Kinetics of fluorination of metallic molybdenum with elementary fluorine

Article abstract of DOI:10.1007/s11167-005-0195-1

The kinetics of the heterogeneous reaction of metallic molybdenum with elementary fluorine under conditions close to those used in actual technological practice at a concentration of fluorine in the gas mixture equal to 20-50 vol % was studied. The kinetic parameters were evaluated using the Arrhenius equation. A regression equation was obtained using the statistical method of experimental design for practical calculations of the rate of fluorination of metallic molybdenum with elementary fluorine. This equation makes it possible to calculate the fluorination rate at any point of the factor space, at fluorine concentrations of 30-50 vol % and initial temperatures of 250-350°C.

Full text of DOI:10.1007/s11167-005-0195-1

Russian Journal of Applied Chemistry, Vol. 77, No. 12, 2004, pp. 1929 1934. Translated from Zhurnal Prikladnoi Khimii, Vol. 77, No. 12, 2004,
pp. 1950 1955.
Original Russian Text Copyright
2004 by Rybakov, Seredenko, Orekhov, Mironov.
PHYSICOCHEMICAL STUDIES
OF SYSTEMS AND PROCESSES
Kinetics of Fluorination of Metallic Molybdenum
with Elementary Fluorine
A. G. Rybakov, A. V. Seredenko, V. T. Orekhov, and B. S. Mironov
All-Union Research Institute of Chemical Technology, Federal State Unitary Enterprise, Moscow, Russia
Received March 10, 2004
Abstract The kinetics of the heterogeneous reaction of metallic molybdenum with elementary fluorine under
conditions close to those used in actual technological practice at a concentration of fluorine in the gas mix-
ture equal to 20 50 vol % was studied. The kinetic parameters were evaluated using the Arrhenius equation.
A regression equation was obtained using the statistical method of experimental design for practical calcula-
tions of the rate of fluorination of metallic molybdenum with elementary fluorine. This equation makes it
possible to calculate the fluorination rate at any point of the factor space, at fluorine concentrations of 30
50 vol % and initial temperatures of 250 350 C.
A study of the kinetics of the heterogeneous reac-
tion of metallic molybdenum with elementary fluorine
to give gaseous molybdenum hexafluoride MoF6 is of
profound practical interest. Molybdenum hexafluoride
is widely used in various fields of the national econ-
omy: for deposition of high-temperature- and corro-
sion-resistant Mo films of prescribed thickness on
metallic articles, for obtaining ultrapure metallic
powders, and as a fluorinating agent in synthesis of
organofluorine substances.
ementary F2 on a continuous weighing setup shown
schematically in Fig. 1.
The setup comprises a VLA-200M analytical bal-
ance 1, induction transducer 2, thermocouple 3, reac-
tion boat 4 with a sample 5, furnace 6, and table 7 for
In [1], the kinetics of fluorination of metallic Mo
with elementary F2 was studied at its concentration of
4 to 13 vol %. The kinetic parameters of the reaction
(activation energy, reaction order) were determined.
At a F2 content in argon equal to 4 13 vol %, the con-
centration of MoF6 in the gas flow is too low. This
may present difficulties in the subsequent stages of
isolation of molybdenum hexafluoride from the gas
flow.
The goal of our study was to examine the kinetics
of the heterogeneous reaction of powdered metallic
Mo with elementary F2 at real technological param-
eters of the fluorination process: concentration of
fluorine in argon in the range 20 50 vol % and initial
temperature of 250 350 C, by the classical and sta-
tistical methods.
EXPERIMENTAL
Fig. 1. Schematic of the continuous-weighing setup for
studying the kinetics of the heterogeneous reaction of
metallic molybdenum with elementary fluorine. (8) Exhaust
hood; for other explanations, see text.
We performed the experiments aimed to study
the kinetics of fluorination of metallic Mo with el-
1070-4272/04/7712-1929 2004 MAIK Nauka/Interperiodica

