1

Kinetics analysis of the nitrogen/oxygen

substitution reaction in phosphate melts by NMR

Francisco Muñoz

Instituto de Cerámica y Vidrio (CSIC), Kelsen 5, 28049 Madrid, Spain

Dr. Francisco Muñoz Fraile

Instituto de Cerámica y Vidrio (CSIC)

Kelsen 5, 28049 Madrid (Spain)

Tel: +34917355840

Fax: +34917355843

e-mail: fmunoz@icv.csic.es

2

Abstract

Nitridation of phosphate glasses is generally performed through reaction of the phosphate

melt under an ammonia flow, after which an important modification of their properties

takes place. It is assumed that nitridation proceeds through the growing of oxynitride

microdomains at the expense of the oxygenated ones, giving rise to an homogeneous

incorporation of nitrogen all through the glass network. In this work, Nuclear Magnetic

Resonance data have been used to follow the concentration of the oxide and oxynitride

species, i.e. PO4, PO3N and PO2N2 tetrahedra, within the glass structure of Li2O-Na2O-

PbO-P2O5 glasses, against the reaction time for temperatures between 600 and 700ºC. It has

been proved that the ammonolysis of phosphate melts by thermal treatment under ammonia

proceeds through a mechanism consisting of two consecutive pseudofirst order reactions

with activation energies of approximately 150 kJ/mol and similar rate constants though

different frequency factors.

Keywords: Oxynitride Phosphate Glasses; Nuclear Magnetic Resonance; Ammonolysis;

Nitridation; Kinetics; Activation Energy

3

1. Introduction

Nitridation, or the way to produce nitride compounds through reaction with ammonia, has

already been extensively used to synthesize nitride and oxynitride inorganic materials [1-4].

Direct reaction with molecular nitrogen does not allow, in general, substitution of oxygen

by nitrogen due to the much greater stability of N2 with respect to O2. A more reactive

nitrogen species like NH3 can be suitably employed at relatively low to medium reaction

temperatures to produce the nitrogen/oxygen substitution. Ceramic oxide precursors are

usually nitrided between 800 and 1200ºC under NH3 flow [1]. However, nitridation of

glasses by ammonolysis is carried out over their melting temperature, hence resulting in a

liquid-gas reaction [5]. In particular, oxynitride phosphate glasses are typically obtained at

temperatures between 600 and as high as 800ºC in order to avoid phosphorous reduction

and difficulties in homogeneity, leading to a great variety of nitrided compositions.

Oxynitride phosphate glasses have been studied from the early 80’s. Since the first work of

Marchand on alkali metaphosphate glasses [6], many other phosphate glass compositions

have been successfully nitrided through ammonolysis from a basic point of view [7-10].

Phosphate and, especially, oxynitride phosphate glasses have had a great interest as sealing

materials due to their particular thermal properties, like higher thermal expansion

coefficients and lower softening points than borate and silicate glasses, which make them

very useful for low temperature seals [11]. However, they did not reach practical

applications yet. The use of phosphate glasses is often limited due to their extremely low

chemical resistance to moisture, but this can be considerably improved through the

substitution of nitrogen for oxygen within the glass network, i.e. by ammonolysis of the

phosphate melts. After nitridation, the chemical durability, as well as the mechanical and

thermal stability of the phosphate glasses, increases significantly.

4

But oxynitride phosphates have also gained much attention due to their increased basic

character after the nitrogen incorporation and their possibility to be used as heterogeneous

catalysts [12-14]. Recently, the development of solid-state electrolytes for lithium

secondary batteries has made the study of the influence of nitrogen on the electrical

conductivity of amorphous and glassy phosphate compounds a very important issue. After

discovering that nitrogen incorporation into lithium phosphate glasses increases their

electrical conductivity, Yu et al. [15] synthesize the first LiPON electrolyte through Radio

Frequency Magnetron Sputtering of a lithium phosphate under nitrogen atmosphere. With a

conductivity about 10-6

S.cm-1

at 25ºC and a good stability window, it resulted to be

compatible with the lithium metallic anode providing the battery system of a very long

active life.

