**Chemical Vapor Transport Reactions–Methods, Materials, Modeling**

Peer Schmidt, Michael Binnewies, Robert Glaum and Marcus Schmidt

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/55547

### **1. Introduction**

### **1.1. Chemical vapor transport reactions**

A variety of processes of crystal growth proceeds via the gas phase. A short comparative overview on gas phase transports is given here. However, in the main we deal with the concept of Chemical Vapor Transport Reactions [1, 2]. The term "*Chemical Vapor Transport*" (CVT) summarizes heterogeneous reactions which show one shared feature: a condensed phase, typically a solid, has an insufficient pressure for its own volatilization. But the pertinent phase can be volatilized in the presence of a gaseous reactant, the *transport agent*, and deposits elsewhere, usually in the form of crystals. The deposition will take place if there are different external conditions for the chemical equilibrium at the position of crystallization than at the position of volatilization. Usually, different temperatures are applied for volatilization and crystallization, Figure 1.

© 2013 Schmidt et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Chemical vapor transport reactions address the formation process of pure and crystalline solids. Especially, the growth of single-crystalline material is of particular value because, among other things, it allows the determination of the crystal structure by diffraction methods. Beyond the aspect of basic research, chemical vapor transport reactions have also gained practical significance: they form the basis of the operating mode of halogen lamps. Further‐ more, an industrial process is based on a chemical transport reaction, the Mond-Langer-Process for the production of ultrapure nickel [3]. Chemical vapor transports likewise occur in nature forming minerals without human influence, in particular at places of high temper‐ atures. Bunsen was the first who observed and described it [4]. He noticed that the formation of crystalline Fe2O3 is associated with the presence of volcanic gases which contain gaseous hydrogen chloride. Van Arkel and de Boer were the first scientists who carried out specific transport reactions in the laboratory from 1925 onwards [5]. They were motivated by the huge interest in finding a process to fabricate pure metals like titanium at that time [6]. Van Arkel and de Boer used the so called *glowing wire method*. In the process, the contaminated metal *M* (e.g. a metal of the 4th group) transforms into a gaseous metal iodide (*M*I*n*) in the presence of iodine as the transport agent. The iodide is formed at the metal surface in an exothermic reaction and vaporizes completely, thus reaching a glowing wire which was heated up to high temperatures. On the glowing wires surface, the back reaction (that is the endothermic reaction) is favored by Le Chatelier's principle. That way the decomposition of the metal iodide via the metals deposition proceeds and the metal is deposited on the hot wire.

The following section shall provide an extensive overview on both principles and mechanisms of chemical vapor transport reactions and on characteristic examples of crystal growth of different substance classes by CVT. A simple thermodynamics basis is given in order to set you in ability to estimate the conditions of vapor transport experiments by own calculations; more complex calculations methods are presented for advanced investigations. Not at least, a short introduction for performing different CVT experiments (ampoule technique, oven setup,

A vast number of reactions involving gas phases hardly differ from each other: If a condensed substance encounters a temperature gradient, it moves from the place of dissolution via the gas phase to the place of deposition, from **source** to **sink**. However, we do not "see" how the substance is led to the gas phase and deposited at another place. The mechanisms of gas phase transports can be deduced from experimental determination of the gas phase composition and/ or from thermodynamic considerations of the pertinent heterogeneous equilibria between the

**Sublimation**: Sublimations occurs without decomposition of the initial solid by forming only one dominating gas species. Substances showing sublimation are often solids constituting of molecular units, which are "bonded" by only weak interactions. The much stronger (covalent) bond in the molecular unit persist even under external energy stress, and the molecule can

() ( ) 2 2 *Is Ig* ¬¾¾ ¾¾® (1)

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sublime undecomposed. Iodine, I2 is a concise example of sublimation.

**Figure 2.** Composition of the gas phase of sublimation of AlCl3.

determination of transport rates, investigation of transport sequences,…) is given.

**2. Vapor transport methods and principles**

**2.1. Overview on vapor transport methods**

solid and the gas phase [25].

A systematic research and description of chemical transport reactions was carried out by Schäfer in the 1950s and 1960s [1]. It became apparent that pure and crystalline species of various solids could be made with the help of chemical transport reactions: metals, metalloid, and intermetallic phases as well as halides, chalcogen halides, chalcogens, pnictides and many others. The current knowledge comprises of thousands of different examples for chemical vapor transport reactions. The results of different periods of investigations are recorded in some review articles [7-13]. Besides, the monographs [1, 2] and an extensive book chapter [14] give an overview on principles and applications of chemical transport reactions referred to the pertinent period of knowledge. To date the chemical vapor transport method developed to be an important and versatile preparative method of solid state chemistry.

Schäfer's endeavour also showed that chemical transport reactions follow thermodynamic regularities [15]; kinetic effects are rarely observed which makes a general description easier. Subsequently, the thermodynamic approaches for detailed description of chemical vapor transports became more sophisticated [16-22]. As a result, complex models for the description of vapor transports of phase mixtures, phases with variable composition, and transports with deposition sequences were established - the "Extended transport model" [18-21] and the "Cooperative transport model" [22]. Thus, the understanding of chemical vapor transport reactions is well developed; predictions on alternative transport agents, optimal reaction conditions and the amount of transported substance are possible and fairly easy accessible via computer programs [23, 24]. Indeed, the proper handling of these programs requires a profound knowledge on thermodynamic data (enthalpy, entropy, heat capacity) of all condenses and gaseous substances that are involved.

The following section shall provide an extensive overview on both principles and mechanisms of chemical vapor transport reactions and on characteristic examples of crystal growth of different substance classes by CVT. A simple thermodynamics basis is given in order to set you in ability to estimate the conditions of vapor transport experiments by own calculations; more complex calculations methods are presented for advanced investigations. Not at least, a short introduction for performing different CVT experiments (ampoule technique, oven setup, determination of transport rates, investigation of transport sequences,…) is given.

### **2. Vapor transport methods and principles**

#### **2.1. Overview on vapor transport methods**

Chemical vapor transport reactions address the formation process of pure and crystalline solids. Especially, the growth of single-crystalline material is of particular value because, among other things, it allows the determination of the crystal structure by diffraction methods. Beyond the aspect of basic research, chemical vapor transport reactions have also gained practical significance: they form the basis of the operating mode of halogen lamps. Further‐ more, an industrial process is based on a chemical transport reaction, the Mond-Langer-Process for the production of ultrapure nickel [3]. Chemical vapor transports likewise occur in nature forming minerals without human influence, in particular at places of high temper‐ atures. Bunsen was the first who observed and described it [4]. He noticed that the formation of crystalline Fe2O3 is associated with the presence of volcanic gases which contain gaseous hydrogen chloride. Van Arkel and de Boer were the first scientists who carried out specific transport reactions in the laboratory from 1925 onwards [5]. They were motivated by the huge interest in finding a process to fabricate pure metals like titanium at that time [6]. Van Arkel and de Boer used the so called *glowing wire method*. In the process, the contaminated metal *M* (e.g. a metal of the 4th group) transforms into a gaseous metal iodide (*M*I*n*) in the presence of iodine as the transport agent. The iodide is formed at the metal surface in an exothermic reaction and vaporizes completely, thus reaching a glowing wire which was heated up to high temperatures. On the glowing wires surface, the back reaction (that is the endothermic reaction) is favored by Le Chatelier's principle. That way the decomposition of the metal iodide

228 Advanced Topics on Crystal Growth

via the metals deposition proceeds and the metal is deposited on the hot wire.

an important and versatile preparative method of solid state chemistry.

condenses and gaseous substances that are involved.

