all air bubbles had disappeared. The procelain crucibles do not react [23] significantly with the melt. The melts were agitated thoroughly to ensure homogeneity and then poured onto a metal plate and quickly covered with a brass block. Since the samples were hygroscopic, the quenching process was done in an atmosphere of dry nitrogen gas. Most samples were sealed in polystyrene vials, but some samples of extremely high hygroscopic character were vacuum-sealed in quartz tubes. The glasses were transparent and showed no sign of devitrification when checked by X-ray diffraction techniques. Varian Associates Wide-Line NMR Spectrometer (V-4200 B) was employed in
Table 2 Values of N4(E), N4(C) and the values of N4 [labelled N4(R)] measured by Raman spectroscopy (23). Sample number
K20 a)
B203 a)
P2Os a)
N4 (E)
N4 (C)
N4 (R)
11 15 25 36 37
25 30 40 23 16.7
50 40 20 54 66.7
25 30 40 23 16.7
0.64 0.75 0.70 0.56 0.43
0.60 0.74 0.75 0.55 0.38
0 0.08 0.26 0.03 0.52
a) Compositions are given by molar%.
Y.H. Yun, P.J. Bray/NMR studies o[glasses
49
connection with a Nicolet Signal Averager (Model 1072). The NMR spectra were obtained at a f~ed frequency of 16 MHz, by sweeping the magnetic field through the resonance condition. All measurements were made with the glass samples at room temperature.
3. Results and discussion The first derivative of the B 11 NMR absorption spectra for all the glasses studied consists of two lines. Examples of experimental spectra are shown in fig. 2. A narrow central line arises from boron atoms in oxygen tetrahedra (BO4 units) while boron atoms at the center of oxygen triangles (BO3 units) yield a broad resonance line due to a larger interaction between the B 11 nuclear quadrupole moment and the electric field gradient present at the boron site [3]. Particular attention was paid to those glasses having a high ratio of potassium oxide to boron oxide (samples no. 6, 10, 14, 19 and 23), since those glasses may contain BO3 units with one or two non-bridging oxygens (denoted as 'asymmetric BO3 units") such as those found in alkali borate glasses of high alkali oxide to boron oxide ratio [11]. Since one or two non-bridging oxygens in a BO3 unit cause the electric field gradient tensor at
glass No. 6 ~K20" I B2Os" ~P~051 glass No. lO -~K20. I B2Os.-~P~,05
'S'~
gless No. 14 }K20. 18203- ½P205 g,ass N o , 9
2K20" I B203'~P205 ' ' ' ' ~
~G"J/
glass No. 2:3 ,._,,,~ 2.5K20 • I B203. I P~05~ "~
~, ~ / '~.j~a ' 28.5 K i l l I
I
Fig. 2. B11 NMR (derivative) spectra at a resonance frequency vo of 16 MHz for samples No. 6, 10, 14, 19, and 23.
50
Y.H. Yun, P.J. Bray/NMR studies of glasses
the boron site to lose axial symmetry, the resulting spectra show definite structure [25]. The present potassium borophosphate glasses do not show this "extra" structure in the broad resonance lines (see fig. 2); therefore, these glasses do not contain an appreciable number of asymmetric BO3 units. The narrow and broad resonance lines can be separated and analyzed [25-29] in order to obtain the quadrupole parameters (i.e. the quadrupole coupling constant and the asymmetry parameter) and the fraction N4 of boron atoms in BO4 units. B 11 quadrupole parameters for all the samples studied appear to be similar to those found for alkali borate [3,7] an alkaline earth borate [8,10] glasses. Further, these parameters are relatively insensitive to changes of glass composition. A new method [30,31 ] of determining N4, involving the use of a signal averager, was employed in this work for samples with K ~< 1. Since the modulation technique [32] was used in the present study, the recorded signals are the first derivative of the absorption curve. The modulation frequency was 80 Hz and the modulation amplitude was 1.03 G which is small enough to ensure that appreciable broadening from the modulation field does not occur. A built-in integrator in the Nicolet signal averager was used to produce the absorption signals shown in fig. 3. The central peak is from boron atoms in BO4 units, and it is easily separated from the broad line. A direct measurement of the area under the central peak with respect to the total area gives the fraction N4. Although this method, called the "area method," has several advantages over the conventional "comparison method" [3] as described elsewhere [30,31], it will not yield accurate results for N4 for large values of N4. Thus for samples having K/> 1, which showed very large N4 values, the conventional comparison method [3] has been employed. N4 values of the K = 1 family of
gloss No.6
gloss No.19 Fig. 3. B 11 NMR spectra (integrated) from samples no. 6 and No. 19, which are used for determination o f N 4 .
