Investigating the dynamic changes of the vapour concentration in a Vapour Phase Soldering oven by simplified condensation modelling

Applied Thermal Engineering 59 (2013) 94e100

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Investigating the dynamic changes of the vapour concentration in a Vapour Phase Soldering oven by simplified condensation modelling Balázs Illés*, Attila Géczy Department of Electronics Technology, Budapest University of Technology and Economics, Egry József str. 18, H-1111 Budapest, Hungary

h i g h l i g h t s
Vapour condensation modelling in Vapour Phase Soldering (VPS) oven.
Dew point model is developed for Galden liquid by experiments.
Effect of soldered assembly on the vapour concentration change is investigated.
Effect of immersion speed on soldering thermal profile is studied.
Describe the balance between the vapour consumption and reproduction.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 28 December 2012 Accepted 3 May 2013 Available online 17 May 2013

The dynamic changes of the vapour concentration during Vapour Phase Soldering (VPS) process was investigated by a board level modelling approach of vapour condensation. This model is based on a process (machine) level model which calculates the vapour and temperature space in the VPS tank. The board level condensation model is embedded into the process level model and runs as a co-simulation. The condensation model applies combined transport mechanisms including heat transport by heat conduction; mass transport by phase change during the condensation of the Galden liquid; and energy transport caused by mass transport. The model uses a special dew point calculation which was developed for Galden liquid by experiments. The model can describe the temperature change of soldered assembly, and the vapour consumption around the assembly. This way the effect of the soldered assembly on the vapour space can be investigated. It was also shown that the heat conduction of the vapour space and the immersion speed of the assembly cannot be neglected. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: Vapour Phase Soldering Condensation Vapour concentration Co-simulation

1. Introduction Vapour Phase Soldering (VPS) is a reflow soldering method, which is an emerging alternative of the conventional forced convection reflow soldering. During the VPS process a vapour space is generated in a closed tank from a special heat transfer liquid (Galden) by a heater (at bottom of the tank) and by a cooler appliance (at top of the tank) which condenses the excess vapour. The prepared assembly is immersed into the vapour space, the vapour then condenses on it. The latent heat of condensation and the heat flow from the surrounding medium heats the assembly above the melting point of the applied solder alloy. The Galden liquid [1] is a specific product composed of perfluoropolyether substance (PFPE):

* Corresponding author. Tel.: þ36 1 463 2755. E-mail address: [email protected] (B. Illés). 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.05.008

(1)

where the flexible ether chain structure is closed with strong carbonefluorine bonds providing stability. Galden liquids with various boiling points (from 150  C up to 240  C) can be chosen according to the melting point of the applied solder alloy. The main advantages of VPS process are the uniform heating and the lack of overheating while the temperature is limited to the boiling point of the liquid [2]. In addition inert atmosphere and condensed film layer keeps oxygen out from the melted solder, avoiding the oxidation of the joints. Main disadvantage of the VPS technology is the rapid heating, which may cause damages in the solder joints such as solder cracking [3], void generation [4],

B. Illés, A. Géczy / Applied Thermal Engineering 59 (2013) 94e100

Nomenclature T E m 4 t V A DG H S

l h CS

r

temperature, K energy, J mass, kg vapour concentration, kg/m3 time, s volume, m3 surface, m2 Gibbs free energy, J enthalpy, J entropy, J/K specific thermal cond., W/m K latent heat, J/kg specific heat capacity, J/kg K density, kg/m3

tombstoning [5], etc. During the VPS process the vapour is the actual heat transfer medium for soldering; therefore the most important parameters are the temperature and the Galden vapour concentration (amount of Galden vapour in a given volume) in the vapour space. The key steps of VPS are the evaporation of Galden liquid and the condensation of vapour on the assembly. The physical description of the Galden evaporation is well known [8], (over the boiling point the influent heat is expended for the evaporation). The condensation is more complicated since it depends on the temperature and the concentration of vapour. In addition there is no dew point model for the Galden vapour. Besides the technical innovations such as application of vacuum atmosphere and soft vapour thermal profiles, there are only a limited amount of researches for the characterization of the VPS process. Few examples show different solutions such as simple thermal profiling [6], measurements by thermovision cameras [7] and observation of the condensed droplets inside the vapour space by optical method [2]. In our previous work we have modelled the evaporation of the Galden liquid and vapour space forming at the level of the VPS process [8]. This paper presents the continued work focussing on the study of the dynamic vapour space change caused by the immersion of the soldered assembly into the oven. A board level vapour condensation model was developed whereby the heating of the assembly and the vapour consumption around it can be studied. The aim was to earn information about balance between the vapour consumption and redevelopment during VPS process.