A systematic research and description of chemical transport reactions was carried out by Schäfer in the 1950s and 1960s [1]. It became apparent that pure and crystalline species of various solids could be made with the help of chemical transport reactions: metals, metalloid, and intermetallic phases as well as halides, chalcogen halides, chalcogens, pnictides and many others. The current knowledge comprises of thousands of different examples for chemical vapor transport reactions. The results of different periods of investigations are recorded in some review articles [7-13]. Besides, the monographs [1, 2] and an extensive book chapter [14] give an overview on principles and applications of chemical transport reactions referred to the pertinent period of knowledge. To date the chemical vapor transport method developed to be

Schäfer's endeavour also showed that chemical transport reactions follow thermodynamic regularities [15]; kinetic effects are rarely observed which makes a general description easier. Subsequently, the thermodynamic approaches for detailed description of chemical vapor transports became more sophisticated [16-22]. As a result, complex models for the description of vapor transports of phase mixtures, phases with variable composition, and transports with deposition sequences were established - the "Extended transport model" [18-21] and the "Cooperative transport model" [22]. Thus, the understanding of chemical vapor transport reactions is well developed; predictions on alternative transport agents, optimal reaction conditions and the amount of transported substance are possible and fairly easy accessible via computer programs [23, 24]. Indeed, the proper handling of these programs requires a profound knowledge on thermodynamic data (enthalpy, entropy, heat capacity) of all

A vast number of reactions involving gas phases hardly differ from each other: If a condensed substance encounters a temperature gradient, it moves from the place of dissolution via the gas phase to the place of deposition, from **source** to **sink**. However, we do not "see" how the substance is led to the gas phase and deposited at another place. The mechanisms of gas phase transports can be deduced from experimental determination of the gas phase composition and/ or from thermodynamic considerations of the pertinent heterogeneous equilibria between the solid and the gas phase [25].

**Sublimation**: Sublimations occurs without decomposition of the initial solid by forming only one dominating gas species. Substances showing sublimation are often solids constituting of molecular units, which are "bonded" by only weak interactions. The much stronger (covalent) bond in the molecular unit persist even under external energy stress, and the molecule can sublime undecomposed. Iodine, I2 is a concise example of sublimation.

$$I\_2\left(\mathcal{s}\right) \overbrace{\longleftrightarrows}^{} I\_2\left(\mathcal{g}\right) \tag{1}$$

**Figure 2.** Composition of the gas phase of sublimation of AlCl3.

The other possible gas species in the system, I(g) is of less importance due to the significant‐ ly lower partial pressures at the temperature of sublimation.

Saline solids can sublime, too. A well-known example is aluminum(III) chloride which is present in the gas phase in large proportion in form of dimeric molecule Al2Cl6, Figure 2. The additional systems gas species, such as AlCl3(g), Cl2(g), and Cl(g) show significantly lower partial pressures at the given temperature and thus not take part in the evaporation process.

$$\text{2 AlCl}\_3\text{(s)} \xleftarrow{\text{Al}} \text{Al}\_2\text{Cl}\_6\text{(g)}\tag{2}$$

As a generalization, the decomposition sublimation of a compound *AB*x can be described by

The gas phase transport of Bi2Se3 by decomposition sublimation gives an example for congru‐ ent dissolution and condensation. Thus, a solid of always the same, constant composition is deposited. Nevertheless, a decomposition sublimation can be incongruent, too. Often, the product of an incongruent decomposition sublimation has the same composition as the initial solid. A simple example of this is copper(II) chloride. If heated at a running pump to several hundred degrees, the steam that is built in subsequent equilibria (7) and (8) contains the

The mechanism of decomposition sublimation is even more complex in the case of Bi6Cl7 [25, 26]. The initial solid is decomposed into a second solid – here elemental bismuth – and the dominating gas species BiCl3 in equilibrium (9). Thereby, the compositions of the gas phase and thus the "solubility" of all components is unequal the initial composition of the solid,

Nevertheless, the gas phase transport of Bi6Cl7 is realized by a second, subordinated equili‐ brium (10). In this case, the composition of the deposited solid strongly depends on the experimental conditions: Congruent deposition of Bi6Cl7 only occurs with low temperature gradients between source and sink. At higher temperature gradients pure BiCl3 is deposited.

As has been shown, the mechanism of gas phase transport will get more complicated if the decomposition leads to a further condensed solid and a reactive gas phase. Subsequent, auto

( ) ( ) *AB A g xB g x* ¬¾¾ ¾¾® + (5)

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( ) ( ) ( ) *AB AB g x y B g x y* ¬¾¾¾¾® + - (6)

( ) ( ) ( ) 2 2 *CuCl s CuCl s Cl g* 1/ 2 ¬¾¾ ¾¾® + (7)

( ) ( ) ( ) 6 7 3 3 / 7 11 / 7 *Bi Cl s* ¬¾¾¾®¾ *Bi s BiCl g* + (9)

( ) ( ) ( ) 6 7 3 2 11 *Bi Cl s BiCl g BiCl g* ¬¾¾ ¾¾® + (10)

*CuCl s CuCl g* ( )¬¾¾ ¾¾® ( ) (8)

the equilibria (5) or (6), respectively.

molecules CuCl, Cu3Cl3, Cu4Cl4 and Cl2.

Figure 4.

transport processes can result.

In a generalized form, the sublimation of a compound *AB*x is described by equilibrium (3).

$$AB\_x(s) \overleftrightarrow{\longleftrightarrow} AB\_x(g) \tag{3}$$

**Decomposition sublimation**: If there is no stable molecular unit which is evaporable, a solid can decompose into various gaseous products while heating. Changing the equilibrium conditions, the initial solid can be recovered out of such a gas phase. This is called decompo‐ sition sublimation.

The gas phase transport of bimuth(III) selenide - Bi2Se3, an important constituent for thermo‐ electric materials - shows the characteristic of that. It decomposes into stoichiometric amounts of BiSe(g) and Se2(g) in the vapor phase, the molecule of the initial composition Bi2Se3(g) does not occur in evaporation process, Figure 3. During cooling, the gas phase condenses completely and solid solid bimuth(III) selenide is formed (4).

$$Bi\_2Se\_3\left(s\right) \xleftarrow{\colon-} 2BiSe\left(g\right) + 1/2\text{ }Se\_2\left(g\right) \tag{4}$$

**Figure 3.** Composition of the gas phase of decomposition sublimation of Bi2Se3.

As a generalization, the decomposition sublimation of a compound *AB*x can be described by the equilibria (5) or (6), respectively.

The other possible gas species in the system, I(g) is of less importance due to the significant‐

Saline solids can sublime, too. A well-known example is aluminum(III) chloride which is present in the gas phase in large proportion in form of dimeric molecule Al2Cl6, Figure 2. The additional systems gas species, such as AlCl3(g), Cl2(g), and Cl(g) show significantly lower partial pressures at the given temperature and thus not take part in the evaporation process.

In a generalized form, the sublimation of a compound *AB*x is described by equilibrium (3).

**Decomposition sublimation**: If there is no stable molecular unit which is evaporable, a solid can decompose into various gaseous products while heating. Changing the equilibrium conditions, the initial solid can be recovered out of such a gas phase. This is called decompo‐

The gas phase transport of bimuth(III) selenide - Bi2Se3, an important constituent for thermo‐ electric materials - shows the characteristic of that. It decomposes into stoichiometric amounts of BiSe(g) and Se2(g) in the vapor phase, the molecule of the initial composition Bi2Se3(g) does not occur in evaporation process, Figure 3. During cooling, the gas phase condenses completely

( ) ( ) 3 2 6 2*AlCl s Al Cl g* ¬¾¾ ¾¾® (2)

() ( ) *AB s AB g x x* ¬¾¾ ¾¾® (3)

( ) () () 2 3 2 *Bi Se s BiSe g Se g* ¬¾¾ ¾¾®2 1/ 2 + (4)

ly lower partial pressures at the temperature of sublimation.

sition sublimation.

230 Advanced Topics on Crystal Growth

and solid solid bimuth(III) selenide is formed (4).