The structure of phosphate glasses is built up of PO4 units linked together through bridging

oxygen atoms (BO). Depending on composition, the number of BO may vary between 3

and 1, from the ultraphosphate to the polyphosphate range. Non-bridging oxygens (NBO)

will be coordinated with modifier cations. During the reaction of nitrogen/oxygen

substitution, both bridging and non-bridging oxygens are substituted by dicoordinated, –N=

(Nd), and tricoordinated, –N< (Nt), nitrogen species [16]. The oxynitride glass network is

then built up of PO4 and the new PO3N and PO2N2 tetrahedra [16], which increase the

cross-linking density giving rise to the notable modification of the glass properties. The

nitridation process is carried out through well established substitution rules based on the

substitution of 3O2-

by 2N3-

. Two nitridation models have been proposed to explain how the

nitrogen/oxygen substitution takes place. According to Reidmeyer et al. [7], the nitridation

proceeds randomly with respect to BO and NBO species and the BO/NBO ratio only

depends on the N/P atomic ratio x:

5

BO/NBO = [1 – 3x/4] / [2 – 3x/4] (1)

On the other hand, the alternative model of Marchand et al. [17] is supported by

substitution rules deriving from the chemical equivalences:

Nt = 3/2BO (2)

Nd = 1NBO + 1/2BO (3)

In this case, the BO/NBO ratio for each nitrogen content in the glasses can be expressed as

a function of the relative proportion of both Nt and Nd nitrogen types:

BO/NBO = (BO/NBO)0 – [1.5Nt] / [2 – 1Nd] (4)

where (BO/NBO)0 is the ratio in the parent oxide glass, i.e. the non-nitrided composition,

and Nd and Nt correspond to the relative amounts of nitrogen atoms in either dicoordinated

or tricoordinated species, respectively, which are determined by N1s X-ray Photoelectron

Spectroscopy (XPS). For a metaphosphate glass, where the network is ideally formed by

infinite chains of tetrahedra, (BO/NBO)0 is equal to 0.5. However, the presence of small

water amounts induces some depolymerisation, and the experimental value is often found

lower. For example, Le Sauze et al. [9] found for the base glass Li0.5Na0.5PO3 a (BO/NBO)0

ratio of 0.45 by XPS. Note that a small deviation from the metaphosphate composition can

also affect this ratio. For these glasses, comparison between experimental BO/NBO values

deduced from O1s XPS analyses and those calculated by using equation (4) showed an

excellent correlation. The nitrogen/oxygen substitution mechanism was explained by the

growing of oxynitride micro-domains at the expense of oxygenated ones, where the

nitrogen atoms replace preferentially the oxygen atoms shared by a PO4 tetrahedron and a

PO3N one.

The characterization of oxynitride phosphate glasses by means of O1s XPS, as reported by

Le Sauze et al. [9] and Muñoz et al. [16], showed the variation in the relative proportions of

6

bridging and non-bridging oxygens as a function of nitrogen content. The results indicated

that the BO/NBO ratio fits the calculated values when using the nitridation model proposed

by Marchand et al. [17], showing a linear decrease in the BO/NBO ratio within the range of

N/P ratio studied, which has also been seen in mixed alkali lead phosphate glasses

according to the same substitutional rules of equations (2) and (3) [18].

Nitridation kinetic studies on alkali and alkaline-earth phosphate glasses have proved that

nitrogen content increases with time up to a maximum value depending on composition of

glasses [7]. A general conclusion arising from these studies is that the higher the ionic field

strength of the modifiers the higher the nitrogen content under the same conditions of

temperature and time. However, nitridation process is also controlled by diffusion of

ammonia throughout the melt and, in consequence, the viscosity of the melt determines the

nitridation rate and can also affect the maximum nitrogen content reached. The higher ionic

field strength of divalent cations than monovalent ones results in stronger bonds with

oxygen, and thus higher values of melt viscosity. This is why introduction of divalent metal

oxides, such as BaO in the glass formulation generally leads to a limited nitridation [8].

PbO is an exception as it provides a low melt viscosity and thus enables incorporation of

high nitrogen contents, as previously demonstrated by Pascual et al. [8,19]. Moreover, PbO

has shown to improve the chemical durability of phosphate glasses while maintaining low

softening points [20]. In this sense Sn and Pb have demonstrated to be suitable elements for

nitridation due to the low viscosity values of the melts than those of glass compositions

containing other different modifiers [10,21].