95

Tb boiling point, K w general variables n,k indexing of the mesh Dx, Dy, Dz resolution of the mesh, mm Dt time step, mm divide constant kc Abbreviations dp dew point cn condensation ev evaporation df diffusion pr process st saturation vp vapour so solid

within the condensate layer [13]. Or the governing equations of the mass and energy transport are formulated separately for the two boundary layers [14], and then they are coupled applying conditions of compatibility at the interface [15]. In our model this last version was applied. 2.1. Physics of the simplified condensation model The layer structure and transport mechanisms of the model can be seen in Fig. 1, where mcn is the condensation mass transport, Ecn is the condensation energy transport, qvpecn is the heat diffusion at the vapourecondensate boundary and qcneso is the heat diffusion at the condensateesolid boundary. The mass diffusion is neglected in the vapour space at the border of the assembly; hence there, the mass change is more intense by condensation than by diffusion. The vapour consumption during the condensation starts significant mass diffusion in the vapour space to compensate the mass loss; this is also calculated in the process model. The convectional energy transport in the condensate is neglected due to the horizontal position of the assembly. The thickness of the condensate is usually supposed to be unknown and dimensionless coordinates are used during the mesh generation [12] or it is approximated by the ratio of the specific thermal conductivity of the condensate and the heat transfer coefficient of the vapour [16]. According to the experimental observations, in the case of VPS the thickness of the condensate is 0.2e 0.3 mm (depends on given surface circumstances of the assembly). This layer is formed immediately after the immersion of the

2. Condensation model When the soldered assembly is immersed to the vapour space, the vapour condenses on it and forms a condensate film layer which surrounds the body. This phenomenon can be described in different ways. If condensation is only an effect of the investigated process, the heat transfer between the solid structure and the vapour is usually approximated by an overall heat transfer coefficient [9] which is determined by direct measurements [10] or by experimental equations [11]. A more sophisticated method shows the presence of the condensate layer between the solid body and vapour phase atmosphere [12]. In these cases the heat transfer between the vapoureliquid and liquidesolid interfaces are separated and described in different ways. A possible model when the heat transfer at the vapoureliquid boundary is described by an overall heat transfer coefficient and thermal diffusion is supposed

Process model Condensation model boundary

Vapour mcn, qvp-cn, Ecn qcn-so

Vapor Condensate boundary Condensate Solid boundary

Condensate

Assembly Fig. 1. Layer structure model of condensation.

96

B. Illés, A. Géczy / Applied Thermal Engineering 59 (2013) 94e100

Dwn ¼ 2

Removable lid

X

ri $Tn ðtÞ þ

i ¼ x;y;z

Cooling pipe

X

  ri $ Tnþ1ðiÞ ðtÞ þ Tn1ðiÞ ðtÞ

in the case of Eq. (2) r coefficients are the following:

Process zone

rx ¼

Test board (with grid)

in the case of Eq. (4) r coefficients are the following:

Heat transfer liquid

rx ¼

Immersion heater

assembly into the vapour and its thickness remains near constant during the process caused by the balance between the gravity force and the force acts by the condensate surface tension. In this application the thickness of the condensate layer is considered to be 0.25 mm. The heat diffusion is described by the heat equation:

! (2)

where t is the time [s], T is the temperature [K], l is the specific thermal conductivity [W/m K], r is the density [kg/m3] and CS is the specific heat capacity [J/kg K]. During the condensation, the phase change generates mass transport at the vapourecondensate boundary. The transported mass generates energy transport contains the internal energy of the mass and latent heat of phase change:

vE vm ¼ ðh þ CS $Tb Þ $ vt vt

l Dt l Dt l Dt ; r ¼ ; r ¼ r$CS Dx2 y r$CS Dy2 z r$CS Dz2

l$A Dt l$A Dt l$A Dt $ ; ry ¼ $ ; rz ¼ $ h þ CS $Tb Dx h þ CS $Tb Dy h þ CS $Tb Dz