**Figure 3.** Composition of the gas phase of decomposition sublimation of Bi2Se3.

$$\mathbf{A} \mathbf{B}\_x \overrightarrow{\mathbf{x} \mathbf{x} \mathbf{x} \mathbf{x}} \mathbf{A} \begin{pmatrix} \mathbf{g} \end{pmatrix} + \mathbf{x} \mathbf{B} \begin{pmatrix} \mathbf{g} \end{pmatrix} \tag{5}$$

$$AB\_x \overbrace{\longleftrightarrow\ } AB\_y \left(g\right) + \left(x - y\right)B\left(g\right) \tag{6}$$

The gas phase transport of Bi2Se3 by decomposition sublimation gives an example for congru‐ ent dissolution and condensation. Thus, a solid of always the same, constant composition is deposited. Nevertheless, a decomposition sublimation can be incongruent, too. Often, the product of an incongruent decomposition sublimation has the same composition as the initial solid. A simple example of this is copper(II) chloride. If heated at a running pump to several hundred degrees, the steam that is built in subsequent equilibria (7) and (8) contains the molecules CuCl, Cu3Cl3, Cu4Cl4 and Cl2.

$$\text{CuCl}\_2\text{(s)} \xrightleftharpoons \text{CuCl(s)} \, +1/2 \, \text{Cl}\_2\text{(g)}\tag{7}$$

$$\mathsf{CuCl}(s) \xrightleftharpoons \mathsf{CuCl}(g) \tag{8}$$

The mechanism of decomposition sublimation is even more complex in the case of Bi6Cl7 [25, 26]. The initial solid is decomposed into a second solid – here elemental bismuth – and the dominating gas species BiCl3 in equilibrium (9). Thereby, the compositions of the gas phase and thus the "solubility" of all components is unequal the initial composition of the solid, Figure 4.

$$\text{13 } \text{7 } \text{Bi}\_6\text{Cl}\_7\text{(s)} \xrightleftharpoons \text{11 } \text{7 } \text{Bi}\text{(s)} + \text{BiCl}\_3\text{(g)}\tag{9}$$

$$2\text{ Bi}\_6\text{Cl}\_7\text{(s)} \xrightleftharpoons 11\text{ BiCl} \text{(g)} + \text{BiCl}\_3\text{(g)}\tag{10}$$

Nevertheless, the gas phase transport of Bi6Cl7 is realized by a second, subordinated equili‐ brium (10). In this case, the composition of the deposited solid strongly depends on the experimental conditions: Congruent deposition of Bi6Cl7 only occurs with low temperature gradients between source and sink. At higher temperature gradients pure BiCl3 is deposited.

As has been shown, the mechanism of gas phase transport will get more complicated if the decomposition leads to a further condensed solid and a reactive gas phase. Subsequent, auto transport processes can result.

**Figure 4.** Composition of the gas phase of decomposition sublimation of Bi6Cl7.

**Auto transport**: The auto transport resembles the appearance of sublimation or decomposition sublimation. Nevertheless, the transported solid does not generate an effective partial pressure on its own. Rather, a transport agent is formed by (incongruent) thermal decomposition of the solid and the substance is transferred into the gas phase at a higher temperature without the addition of an external transport agent. The crystallization of MoBr3 serves as an example of auto transport processes. The compound decomposes incongruently under formation of solid MoBr2(s) releasing a gas phase of the dominant species MoBr4 and Br2 in equilibria (11) and (12), see Figure 5. The heterogeneous equilibria of MoBr4 and Br2 with the initial solid MoBr3 can lead at higher temperature to the vapor transport equilibrium (13).

$$2MoBr\_3\left(s\right) \xrightarrow{\longrightarrow} MoBr\_2\left(s\right) + MoBr\_4\left(g\right) \tag{11}$$

() ( ) ( ) *AB s nB g AB g x x n*+ + ¬¾¾ ¾¾® (15)

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( ) () ( ) 3 22 *MCl s MCl s Cl g* ¬ ¾ ¾¾®¾ + 1/ 2 (16)

() ( ) ( ) 32 4 *MCl s Cl g MCl g* + 1/ 2 ¬¾¾¾®¾ (17)

Auto transports are generally endothermic reactions like sublimation and decomposition sublimation (deposition in the direction form source to sink: hot to cold). The transport equilibrium can only be effective if two conditions are met: First, the partial pressure of *B* must be sufficiently high and second, the transporting phase *AB*x(s) must remain in equilibrium, thus *AB*x(s) must not be decomposed completely. *B* stands for a gaseous decomposition product in the sense of equation (14). Thus, *B* can be an atom (e.g. an bromine atom), a

There may be a smooth transition of the described phenomena of sublimation or decomposi‐ tion sublimation to the mechanism of auto transport. The dissolution of CrCl3 in the gas phase represents such a complex behavior. One can find congruent sublimation, the formation of gaseous chromium(III) chloride, and of an incongruent decomposition at the same time. In a consecutive reaction chlorine can react with the primary solid CrCl3, thus becoming the transport agent. The transport effective gaseous molecule is CrCl4, Figure 6. In case of the chlorides MoCl3 or VCl3, the gas molecules *M*Cl3 are too unstable or unknown and the movement in the temperature gradient takes place only through auto transport according to

The principle of auto transport is to apply also for other substance classes, such as oxides, chalcogenides and above all chalcogenide halides. As an example of the auto transport of an oxide, the crystallization of IrO2 is presented. At temperatures of about 1050 °C the phase

homonuclear molecule (Cl2, Br2, O2,…) or a heteronuclear molecule.

**Figure 5.** Composition of the gas phase for the auto transport of MoBr3.

the equilibria (16) and (17) (*M* = Cr, Mo, V).

$$MoBr\_3\left(s\right) \xrightarrow{\longrightarrow} MoBr\_2\left(s\right) + 1/2\text{ }Br\_2\left(g\right) \tag{12}$$

$$MoBr\_3\left(s\right) + 1 / \text{ 2 }Br\_2\left(g\right) \overbrace{\longleftrightarrow}MoBr\_4\left(g\right) \tag{13}$$

Based on this example, one can formulate the course of the auto transport in general terms [25]: A compound *AB*x(s) does not generate a transport effective partial pressure of the gas species *AB*x(g) or *A*(g)+*B*(g) (*AB*(g)+*B*(g)) on its own. The auto transport is based on two coexisting solid phases *AB*x(s) and *AB*x–n(s) as well as a gas phase which is generated through a decom‐ position reaction (14). The formed gaseous species *B* then reacts under the formation of only gaseous product *AB*x+n in the sense of CVT reactions (15).

$$AB\_x(\mathbf{s}) \overleftrightarrow{\longleftrightarrow} AB\_{\mathbf{x}-\mathbf{n}}(\mathbf{s}) + \mathbf{n}B(\mathbf{g}) \tag{14}$$

**Figure 5.** Composition of the gas phase for the auto transport of MoBr3.

**Auto transport**: The auto transport resembles the appearance of sublimation or decomposition sublimation. Nevertheless, the transported solid does not generate an effective partial pressure on its own. Rather, a transport agent is formed by (incongruent) thermal decomposition of the solid and the substance is transferred into the gas phase at a higher temperature without the addition of an external transport agent. The crystallization of MoBr3 serves as an example of auto transport processes. The compound decomposes incongruently under formation of solid MoBr2(s) releasing a gas phase of the dominant species MoBr4 and Br2 in equilibria (11) and (12), see Figure 5. The heterogeneous equilibria of MoBr4 and Br2 with the initial solid MoBr3

Based on this example, one can formulate the course of the auto transport in general terms [25]: A compound *AB*x(s) does not generate a transport effective partial pressure of the gas species *AB*x(g) or *A*(g)+*B*(g) (*AB*(g)+*B*(g)) on its own. The auto transport is based on two coexisting solid phases *AB*x(s) and *AB*x–n(s) as well as a gas phase which is generated through a decom‐ position reaction (14). The formed gaseous species *B* then reacts under the formation of only

( ) () ( ) *AB s AB s nB g x x n*- ¬

( ) () ( ) 3 24 2*MoBr s MoBr s MoBr g* ¬ ¾ ¾¾¾® + (11)

( ) () ( ) 3 22 *MoBr s MoBr s Br g* ¬ ¾ ¾¾®¾ + 1/ 2 (12)

() ( ) ( ) 32 4 *MoBr s Br g MoBr g* + 1/ 2 ¬¾¾ ¾ ®¾ (13)

¾ ®¾¾¾ + (14)

can lead at higher temperature to the vapor transport equilibrium (13).

