V. Pereslavtsev, Yu.M. Pustovoit,
RRC "Kurchatov Institute", 123182, Kurchatov sq Moscow, Russia
The problem of hydrogen evacuation by getters and metal membranes at low pressures is being discussed last decades [1-3]. The work is devoted to the study of hydrogen evacuation by one or two layer metal membrane. One can use the phenomenology approach of absorption-desorption processes in the system hydrogen -nonevaporated getter for the description of absorption-desorption processes in the system hydrogen - metal membrane [4]. The hydrogen flux desorbed by metal surface is described by the square law Iout = ¡3 ■ c2, where c is the surface concentration of gas atoms in metal, and ¡3 is the desorption coefficient. Such a model of the dehydridisation of metals was offered by Sieverts for a wide range of hydrogen concentration. According to the Sieverts law, the equilibrium gas pressure near the metal surface is proportional to the square of atomic gas concentration in metal p = K ■ c2, where K is the equilibrium constant, K = K0 ■ exp(- EjRT), Es is the
activation energy of solubility. One can determine ¡3 = a K/V2n mkT .
The hydrogen flux adsorbed by a surface can be calculated by the formula J 0 = p/y/2nkmT = nv/4, where p and T are the pressure and the temperature of the gas, m is the gas molecule mass, n is the gas density, v is the average molecular speed, O < 1 is the sticking coefficient taking into account the existence of a surface energy barrier limiting the adsorption of molecules by a surface: O = O0 ■ exp(- Ea/RT), Ea is the activation energy
for the adsorption of molecules. In a common case, the gas flux qin adsorbed by a surface, consists of the
various parts taking into account in particular the interaction of atoms and ions with metal. Atoms and ions have own "sticking coefficients", and these coefficients differ from the molecular ones.
1. ONE-LAYER MEMBRANE. The hydrogen concentration c(x,t) in a membrane (Fig. 1) at time t in a position x is described by the diffusion equation:
EVACUATION OF HYDROGEN BY GETTERS AND METAL MEMBRANES AT LOW PRESSURES
dc{x,t) d2 c{x,t)
—d-- = D—^^ (1)
ot ox y '
with boundary conditions: on a surface 1 (x=0): „ dc(0,t) _
-D ' _ qiin- qiout (2)
O x ' y '
on a surface 2 (x=l): dc(l,t)
-D ¿x ~ q2out- q2in. (3)
where qin _ apj„^2nmkT~g is the hydrogen flux adsorbed by the surface of a membrane, q1out _ ¡1 c(0,t)2 is the hydrogen flux desorbed by the surface of a membrane, ni, pi and Tg is concentration, pressure and
temperature of hydrogen on the side 1 of membrane accordingly; a _a0 • exp(-EjRT) is the probability of adsorption, D _D0■ exp(-Ed/RT) is the diffusion coefficient, ¡5 _ aKj2nmkTg is the desorption
constant determined by the constant of an equilibrium K _K0■ exp(-EjRT) (the equilibrium pressure of hydrogen at membrane surface isp _ Kc2 and qin _ qout), Ea, Ed e Es is the activation energy of adsorption, diffusion and solubility accordingly.
The solution of the diffusion equation with square-law boundary conditions in a common case is resulted in work [5].
The diffusion equation solution of the hydrogen evacuation by metal membrane for the stationary case (t ^^ and q _ Const) is considered in works [5,6]. The hydrogen flux pumped out by a membrane is described by the equation:
i
Pi - 2pmkTgl - J 2pmhTg 2 + p2 - = 0- (4)
The evacuation probability of hydrogen molecule by a membrane X_ q^2n mkTg jp1 at Tg1 _ Tg2 is described by the equation:
HZ-XK=0 (5)
]j a1 \a2 p1 A D pnmkTg The equation (5) has two asymptotic solutions.
1) The hydrogen flux pumped out by a membrane is limited by the diffusion process a in a membrane, p1 >> p2 and x << a1:
J2nmkTg d
<6)
2) The hydrogen flux pumped out by a membrane is limited by an adsorption at low pressure X^Pi ^ 0, (Pi >> P2):
X = (l/ai + 1ja2 ), (7)
for a1 =a2 = a, x =al2.
The experimental results of hydrogen evacuation by the cylindrical palladium membrane (the diameter is 56 mm, length is about 100 mm and thickness is 20 microns) [6] are shown in Fig. 2. The hydrogen, diffused through a membrane are oxidized by oxygen up to water.
One can determine the hydrogen adsorption probability a= 0.85 -exp(-670¡T) at a1 =a2 =a, the
hydrogen diffusion coefficient D = 7 ■ 10~6 ■ exp(-4700¡T) m2/s, (atK = 31 ■ exp(-2000/T) Pa/(m3Pa/kg)2 [7]) by means of these data [6] and to calculate the dependence of evacuation probability of hydrogen molecule by the mentioned above palladium membrane on pressure (Fig. 3).
2. TWO-LAYER MEMBRANE. The hydrogen concentration c(x,t) in a two-layer membrane [8] (Fig. 4) at time t in a position x is also described by the diffusion equation (1) with boundary conditions (2) on surface 1 (x=0): dc, (0,t ) a r 2/ m
-Ö<^=7nfcr['-K'c'(04 (8)
and (3) on surface 2 (x=li+l2):
n dcn (l1 + lII,t ) a2 2 ij + , A 1
- D" dx =~nTg [+w)-p ].