(3)

dp

Tn > Tnþi

(6.3)

(6.4)

The dew point model of the Galden vapour will be presented in the Verification section. The condensation causes a loss of mass in vapour cell n and results in a mass increase in the condensate cell whereon the condensation happened. However the volume of the condensate layer is considered to be constant, it is supposed that during condensation the same amount of Galden liquid left the condensate layer as the amount of the condensing mass. (Practically the exceeding Galden amount drips back to the bottom of the tank.) Therefore in the case of the condensate cells the mass transport generated energy transport (Eq. (3)) can be calculated according to latent heat of condensing mass and the internal energy difference between the condensing and the leaving mass:

DEncn ¼ ðCS $ðTb  Tn Þ þ hÞ$Dmn

DEnvp ¼ ðCS $Tb Þ$Dmn

  l$A vm vT vT vT $ ¼ þ þ vt h þ CS $Tb vx vy vz

D4n ¼  (4)

where h is the latent heat of the Galden [J/kg] and A is the surface whereon the condensation is happened [m2]. The condensing mass causes concentration decrease at the vapour boundary:

(5)

where 4 is the concentration [kg/m3] and V is the volume [m3]. 2.2. Numerical solution The model was designed by MATLAB with the application of the Finite Difference Method (FDM). The previously defined Partial Differential Equations (PDEs) are solved by the three dimensional explicit Forward Time Central Space (FTCS) method. The governing equations (Eqs. (2) and (4)) have the following form:

(7.1)

In the case of the vapour cells the mass transport generated energy transport means the internal energy loss of the cells:

where Tb is the given boiling temperature of the Galden liquid [K] and m is the mass [kg]. The energy transport has to be proportional with the heat flux into the condensate film [15], therefore the transported mass can be calculated:

v4 1 vm ¼  vt V vt

(6.2)

where w is a general variable (T or m), n is the indexing of the mesh, Dt is the time step [s] and Dx, Dy, Dz is the mesh size [m]. The necessary condition of Eq. (6.1) in the case of mass transport is that the dew point temperature of the vapour cell n is over the temperature of the neighbouring cell whereon the condensation is happened:

Fig. 2. The applied VPS station with numerical grids of the models.

l vT v2 T v2 T v2 T $ þ þ ¼ r$CS vx2 vy2 vz2 vt

(6.1)

i ¼ x;y;z

(7.2)

The condensing mass caused concentration decrease in a given vapour cell is (Eq. (5)):

Dmn

(8)

Vn

On the whole the temperature change in a given cell can be defined according to the heat diffusion (Eq. (6.1) with Eq. (6.2)) and the mass change induced energy transports (Eq. (6.1) with Eq. (6.3) and Eqs. (7.1) and (7.2)):

DTn ¼ DTndf þ

DEn Cn

(9)

The initial temperature condition for the soldered assembly is T(0) ¼ 40  C. It was a bit higher than the ambient temperature due to the preheating effect of the assembly positioning at the top of the VPS tank. The initial condition of the vapour space is defined by the pre-calculation of the process model [8]. 2.3. Embedded construction of the condensation model As it was discussed in the Introduction section the board level condensation model is embedded into a VPS process model

B. Illés, A. Géczy / Applied Thermal Engineering 59 (2013) 94e100

(presented in Ref. [8]). The VPS process model calculates the temperature and the concentration of the vapour space, from the start of the Galden evaporation until the saturation of the vapour space (prepared for soldering). The process and the condensation models are linked together and run together. After each calculation step of the process model, the condensation model receives the actual vapour space parameters. After the calculation of the condensation model, the process model gets back the modified vapour space parameters. The vapour cells around the assembly are the connection points between the process and the condensation model. Data transfer from the process to the condensation model is defined: vp vp TnðcnÞ ðtÞ ¼ TkðprÞ ðtÞ

(11.1)

