Z4 – Crystal growth from the vapour phase __________________________________________________________________________________

Z4- Vapour Phase Crystal growth The aim of this experiment is the sublimation of elemental Iodine (I2) in a sealed Ampoule (Physical Vapour Transport, PVT). The students are expected to be familiar with the general aspects of crystal growth from the vapour phase and also with the differences of this growth method compared to others. A first insight into the dominant transport mechanisms in the PVT can be seen in the next pages. A literature overview is also given in attachment. Furthermore, it is important to know the crystallographic properties of iodine, the vapour pressure curve and the general rules of handling hazardous materials.

Exercise The students will get an ampoule filled with Iodine. After installation in the growth apparatus (Fig. 1), the transportation rates should be determined as a function of the temperature maximum and the set temperature difference between source and condensation room. Furthermore, the shape of the phase boundary should be described and correlated with the growth parameters.

Z4 – Crystal growth from the vapour phase __________________________________________________________________________________

Fig. 1: Vapour phase growth furnace

Theory of the PVT In contrast to the epitaxial vapour phase method, the bulk crystal growth from the vapour phase is carried out at relatively high pressures (i.e p>> 1 hPa). The mean free path of the gas molecules is then much smaller than the gas zone and the gas can then be handled as a fluid.

Z4 – Crystal growth from the vapour phase __________________________________________________________________________________

The individual process steps can be specified as follows: General 1. Phase change to the gaseous form 2. Transport 3. Deposition 4. Back transportation of surplus components, volatile impurities, inert gas or of a gas transport (CVT)

Experiment Sublimation of I2-molecules: I2(s) →I2(g), ∆S>0 Transport of the I2-molecules Condensation: I2(g) →I2(s) No other gas is filled into the ampoule. Since silica glass is used as a crucible material, one must expect (at least) H2O impurities.

The transport is initiated by a difference in the partial pressures of the species to be transported. The movement is from higher to lower partial pressure, i.e for a Sublimation reaction from higher temperature region to lower temperature region. If on the other hand a chemical vapour transport (CVT) is considered, one can also find examples of transport reactions, where a higher partial pressure of the species to be transported is adjusted in the region of lower temperature.

E.g.: 1. Si(s) + 2H2(g) → SiH4(g), ∆S

𝑡𝑜𝑡 𝐽𝑅𝑒𝑠𝑡 =0

𝐼2 ).

(2.2)

The diffusive flow (unit: mol/s) is derived from the Fick’s law: 𝑑𝑖𝑓𝑓

𝐽𝛼

= −𝐴𝑁𝐷

𝑑𝑐𝛼 𝑑𝑥

(2.3)

Where A is the cross sectional area, 𝑐𝛼 the konzentration (=partial pressure of α/total pressure), N the amount of material/volume, D the diffusion coefficient and x the region in the ampoule.

Z4 – Crystal growth from the vapour phase __________________________________________________________________________________

The sum of the concentration of the main components (index H; in experiment Iodine) and the residual gas (index Rest; in experiment 𝐻2 𝑂 ) is 1 (independent of x). 𝑐𝐻 + 𝑐𝑅𝑒𝑠𝑡 = 1 ∀𝑥 From (2.3) follows that the sum of the diffusive flows disappears: 𝑑𝑖𝑓𝑓

𝐽𝐻

𝑑𝑖𝑓𝑓

+ 𝐽𝑅𝑒𝑠𝑡 = 0

(2.4)

With the addition of equation (2.1) for the main component and the residual gas follow (2.2): 𝑑𝑖𝑓𝑓

𝑡𝑜𝑡 𝐽𝐻𝑡𝑜𝑡 + 0 = 𝐽𝐻𝑡𝑜𝑡 + 𝐽𝑅𝑒𝑠𝑡 = 𝐽𝐻𝑙𝑎𝑚 + 𝐽𝐻

𝑑𝑖𝑓𝑓

𝑙𝑎𝑚 𝑙𝑎𝑚 + 𝐽𝑅𝑒𝑠𝑡 + 𝐽𝑅𝑒𝑠𝑡 = 𝐽𝐻𝑙𝑎𝑚 + 𝐽𝑅𝑒𝑠𝑡

(2.5)

In a laminar flow, the gas volume will be moved as a whole. The laminar flow of a component results from the concentration in the unit volume. 𝑙𝑎𝑚 𝐽𝛼𝑙𝑎𝑚 = 𝑐𝛼 𝐽𝐻𝑙𝑎𝑚 + 𝐽𝑅𝑒𝑠𝑡 = 𝑐𝛼 𝐽𝐻𝑡𝑜𝑡

(2.6)