Alkali-lead containing phosphate glasses belonging to the system of composition Li2O-

Na2O-PbO-P2O5 were chosen as a model due to their ability for nitrogen incorporation,

which have been previously studied for their characteristics properties relevant for low

7

temperature sealing applications. The purpose of the present contribution has been to

analyze the kinetics of the reaction of nitrogen for oxygen substitution in phosphate glasses

from previous NMR data describing the phosphate species found in the LiNaPbPON

oxynitride glasses. A quantitative measure of the concentration of PO4, PO3N and PO2N2

oxynitride species by 31

P Nuclear Magnetic Resonance has been used assuming a

mechanism formed by two consecutive pseudofirst order reactions, from which the

activation energies and rate constants can be derived.

2. Experimental

The synthesis of a phosphate glass of composition 12.5Li2O.12.5Na2O.25PbO.50P2O5 and

the oxynitride glasses used for this study has been described in a previous work [10]. The

oxynitride glasses are formulated according to their molecular formula, i.e.

Li0.25Na0.25Pb0.25PO3-3x/2Nx, and the nitrogen content expressed as the N/P ratio (x in the

glass formulation). On the other hand, the variation of the different oxynitride species

coexisting within the glass network in Li0.25Na0.25Pb0.25PO3-3x/2Nx glasses was studied

through 31

P MAS and DQ-MAS NMR as a function of the nitrogen content in Ref. [16].

During the course of the nitridation reaction, the NH3 flow is kept very high in order to

avoid rapid decomposition of ammonia into N2 and H2, which otherwise would prevent

nitridation, thus ensuring an excess of ammonia throughout the process.

3. Results and discussion

3.1. Concentration of nitrogen as a function of reaction parameters

Figure 1 depicts a 3D-plot representing the increase of N/P ratio as a function of both

temperature and time for the series of oxynitride glasses Li0.25Na0.25Pb0.25PO3-3x/2Nx, using

8

the complete set of data gathered in reference [10]. As it was pointed out, nitridation

behaves like a diffusion-controlled process [10], so that nitrogen incorporation may be

assumed to depend on the square-root of time through the equation:

(N/P)T = KTt1/2

(5)

where (N/P)T is the nitrogen content introduced in the glass at temperature T, i.e. x in the

glass formulation Li0.25Na0.25Pb0.25PO3-3x/2Nx, t is the treatment time and KT is a

proportionality constant. It was observed that KT increases for an increasing treatment

temperature [10] and, at the same time, nitrogen content increases linearly as a function of

temperature for a constant treatment time. Figure 2 shows the variation of KT as a function

of temperature (a) and log KT with reciprocal temperature (b) for the glasses

Li0.25Na0.25Pb0.25PO3-3x/2Nx. Data points in Fig. 2b have been fitted to an Arrhenius

equation, from which an activation energy of 65 kJ.mol-1

can be obtained. If it is assumed

that KT stands for a constant which is determined by the viscosity of the melt at temperature

T, this activation energy may be related with the thermally activated process of ammonia

diffusion within the melt.

3.2. Analysis of the rate constants and activation energy of the reactions

The behavior of P(O,N)4 groups for increasing nitrogen contents has been described by

Muñoz et al. in [16]. For a given N/P ratio and KT constant, it is possible to calculate the

time for each nitrogen content reached according to equation (5). Therefore, the variation of

P(O,N)4 groups may be expressed as a function of the reaction time, which is represented in

Fig. 3 for KT determined at 700ºC. During the course of the nitrogen substitution for

oxygen, the concentration of PO4 groups progressively decreases with time. The amount of

9

PO3N groups first increases rapidly and then reaches a maximum at around 2 h and then

PO2N2 tetrahedra start increasing as well as Q1 groups though in a much lower amount.

The nitridation of the metaphosphate glasses can be represented by the general reaction:

Li0.25Na0.25Pb0.25PO3 + xNH3 Li0.25Na0.25Pb0.25PO3-3x/2Nx + 3x/2H2O (6)

This process is carried out through well established substitution rules defined by the

equivalences 2Nt=3BO and 2Nd=2NBO + 1BO, which are based on the substitution of 3O2-

by 2N3-

, as proposed by Marchand et al. [17]. The validation of this model is made through

comparison of the calculated BO/NBO ratio from the substitution rules and the

experimental determination of the BO/NBO ratio by O1s XPS as a function of the nitrogen

content. This has already been done in Li-Na-P-O-N [9], as well as in Li-Na-Pb-P-O-N

glasses [18]. The results indicate that BO/NBO ratio decreases linearly with the nitrogen

content.

