New lithium gas sorbent. III. Experimental data on evaporation

Article abstract of DOI:10.1016/j.jallcom.2007.06.055

The kinetics of lithium evaporation from Ag-Li wire has been studied experimentally in the temperature interval 520-630 °C. The initial stage of the process takes place in the kinetic regime and finishes with the formation of a thin layer of silver on the surface of the alloy. Then the process moves to the diffusion region where the evaporation flow and the mass of the deposited film can be described quantitatively with the help of simple analytical expressions.

Full text of DOI:10.1016/j.jallcom.2007.06.055

Journal of Alloys and Compounds 460 (2008) 357–362
New lithium gas sorbent
III. Experimental data on evaporation
K. Chuntonova,∗, J. Setinab, A. Ivanovc, D. Permikinc
a Nanoshell Materials R&D GmbH, Primoschgasse 3, 9020 Klagenfurt, Austria
b Institute of Metals and Technology, 1000 Ljubljana, Slovenia
c Ural State University, Lenin Avenue 51, 620083 Ekaterinburg, Russia
Received 4 May 2007; received in revised form 14 June 2007; accepted 15 June 2007
Available online 19 June 2007
Abstract
The kinetics of lithium evaporation from Ag–Li wire has been studied experimentally in the temperature interval 520–630 ◦C. The initial stage
of the process takes place in the kinetic regime and finishes with the formation of a thin layer of silver on the surface of the alloy. Then the process
moves to the diffusion region where the evaporation flow and the mass of the deposited film can be described quantitatively with the help of simple
analytical expressions.
© 2007 Elsevier B.V. All rights reserved.
Keywords: Lithium films; Solid solutions; Evaporation rate; Cover layer; MEMS
1. Introduction
packed micro electro-mechanical systems (MEMS) [4–7], a
rapidly developing and very specific sector of new technologies.
The presence of moving parts inside MEMS, extremely small
sizes of enclosed cavities with a correspondingly high surface-
to-volume ratio of cavity, as well as a long operating lifetime
require a high sorption capacity of getters and the absence of
loose particles [8–10]. However, it should be recognized that
these requirements are mutually exclusive if one bears in mind
traditional non-evaporative getters (NEGs), based on transition
metals such as Ti, Zr, etc. [11–13]. Gas sorption by transition
metals at room temperature continues only until the surface
is saturated (one or, in the best case, several molecular lay-
ers). Therefore, though dense films of the given metals satisfy
the requirement of the absence of loose particle formation, at
the same time, they have a negligibly small sorption capacity.
High porosity sintered materials such as high porosity thin film
(HPTF) [14], the sorption capacity of which is approximately
two orders of magnitude higher than that of dense films, generate
free particles [15,16] due to their powder origin.
Solid solutions of Li in Ag, Cu and some other metals are
a very convenient getter material, which is easily passivated by
several methods and is also easily activated by means of heat-
ing to 150–350 ◦C [1]. When the temperature of these alloys is
raised to 450–600 ◦C they turn into vapor sources of Li, which
condensing on the substrate, forms active getter layers character-
ized by high sorption activity especially with respect to oxygen
and oxygen containing gases [2,3].
In this connection, it is possible to discuss two different direc-
tions in the development of getter technologies based on lithium
alloys. One consists of developing vacuum pumps or gas puri-
fiers, which use the sorption potential of heated foils or plates.
The foils or plates can be produced mechanically by rolling the
ingots [1]. We will discuss these issues in our next paper.
Another direction refers to the field of film technologies,
when lithium or its alloy is deposited onto the set surface in
the form of a getter film for maintaining vacuum inside sealed-
off devices. In the first place we should mention here vacuum
But even HPTF-getters are not able to ensure conditions nec-
essary through the lifetime of the MEMS. A simple calculation
using typical MEMS-level values shows that, e.g. to maintain a
pressure of ∼10−3 mbar in a cavity with a volume of ∼1 mm3
over 20 years at a standard leak rate of 10−10 atm cc/s, it would
∗
Corresponding author. Tel.: +43 650 62 03 565.
E-mail address: konstantin@chuntonov.com (K. Chuntonov).