Y.H. Yun, P.Z Bray / NMR studies of glasses
51
the samples were measured by employing both methods. The two N4 values for a given sample agreed within experimental error. Since the N4 values depend on glass composition much more strongly than do values of the quadrupole parameters, the behavior of N4 as a function of composition will be discussed extensively. N4 values of binary alkali borate glasses have been analyzed [11] by plottingN4 as a function of R (= mol.% alkali oxide/mol.% B20a). For R < 0.5, the N4 values fall on the straight line N4 ---R whose slope is one half [11] of the rate of conversion of BOa units to B04 units due to the oxygens introduced by alkali oxides. Each oxygen added by an alkali oxide is capable of converting two boron atoms from BOa to B04 units, and N4 can be written as N, =½ aR
(1)
where a, the conversion rate, equals (+2) for R < 0.5. N4 values for the ternary glasses in the system K 2 0 - B 2 0 3 - P 2 0 5 are analyzed accordingly. The molar fractions of K20, B203, and P2Os are denoted byx, y, and z, respectively. R and K are thus defined as R = x/y,
(2)
K = z/y.
The measured values of N4 are listed in table 1 and plotted as a function of R for fixed K in fig. 4. The plots are separated into eight families, each corresponding to one K value. A least-square fit of the N 4 data yields K
N4
1
0.63R 0.32R O.09R -0.09R
!3 l2 3
+ 0.12 + 0.34 + 0.58 + 0.82
K
N4
1 2 3 9
-0.19R -0.14R -0.13R -O.06R
+ 0.96 + 1.06 + 1.06 + 1.01
(3)
The linearity between N4 and R suggests that N4 can be formulated as N4 = ~ aR +/3,
(4)
where ~a and/3 are constants depending upon the K value. Figure 5 shows a plot of/3 as a function of K. The value of/3, equivalent to N4 for binary borophosphate glasses, increases with K up to K = 1 and remains near/3 = 1 for K > 1. This might indicate that if the binary borophosphate system forms a glass, there exist BO4 units - presumably in the form of BPO4 units - which will form to the extent that equal amounts of B203 and P2Os are available. If this is the case, it can be reasonably assumed that a binary borophosphate glass having more B203 than P2Os consists o f a BPO4 network and B203, and also that a binary borophosphate glass having more P2Os than B20~ consists of a BPO4 network and P2Os. In other words, (vB203 + zP205) = (v - z) B203 + 2zBPO4 , = ( z - y ) P2Os + 2yBPO4,
for K ~< 1 forK~> 1 .
(5)
Y.H. }run, P.J. Bray/NMR studies of glasses
52 ,q.
z
/
O.e
/
0.6 0.4
K={
.t /
K={
Z
0.2
R
R
2
z [ K:{ ,q.
I
Ir
z
K=I
°"r"..-.-~.. ] --
°"f,
t
R
K--2
\:',~.. R
!
R i
2
2
Z
0.6
0.4
z
i Z
%,
,R
!
i !
3
.~
K:3
K:9
0.2
R
R
Fig. 4. The fraction N4 of boron atoms in BO4 units versus R. The values of N4 indicated by closed and open ckcles were measured by the area method and comparison method, respectively. Since a BP04 unit consists o f one B04 unit and one P04 unit,/3 is given by
= 2z/2y = K , =2y/2y =1,
for K ~< 1 , forK1>1.
(6)
Y.H. ]Tun,P.Z Bray/NMR studies of glasses
P
t
I.O
O.0
0.6
0.4
] ,,
53
]
l
0.2
i I I II I K I 2 3 9 Fig. 5. # versusK. The solid line indicates # = K for K ~ 1, # = 1 for K ~ 1.