**Figure 4.** Composition of the gas phase of decomposition sublimation of Bi6Cl7.

232 Advanced Topics on Crystal Growth

gaseous product *AB*x+n in the sense of CVT reactions (15).

$$AB\_x(\text{s}) + nB(\text{g}) \xleftarrow{} AB\_{x+n}(\text{g}) \tag{15}$$

Auto transports are generally endothermic reactions like sublimation and decomposition sublimation (deposition in the direction form source to sink: hot to cold). The transport equilibrium can only be effective if two conditions are met: First, the partial pressure of *B* must be sufficiently high and second, the transporting phase *AB*x(s) must remain in equilibrium, thus *AB*x(s) must not be decomposed completely. *B* stands for a gaseous decomposition product in the sense of equation (14). Thus, *B* can be an atom (e.g. an bromine atom), a homonuclear molecule (Cl2, Br2, O2,…) or a heteronuclear molecule.

There may be a smooth transition of the described phenomena of sublimation or decomposi‐ tion sublimation to the mechanism of auto transport. The dissolution of CrCl3 in the gas phase represents such a complex behavior. One can find congruent sublimation, the formation of gaseous chromium(III) chloride, and of an incongruent decomposition at the same time. In a consecutive reaction chlorine can react with the primary solid CrCl3, thus becoming the transport agent. The transport effective gaseous molecule is CrCl4, Figure 6. In case of the chlorides MoCl3 or VCl3, the gas molecules *M*Cl3 are too unstable or unknown and the movement in the temperature gradient takes place only through auto transport according to the equilibria (16) and (17) (*M* = Cr, Mo, V).

$$\text{MCl}\_3\text{(s)} \xrightleftharpoons \text{MCl}\_2\text{(s)} + 1/2 \text{ Cl}\_2\text{(g)}\tag{16}$$

$$\text{MCl}\_3\text{(s)} + 1/2 \text{ Cl}\_2\text{(g)} \xrightleftharpoons \text{MCl}\_4\text{(g)}\tag{17}$$

The principle of auto transport is to apply also for other substance classes, such as oxides, chalcogenides and above all chalcogenide halides. As an example of the auto transport of an oxide, the crystallization of IrO2 is presented. At temperatures of about 1050 °C the phase

**Figure 6.** Composition of the gas phase for vapor transport processes of CrCl3.

decomposes into the metal and molecular oxygen (18). In a subsequent heterogeneous equilibrium (19), oxygen reacts with the primary solid to form the transport effective gas species IrO3, Figure 7. The back reaction takes place at lower temperature and IrO2 is deposited.

$$IrO\_2(s) \xrightarrow{\quad} Ir(s) + O\_2(g) \tag{18}$$

open systems oxygen stream (*p*(O2) = 1 bar) leads to the formation of pure IrO2 [1]. The transport behavior of RuO2 is to discuss in the same way: by auto transport RuO1.998 is obtained while RuO2.0 crystallizes in vapor transport experiments with excess of oxygen [5]. Even if the change in composition is very small, the physical properties can differ significantly. Thus the specific electrical resistance of RuO2 is of more than one order of magnitude higher than of RuO2−x [27].

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If at least one of the components of *AB*x does not form a gas species with sufficient vapor pressure which is suitable for a substance transport (sublimation, decomposition sublimation,

**Chemical Vapor transport reaction**: A chemical vapor transport reaction is characterized by the fact that another substance, the *transport agent*, is required for the dissolution of a solid in the gas phase. This characteristic is to illustrate by the example of vapor transport of zinc oxide by addition of chlorine. ZnO decomposes forming its own vapor phase with only small extent. Thus, the equilibrium pressure at a temperature of 1000 K is below 10−10 bar, Figure 8. By adding chlorine, the transport effective gas species ZnCl2 and O2 are formed in heterogeneous equilibrium (20). Here, the substances that appear in the vapor are different to those in the solid. Thereby transport effective vapor pressures (*p*(*i*) > 10−4 bar) of the gas species can be

() ( ) () () 2 22 *ZnO s Cl g ZnCl g O g* + ¬¾¾¾®¾ + 1/2 (20)

¾¾®¾¾ + (21)

auto transport), the addition of an external transport agent will be necessary.

observed already below 600 K, Figure 9.

**Figure 8.** Composition of the gas phase for the thermal decomposition of ZnO.

The chemical vapor transport of ZnO is also possible by addition of hydrogen chloride. Likewise for the transport with chlorine ZnCl2 is formed as the transport effective species for the transfer of zinc from source to sink, Figure 10. Otherwise the used transport agent HCl can react with oxygen, too. Thus the oxygen transferring species H2O is formed in equilibrium (21).

() ( ) () () 2 2 *ZnO s HCl g ZnCl g H O g* + 2 ¬

$$2IrO\_2\left(s\right) + O\_2\left(g\right) \xrightleftharpoons 2IrO\_3\left(g\right) \tag{19}$$

**Figure 7.** Composition of the gas phase for the auto transport of IrO2.

Generally, all the auto transports are feasible as "regular" chemical vapor transport reactions. In these cases, the transport is possible as well through the addition of the transport agent without the preceding decomposition reaction. An important difference in both experiments can be observed: As the auto transport is based on a decomposition reaction, crystals of a different (metal rich) composition can be deposited. Thus the auto transport of IrO2 leads to the deposition of IrO2−x (depleted by oxygen). Otherwise, the regular vapor transport in an open systems oxygen stream (*p*(O2) = 1 bar) leads to the formation of pure IrO2 [1]. The transport behavior of RuO2 is to discuss in the same way: by auto transport RuO1.998 is obtained while RuO2.0 crystallizes in vapor transport experiments with excess of oxygen [5]. Even if the change in composition is very small, the physical properties can differ significantly. Thus the specific electrical resistance of RuO2 is of more than one order of magnitude higher than of RuO2−x [27].

If at least one of the components of *AB*x does not form a gas species with sufficient vapor pressure which is suitable for a substance transport (sublimation, decomposition sublimation, auto transport), the addition of an external transport agent will be necessary.

**Chemical Vapor transport reaction**: A chemical vapor transport reaction is characterized by the fact that another substance, the *transport agent*, is required for the dissolution of a solid in the gas phase. This characteristic is to illustrate by the example of vapor transport of zinc oxide by addition of chlorine. ZnO decomposes forming its own vapor phase with only small extent. Thus, the equilibrium pressure at a temperature of 1000 K is below 10−10 bar, Figure 8. By adding chlorine, the transport effective gas species ZnCl2 and O2 are formed in heterogeneous equilibrium (20). Here, the substances that appear in the vapor are different to those in the solid. Thereby transport effective vapor pressures (*p*(*i*) > 10−4 bar) of the gas species can be observed already below 600 K, Figure 9.

$$ZnO\text{(s)} + Cl\_2\text{(g)} \xrightarrow{\text{C}} ZnCl\_2\text{(g)} + 1/2O\_2\text{(g)}\tag{20}$$

**Figure 8.** Composition of the gas phase for the thermal decomposition of ZnO.

decomposes into the metal and molecular oxygen (18). In a subsequent heterogeneous equilibrium (19), oxygen reacts with the primary solid to form the transport effective gas species IrO3, Figure 7. The back reaction takes place at lower temperature and IrO2 is deposited.