0925-8388/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.jallcom.2007.06.055

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K. Chuntonov et al. / Journal of Alloys and Compounds 460 (2008) 357–362
be necessary to use a getter with HPTF properties, which is many
times larger in volume than the cavity itself.
A really high sorption capacity at room temperature can only
be achieved in materials containing chemically active metals:
alkalis, alkali-earths, and rare-earths. In this case, gas sorption
takes place according to the known mechanism of oxidation of
metals, namely, by the growth of a layer of reaction products
on the metal/gas boundary [17,18]. Under vacuum conditions,
when the process kinetics is small due to the negligible density
of one of the components, even active metals form on their sur-
face, not porous, but dense layers of oxides, nitrides and other
compounds without loose particle formation, having a structure
close monocrystalline. The sorption capacity in film getters of
this nature can approach their theoretical limit that is about four
orders of magnitude higher than in the case of HPTF-getters.
Of the active metals, lithium is the most suitable candidate to
take the role of the main getter in MEMS technologies. Possess-
ing the highest diffusion mobility, lithium allows maintaining
the sorption kinetics at the maximum high level. Moreover, the
uniqueabilityoflithiumtoformsolidsolutionsinawideconcen-
tration range with Ag, Au, Co and Cu [19] makes it possible to
overcome easily all of the technological limits connected with
the chemical activity of lithium itself. Finally, alloys Ag–Li,
Cu–Li, etc. due to their ductility are ideal vapor sources for
thermal deposition of films of uniform thickness onto substrates
of any shape. By shaping the alloy into beads, wire, or strips, it
is possible to obtain evaporation flows for all types of symmetry.
However, to control the deposition processes, it is neces-
sary to know how the rate of lithium evaporation from its solid
solutions changes with temperature and time.
Previously, Ag–Li films have already been used as a reser-
voir for Li atoms in laser sources of lithium ions for accelerators
[20–23]. The focus of these studies was on the diagnostics
of lithium plasma but not on the evaporation kinetics and the
changes in the film, which accompany evaporation.
The aim of the present paper is to provide concrete knowledge
for the case of wire vapor sources taking into consideration the
results of formal theoretical analysis of the processes taking
place in the alloy itself [24]. The conclusions obtained for linear
vapor sources can easily be generalized for the case of point or
planar sources.
Fig. 1. Design of a deposition cell: (1) Ag–Li filament; (2) quartz tube; (3)
thermocouple; (4) connecting wires; (5) steel ring; (6) string.
with filament 1. The tube 2 was 29 mm in diameter and 120 mm high, and
provided capturing of the entire evaporation flow along the filament region of
40 mm.
In the second set of measurements, an Ag–25 at.% Li alloy served as the
lithium source and steel tube ring 5, fixed with the help of wire string 6 in a
symmetric position with respect to 1, served as the substrate. The ring 5 was
8 mm high. The dimensional proportions of the assembly are more or less exactly
shown in Fig. 1.
Both sets of measurements consisted of several single depositions, the first
of which was started after a preliminary bakeout of the entire cell at 300–350 ◦C
for about 12 h and the next one, directly after a basic pressure of 10−7 mbar
had been achieved without heating, i.e. at room temperature. During lithium
evaporation, while heating of filament 1 by current, the total pressure in the
system increased approximately by one order of magnitude. After each single
deposition operation, the corresponding substrate, 2 or 5, was taken out through
the upper port of the vacuum chamber for chemical analysis of the condensate
and replaced by a new one.
Ag–Li wire was manufactured using an ordinary wire-drawing technique
from alloys obtained by melting the initial metals and further homogenizing of
the mixture in evacuated steel ampoules [1]. Ag (Alfa Aesar, 99.999%) and Li
(Chemetal, 99.9%) were used as the alloy components.
2. Experimental method
The process of Li evaporation from Ag–Li wires was studied by a rather
simple but reliable method: by determination of the mass of condensate ꢀmLi
obtained by deposition during time ꢀt at temperature T of the wire. The mass of
the lithium film was calculated from the data on the concentration of the solution
formed as a result of washing the film with a known amount of pure water [3].