1930
RYBAKOV et al.
of argon. The variation of temperature in the course
of time was recorded with the ChA thermocouple
and a secondary EPP-09 potentiometer. Then the zero
level was set and the loss of mass by the sample in
the course of fluorination was monitored. Fluorine
with the content of the main component of 92
96 vol % was used in the study; argon of A brand
served to dilute fluorine.
Before the experiments, we passivated the setup at
a temperature of 300 400 C and F2 concentration in
argon of about 30 vol % until a stable fluoride film
was formed on the surface. The ChA thermocouple
was placed within a corundum straw, with only its
junction contacting with the fluorine argon mixture.
The error in weighing in the range 0 500 mg did not
exceed 1 2%.
The heterogeneous reaction between metallic Mo
and elementary F2 occurs in accordance with the fol-
lowing overall equation
Fig. 2. Variation of the sample mass, (m
of temperature T in the reaction between metallic molyb-
denum and elementary fluorine with time
m)/m , and
0
0
.
Mo + 3F2
MoF6.
moving the reactor up and down in the furnace.
The iron core of the induction transducer 2 is sus-
pended on the right arm of the balance, and the ther-
mocouple 3 and the reaction boat 4, on the left arm.
At the technological parameters used in actual prac-
tice, the reaction of fluorination is strongly exothermic
and, therefore, certain difficulties were encountered in
experimental data processing. The results obtained
using the procedure we suggested are shown in Fig. 2:
after a stable temperature Ti was reached at an instant
of time i, the derivative of the curve describing
the variation of the sample mass with time was found
The unbalance of the balance leads to motion of
the iron core in the induction coil 2, which gives rise
to an induction voltage proportional to the change in
the mass of the sample as a result of the reaction of
metallic Mo with elementary F2. The induction trans-
ducer 2 is connected into an arm of the differential-
transformer circuit of a DSR-35 instrument. The linear
portion of the plot of the change in mass against
the induction voltage corresponded to variation of
the sample mass in the range 0 500 mg. The con-
version of the metallic Mo was determined from
the loss of mass by the sample as a result of the for-
mation of gaseous MoF6. The variation of the mass of
a sample of metallic Mo was continuously monitored
with a secondary DSR-35 instrument. The completion
of the reaction was judged from termination of varia-
tion of the sample mass.
graphically at
[2]. This derivative is numerically
i
equal to the rate constant of fluorination, kT , at a
temperature Ti. The rate constants were determined
at two temperatures and the apparent activation energy
(kJ mol ) of the heterogeneous reaction between
powdered Mo and elementary F2 was calculated using
the equation
i
1
kT
19.1479T2T1
2
E =
log
.
(1)
kT
T2 T1
1
We carried out more than 40 experiments, and typ-
ical S-shaped curves describing the variation of
the mass of metallic Mo in the course of fluorination
were obtained. During the first 2 min, there is no re-
action, i.e., an induction period is observed. Further,
the sample mass somewhat increases because of the
formation of solid molybdenum fluorides MoF5 and
MoF4. Then volatile MoF6 starts to be formed, which
leads to a decrease in the sample mass.
A weighed portion ( 400 mg) of powdered metallic
molybdenum (particle size 20 50 m) was charged
into a cylindrical nickel boat 15 mm in diameter and
3 mm high. The boat with the sample was attached
with a special clamp to the suspended Chromel
Alumel (ChA) thermocouple so that the thermojunc-
tion was close to the sample surface.
After that the fluorination reactor was hermetically
sealed and heated to a required temperature in a flow
We processed the results of the experiments on
the kinetics of fluorination of metallic Mo with
RUSSIAN JOURNAL OF APPLIED CHEMISTRY Vol. 77 No. 12 2004