VnðcnÞ mnðcnÞ ðtÞ ¼ mkðprÞ ðtÞ$ VkðprÞ

(11.2)

where k is the index of the cell in the process model wherein the cell of the condensation model is currently located. Hence the cell size of the process and the condensation model is different (will be discussed in Section 3); the amount of vapour (Eq. (11.2)) has to be calculated according to the volume ratio of the cells. After each calculation steps the condensation model modifies the vapour space parameters in the process model with the consumed energy and mass. In this case the cell volume ratio has to be considered at the temperature modification: vp vp TkðprÞ ðt þ 1Þ ¼ TkðprÞ ðtÞ 

j X

VnþiðcnÞ vp TnþiðcnÞ ðtÞ$ VkðprÞ i¼0

mkðprÞ ðt þ 1Þ ¼ mkðprÞ ðtÞ 

j X

DmnþiðcnÞ ðtÞ

(12.1)

(12.2)

i¼0

where j is the number of the cells of the condensation model which are currently located in cell k of the process model. This cosimulation structure ensures much faster operation than a combined (process and condensation) model with a finer resolution in the whole vapour area.

3. Parameters and space discretization The investigated batch type VPS system has a stainless steel tank with double wall: width (x axis) 180 mm; length (y axis) 280 mm; height (z axis) 170 mm; and wall thickness 0.5 mm. The tank is covered by a removable metal lid with apertures for probes and a heat-resistant glass window. The immersion resistor heater (⌀10 mm stainless steel tube, ceramic filler and ⌀1 mm heater filament with w25 U resistance) is positioned 10 mm from the bottom of the tank. The cooling is solved by a copper tube, positioned 10 mm under the top edge of the tank and led outside through the lid. Ambient temperature water is circulated inside the tube. For the verification measurements 1.3 dm3 HT170 type Galden (170  C boiling point) was used. This Galden type was chosen to achieve faster experimental validation results; hence the heating up and cooling down cycles are much shorter in this case than in the case of Galden for lead-free soldering at 230  C. HT170 is also relevant from the aspect of soldering with low melting point solder alloys, such as SneBi types. During the investigations a simple FR4 board (with 80  80  1.6 mm3 size) was studied with 550 W heating and 50 W cooling power.

97

The condensation model contains cuboid and cubic cells in a non-uniform grid with the following cell types: FR-4 (test board), Galden liquid, vapour cells (pure Galden vapour in a saturated cell and otherwise mixture of air and Galden vapour). Physical parameters of the materials can be seen in Table 1. The resolution of the space was reduced from a starting value to a final value from which the numerical solution shows no significant variation. An acceptable resolution is obtained at 5  5  0.4 mm3 cell size with 16 cells along the x and y axis and with 4 cells along the z axis (height of the board). A Galden liquid layer is defined around the board with 0.25 mm thickness. A vapour cell layer is defined around the Galden liquid layer with 0.4 mm thickness. The numerical grid contains altogether 3200 cells. The process model works with much lower resolution (the typical cell size is 10  10  10 mm3) with 10,800 cells [8]. The applied VPS station with the grids of the process and the condensation model can be seen in Fig. 2. The stability and the convergence criterion of FTCS is:

rx þ ry þ rz  0:5

(13)

and the truncation error is: O(Dt, Dx2, Dy2, Dz2). The maximum time step is found at Dt < 0.016 s. However, Dt ¼ 0.01 s is used in order to reduce truncation error without the increase of complexity. This increases the number of calculation steps together with the round error. The round error is decreased by the application of double words. In order to avoid the large memory demand, sparse vectors are used which reserve memory space only for the non-zero elements. In addition, the sparse vectors increase the calculation velocity with omitting those calculation steps where they have no elements. 4. Verification and dew point model The condensation model was verified by dynamic temperature measurements and by detection of concentration changes. The temperature measurements were carried out with K-type thermocouples (absolute measurement accuracy is 0.5  C) attached with SMD adhesive into small bores on the surface of the test board. The concentration changes result in pressure changes which were detected by a Sensirion SDP1108 differential pressure sensor (absolute measurement accuracy 0.002 Pa, but estimated accuracy in the case of low flow rates 0.1 Pa) under the test board at centre position. From the measured pressure the concentration (density) change can be calculated by the general gas law. The measurements have started after the saturation of the vapour space (means 170  C vapour temperature and 18 kg/m3 vapour concentration). The first aim of the verification was to determine the dew point temperature of the Galden vapour. The dew point depends on the temperature and the concentration (or Relative Humidity, RH) of the vapour as it is presented in a simple expression for water vapour [17]:

Tdp ¼ T 

100  RH 5

(14)

Table 1 Physical parameters of materials.