Le Sauze et al. described the nitridation mechanism as a process by which PO4 groups are

substituted first, giving rise to PO3N ones and, subsequently, nitrogen atoms substitute for

oxygen belonging to adjacent PO4 and PO3N groups, so that the reaction progresses by the

growing of oxynitride domains at the expense of the oxygenated ones, which takes place

homogeneously within the glass network [9,16].

The different P(O,N)4 groups coexisting within the glass network can be considered as the

“molecular species” that take part into the reaction mechanism, i.e. PO4, PO3N and PO2N2.

A simple way to show a general reaction mechanism, based on the model discussed above,

might be the following:

PO4 + NH3 PO3N + H2O (7)

PO4-PO3N + NH3 PO3N-PO2N2 + H2O (8)

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The nitrogen/oxygen substitution on each PO4 group leads to two or three adjacent PO3N

ones, depending on whether nitrogen appears as dicoordinated, Nd, or tricoordinated, Nt to

neighbouring phosphorous atoms. Then, the substitution of nitrogen for oxygen atoms in

PO4 tetrahedra gives rise to a PO2N2 groups and one additional PO3N, and the nitridation

mechanism may be expressed by a two consecutive first-order reactions system as follows:

PO4 PO3N PO2N2 (9)

where PO4, PO3N and PO2N2 are the initial, intermediate and final reaction product,

respectively. Since NH3 concentration is kept in excess during the nitridation process to

allow reaction of ammonia within the melt before it decomposes, and the reactions depend

on the concentration of PO4 and PO3N only, they are considered pseudofirst-order

reactions.

In a classical system of two consecutive reactions, the concentration of the intermediate

product follows a function of time up to a maximum and then it begins to decrease. In the

present case, at the same time that PO2N2 groups are formed, PO3N groups are also formed.

Thus, the concentration of the PO3N groups never decreases down to zero, remaining at a

constant value (see Fig. 3 and ref. [16]). Assuming a pseudofirst-order reaction, the

corresponding expression for the reaction rate of equation (7) would be:

v1 = d[PO4]/dt = -k1[PO4] (10)

where k1 is the rate constant of equation (7) for a given temperature.

The integration of eq. (10) gives rise to the following expression for the concentration of

PO4 groups as a function of the reaction time:

[PO4] = [PO4]0e-k

1t (11)

11

being k1 the rate constant and [PO4]0 the initial concentration of PO4 groups in the base

glass. From the least-square fitting of log [PO4] as a function of time, k1 rate constants can

be calculated at each reaction temperature. Figure 4 presents ln k1 as a function of the

reciprocal temperature, where the data points have been fitted to an Arrhenius equation,

from which an activation energy value of 148 kJ.mol-1

is obtained.

In the same way, the expression for the reaction rate of the formation of PO2N2 groups can

be given as:

v2 = d[PO3N]/dt = k1[PO4] - k2[PO3N] (12)

being k1 and k2 the rate constants of equations (7) and (8), respectively. From the

integration of (12) and (11), the concentrations of the PO3N and PO2N2 groups can be

deduced:

[PO3N] = [PO4]0[k1/(k2-k1)](e-k

1t - e

-k2t) (13)

[PO2N2] = [PO4]0 - [PO4]0e-k

1t - [PO4]0[k1/(k2 - k1)](e

-k1t - e

-k2t) (14)

In order to estimate the rate constants for the reaction of formation of PO2N2 groups, k2, the

following approximation is assumed: from the total amount of PO3N groups we need to

subtract the amount of the PO3N groups that are formed at the same time that PO2N2 groups

due to the fact that each new PO2N2 tetrahedra gives rise to a new PO3N one, as it can be

seen in equation (8). Then, it is possible to plot the concentration of the intermediate PO3N

species, effective percentage of PO3N groups ([PO3N]eff) that are responsible for the

formation of PO2N2 ones, as a function of time. As an example, a representation of

([PO3N]eff) groups concentration at 700ºC is given in Fig. 5. As it is the case of a two

consecutive first-order reactions system [22], there is a certain time for which [PO3N]eff

reaches a maximum value, named tmax, and is given by the equation:

tmax = [1/(k1 – k2)]ln(k1/k2) (15)

12

Here, tmax can be calculated, at each temperature, if [PO3N]eff values are fitted to functions

of the type:

[PO3N]eff = a1exp(-t/r1) + a2exp(-t/r2) (16)

being a1,2 and r1,2 amplitudes and rates, respectively.