**Figure 6.** Composition of the gas phase for vapor transport processes of CrCl3.

234 Advanced Topics on Crystal Growth

Generally, all the auto transports are feasible as "regular" chemical vapor transport reactions. In these cases, the transport is possible as well through the addition of the transport agent without the preceding decomposition reaction. An important difference in both experiments can be observed: As the auto transport is based on a decomposition reaction, crystals of a different (metal rich) composition can be deposited. Thus the auto transport of IrO2 leads to the deposition of IrO2−x (depleted by oxygen). Otherwise, the regular vapor transport in an

**Figure 7.** Composition of the gas phase for the auto transport of IrO2.

() () ( ) 2 2 *IrO s Ir s O g* ¬¾¾ ¾¾® + (18)

() ( ) ( ) 22 3 2 2 *IrO s O g IrO g* + ¬¾¾ ¾¾® (19)

The chemical vapor transport of ZnO is also possible by addition of hydrogen chloride. Likewise for the transport with chlorine ZnCl2 is formed as the transport effective species for the transfer of zinc from source to sink, Figure 10. Otherwise the used transport agent HCl can react with oxygen, too. Thus the oxygen transferring species H2O is formed in equilibrium (21).

$$\text{ZnO} \text{(s)} + 2\text{HCl} \text{(g)} \xrightleftharpoons \text{ZnCl}\_2 \text{(g)} + \text{H}\_2\text{O} \text{(g)}\tag{21}$$

different place with another temperature under the release of the transport agent. In a closed system, typically a sealed ampoule, the transport agent remains in the system and constantly re-enters the reaction. Thus, in a closed system, a much smaller amount of the transport agent is needed. In some cases only few milligrams of the transport agent are sufficient to cause a transport effect. In the laboratory one predominantly works with closed systems. An easy closed system is a sealed glass tube. Such a *transport ampoule* has a typical length of 100 to 200 mm and a diameter of 10 to 20 mm. It includes about one gram of the solid which is to be transported, and as much transport agent as is needed to raise the pressure in the ampoule to

Chemical Vapor Transport Reactions–Methods, Materials, Modeling

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237

It is of prime interest for preparative working chemists whether a certain solid can be prepared with the aid of chemical vapor transport reactions, which transport agents are suitable and under which conditions a transport can be expected. At this point, we want to appoint some

The vapor transport reaction has to realize, that all formed products are gaseous under the reaction conditions. Thus a suitable transport agent is to select, which can transfer all compo‐

The equilibrium position of the transport reaction must not be extreme, so that dissolution into the gas phase and re-condensation of the solid are possible under slightly changed experi‐ mental conditions. In cases of an extreme equilibrium no dissolution occurs (evaporation reaction unfavored) or the formation of gaseous products is not reversible (back reaction under

The temperature at which the numerical value of the equilibrium constant *Kp* equals 1 (Δr*G*0

The transport is caused in almost every case by different temperatures and therefore changed equilibrium position in source and sink. It is common to characterize the volatilization (source) and the deposition temperature (sink) with *T*1 and *T*2, respectively, *T*1 representing the lower temperature. The *transport direction* results from the sign of the reaction enthalpy of the transport reaction based on Le Chatelier's principle. Therefore, exothermic transport reactions always transport to the zone of higher temperature - from *T*1 to *T*2 (*T*1 → *T*2), endothermic

A chemical vapor transport reaction can be divided into three steps: the *forward reaction* at the source material; the *gas motion*; and the *back reaction* leading to the formation of the solid in the crystallization zone. In most cases, the slowest and therefore the rate-determining step is the

T

T / Δr*S*0 T).

re-condensation unfavored). In both cases no vapor transport is observed.

= 0) is referred to as optimal transport temperature *T*opt (*T*opt = Δr*H*0

reactions transfer the solid to the cooler zone - from *T*2 to *T*1 (*T*2 → *T*1).

one bar or less during the reaction.

general qualitative considerations.

**• The suitable temperature**

**• The transport direction**

**• The rate of mass transport**

nents of the initial solid into the gas phase.

**• The basic precondition for successful CVT**

**• The suitable transport agent for the investigated system**

**Figure 9.** Composition of the gas phase for the CVT of ZnO with chlorine.

**Figure 10.** Gas phase composition for the CVT of ZnO with hydrogen chloride.

Here, the general principle of transport reactions can be seen clearly: The source material is transformed reversibly into gaseous products by the use of the transport agent. The transfer of the solid can be realized in different ways by formation of both heteronuclear species (like ZnCl2 and H2O) and atomar or homonuclear species (O2).

$$A B\_x(\mathbf{s}) + n \mathcal{C}(\mathbf{g}) \overbrace{\longleftrightarrow} A \mathcal{C}\_n(\mathbf{g}) + \mathbf{x} / y B\_y(\mathbf{g}) \tag{22}$$

$$A B\_x(\mathbf{s}) + n \mathbf{C} D(\mathbf{g}) \overbrace{\longleftrightarrow} A \mathbf{C}\_n(\mathbf{g}) + \mathbf{x} / y \mathbf{B}\_y \mathbf{D}(\mathbf{g}) \tag{23}$$

#### **2.2. Principles and thermodynamic considerations on CVT**

In principle, two working methods are applied for the practical realization in the laboratory: the transport in open or closed systems. An open system is applied with an on both sides opened tube made of glass or ceramic material. Inside, a continuous flow of the transport agent is led over the source material; the solid, which is kept at a certain temperature, deposits at a different place with another temperature under the release of the transport agent. In a closed system, typically a sealed ampoule, the transport agent remains in the system and constantly re-enters the reaction. Thus, in a closed system, a much smaller amount of the transport agent is needed. In some cases only few milligrams of the transport agent are sufficient to cause a transport effect. In the laboratory one predominantly works with closed systems. An easy closed system is a sealed glass tube. Such a *transport ampoule* has a typical length of 100 to 200 mm and a diameter of 10 to 20 mm. It includes about one gram of the solid which is to be transported, and as much transport agent as is needed to raise the pressure in the ampoule to one bar or less during the reaction.

It is of prime interest for preparative working chemists whether a certain solid can be prepared with the aid of chemical vapor transport reactions, which transport agents are suitable and under which conditions a transport can be expected. At this point, we want to appoint some general qualitative considerations.

### **• The suitable transport agent for the investigated system**

The vapor transport reaction has to realize, that all formed products are gaseous under the reaction conditions. Thus a suitable transport agent is to select, which can transfer all compo‐ nents of the initial solid into the gas phase.

### **• The basic precondition for successful CVT**

The equilibrium position of the transport reaction must not be extreme, so that dissolution into the gas phase and re-condensation of the solid are possible under slightly changed experi‐ mental conditions. In cases of an extreme equilibrium no dissolution occurs (evaporation reaction unfavored) or the formation of gaseous products is not reversible (back reaction under re-condensation unfavored). In both cases no vapor transport is observed.

#### **• The suitable temperature**

**Figure 10.** Gas phase composition for the CVT of ZnO with hydrogen chloride.

**Figure 9.** Composition of the gas phase for the CVT of ZnO with chlorine.

236 Advanced Topics on Crystal Growth

ZnCl2 and H2O) and atomar or homonuclear species (O2).

**2.2. Principles and thermodynamic considerations on CVT**

Here, the general principle of transport reactions can be seen clearly: The source material is transformed reversibly into gaseous products by the use of the transport agent. The transfer of the solid can be realized in different ways by formation of both heteronuclear species (like

In principle, two working methods are applied for the practical realization in the laboratory: the transport in open or closed systems. An open system is applied with an on both sides opened tube made of glass or ceramic material. Inside, a continuous flow of the transport agent is led over the source material; the solid, which is kept at a certain temperature, deposits at a

() ( ) ( ) ( ) / *AB s nC g AC g x yB g x n y* + + ¬¾¾ ¾¾® (22)

() ( ) ( ) ( ) / *AB s nCD g AC g x yB D g x n y* + + ¬¾¾ ¾¾® (23)

The temperature at which the numerical value of the equilibrium constant *Kp* equals 1 (Δr*G*0 T = 0) is referred to as optimal transport temperature *T*opt (*T*opt = Δr*H*0 T / Δr*S*0 T).