These relationships are shown in fig. 5 by the solid lines. Comparison with the experimental values shows that the agreement is reasonably good to within experimental error. To confirm the above results, two binary borophosphate glasses were prepared and tested. Although most of the binary borophosphate system does not form a glass, it has been reported that clear glasses can be obtained with a P2Os concentration less than 5 weight % [33]. One and two molar% P2Os binary borophosphate glasses (samples no. 1 and 2) were carefully prepared by using platinum crucibles and vacuum-sealed in a quartz tube. Fig. 6A shows the first derivative of the B 11 NMR absorption spectra of the samples along with that of pure B2Os glass for comparison. Figure 6B shows the integration of fig. 6A, from which N4 values were obtained. The determination of the dotted lines in fig. 6B was guided by visual comparison with the absorption spectrum of the 100% B203 glass sample shown in fig. 6B. As listed in table 1, the N4 values of these two binary borophosphate glasses agree with the values predicted by eq. (6). According to fig. 4, the addition of K20 to borophosphate glasses increases or decreases the N4 values depending on the value of K. The slopes of the linear relationships between N4 and R in eqs. (3), S(K), are plotted in fig. 7 as a function of K. The values of the slope sharply decreases from +1 to -0.19 when K is increased from 0 to 1. As the K value is further increased the values of the slope increase slowly, but remain less than zero. It has been well-known [3,11] that in binary alkali borate glasses with up to 33~ mol.% alkali oxide content the N4 values are increased by adding alkali oxides and the conversion rate of BOa units to BO4 units is (+2). This has been explained by the structural model developed by Kroh-Moe [34] in which alkali borate glasses
[A]
[8]
glass 100% Bz03 glass 99Bz03. I PzOa
glass 98 B~33"2 PzOa
28.SKHz I
I
Fig. 6. (A) B 11 NMR (derivative) spectra at a resonance frequency v0 o f 16 KHz for binary b o r o p h o s p h a t e glasses. (B) B 11 NMR (integrated) spectra o f binary b o r o p h o s p h a t e glasses which are used for the determination o f N 4.
0
U)
2 0
Fig. 7. S(K) versus K. T h e solid line indicates that S(K) = (1 - 1.38K)/(1 + K ) , S(K) = - 0 . 3 8 / ( 1 + K ) ,
for K < 1 , for K ~ 1 .
3
9
K
Y.H. Yun, P.J. Bray / NMR studies of glasses
55
are viewed as a random mixture of boroxol units, tetraborate units, and diborate units which occur in crystalline alkali borate compounds. If the alkali content is over 33] mol.%, N4 decreases on addition of more alkali oxide. The decrease of N4 is always accompanied [11] by the creation of asymmetric BOa units. This has recently been explained [16] by the formation of metaborate units and loose BO4 units at the expense of diborate units on addition of alkali oxides. As a result, the conversion rate of BO4 units to asymmetric BO3 units equals (-0.5). The decrease of N4 in the ternary potassium borophosphate glass system, however, cannot be explained by this process because an appreciable number of asymmetric BO3 units has not been observed. A similar decrease of N4 without the formation of asymmetric BOa units has been observed in lead borate [4] and lead borosilicate [15] glasses. This has been explained [4] by assuming that at high lead content, some of the lead enter the glass as a covalent network former in the form of PbO4 pyramids. A Pb 2°7 NMR study of lead borosilicate glasses [15] has supported this explanation. However, this cannot be the case for the potassium borophosphate glasses because K20 is believed to be solely a network modifier due to its chemical characteristics, such as the single-bond energy or electronegativity, which serve as criteria [33] to determine whether or not a metal oxide will form a glass network. Thus, a completely different process must be taken into account in order to explain the decrease o f N 4 in this ternary system. Particular attention has been paid to the K = 1 family of K:O-B203-P2Os glasses since from the analysis of 13, it appears that the hypothetical glass of composition B203 • P2Os consists