For the main component follows from (2.1),(2.3),(2.6): 𝐽𝐻𝑡𝑜𝑡 = 𝑐𝐻 𝐽𝐻𝑡𝑜𝑡 − 𝐴𝑁𝐷

𝑑𝑐𝐻 𝑑𝑥

2.7

By transforming the equation to: 𝐽𝐻𝑡𝑜𝑡 = −

𝐴𝑁𝐷 𝑑𝑐𝐻 𝐴𝑁𝐷 𝑑𝑐𝐻 =− (1 − 𝑐𝐻 ) 𝑑𝑥 𝑐𝑅 𝑑𝑥

2.8

It becomes clear that the total flow (and also the laminar flow from eq. (2.6)) is limited in presence of a residual gas component. In a similar form, in older literature [e.g. Faktor Garret] the equation (2.8) is handled as the Stefan flow.

Z4 – Crystal growth from the vapour phase __________________________________________________________________________________

Equation (2.7) is a normal 1st order differential function 𝐶𝐻 (𝑥) . A similar differential function also follows for 𝐶𝑅𝑒𝑠𝑡 (𝑥) . An approach to solving differential functions of this type can be found in [Walter]. The differential function (2.7) or the problem with the corresponding initial value has the following solutions: 𝑐𝛼 𝑥 = 𝑐𝛼 𝑥0 − 𝑘𝛼 . 𝑒𝑥𝑝

𝐽𝐻𝑡𝑜𝑡 . (𝑥 − 𝑥0 ) + 𝑘𝛼 𝐴𝑁𝐷

𝑤𝑖𝑡𝑕 𝑘𝛼 =

1, 𝑓𝑜𝑟𝛼 = 𝐻 (2.9) 0, 𝑓𝑜𝑟𝛼 = 𝑅𝑒𝑠𝑡

Exercise: Check if equation (2.9) is really the solution of the differential function (2.7). One can insert (2.9) in (2.7) and check if the resulting equation is generally valid. With known partial pressure at the phase boundary and known total pressure, the transport flow and so the growth rate can be calculated. N is obtained approximately from the: P=NRT (unit of N here: mol/m3). The diffusion constant is dependent on pressure and temperature [see Faktor Garrett p.101]: 𝑃0 𝑇 𝐷=𝐷 𝑃 𝑇0 0

1.8

2.10

With D0: diffusion constant at normal conditions, for a molecule with two atoms approx. 0.2 cm2/s; T0 =273K; P0 = 1013 hPa; P: total pressure

The latent heat flow is to be considered for exact transport experiments. The latent heat causes in an exothermic (endothermic) reaction an increase in temperature at the reaction region. That means the higher the transport rate, the lower the temperature difference between the surface of the feed material and the crystal. Poor thermal contact (e.g. glass, air gap) of the system and the growth furnace favours this effect.

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Because of the two unknown parameters (exact temperature and total pressure), a quantitative comparison of theory and practical experiment must be avoided. Nevertheless, the student should plot a diagram showing the partial pressure p(x). If possible, the parameters (e.g. total flow) should be determined from the experiment. One can choose any plausible value for the total pressure.

Instructions Adjustment of the magnetic stirrer: temperature 50°C, rotation: 650 rpm (increase very slowly) The temperature of the oil bath is to be maintained at 75°C (shown on the mercury thermometer). This should be kept constant since the temperature changes only slowly due to high heat capacity. If the bath temperature of the growth experiment must be changed, the set temperatures must not exceed the melting point of iodine (113, 6°C). It should be noted that the flash point of silicon oil is 300°C! To cleanse the crystallization region of impurity seeds, it is important to set the temperature of the upper heating zone higher than the oil bath at the beginning (i.e. 85°C). If the crystallization peak is free of seeds for a long period, the temperature of the upper zone should be lowered gradually to the temperature of the oil bath. The temperature can then be set to a desired value below the oil bath. After the temperature has been kept constant for a long time, the pulling of the ampoule can be started. The experimental protocol should provide a brief overview of the growth method from the vapour phase, containing the fundamental thermodynamic principles and also describing the experimental procedure. In addition, as described in the script, a vapour pressure curve and the spatial distribution p(x) of the iodine partial pressure should determined (diagrams).

Z4 – Crystal growth from the vapour phase __________________________________________________________________________________

Literature H. Schäfer; Chemische Transportreaktionen, Verlag Chemie, Weinheim 1962 M.M. Faktor, I. Garret, Growth of Crystals from the Vapor, Chapman and Hall, London 1974 F. Rosenberger, Fundamentals of Crystal Growth I, Macroscopic Equilibrium and Transport Concepts; Springer Verlag, Heidelberg, N.Y. 1979 Wilke, Bohm, Kristallzüchtung; Deutscher Verlag der Wissenschaften, Berlin 1988 O. Knacke

Z4 – Crystal growth from the vapour phase __________________________________________________________________________________