#### **• The transport direction**

The transport is caused in almost every case by different temperatures and therefore changed equilibrium position in source and sink. It is common to characterize the volatilization (source) and the deposition temperature (sink) with *T*1 and *T*2, respectively, *T*1 representing the lower temperature. The *transport direction* results from the sign of the reaction enthalpy of the transport reaction based on Le Chatelier's principle. Therefore, exothermic transport reactions always transport to the zone of higher temperature - from *T*1 to *T*2 (*T*1 → *T*2), endothermic reactions transfer the solid to the cooler zone - from *T*2 to *T*1 (*T*2 → *T*1).

#### **• The rate of mass transport**

A chemical vapor transport reaction can be divided into three steps: the *forward reaction* at the source material; the *gas motion*; and the *back reaction* leading to the formation of the solid in the crystallization zone. In most cases, the slowest and therefore the rate-determining step is the gas motion. At a pressure of about 1 bar, the gas motion mainly takes place through diffusion; thus, the diffusion laws determine the velocity of the whole process. As we are observing the diffusion of gases, it is practicable to introduce the partial pressure gradient d*p*/d*s*. Thus, the transported amount of substance per time is proportional to the partial pressure gradient.

To intensify the theoretical understanding of chemical vapor transport reactions in a compre‐ hensible way the representative experiment of the transport of tungsten(IV) oxide is illustrated. With the help of the clear example of the transport of WO2, the mentioned general considera‐ tions can be tackled:

**The suitable transport agent for the investigated system.** The solid WO2 does not have an own measurable vapor pressure which would be suitable to transfer the compound to the gas phase in the sense of a sublimation. The phase rather decomposes at 1000 K with an oxygen partial pressure of 10−20 bar towards metallic tungsten. Here, the addition of a transport agent is necessary. As a general rule, the halogens chlorine, bromine and iodine (24) or halogen compounds (25), such as the hydrogen halides H*X* (*X* = Cl, Br, I) are suitable as transport agents. For the transport of WO2 the gas species WO2*X*2 can be effective for vapor transport. Thus all the components of the system – tungsten, oxygen, and chlorine – are present in the gas phase.  During a highly endergonic reaction Δr*G*0

, *ΔrS* 0

, *ΔrS* 0

, *Kp*, 1000 ≈ 103

, *ΔrS* 0

, *ΔrS* 0

, *Kp*, 1000 ≈ 1013

, *Kp*, 1000 ≈ 10–2

, *Kp*, 1000 ≈ 108

< –100 kJ mol–1 (*Kp* > 104

into the gas phase. That sounds great. But: The back reaction under deposition of the solid phase is not possible in thermodynamic terms. That means that on the source side the trans‐ porting compound is almost completely transferred into the gas phase without depositing on

hardly transferred into the gas phase, thus a transport cannot take place. With the help of thermodynamic data of the substances involved in the reaction, the values of the Gibbs energy, respectively the equilibrium constants of possible transport reactions can be calculated.

1000 =73.2 *J* · *mol* –1 · *K* –1

1000 =74.7 *J* · *mol* –1 · *K* –1

1000 = 84.6 *J* · *mol* –1 · *K* –1

( ) ( ) ( ) ( ) 2 22 2 *WO s HCl g WO Cl g H g* + 2 ¬

1000 = 283.4 *J* · *mol* –1 · *K* –1

( ) ( ) ( ) *WO s Cl g WO Cl g* 2 2 2 2 + ¬¾¾ ¾¾® (27)

( ) ( ) ( ) *WO s Br g WO Br g* 2 2 2 2 + ¬¾¾ ¾¾® (28)

( ) ( ) ( ) *WO s I g WO I g* 2 2 2 2 + ¬¾¾ ¾¾® (29)

¾¾®¾¾ + (30)

) shows a high dissolution of the solid

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239

Chemical Vapor Transport Reactions–Methods, Materials, Modeling

> 100 kJ mol–1 (*Kp* < 10−4) the solid is

$$2\text{ }\text{WO}\_2\text{(s)} + 2\text{ }\text{HX}\text{(g)} \xrightleftharpoons \text{WO}\_2\text{X}\_2\text{(g)} + \text{H}\_2\text{(g)}\tag{25}$$

Also, adding mercury halides, which are solid at room temperature, is potentially suitable to transport both components of the solid phase – tungsten as well as oxygen – into the gas phase (26).

$$\text{WO}\_2\text{(s)} + \text{HgX}\_2\text{(g)} \xrightleftharpoons \text{WO}\_2\text{X}\_2\text{(g)} + \text{Hg}\text{(g)}\tag{26}$$

At temperatures above 300 °C the mercury halides evaporate completely. Afterwards the gas species WO2*X*2 is formed in addition to mercury. Here, only gaseous species (WO2*X*2(g)+Hg(g)) are formed, too.

**The basic precondition for successful CVT.** Basic precondition for chemical vapor transport reactions is a balanced equilibrium position: For reactions which are described by *one* independent reaction equation, transports can be expected for equilibrium constants *Kp* in the range from 10–4 up to 104 respectively Gibbs energies Δr*G*0 of approx. –100 to +100 kJ mol–1. The partial pressure gradient Δ*p* as a driving force for the material transport between dissolution and deposition site is achieved by a temperature gradient.

A highly exergonic reaction Δr*G*0 < –100 kJ mol–1 (*Kp* > 104 ) shows a high dissolution of the solid into the gas phase. That sounds great. But: The back reaction under deposition of the solid phase is not possible in thermodynamic terms. That means that on the source side the trans‐ porting compound is almost completely transferred into the gas phase without depositing on the sink side. During a highly endergonic reaction Δr*G*0 > 100 kJ mol–1 (*Kp* < 10−4) the solid is hardly transferred into the gas phase, thus a transport cannot take place. With the help of thermodynamic data of the substances involved in the reaction, the values of the Gibbs energy, respectively the equilibrium constants of possible transport reactions can be calculated.

$$\text{WO}\_2\text{(s)} + \text{Cl}\_2\text{(g)} \xrightleftharpoons \text{WO}\_2\text{Cl}\_2\text{(g)}\tag{27}$$

$$
\begin{aligned}
\left(\Delta\_r H^{\text{\textdegree}}\right)\_{1000} &= -86.5 \text{ kJ} \cdot \text{mol}^{-1}, \ \Delta\_r S^{\text{\textdegree}}\ \_{1000} = 73.2 \text{ J} \cdot \text{mol}^{-1} \cdot K^{-1} \\\\
\left(\Delta\_r G^{\text{\textdegree}}\right)\_{1000} &= -159.7 \text{ kJ} \cdot \text{mol}^{-1}, \ \text{K}\_{p,1000} \approx 10^8
\end{aligned}
$$

gas motion. At a pressure of about 1 bar, the gas motion mainly takes place through diffusion; thus, the diffusion laws determine the velocity of the whole process. As we are observing the diffusion of gases, it is practicable to introduce the partial pressure gradient d*p*/d*s*. Thus, the transported amount of substance per time is proportional to the partial pressure gradient.

To intensify the theoretical understanding of chemical vapor transport reactions in a compre‐ hensible way the representative experiment of the transport of tungsten(IV) oxide is illustrated. With the help of the clear example of the transport of WO2, the mentioned general considera‐

**The suitable transport agent for the investigated system.** The solid WO2 does not have an own measurable vapor pressure which would be suitable to transfer the compound to the gas phase in the sense of a sublimation. The phase rather decomposes at 1000 K with an oxygen partial pressure of 10−20 bar towards metallic tungsten. Here, the addition of a transport agent is necessary. As a general rule, the halogens chlorine, bromine and iodine (24) or halogen compounds (25), such as the hydrogen halides H*X* (*X* = Cl, Br, I) are suitable as transport agents. For the transport of WO2 the gas species WO2*X*2 can be effective for vapor transport. Thus all the components of the system – tungsten, oxygen, and chlorine – are present in the gas phase.