KINETICS OF FLUORINATION OF METALLIC MOLYBDENUM WITH ELEMENTARY FLUORINE 1931
Table 1. Averaged calculated values of the kinetic parameters of fluorination of metallic molybdenum with elementary
fluorine
Concentration of F2
in argon, vol %
Apparent activation energy
Pre-exponential factor k0,
1
Rate constant k, min
1
1
E, kJ mol
min
20
30
40
50
55.447
76.221
84.108
95.497
6.7
9.7
12.9
14.1
2.237 104
1.392 105
4.196 106
1.651 107
Table 2. Matrix of the orthogonal CCD for two factors (cF , T)
2
X 12
X 22
cF ,
Y,
System
vol 2%,
X 12
X 22
X1X2 X 21
X 12
Ycalc
Run
no.
T, C,
X2
2
N
N
kg h 1 m
X1
0
40
10
50
30
1
300
50
350
250
1
+1
1
1
Complete factorial
experiment
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
+1
1
1
+1
0
0
0
0
0
0.33
0.33
9.3373
15.6238
9.0984
13.7215
8.6850
14.0453
13.1831
11.5654
12.3486
9.4743
15.4383
8.2243
13.6483
8.8493
14.2733
12.9838
11.7338
12.3588
2
3
4
5
6
7
8
9
+1
1
+1
1
+1
0
0
1
0.33
0.33
0.33
0.33
0.33
0.67
0.67
0.67
0.33
0.33
0.33
0.67
0.67
0.33
0.33
0.67
+1
+1
0
0
1
Experiments at
star points
+1
0
Experiment at
0
the center of design
elementary F2, using the Arrhenius equation [3 5].
The averaged values of the kinetic parameters are
listed in Table 1.
In accordance with the values of the apparent ac-
tivation energy (Table 1), the process is limited by
diffusion of F2 into a layer of metallic Mo. The reac-
tion order with respect to F2 is close to unity. Raising
the concentration of F2 in the gas mixture leads to
a considerable exothermic effect.
The kinetic equation of the heterogeneous reaction
of metallic Mo with elementary F2 can be written in
the general case as
Practical calculations of the rate of fluorination of
metallic Mo with elementary F2 require simpler and
more precise relations. We solved this problem by
using the experimental-statistical method of exper-
iment design [6, 7], orthogonal central composite
design (CCD). The necesary number of experiments
can be calculated by the formula
E/RT
k = k0 e
.
(2)
At technological parameters used in the actual
practice, the reaction between metallic Mo and el-
ementary fluorine proceeds with a considerable heat
release, and reproducibility could not be achieved
in parallel experiments. As a result, the error in de-
termining the numerical values of the kinetic pa-
rameters was 35% at 20 vol % F2 in the reaction
mixture and about 60% at a concentration of 40
50 vol %.
N = 2n + 2n + 1,
(3)
where n is the number of factors constituting a com-
plete factorial experiment; 2n, number of star points;
RUSSIAN JOURNAL OF APPLIED CHEMISTRY Vol. 77 No. 12 2004

1932
RYBAKOV et al.
Table 3. Results of parallel experiments in studying the rate of fluorination of metallic molybdenum with elementary
fluorine
2
Parameter
cF , vol %
Rate of fluorination kg h 1 m
2
2
Run no.
Yav, kg h 1 m
j
T,
C
Y1
Y2
Y3
Y4
2
1
2
3
4
5
6
7
8
9
250
30
50
40
30
40
50
30
40
50
8.4389
16.5513
13.1047
8.8785
12.8551
13.1047
9.6506
8.3586
15.9046
13.2017
8.8785
11.8449
14.2705
8.6229
10.1925
14.1456
13.2430
8.2912
12.3839
14.7608
9.0217
10.3592
9.3373
15.6238
13.1831
8.6850
12.3613
14.0453
9.1029
1.1802
1.5621
0.0050
0.1123
0.2595
0.2813
0.1791
0.5372
1.1370
250
250
300
300
300
350
350
350
11.2030
14.5229
12.4089
14.1304
11.0840
12.5113
11.5654
13.7215
5.2467
and 1 corresponds to an experiment at the center of
design (at the point with zero level of the factors).
The experimental conditions and the results ob-
tained are listed in Table 2.
As independent parameters of the fluorination pro-
cess were taken the concentration of F2 in argon
Each experiment in the design matrix was carried
out no less than three times. The results of parallel
experiments performed to study of the rate of fluo-
rination of metallic Mo with elementary F2 are listed
in Table 3. Table 2 lists the averaged values of the
rate Y [kg Mo/(h m2)], calculated from the experi-
mental data in Table 3. A statistical processing of the
(cF , vol %), X1, and the initial temperature in the
2
fluorination zone ( C), X2. The rate of fluorination of
2
metallic Mo, Y (kg h 1 m ), was chosen as the re-
sponse function (output parameter).
It was established experimentally that the fluo-
rination occurs on the outer surface of the sample,
equal to the area of the reaction boat. This is also
confirmed by the fact that, if the weighed portion
(layer thickness) of metallic Mo is lowered by a fac-
tor of 2 4 (200, 100 mg) at initial temperatures of
250 350 C and F2 concentration of 20 50 vol %,
the fluorination rates remain virtually unchanged.
The specific surface area of the metallic powder is
apparently larger than the outer surface area of
the sample, and, therefore, the calculated rates are
underestimated. No quantitative estimates were per-
formed.
results obtained made it possible to calculate the rms
2
deviation of the output response function to be
=
y
0.583, at a variance of the average, 2y/n = 0.583/3 =
0.1943.
The reproducibility of the results of experiments is
commonly verified by finding the ratio of the largest
estimated variance to the sum of all estimates of var-
iances (Cochrane criterion):
2
max
j
1.5621
6.2467
Gcalc
=
=
= 0.29.
2
j
The center of the design (zero level) corresponded
to a F2 concentration in argon of 40 vol % and the ini-
tial temperature in the reaction zone equal to 300 C;
the range of variation of the independent parameters
was taken to be 10 vol % for the concentration of F2
and 50 C for temperature.
For the confidence probability P = 0.95, f =
1 = 2 and N = 9, Gtab = 0.478, and the experiments
are considered to reproducible, and the estimates
of the variance, to be uniform, because Gcalc Gtab
(0.29 < 0.478).
3
The regression equation obtained in this case with
the use of an orthogonal CCD is as follows:
The regression coefficients were calculated by
the formulas
Y = b0 + b1X1 + b2X2 + b12X1X2
N
b0 = 1/N yj ,
(5)
+ b11X21 + b22X22.
(4)
j
= 1
RUSSIAN JOURNAL OF APPLIED CHEMISTRY Vol. 77 No. 12 2004