On the other hand, from equation (15) we arrive to the following relation:

ln k2 – k2tmax = ln k1 – k1tmax (17)

and assuming that |ln k2| >> |k2tmax|, it is possible to calculate k2 constants at every

temperature. Table 1 gathers k1 and k2 rate constants and tmax for temperatures between 600

and 700ºC. Figure 6 gives the Arrhenius fit of Log k2 constants as a function of the

reciprocal temperature, from which the activation energy for PO2N2 groups formation takes

the value of 146 kJ.mol-1

. This value being very close to that of the reaction of formation of

PO3N groups.

Figure 7 depicts the variation of both k1 and k2 rate constants as a function of temperature,

from which a typical behavior of first-order reactions can be seen. From the comparison of

the rate constants k1 and k2 for the reactions of formation of both PO3N and PO2N2 groups,

respectively, it can be observed that they are of the same order of magnitude though k1

constants are greater than the k2 ones (Table 1). Table 2 summarizes the activation energy

and frequency factors for both reactions. Both reactions have similar values of activation

energy, which indicates that the substitution of nitrogen for oxygen is equally permitted in

both PO4 and PO3N groups. The difference arises from the frequency factor of each

reaction, being higher in the case of reaction (7), i.e. formation of PO3N, than in (8)

corresponding to the PO2N2 case, since a much higher number of PO4 are available for

nitridation than PO4-PO3N regions where nitridation has already taken part.

13

4. Conclusions

From the NMR characterisation of oxynitride glasses belonging to the

12.5Li2O.12.5Na2O.25PbO.50P2O5 composition, the nitrogen concentration data against the

reaction time have been used to model the kinetics of the nitrogen substitution for oxygen

by ammonolysis at temperatures between 600 and 700ºC. The reaction of nitridation in

phosphate melts has been explained through a mechanism consisting of two consecutive

pseudo-first order reactions by which PO3N tetrahedra are firstly formed from the PO4

ones, and the PO2N2 from the PO3N existing before, proving that the intermediate PO3N

groups reach a maximum concentration at tmax. Both reactions have similar rate constants

and activation energies of the order of 150 kJ/mol. The results are in agreement with a

model previously proposed and experimentally verified by which oxynitride domains grow

at the expense of the oxygenated regions.

Acknowledgment

The author expresses his gratitude to R. Marchand, L. Montagne, J. Rocherullé, A. Durán

and L. Pascual for the fruitful collaboration on oxynitride glasses.

14

References

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oxynitrides : preparation, crystal chemistry and properties, J. Eur. Ceram. Soc., 1991, 8,

197-213.

[2] Marchand R., Tessier F., Le Sauze A. & Diot N., Typical features of nitrogen in nitride-

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173-178.

[7] Reidmeyer M.R. & Day D.E., Phosphorus oxynitride glasses, J. Non-Cryst. Solids

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metaphosphate glasses : a comparative structural analysis of the Na-P-O-N and Li-Na-P-O-

N systems, J. Non-Cryst. Solids 2001, 293&295, 81-86.

15

[10] Muñoz F., Durán A., Pascual L. & Marchand R., Synthesis and properties of nitrided

phosphate glasses in the system R2O-R’2O-PbO-P2O5 (R,R’=Li,Na), Phys. Chem. Glasses

2002, 43C, 113-118.

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metal seals and coatings, J. Mat. Sci. 1993, 28, 2841-2886.

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P., A novel family of mixed gallium aluminum phosphorus oxynitrides: their synthesis,

characterization and utilization in heterogeneous catalysis, Mat. Sci. Eng. B 1997, 47, 177-

183.