mainly of BPO4 units. The decrease of N4 in the K = 1 family might be attributed to the destruction of BPO4 units by addition of K20 in order to form other structural units. It would be of substantial interest and value to determine the kinds of structural units which are formed a t t h e expense of BPO4 units by added K20. However, it was not possible to secure that information in the present investigation because the B 11 and p31 NMR spectra employed in this work were not able to identify each structural unit that exists in the glasses. It has been known [28] for some time that B al NMR spectra are not sufficiently senstive to distinguish each kind of structural unit in the alkali borate glasses because the dipole-dipole interaction and the distributions [28,35,36] of quadrupole parameters smear out the details of the spectrum which might be characteristic of each structural unit. p31 NMR spectra for the K 2 0 - B 2 0 3 - P 2 O s glasses were obtained at 16 MHz in the hope that they might be used to distinguish the alkali phosphate units which exist in alkali phosphate compounds. Since p31 has a nuclear spin ~, it has no electric quadrupole moment, but there are chemical shift interactions [6,7,37] which are available to probe, the bonding and structure. Slightly different p31 NMR spectra have been reported by Bray [38] from two crystalline alkali phosphate compounds. However, all of the p3~ NMR spectra obtained from potassium borophosphate glasses were structureless and quite symmetric, and the line widths were between one and two gauss. Although it is not possible at this time to describe the destruction process of
56
Y.H. Yun, P.J. Bray/NMR studies of glasses
BPO4 units by the addition of K20, the conversion rate of BO4 units into other units due to the destruction of BPO4 units can be experimentally determined from eq. (5) by considering the K =1 family. From eq. (3) with K = 1, and eq. (4), the destruction rate of BO4 units in the borophosphate (BPO4) network is given by (-0.38); that is, each oxygen added as K20 destroys 0.38 BO4 units. The production rate of BO4 units in a borate network has already been given [ 11 ] as (+2). Since for ternary glasses having K < 1 there are two kinds of networks [i.e. the borate network and a borophosphate (BPO4) network], there might be a sharing of K+1 ions between the two networks. Proportional sharing of cations between two networks has been observed in the glass systems PbO-B203-SiO2 [ 15] and N a 2 0 B203-SIO2 [16]. If it is assumed that the K+1 ions are proportionally shared between the borate network and the borophosphate (BPO4) network, then the number of oxygens which can modify each network would be reduced by the factor O'
-
z)/[(y
- z ) + 2z] = (1 - K ) / ( 1 + K )
for the borate network and 2z/[(y - z) + 2z] = 2K/(1 +K)
for the borophosphate (BPO4) network [see eq. (5)]. Thus, the conversion rate a(K) of BO4 units for the K ~< 1 families is given by a(K) = 2[(1 - K ) / ( 1
+K)] + (-0.38)[2K/(1
= (2 - 2.76K)/(1 + K ) ,
+K)I (7)
for K ~< 1 .
If it also assumed that for K > 1 families the K+l ions are shared between the borophosphate (BPO4) network and phosphate network, then the number of oxygens which can modify the borophosphate (BPO4) network would be reduced by the factor 2y/[2y + (z - y ) ] = 2/(1 +K)
[see eq. (5)]. Thus the conversion rate a(K) of BO4 units for the K > 1 families is given by o~(K) = (-0.38)[2/(1 +K)] =-0.76/(1 + K ) ,
forK~> 1 .
(8)
From eqs. (7) and (8), the slope S(K), which is one half of a(K), is given by S(K) = (1 - 1.38K)/(1 + K ) , = -0.38/(1 + K ) ,
for K ~< 1
(9)
for K I> 1.
Plots of the two parts of eq. (9) are shown as the solid lines in fig. 7 and compared with the experimental values. The agreement is reasonably good within experimental error and considering the additional uncertainties involved in the simplified
Y.H. Yun, P.J. Bray/NMR studiesof glasses
57
model, which will be discussed later. Thus, from eqs. (6) and (9) N4 can be formulated as a function of K and'R according to the structural model proposed in this paper; N4 = [(1 - 1.38K)/(1 + K)] R + K , = [(-0.38)/(1 + K)] R + 1 ,
for K ~< 1 for K >t 1 .