A Perkin-Elmer 2380 flame atomic absorption spectrometer was used for this
purpose. The deviation in determination of the mass of Li did not exceed 7%.
The principal scheme of a deposition cell is given in Fig. 1. Inside a vacuum
chamber, a tested wire 1 with diameter of 0.5 mm was connected vertically to
two contacts Ni-conductors 4, which were strong enough for holding wire 1. A
thermocouple 3 with diameter 0.1 mm was spot-welded to the lower part of the
heated region 1. This installation of the wire was used for several deposition
operations.
3. Results and discussion
Two sets of measurements were performed using different materials and
substrate sizes. In the first set of measurements, lithium deposition was per-
formed from an Ag–28.5 at.% Li alloy onto a quartz tube 2 which was coaxial
Sorption studies of lithium films [3] showed that the material
works most effectively when the film thickness is 120–200 A.
˚

K. Chuntonov et al. / Journal of Alloys and Compounds 460 (2008) 357–362
359
Table 1
At the same time, the curves are similar in shape and both
are characterized by the presence of a minimum, which is con-
siderably shifted to the initial region of each deposition set. At
first sight, such a minimum seems to be an anomaly as both
constituents of the evaporation process, namely, the transfer of
lithium atoms into the vapor phase and the diffusion of these
atoms from the volume of the wire to the surface, are increasing
functions of the temperature. Meanwhile, the above-mentioned
Experimental data for deposition of lithium onto a quartz substrate
¯
˚
No.
T (K)
ꢀt (s)
c0 (at.%) Li
ꢀmLi (mg)
ꢀh (A)
1
2
3
4
5
793
823
838
848
903
140
690
505
600
265
28.5
28.4
28.3
28.2
28.0
0.016 0.001
0.029 0.002
0.040 0.0025
0.055 0.003
0.072 0.005
83
150
207
285
373
¯
behavior of the curves j − T is to be expected, and the following
two facts are important in understanding what is taking place:
¯
This predetermined both the general planning and details of the
present experiment.
The data for the first set of depositions (quartz substrate) are
given in Table 1. Here c0 is the gross composition of the Ag–Li
wire after introduction of the correction for the loss of lithium
during the previous deposition procedure, and ꢀh is the average
thickness of the lithium layer on the substrate.
As can be seen, the deposition of films of thickness
100–300 A is accompanied by a rather marginal change in the
total concentration of the evaporated component. This means
that a vapor source such as an Ag-Li wire allows performing
multiple depositions of thin lithium layers with a practically
constant rate within the bounds of a single deposition.
the implicit dependence of the j − T curves on time and the
diffusionless character of evaporation in the initial stage of the
process.
According to our deposition procedure, the series of experi-
mental points that form curves 1 and 2 (Fig. 2) is an evolutionary
sequence. From deposition to deposition, not only is a change
in the total concentration of lithium in the wire taking place, but
also the development of high chemical non-homogeneity in it.
In fact, this non-homogeneity determines the value of the evap-
oration flow. In essence, the graphs in Fig. 2 show the function
¯
˚
¯
j(T, t), of which it is known that ∂j(T, t)/∂T > 0, and ∂j(T, t)/∂t < 0
¯
[24]. Hence, the appearance of the minimum in curves j(T, t) is
inherent in the very nature of this function.
According to the data in Table 1, the linear rate of film growth
To make it clearer, let us establish the physical meaning of
the processes taking place in a wire that is periodically heated.
During the first heating of the initially chemically homogeneous
wire, onlylithiumatomsfromthesurfaceandfromthebordersof
the surface thin layer evaporate. The evaporation rate at this stage
is maximal. As a result of the loss of lithium, a thin layer which
almost completely consists of atoms of the non-volatile metal,
is created on the surface. That is, a diffusion barrier is formed
in the material, which abruptly decreases the evaporation rate.
At the same time, raising the temperature of the source in
every next deposition operation leads to the increase in evap-
oration flow (Fig. 2). The growth of the evaporation rate is
conditioned, in particular, by the fact that for the discussed mate-
rials, the energy of the diffusion activation is higher than the
energy of evaporation. So, although the thickness of the cover
layer depleted in lithium increases with time, the surface lithium
concentration also grows due to the temperature rise and this
becomes a cause for the growth of j [24].