( ) ( ) ( ) *WO s X g WO X g* 2 2 2 2 + ¬¾¾ ¾¾® (24)

¾¾®¾¾ + (25)

¾¾®¾¾ + (26)

of approx. –100 to +100 kJ mol–1. The

Finally, the transport equations can reflect the formation of only gaseous species.

( ) ( ) ( ) ( ) 2 22 2 *WO s HX g WO X g H g* + 2 ¬

( ) ( ) ( ) ( ) *WO s HgX g WO X g Hg g* 2 2 2 2 + ¬

Also, adding mercury halides, which are solid at room temperature, is potentially suitable to transport both components of the solid phase – tungsten as well as oxygen – into the gas phase

At temperatures above 300 °C the mercury halides evaporate completely. Afterwards the gas species WO2*X*2 is formed in addition to mercury. Here, only gaseous species (WO2*X*2(g)+Hg(g))

**The basic precondition for successful CVT.** Basic precondition for chemical vapor transport reactions is a balanced equilibrium position: For reactions which are described by *one* independent reaction equation, transports can be expected for equilibrium constants *Kp* in the

partial pressure gradient Δ*p* as a driving force for the material transport between dissolution

respectively Gibbs energies Δr*G*0

and deposition site is achieved by a temperature gradient.

tions can be tackled:

238 Advanced Topics on Crystal Growth

(26).

are formed, too.

range from 10–4 up to 104

$$\text{WO}\_2\text{(s)} + \text{Br}\_2\text{(g)} \xrightleftharpoons \text{WO}\_2\text{Br}\_2\text{(g)}\tag{28}$$

$$
\Delta\_r H^0\_{\,1000} = 13.0 \text{ kJ} \cdot mol^{-1}, \ \Delta\_r S^0\_{\,1000} = 74.7 \text{ J} \cdot mol^{-1} \cdot K^{-1}
$$

$$
\Delta\_r G^0\_{\,1000} = -61.7 \text{ kJ} \cdot mol^{-1}, \ K\_{p\_{\,1000}} \approx 10^3
$$

$$\text{WO}\_2\text{(s)} + \text{I}\_2\text{(g)} \xrightleftharpoons \text{WO}\_2\text{I}\_2\text{(g)}\tag{29}$$

$$
\begin{aligned}
\Delta\_r H^{\circ 0}{}\_{1000} &= 112.4 \text{ kJ} \cdot mol^{-1}, \ \Delta\_r S^{\circ 0}{}\_{1000} = 84.6 \text{ J} \cdot mol^{-1} \cdot K^{-1} \\\\
\Delta\_r G^{\circ 0}{}\_{1000} &= 27.8 \text{ kJ} \cdot mol^{-1}, \ \text{K}\_{p, 1000} \approx 10^{-2}
\end{aligned}
$$

$$\text{WO}\_2\text{(s)} + 2\text{ }\text{HCl(g)} \xrightleftharpoons \text{WO}\_2\text{Cl}\_2\text{(g)} + \text{H}\_2\text{(g)}\tag{30}$$

$$
\Delta\_r H^0\_{\,1000} = \text{31.0 kJ} \cdot mol^{-1}, \ \Delta\_r S^0\_{\,1000} = \text{283.4 J} \cdot mol^{-1} \cdot K^{-1}
$$

$$
\Delta\_r G^0\_{\,1000} = -252.4 \text{ kJ} \cdot mol^{-1}, \ K\_{p\_{\,1000}} \approx 10^{13}
$$

$$\text{WO}\_2\text{(s)} + 2\text{ HBr}\text{(g)} \xrightleftharpoons \text{WO}\_2\text{Br}\_2\text{(g)} + \text{H}\_2\text{(g)}\tag{31}$$

() ( ) () () *WO s HgBr g WO Br g Hg g* 2 2 2 2 + ¬

*bar*

*bar*

() ( ) () () *WO s HgI g WO I g Hg g* 2 2 2 2 + ¬

= 170.5 *J* · *mol* –1 · *K* –1

= 179.2 *J* · *mol* –1 · *K* –1

**The suitable temperature.** The optimum average temperature [*T*¯ = (*T*2+*T*1)/2] for chemical vapor transports results from the requirement of Δr*G*0 ≈ 0. If the thermodynamic data of the reaction are known, which can easily be obtained from the values of the involved species according to Hess's law, the optimum average temperature can be calculated from quotient of the reaction enthalpy and entropy (38). Vant`t Hoff`s equation (37) establishes the link between the equilibrium constant *K* and the thermodynamic data of the reaction enthalpy and entropy. The better the data, the more realistic are the results. With the help of standard data given for 298 K, the first estimation of the optimum transport temperature can be made. The results of this calculation are not to be met to the exact degree. One rather finds a range of ± 100 K which

> 0 *r* - *T* ⋅ ∆ *ST*

0 *r* R ⋅ *T* + ∆ *ST* 0 *r*

0

*r* (36)

R (37)

1000

1000

**Figure 11.** Equilibrium constants of transport reactions of WO2(s) with Hg*X*2(g), *X* = Cl, Br, I.

∆ *GT* 0 *r* = - ∆ *HT*

ln*K* = - ∆ *HT*

*ΔrH* 0 1000

*ΔrG* 0 1000

*ΔrH* 0 1000

*ΔrG* 0 1000 = 190.5*kJ* · *mol* –1, *ΔrS* 0

= 249.6 *kJ* · *mol* –1, *ΔrS* 0

is suitable for the transport.

= 70.4 *kJ* · *mol* –1, *Kp*, 1000 ≈ 10−4

= 20.0 *kJ* · *mol* –1, *Kp*, 1000 ≈ 10−1

¾¾®¾¾ + (34)

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241

¾¾®¾¾ + (35)

$$
\Delta\_r H^0 \underset{1000}{\mathop{\cdot}} = 105.7 \ kf \cdot mol^{-1}, \ \Delta\_r S^0 \underset{1000}{\mathop{\cdot}}^0 = 296.1 \ l \cdot mol^{-1} \cdot K^{-1}
$$

$$
\Delta\_r G^0 \underset{1000}{\mathop{\cdot}}^0 = -190.4 \ kf \cdot mol^{-1} K\_{p\_{\cdot \, 1000}} \approx 10^{10}
$$

$$
\mathop{\cdot} \underset{2}{\mathop{\cdot}} \text{(s)} + 2 \ H \text{(g)} \underset{1 \text{---}}{\mathop{\cdot}} \underset{1 \text{---}}{\mathop{\cdot}} \text{WO}\_2 \text{I}\_2 \text{(g)} + H\_2 \text{(g)} \tag{32}
$$

$$
\begin{aligned}
\Delta\_r H \stackrel{0}{\underset{1000}{0}} &= 174.6 \text{ kJ} \cdot \text{mol}^{-1}, \ \Delta\_r S \stackrel{0}{\underset{1000}{0}} = 314.3 \text{ J} \cdot \text{mol}^{-1} \cdot K^{-1} \\\\
\Delta\_r G \stackrel{0}{\underset{1000}{0}} &= -139.7 \text{ kJ} \cdot \text{mol}^{-1}, \ \text{K}\_{p, 1000} \approx 10^7
\end{aligned}
$$

The calculations' results give a realistic outlook on the prospective results of transport experiments: Using halogens the transport with iodine seems to be promising (29). In the case of bromine, the transport seems at least possible (28) whereas chlorine causes an extreme equilibrium position under the formation of WO2Cl2(g) – a transport should not be possible (27). With the hydrogen halides equilibria are far on the side of the reaction products (30 – 32). This is due to clearly higher gain of entropy during the reaction. Although one can observe gradations in the equilibrium position for transports with HI and HBr compared to HCl, transports are principally not expected.