(10)
The treatment of N4 given above is based on a simplified model. The real glasses are not as simple in several respects. First, asymmetric BO3 units are completely ignored in the analysis on the basis of characteristics of the B 1~ NMR spectra for the three-coordinated borons. Since small concentrations of asymmetric BO3 units (involving less than perhaps 5% of the total borons) are not easily detectable in B 1 NMR spectra, the glasses may contain small quantities of asymmetric BO3 units. Second, the proportional sharing of IC l ions between the two networks may not be exactly according to eqs. (7) and (8). As shown in fig. 7, the experimental values of S(K) are generally a bit lower than the values predicted by eq. (9). This might indicate that some preferential association of K*~ ions with the borophosphate (BPO4) network rather than the borate network or phosphate network occurs. Similar preferential association of metal ions with one of the two networks in borosilicate glass systems has been reported [ 15,16]. Third, the conversion rate (-0.38) of BO4 units to other units in the borophosphate (BPO4) network has an experimental uncertainty (+0.10). Careful studies of these K20-B203-P2Os glasses by means of B 1° NMR and Raman spectroscopy are desirable to obtain more precise information concerning both the destruction process of BPO4 units and the conversion rate of BO4 units to other units due to the destruction of BPO4 units. All of the approximations noted above introduce some additional uncertainties into the calculated values of N,. Nevertheless, the simplified model proposed here permits a useful determination of the N4 values in ternary potassium borophosphate glasses from a knowledge of glass composition (i.e. from K and R). Table 1 lists the experimental values of N4 and the calculated values of N4 obtained from the model presented above. In fig. 8, all of the experimentalN4 data in table 1 are shown and compared with the calculated values. The agreement is good within the experimental error and the additional uncertainties involved in the simplified model. Raman spectroscopy has recently been employed [23] to extract quantitative values of N4 for this ternary glass system. The Raman technique has proved to be extremely useful in helping to identify structural units in glasses by means of band frequencies, but evaluation of N4 depends on a determination of band intensities which are sometimes uncertain, particularly in cases of overlap and fluorescence. Five glasses in table 2 have the same compositions as those studied by Raman techniques [23]. The results of N4 measurements for those samples using B 11 NMR are shown in table 2, along with the N4 values from Raman studies [23] and also with the calculated values of N4 from their corresponding compositions according to the
Y.H. ]run, P.J. Bray /NMR studies of glasses
58
/," ,/
%,
O
•
*
I
// /t / m
6 //
/
./
,~'"
,/ :.'"
I
I o.2
I
I o 4
I
I. o a
I
I o.a
t
| Lo
N4(E)
Fig. 8. Experimental values of N4(E ) versus the values of N4(c) calculated from their corresponding compositions according to the model proposed in this paper. The solid line indicates N4 (E) = N4 (C).
model proposed in this paper. The differences between the N4 values of the same sample as measured by NMR and Raman spectroscopy are obvious.
4. Summary The B 11 NMR spectra obtained from glasses in the system K20-B203-P2Os consists of a broad resonance line and narrow resonance line which indicate that these glasses contain both BO3 and BO4 units, but no appreciable numbers of BO3 units with one or two non-bridging oxygens are present. The values of N4 were measured by the area method, which involves the use of a signal averager, for samples with K < 1. For samples having K i> 1, the conventional comparison method was employed to measure N4 (K = mol.% P2Os/mol.% B2Oa). Equations which predict the behavior of N4 as a function of composition are formulated according to a simplified model containing the following elements. (1) If the binary borophosphate system forms glasses, they consist of a borophosphate (BPO4) network and a borate network for K < 1, or a borophosphate (BPO4) network and a phosphate network for K > 1. (2) The conversion rates of BO4 units in the borate network and the borophosphate (BPO4) network are given as (+2) and ( - 0 . 3 8 ) , respectively. (3) K"~1 ions are propo~ionally shared between the two net-
Y.H. Yun, P.J. Bray/NMR studies of glasses
59
works; (i.e. between the borate and borophosphate (BPO4) networks for K < 1, and between the phosphate and bo'rophosphate (BPO4) networks for K > 1).
Acknowledgments The authors express their appreciation to Mr. R. Kershaw for taking X-ray diffraction patterns of the samples, and also to S.A. Feller and F. Bucholtz for assistance in preparing the manuscript.
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Y.H. Yun, P.J. Bray/NMR studies of glasses
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