¯
v = ꢀh/ꢀt on the inside cylindrical surface with a diameter
˚
from 10 to 100 mm is within the range of 0.1–4.0 A/s. At these
values of v, the process of deposition of monoatomic Li-layers
can be easily controlled automatically or manually.
However, the gradual decrease in the total concentration of
lithium in the source leads to the monotonic decrease in the
evaporation rate. To compensate for this decrease, it is necessary
to raise the temperature of the wire accordingly or to increase
the deposition interval ꢀt.
¯
Graphs j − T in Fig. 2 give some idea of how the evaporation
flow changes with temperature and time. Here curve 1 refers to
the set of depositions onto the quartz substrate, curve 2 refers
¯
to the set of depositions onto the steel substrate, and j is the
average evaporation rate during the time ꢀt. It can be seen that
curve 2 is situated a little lower than curve 1, which is connected
to the lower lithium content in the source in the deposition of
the second set.
¯
Thus, the unusual appearance of the experimental curves j −
T is sensibly explained from the position of the theory [24]
which predicts the formation of a thin film of non-volatile metal
on the surface of a solid solution when its volatile component
evaporates. These ideas are applied below in the derivation of
a simplified method of calculation of evaporation flow in metal
systems with intensive evaporation of one of the components.
4. Calculation of the evaporation flow
Let us consider the problem of evaporation of metal A from
a solid solution where the second component B has vapor pres-
sure many orders of magnitude lower than A. The vapor source
consists of a wire with length l and radius r0 and with initial con-
centration of volatile metal c0. The wire is placed along an axis
of an evacuated tube and heated with the current to a temperature
¯
Fig. 2. Curves j − T according to the data of Table 1: (1) quartz substrate; (2)
steel substrate.

360
K. Chuntonov et al. / Journal of Alloys and Compounds 460 (2008) 357–362
T, after which evaporation of A starts and the vapor condenses
on the inner wall of the tube. It is required to define the evap-
oration rate of A from the wire and the mass of the condensate
which appears on the wall during time t.
The general solution for a problem of this kind is given in
[24], but now our target is to obtain a working formula for cal-
culating a flow j(T, t) taking into account the real behavior of the
material, i.e. taking into account the data contained in Table 1
and Fig. 2. These data as well as the conclusions from the the-
oretical analysis [24] indicate that already during the first few
seconds of heating, the source surface gets covered with a thin
layer, which is practically deprived of the volatile component.
This layer determines further process behavior.
4.1. Approximation of the cover layer
The mathematical model of the process is presented in the
Appendix. In the assumed variables, the evaporation flow is
equal to
Fig. 4. Dependence of dimensionless mass q on evaporation time at differ-
ent values of H: (1) H = 1000; (2) H = 100; (3) H = 10; lines—formula (7);
circles—strict solution [24].
j = hc0u(τ, 1),
(1)
the outer layer B becomes thicker with time and the surface
concentration u(τ, 1) of the volatile metal continues to decrease,
which in accordance with (1), sets the pace of evaporation.
By substituting (4) into (1) and passing on to the dimension
variables, after certain transformations, we arrive at a formula
for the evaporation flow for the case of a source with a cover
layer
where h = (RT/2πM)1/2 exp (–E/RT), R is the gas constant, M the
molar mass of the volatile metal, and E is the molar energy of
evaporation of the same metal. For lithium alloys with Ag, Cu
and some other transition metals, the mass transfer parameter
H = hr0/Dc ꢀ 1, where Dc = D0 exp(−Q/RT), D0 is a preexpo-
nential factor and Q is the molar activation energy of diffusion.
In this case, a radial distribution of the volatile component con-
centration u(τ, x) is described by relation (4) as shown in the
Appendix.
ꢀ
ꢂ
ꢁ
Dc
πt
Dc
j(t) ≈ c0
−
.