KINETICS OF FLUORINATION OF METALLIC MOLYBDENUM WITH ELEMENTARY FLUORINE 1933
9.3373 + 15.6238 + 9.0984 + 13.7215 + 8.6850 + 14.0453 + 13.1831 + 11.5654 + 12.3613
b0
=
= 12.4386,
9
bi = xij yj / N (xij),
N
(6)
1
1
9.3373 + 15.6239 0.0984 + 13.7215 8.685 + 14.0493
6
b1
=
= 2.7117,
9.3373 15.6238 + 9.0984 + 13.7215 13.1831 + 11.5654
6
b2
=
=
0.6265,
N
N
/
xij xikyj / xijxik,
/
1
bik
=
(7)
(8)
1
9.3373 15.6238 9.0984 + 13.7215
b12
=
= 0.4159,
4
N
bii
=
xijyj / N (xij)2,
1
1
0.33(9.3373 + 15.6238 + 0.0984 + 13.7215 + 8.6850 + 14.0453) 0.67(13.1831 + 11.5654 + 12.3613)
b11
=
=
0.7975,
0.332 6 + ( 0.67)2
3
0.33(0.3373 + 15.6238 + 0.0984 +13.7215 + 13.1831 + 11.5654) 0.67(8.685 + 14.0453 + 12.3613)
b22
=
= 0.2117.
0.332 6 + 0.672
3
To determine the significance of the coefficients
obtained, we calculated their variances
The equation for the rate of fluorination of metallic
Mo is written in the code variables as
2
2
Y = 12.3484 + 2.7117X1 0.6265X2 0.7975X21.
=
av /N = 0.1943/6 = 0.0324,
(10)
bi
2
= 0.1943/4 = 0.0483,
Let us pass from the code variables to technological
parameters:
bix
= 0.1943/[0.33 6 + ( 0.67)2 3] = 0.0971,
2
bii
X1 = (cF
X2 = (T
40)/10 = (0.1cF
4),
6).
(11)
(12)
2
2
2
= 0.2549.
b0
300)/50 = (0.02T
It is commonly believed that a regression coef-
ficient is significant if the following condition is
satisfied
Substituting the values of X1 and X2 in the code
equation and simplifying it, we have
b
b t,
(9)
2
Y = 0.9092cF 0.0125T 0.7975 10 c2F 7.4992,
(13)
2
2
where t is the value of Student’s criterion.
cF = 30 50 vol %, T = 250 350 C.
2
In the given case, for the confidence probability
P = 0.95: f = 9 1 = 8, t = 2.31, b0 t = 1.167,
Substituting the values of the independent param-
eters into this equation, we obtain the calculated
fluorination rates (Table 4).
bi t = 0.416,
bik t = 0.508,
bij t = 0.720;
b0 = 12.3486 > 1.167, b1 = 2.7117 > 0.416,
b2 = 0.6265 > 0.416, b11 = 0.7975 > 0.720;
b22 = 0.2117 < 0.720, b12 = 0.4159 < 0.508.
The adequacy of the equation was assessed by
the Fisher criterion for a confidence probability of
0.95:
Thus, the regression coefficients b22 and b12 are
nonsignificant and should be excluded from the re-
gression equation.
Fcalc = 0.2549/0.1943 = 1.312.
RUSSIAN JOURNAL OF APPLIED CHEMISTRY Vol. 77 No. 12 2004