The boundary condition between the layer I and the layer II is
dcj (lj,t) d Cjj (lI,t)
D
(10)
ox ox
Where cI (x,t) and cu (x,t) is the hydrogen concentration in layer, lj and ljj is the thickness of layer, D1 and Djj is the diffusion coefficient in layer material, K1 and K11 is the equilibrium constant of hydrogen and layer material for the layer I and layer II accordingly.
There is no diffusion flux in a membrane in p1 = p2 = p case and the equilibrium takes place p=ki ■ cï=kii ■ cli, ci = cii KnlKiandcii = ci ■4KJKû.
One can write the equation (4) for a two-layer membrane in a stationary case (t q(x) = Const ):
Pi
- qppmkl, - JqppmkTg2 + p2 - q(/Di + l^/D, ) =
'6.
0
(11)
and the equation (5) for evacuation probability of hydrogen molecule by a two -layer membrane at Tg1 = Tg2 :
Vp7
VirV67v/62 + pjpi - v-.——
^2pmkTg
li"\lKi , lii ^^ ii
D,
+ •
D,
= 0
(12)
The equation (12) has two asymptotic solutions by the analogy equation (5):
1) The hydrogen flux pumped out by a membrane is limited by the diffusion process in a membrane, p1 >> p2 and X << a1:
42nmkTs (hJK injKn
x =
4pi
Dr
D
ii
(13)
2) The hydrogen flux pumped out by a membrane is limited by an adsorption, the probability of hydrogen evacuation is determined by the expression (7).
The experimental model of two-layer membrane supposed by us was used for the experimental researches of hydrogen evacuation. The extension surface of palladium tube (the diameter of tube is 6 mm, the length is 95 mm, the wall thickness is 0.2 mm) was covered by the layer of titanium nonevaporated getter with the thickness
of 1 mm. The hydrogen evacuated was adsorbed by titanium getter, diffused through the tube's wall and was oxidized on internal palladium surface by oxygen. The tube's heating was executed by electrical current. The experimental results of measurement of evacuation probability of hydrogen upon pressure at temperature 750°C are shown on Fig. 5. The dependence of hydrogen evacuation probability on pressure calculated by the equation (13) is plotted by the continuous line on Fig. 5. An equilibrium constant of hydrogen - titanium obtained by the
data of solubility in [7] is K = 4,839-exp(-9525/T) Pa/(m3Pa/kg)2
The coefficient of hydrogen diffusion in titanium a getter covered the palladium tube in the experiment is D = 0,8-10~6 -exp(-5200/T) m2/s.
The value of diffusion coefficient is less than usual diffusion coefficient for titanium nonevaporated getter (D = 1,07 ■ 10"5 ■ exp(-5200/T) m2/s).
One can explain the low diffusion coefficient by the technology used for the covering the tube by getter. The getter was rendered on a palladium tube as the mixture of a powder titanium with organic binder. The binder was "burnt out" in vacuum furnace at the temperature 800°C.
The accepted probability of hydrogen adsorption on a surface titanium getter was aj = 0.125.
The two-layer permeable membrane may be used in non-stationary mode. The above two layer membrane tube
was used as a membrane for the hydrogen evacuation in pulsed mode.
Hydrogen was inputted in vacuum chamber in pulsed mode (10 s) and oxygen was inputted the into the tube in continuous mode. The period of pulses is equal to 60 s. The experimental results of hydrogen pumping by two-layer membrane in intermittent regime are shown in Fig. 6.
The pumping speed of hydrogen in maximum is equal to ~ 12 l/s. It is more than that in stationary regime. The mechanism of the increasing of pumping speed is based on that the time of absorption process is more than the time of diffusion process and the absorption of hydrogen in non-evaporated getter layer is the limit process but not the diffusion process as it is in stationary case. The sorbed hydrogen diffused in the direction of minimum of its concentration to the internal palladium layer of the tube. Such mechanism may be used for the creation of pumping units on the base of two-layer permeable membrane for the hydrogen in pulsed mode.
3. EVACUATION OF HYDROGEN FROM PLASMA BY METAL MEMBRANES The hydrogen flux adsorbed by the surface 1 of a membrane (Fig. 1) qin consists of the hydrogen molecule flux
qH^ = a1 pj-yj2n mkTg (per unit surface area), the hydrogen's ion flux H + qH + = jH + /2e , the hydrogen's molecular ion flux H + qH + = jH +je ~ and hydrogen atoms' flux qH 0 = piH 0 j'l^jn mkTg at the presence of plasma. jH + and jH + are the currents of ions per surface area unit, e is the charge of electron. We assume the
H 2
absence of surface absorption barrier for atoms and ions i.e. there are no power expenses on the dissociation of
aiPi + -
molecules. One can write the flux q1in in a boundary condition (2) as: q1i The boundary condition (2) is:
V2
mkTg
JH + Jh 2 + -H- + -2
2e-
D-
6,
ob(0,t)__
dx ^2pmkTgl
pl +p6 - KM
+jh ++ 2jh+12e
(14)
We assume there is no plasma on the side 2 of membrane. One can write the equation (4) at the plasma presence as:
Pi +
1H0
V261
+
pPmkTgi
26,
jh + + 2jh
2q
1
6~PPmk Tg2 + P2 - ^DT _
0
(15)
We shall consider some practical case: Let the hydrogen pressure at the side 2 of a membrane is the f
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