(2)
2r0
A graphic representation of the function u(τ, x) is given in
Fig. 3. It can be seen that the core of the material is slowly
involved in the process whereas the surface, on the other hand,
immediatelylosescomponentAandispracticallycoveredwitha
filmofmetalB. Duringevaporationunderisothermalconditions,
The amount of evaporated metal is found by integrating the
evaporation rate with respect to time
ꢀ
ꢂ
ꢃ
t
M
N
Dct
r02
m(t) ≡ 2πr0l
j(t) dt = 2πr02lMc0q
(3)
0
where c0 is expressed in mol/m3, N is Avogadro’s constant, and
for calculating q = q(τ) the model provides two possibilities (see
Appendix): a rather complicated but exact eq. (7) or a simplified
eq. (8). To make the choice easier in Figs. 4 and 5, the results of
the calculations of the evaporated masses according to a strict
solution [24] are compared with the results based on (7) and (8),
respectively. It can be seen that, while approximation (7) almost
exactly reproduces the data for the strict solution (Fig. 4), in the
case of (8) there are certain deviations from it, which gradually
grow with the decrease in the value H (Fig. 5).
4.2. Comparison with the experiment
Formula (3) allows calculating the amounts of metal
deposited by a wire of known composition at a temperature
T during time t. In our case, the values necessary for calcula-
tions were found from the thermodynamic properties of Ag–Li
alloys [3] and by fitting of the data of Table 1. It was found that
E = 137 kJ/mol, Q = 220 kJ/mol and D0 = 3.0 m2/s.
Fig. 3. Dependence of dimensionless concentration u on relative coordinate
x at H = 500 at different moments of time τ: (1) τ = 10−5; (2) τ = 10−4; (3)
τ = 5 × 10−4; (4) τ = 10−3; lines—formula (4); circles—strict solution [24].

K. Chuntonov et al. / Journal of Alloys and Compounds 460 (2008) 357–362
361
Table 2
Calculation results and experimental data for deposition of lithium films from Ag–28.5 at.% Li wire with diameter 0.5 mm
exp
Li
exp
Li
th
th
Li
No.
T (K)
ꢀt (s)
Dc (m2/s)
ꢀm (g)
ꢀm (mg)
Li
m
/ꢀm
1
2
3
4
5
793
823
838
848
903
140
690
505
600
265
1.06 × 10−14
1.4 × 10−14
5.7 × 10−14
1.16 × 10−13
5.5 × 10−13
0.016
0.029
0.040
0.055
0.072
0.0164
0.0292
0.0402
0.0553
0.0723
0.98
0.99
1.0
0.99
1.0
Appendix A
The mathematical model of the evaporation process is:
ꢄ
ꢅ
∂c
∂t
Dc ∂
r ∂r
∂c
∂r
=
r
,
t > 0, 0 < r < r0
c(0, r) = c0
∂c
−Dc = hc, t > 0, r = r0,
∂r
where r is a radial coordinate, c(t, r) is the distribution of the
concentration of component A at the moment of time t, Dc is the
coefficient of diffusion of A in a lattice of metal B, and h is the
evaporation coefficient.
Let us introduce dimensionless variables and functions:
coordinate x = r/r0, 0 < x < 1; time τ = tDc/r02; concentration
u = c/c0; mass exchange coefficient H = hr0/Dc.
Fig. 5. Dependence of dimensionless mass q on evaporation time: line—formula
(8); symbols—strict solution [24] for different values of H (circles: H = 1000;
squares: H = 100; rhombs: H = 50).
In the new variables, the problem has a form
ꢄ
ꢅ
∂u
∂τ
1 ∂
x ∂x
∂u
∂x
=
x
,
τ > 0, 0 < x < 1
The calculations were made for an initially homogeneous
Ag–Li wire ofcomposition c0 = 28.5 at.%Li. Theresulting value
of lithium distribution of each preceding calculation was taken
further as the initial value for the following calculation. The
u(0, x) = 1
th
Li
theoretical values of ꢀm are compared with the experimental
∂u
−
= Hu, τ > 0, x = 1
values of ꢀmeLxip in Table 2.