1934
RYBAKOV et al.
Table 4. Calculated values of the fluorination rate
(2) A regression equation (13) for practical calcu-
lations was derived using the statistical method of
experiment design. This equation relates the rate of
fluorination of metallic Mo to temperature and con-
centration of fluorine. It can be used to calculate
the rate of fluorination of metallic Mo at any point of
the factor space at F2 concentrations of 30 50 vol %
and temperatures of 250 350 C.
2
no.
Yicalc
Yiexp
Yicalc Yiexp (Ycalc Yexp)
1
2
3
4
5
6
7
8
9
9.4743
15.4383
8.2243
13.6483
8.8493
14.2733
12.9838
11.7338
12.3588
9.3373
15.6238
9.0984
13.7215
8.6850
14.0453
12.1831
11.5654
12.3613
0.137
0.186
0.874
0.073
0.164
0.228
0.801
0.168
0.003
0.0188
0.0344
0.7640
0.0054
0.0270
0.0520
0.6411
0.0284
0.0001
REFERENCES
1. Andreev, G.G., Guzeeva, T.N., Krasil’nikov, V.A., and
Makarov, F.V., Sovremennye neorganicheskie ftoridy:
Sbornik trudov, Sib. Otd. Ross. Akad. Nauk (Modern
Inorganic Fluorides: Coll. of Works, Sib. Div., Russian
Acad. Sci.), Novosibirsk, 2003, pp. 26 29.
2.0392*
*
2
=
N 2.0392/(N 1) = 0.2549.
2. Batuner, L.M. and Pozin, M.E., Matematicheskie me-
tody v khimicheskoi tekhnike (Mathematical Methods
in Chemical Technology), Leningrad: Gostekhizdat,
1963.
1
At f = 2 and N = 9, the tabulated values of the
Fisher criterion Ftab = 4.26 and, therefore, Fcalc Ftab
(1.312 4.26). Hence follows that the regression
3. Emanuel’, N.M. and Knorre, D.G., Kurs khimicheskoi
kinetiki (Course of Chemical Kinetics), Moscow: Vys-
shaya Shkola, 1962.
equation obtained is adequate to the experimental re-
sults. This equation can be used for calculating the
numerical value of the rate of fluorination of metallic
4. Panchenkov, G.M. and Lebedev, V.P., Khimicheskaya
kinetika i kataliz (Chemical Kinetics and Catalysis),
Moscow: Khimiya, 1985.
2
Mo (kg h 1 m ) at any point of the factor space:
cF = 30 50 vol % and T = 250 350 C.
2
5. Shcherbakov, V.I., Zuev, V.A., and Parfenov, A.V.,
Kinetika i mekhanizm ftorirovaniya soedinenii urana,
plutoniya, neptuniya ftorom i galogenftoridami (Ki-
netics and Mechanism of Fluorination of Uranium,
Plutonium, and Neptunium Compounds with Fluorine
and Halofluorides), Moscow: Energoatomizdat, 1985.
CONCLUSIONS
(1) The kinetics of the heterogeneous reaction of
metallic molybdenum with elementary fluorine was
studied experimentally. The results obtained make it
possible to calculate, using the Arrhenius equation,
averaged values of the kinetic parameters (rate con-
stant, apparent activation energy) for conditions close
to those used in actual technological practice of fluo-
rination. It was found that, as the concentration of F2
in the gas mixture is raised from 20 to 50 vol %,
the error in determining the kinetic parameters in-
creases from 35 to 60%.
6. Nalimov, V.V. and Chernova, N.A., Statisticheskie
metody planirovaniya ekstremal’nykh eksperimentov
(Statistical Methods for Design of Extremal Exper-
iments), Moscow: Nauka, 1965.
7. Sautin, S.N., Planirovanie eksperimenta v khimii i
khimicheskoi tekhnologii (Experiment Design in Chem-
istry and Chemical Technology), Moscow: Khimiya,
1975.
RUSSIAN JOURNAL OF APPLIED CHEMISTRY Vol. 77 No. 12 2004