[14] Fripiat N., Conanec R., Marchand R., Laurent Y. & Grange P., Synthesis and

characterization of a new oxynitride catalyst: The ZrPON solids, J. Eur. Ceram. Soc., 1997,

17, 2011-2015.

[15] Yu X., Bates J.B., Jellison Jr. G.E. & Hart F.X., A stable thin-film lithium electrolyte:

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J. Non-Cryst. Solids 2003, 324, 142.

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16

[19] Pascual L. & Durán A., Nitrided phosphate glasses for soldering applications, Proc.

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17

Figure captions

Figure 1. 3D plot representing the nitrogen content in Li0.25Na0.25Pb0.25PO3-3x/2Nx glasses,

expressed as the N/P ratio x, as a function of both reaction time and temperature.

Figure 2. Proportionality constant KT in equation (5) as a function of temperature (in K) (a)

and variation of Log KT as a function of the reciprocal temperature (b). The line in Fig. 2a

has been drawn as a guide for the eyes. Data points of Fig. 2b have been fitted to an

Arrhenius equation.

Figure 3. Variation of P(O,N)4 groups as a function of the reaction time at a constant

temperature of 700ºC.

Figure 4. Variation of the ln of k1 rate constants as a function of the reciprocal temperature.

Data points have been fitted to an Arrhenius equation.

Figure 5. Variation of PO4, PO3Neff and PO2N2 groups as a function of the reaction time at

700ºC.

Figure 6. Variation of the ln of k2 rate constants as a function of the reciprocal temperature.

Data points have been fitted to an Arrhenius equation.

Figure 7. Variation of the k1 and k2 rate constants as a function of the reaction temperature.

Lines have been drawn as a guide for the eyes.

Table captions

Table 1. Rate constants k1 and k2 and tmax for PO3N groups at temperatures from 600 to

700ºC.

Table 2. Activation energy and pre-exponential factor for the reactions of formation of

PO3N and PO2N2 groups.

18

Figure 1

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Nitro

gen

con

tent

(N/P

ra

tio)

Temperature (ºC)

time

(h)

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Nitro

gen

con

tent

(N/P

ra

tio)

Temperature (ºC)

time

(h)

19

Figure 2

850 875 900 925 950 975

Temperature (K)

0.00

0.05

0.10

0.15

0.20

0.25

0.30K

T (

s-1

/2)

1.00 1.05 1.10 1.15

103/T (K-1)

-2.5

-2.0

-1.5

-1.0

log (

KT in s

-1/2

)

a) b)

20

Figure 3

0 1 2 3 4 5 6 7 8 9 10

time (h)

0

10

20

30

40

50

60

70

80

90

100%

P(O

,N) 4

gro

ups

PO4 (Q2)

PO3N

PO2N2

Q1 (pyrophosphate)

21

Figure 4

1.00 1.05 1.10 1.15 1.20

103/ T (K-1)

-12.0

-11.5

-11.0

-10.5

-10.0

-9.5ln

k1(k

1in

s-1

)

22

Figure 5

0 2 4 6 8 10

time (h)

0

20

40

60

80

100

% P

(O,N

) 4 g

roups

PO3Ntotal - PO2N2 = PO3Neff

PO4 (Q2)

PO2N2

23

Figure 6

1.0 1.1 1.2

103/ T (K-1)

-12.0

-11.5

-11.0

-10.5

-10.0

-9.5

ln k

2(k

2 in s

-1)

24

Figure 7

850 875 900 925 950 975

Temperature (K)

0

1

2

3

4

5

6

7

(k1, K

2)

x 1

05 (

seg

-1)

K1

K2

25

Table 1. Rate constants k1 and k2 and tmax for PO3N groups at temperatures from 600 to

700ºC.

Temperature (ºC) k1 (x 10-5

s-1

) tmax for [PO3N]max (s) k2 (x 10-5

s-1

)

600 0.84

13367 0.75

625 1.09 11247 0.97

650 2.35 6126 2.03

675 3.71 3554 3.26

700 6.32 2214 5.49

26

Table 2. Activation energy and pre-exponential factor for the reactions of formation of

PO3N and PO2N2 groups.

Reaction Ea (KJ.mol-1

) A (x10-3

s-1

)

PO4 PO3N 148 5.6

PO3N PO2N2 146 3.9