∂x
The presented data show that the divergence between the
calculated and the observed values does not exceed 2%. Hence,
eqs. (2) and (3) can be used in the practice of deposition of
lithium films from solid solutions of Ag–Li, Cu–Li, etc.
The strict solution of the problem has a form [24]
ꢀ
ꢂ
ꢄ
ꢅ
λ2kDt
r02
ꢆ∞
λkr
r0
c(t, r) = c0 k=1CkJ0
exp
−
,
ꢀ
ꢂ
5. Conclusions
λ2kDt
r02
ꢆ∞
j(t) = hc0 k=1CkJ0(λk) exp
where expansion coefficients Ck
−
,
1. Wires of Ag–Li alloys with lithium concentrations not higher
than ∼30 at.% are well-controlled and convenient direct
filament lithium vapor sources in the temperature range
520–630 ◦C. In this range, the linear rates of Li-film growth
are values of approximately 0.1–10 A/s.
2. Experimental curves j(T, ) obtained in a sequence of deposi-
1 J0(λkx)x dx
1 J0(λkx)2x dx
2H
0
Ck =
=
,
˚
J0(λk)(λ2k + H2)
¯
0
tions with elevated temperature from one source have a clear
minimum in the initial region of the curve, which is con-
ditioned by a transition from a kinetic stage of evaporation
to a diffusion one. This initial stage is responsible for the
formation of the Ag cover layer on the source surface.
3. Simple analytical expressions have been obtained for calcu-
lation of the evaporation flow and the deposited mass (eqs.
(2) and (3), respectively).
λk are eigenvalues, which are found from a solution of the tran-
scendental equation
λkJ1(λk) = H J0(λk), k = 1, 2, 3 . . . ,
and J0 (z) and J1 (z) are the Bessel zero- and first-order functions,
respectively.
This solution is difficult to use due to the slow convergence
of the corresponding series.

362
K. Chuntonov et al. / Journal of Alloys and Compounds 460 (2008) 357–362
ꢁ
A simple approximation with acceptable accuracy for the
τ
τ
q(τ) = 2
−
.
(8)
basic function u(τ, x) can be obtained with the assumption that
H ꢀ 1 and that the initial stage of evaporation takes place only
with the participation of surface layers. Then for u(τ, x), we can
write [24]
π
2
References
ꢄ
ꢅ ꢄ
ꢅ
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1 − x
1
∼
√
u(τ, x) 1 − erfc
1 +
=
2 τ
2H
ꢇ
ꢈ
√
2 τ
(1 − x)2
√
+
exp −
,
(4)
π(1 − x + 2Hτ)
4τ
where erfc (z) is an additional error integral:
ꢃ
∞
2
exp(−z2) dz.
√
erfc(z) =
π
z
From here we come to dimensionless evaporation flow
√
y(τ) ≈ exp (H2τ) erfc(H τ)
ꢉ
ꢊ
√
1 − exp(H2τ/4) erfc(H τ/2)
−
, H >> 1.
(5)
2H
Eq. (5), which is exact everywhere except for a small neigh-
borhood of point τ ≈ 0, can be substituted with a small sacrifice
of accuracy for the asymptotic expression
ꢄ
ꢅ
1
1
1
2
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√
y(τ) ≈
−
,
(6)
H
πτ
which is a dimensionless equivalent of eq. (2). The amount of
evaporated metal is found by integration of (5) with respect to
time
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tion of Lithium for LEVIS Ion Source, Technical Report SAND-93-2183,
Sandia National Labs, Albuquerque, NM, 1994.
ꢁ
ꢃ
τ
τ
τ
q(τ) ≡ H
y(τ) dτ = 2
−
√
π
2
0
ꢁ
ꢋ
ꢌ
1
τ
+
+
exp(H2τ) erfc(H t) − 1 + 2
H
π
√
ꢋ
ꢄ
ꢅ
ꢄ
ꢅ
ꢌ
1
H2
H2τ
H
τ
[24] K. Chuntonov, A. Ivanov, D. Permikin, J. Alloys Compd. 456 (2008) 187.
exp
erfc
− 1 .
(7)
4
2
At very large values of H, a radical simplification of (7) is
admissible