Air Galden liq. Galden vp. FR4

Density [kg/m3]

Spec. heat cap. [J/kg K]

Spec. therm. cond. [W/m K]

Latent heat [J/kg]

1 1820 20a 2100

1009 973 973 570

0.03 0.07 0.07 0.76(x,y) 0.53(z)

e 63,000 63,000 e

x, y and z represent x axis, y axis and z axis respectively. a Saturation vapour concentration at 170  C.

B. Illés, A. Géczy / Applied Thermal Engineering 59 (2013) 94e100

We modified the dew point model of the water vapour (Eq. (14)) according to experimental approximation of the calculated results to the measured temperature curves.

160

1.6

140

1.4 1.2

120

Meas. temperature Meas. concentration

100

1

Calc. temperature Calc. conc. above Calc. conc. below

80

0.8

60

0.6

40

0.4

20

0.2

0

T dp ¼ T 

0 0

5

10

15

20

25

Time [s] Fig. 3. Temperature change and Galden vapour consumption with dew point (continuous curves) and without dew point (dashed curves).

Unfortunately there is no available model for dew point calculation of Galden. Pure application of Eq. (14) is not possible; the enthalpy (H, [J]) of the Galden vapour is much larger than enthalpy of the water vapour (mainly caused by the one order of magnitude molecular weight difference). Therefore larger entropy change (DS, [J/K]) is necessary for the Galden to start the phase change (condensation) and fulfil the Gibbs free energy condition:

DG ¼ H  T$DS < 0

a)

(15)

1  m $ 1  st $100 kc m

(16)

In a VPS system the application of vapour concentration is obvious instead of RH. According to the Gibbs free energy (Eq. (15)), the dew point temperature of Galden vapour has to be lower (for the larger entropy change) than in the case of water vapour. So, approximation of the kc value was performed from 4.9 to 1 in 0.1 steps. The best match was found at kc ¼ 2.15. In Fig. 3 the calculated and measured parameters are compared with and without the application of dew point. The consumption of the Galden vapour is presented in the cells above and under the centre cell of the test board at the soldering position. The immersion speed of the test board was 50 mm/s results in 2 s immersion time until the soldering position (located 70 mm above the bottom of the tank). With the dew point model (continuous curves), the calculated and measured temperature values almost agree. In the case of the vapour concentration the error is higher which was probably caused by the very low flow rates in the vapour space results in measurement failure of the manometer. A minimal flow is necessary for the differential manometer to the accurate detection. The Galden vapour consumption is relatively high in 2e3 s. The barely visible breaks of the calculated concentration curves indicate that the condensation fluctuates during the process. The “shadowing effect” of the test board is also visible which means that vapour reproduction is better under the test board than over it. Without the application of dew point (dashed curves) the Galden vapour would consume in the cells around the board and would also cause considerable calculation error in the temperature values. Since the dramatic vapour consumption results in dramatic heat

18 16

14 12 10 8 6

4 2

b)

0 18 16

14 12 10 8 6

4 2

c)

0 18 16

14 12 10 8 6

4 2

Concentration [kg/m 3 ]

1.8

Concentration [kg/m3]

Temperature [°C]

180

Concentration [kg/m 3 ]

-5

x 10

Concentration [kg/m 3 ]

98

0

Fig. 4. Vapour distributions along y ¼ 150 mm (right) and x ¼ 100 mm (left) with 50 mm/s immersion speed at: a) 1 s, b) 3 s and c) 25 s.

17mm/s

25mm/s

18 16

14 12 10 8 6

4 2

b)

25mm/s

50mm/s

17mm/s

0 18 16

14 12 10 8 6

4 2

c)

50mm/s

17mm/s

25mm/s

0 18 16

14 12 10 8 6

4 2

Concentration [kg/m 3]

50mm/s

Concentration [kg/m 3]

a)

99

Concentration [kg/m 3]

B. Illés, A. Géczy / Applied Thermal Engineering 59 (2013) 94e100

0

Fig. 5. Vapour distributions along y ¼ 150 mm plane with 50, 25 and 17 mm/s immersion speeds at: a) 1 s, b) 3 s and c) 25 s.

capacity decrease in the vapour cells which causes the fall of the energy transported via heat diffusion (Eq. (6.1) with Eq. (6.2)). 5. Results and discussion

180

0.061

160

0.06

140

Temperature Total amount of vapor

0.059

120

Immersion speed 50 mm/s Immersion speed 25 mm/s Immersion speed 17 mm/s

0.058

100

0.057

80

0.056

60

0.055

40

0

5

10

15

20

Total amount of vapour [kg]

Temperature [° C]

The main aim of the simulations was to investigate the dynamic vapour space change caused by the immersion of a test board into the oven and to earn information about balance between the vapour consumption and reproduction during VPS process in the case different immersion speeds. In Fig. 4a the vapour concentration distributions can be seen in 2D graphs along the planes y ¼ 150 mm (right) and x ¼ 100 mm (left) at different time (with 50 mm/s immersion speed). The calculations have started after the saturation of the vapour space

0.054 25

Time [s] Fig. 6. Temperature change of the test board and the total amount of vapour in the oven.

(at 170  C and 18 kg/m3). The previously defined optimal borders of the processing volume [8] are marked by the white dashed rectangles. As it was also observed during the verification (Fig. 3), the test board causes significant vapour consumption around itself at the beginning of the immersion. In addition it rearranges the state of the vapour concentration in the tank to the end of the heating process (Fig. 4c) compared to the starting state (Fig. 4a). This vapour space rearrangement highly depends on the immersion speed of the test board. In Fig. 5 the vapour concentration distributions can be seen along the plane y ¼ 150 mm at different time calculated with different immersion speeds. In the case of fast immersion (like 50 mm/s) the vapour consumption is more even along the z direction of the oven compared to the slower immersion speeds. In the case of the slower immersion (like 25 and 17 mm/s) most of the vapour consumption is happened at the top part of the vapour space, since the test board almost reaches the saturation temperature there. In Fig. 6 the temperature changes of the test board and the total amount of vapour in the tank is shown in the case of different immersion speeds. As it is visible in Fig. 6; the immersion speed effects also on the shape of the thermal profile. The decrease of the immersion speed results in the decrease of the temperature gradient in the ramp up period; however, delays the brake down of the temperature curve in the saturation period (Table 2). The results predict that the shape of the VPS thermal profile can also be influenced by the immersion speed and not only by the amount of vapour in the tank (controlled by the heating power of the Galden liquid). Table 2 Thermal profile parameters. Immersion speed [mm/s]

Temperature gradient of the ramp up [ C/s]

Brake down temperature [ C]

50 25 17

22.5 18.9 15.2

113 130 140

100

B. Illés, A. Géczy / Applied Thermal Engineering 59 (2013) 94e100

The change of the total vapour amount in the oven was between 3.7 and 5.5 g (6e9%) in the case of the different immersion speeds (Fig. 6). It has to be noted that these are relative decreases hence the vapour evaporation continues during the process. These values and the differences between them are not as significant as the proper place of consumption (Fig. 5) or the consumption around the board (Fig. 4).

6. Conclusions A simplified modelling approach of vapour condensation at board level during the VPS process was presented. The model is embedded into a process level model which calculates the formation of the vapour space in the VPS tank [8]. With the embedded structure the board level condensation model can work in refined resolution compared to the process model without the increase of the complexity and the calculation time. The model can calculate the temperature change of the soldered assembly and the vapour consumption around it. A novel dew point model for Galden vapour was introduced via experimental procedures, since without the application of dew point the calculations were inaccurate. It was observed that the vapour consumption is considerable around the assembly during the VPS process and significant amount of heat is transferred via heat diffusion from the vapour. The heat capacity reduction caused by vapour consumption could result in significant heating gradient decrease. The immersion of the board rearranges the vapour space according to the immersion speed which also controls the shape of the VPS thermal profile. The change of the total amount of vapour in the tank during the soldering is not as significant as the place of consumption or the consumption around the board. Presented results may serve as an initial step to achieve calculation of soldering profiles recommended for mass surface mount technology production.

Acknowledgements This paper was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.

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