The transport of WO2 with mercury halides seems possible for all three transport agents Hg*X*2 (*X* = Cl, Br, I): The equilibrium constants are within the limits of 10−4 < *Kp* < 104 . Thus, these systems are ideal to foster the understanding of a systematic approach and particularly to extend the understanding of chemical vapor transports. In the following, we shall focus on the transport of WO2 with mercury halides. Using mercury bromide as a transport agent, the equilibrium position is least extreme (34) – in this case, the best transport results can be expected, see Figure 11. Using HgCl2(g) for the transport, the equilibrium position is shifted to the right (33); that means, the solid WO2 is transferred well into the gas phase. However, the deposition of the solid on the sink side is only possible to a limited degree. Even when the temperature is decreased, the equilibrium position is still on the product side. The equilibrium constant for the transport with HgI2(g) indicates that the solid is hardly dissolved – the equilibrium position is shifted to the left (35). Thus, these are adverse conditions for a transport.

$$\text{WO}\_2\text{(s)} + \text{HgCl}\_2\text{(g)} \xrightleftharpoons \text{WO}\_2\text{Cl}\_2\text{(g)} + \text{Hg(g)}\tag{33}$$

$$
\Delta\_r H^0\_{\; 1000} = 115.5 \text{ kJ} \cdot mol^{-1}, \ \Delta\_r S^0\_{\; 1000} = 171.9 \text{ J} \cdot mol^{-1} \cdot K^{-1}
$$

$$
\Delta\_r G^0\_{\; 1000} - 56.4 \text{ kJ} \cdot mol^{-1}, \ K\_{p\_{\; 1000}} \approx 10^3 bar
$$

$$\text{MO}\_2\text{(s)} + \text{HgBr}\_2\text{(g)} \xrightleftharpoons \text{NO}\_2\text{Br}\_2\text{(g)} + \text{Hg}\text{(g)}\tag{34}$$

*ΔrH* 0 1000 = 190.5*kJ* · *mol* –1, *ΔrS* 0 1000 = 170.5 *J* · *mol* –1 · *K* –1 *ΔrG* 0 1000 = 20.0 *kJ* · *mol* –1, *Kp*, 1000 ≈ 10−1 *bar*

$$\text{WO}\_2\text{(s)} + \text{H}\_3\text{I}\_2\text{(g)} \xrightleftharpoons \text{WO}\_2\text{I}\_2\text{(g)} + \text{H}\_3\text{(g)}\tag{35}$$

*ΔrH* 0 1000 = 249.6 *kJ* · *mol* –1, *ΔrS* 0 1000 = 179.2 *J* · *mol* –1 · *K* –1

*ΔrG* 0 1000 = 70.4 *kJ* · *mol* –1, *Kp*, 1000 ≈ 10−4 *bar*

( ) ( ) ( ) ( ) 2 22 2 *WO s HBr g WO Br g H g* + 2 ¬

( ) ( ) ( ) ( ) 2 22 2 *WO s HI g WO I g H g* + 2 ¬

1000 = 314.3 *J* · *mol* –1 · *K* –1

The calculations' results give a realistic outlook on the prospective results of transport experiments: Using halogens the transport with iodine seems to be promising (29). In the case of bromine, the transport seems at least possible (28) whereas chlorine causes an extreme equilibrium position under the formation of WO2Cl2(g) – a transport should not be possible (27). With the hydrogen halides equilibria are far on the side of the reaction products (30 – 32). This is due to clearly higher gain of entropy during the reaction. Although one can observe gradations in the equilibrium position for transports with HI and HBr compared to HCl,

The transport of WO2 with mercury halides seems possible for all three transport agents Hg*X*2 (*X* = Cl, Br, I): The equilibrium constants are within the limits of 10−4 < *Kp* < 104

these systems are ideal to foster the understanding of a systematic approach and particularly to extend the understanding of chemical vapor transports. In the following, we shall focus on the transport of WO2 with mercury halides. Using mercury bromide as a transport agent, the equilibrium position is least extreme (34) – in this case, the best transport results can be expected, see Figure 11. Using HgCl2(g) for the transport, the equilibrium position is shifted to the right (33); that means, the solid WO2 is transferred well into the gas phase. However, the deposition of the solid on the sink side is only possible to a limited degree. Even when the temperature is decreased, the equilibrium position is still on the product side. The equilibrium constant for the transport with HgI2(g) indicates that the solid is hardly dissolved – the equilibrium position is shifted to the left (35). Thus, these are adverse conditions for a transport.

( ) ( ) ( ) ( ) *WO s HgCl g WO Cl g Hg g* 2 2 2 2 + ¬

*bar*

1000 = 171.9 *J* · *mol* –1 · *K* –1

1000 = 296.1 *J* · *mol* –1 · *K* –1

*ΔrH* 0

*ΔrG* 0

*ΔrH* 0

*ΔrG* 0

*ΔrH* 0

*ΔrG* 0

1000 = 115.5 *kJ* · *mol* –1

1000 −56.4 *kJ* · *mol* –1

, *ΔrS* 0

, *Kp*, 1000 ≈ 103

1000 = 105.7 *kJ* · *mol* –1

240 Advanced Topics on Crystal Growth

1000 = −190.4 *kJ* · *mol* –1

1000 = 174.6 *kJ* · *mol* –1

1000 = −139.7 *kJ* · *mol* –1

transports are principally not expected.

, *ΔrS* 0

, *ΔrS* 0

*Kp*, 1000 ≈ 1010

, *Kp*, 1000 ≈ 107

¾¾®¾¾ + (31)

¾¾®¾¾ + (32)

¾¾®¾¾ + (33)

. Thus,

**Figure 11.** Equilibrium constants of transport reactions of WO2(s) with Hg*X*2(g), *X* = Cl, Br, I.

**The suitable temperature.** The optimum average temperature [*T*¯ = (*T*2+*T*1)/2] for chemical vapor transports results from the requirement of Δr*G*0 ≈ 0. If the thermodynamic data of the reaction are known, which can easily be obtained from the values of the involved species according to Hess's law, the optimum average temperature can be calculated from quotient of the reaction enthalpy and entropy (38). Vant`t Hoff`s equation (37) establishes the link between the equilibrium constant *K* and the thermodynamic data of the reaction enthalpy and entropy. The better the data, the more realistic are the results. With the help of standard data given for 298 K, the first estimation of the optimum transport temperature can be made. The results of this calculation are not to be met to the exact degree. One rather finds a range of ± 100 K which is suitable for the transport.

$$
\Delta\_r G\_T^{\;0} = -\Delta\_r H\_T^{\;0} - T \cdot \Delta\_r S\_T^{\;0} \tag{36}
$$

$$\ln K = -\frac{\Delta\_r H\_T^{\circ 0}}{R \cdot T} + \frac{\Delta\_r S\_T^{\circ 0}}{R} \tag{37}$$

For the precondition of balanced equilibrium position at *K* = 1 (Δr*G*0 *T* = 0) results:

$$T\_{opt} = \frac{\Delta\_r H\_T^{\circ}}{\Delta\_r S\_T^{\circ}} \tag{38}$$

**The transport direction.** If a transport operation can be described in good approximation by only *one* reaction, the direction of the transport results from the heat balance of the heteroge‐ neous equilibrium according to the van 't Hoff equation respectively to the Clausius–Clapeyr‐

> = - ∆ *HT* 0 *r*

In a reaction with negative reaction enthalpy (exothermic dissolving reaction), the equilibrium constant *Kp* increases with decreasing temperatures – thus dissolution takes place at low, deposition at high temperatures. To put it in other words: The transport is directed to the hotter

In a reaction with positive reaction enthalpy (endothermic dissolving reaction), *Kp* increases with increasing temperatures – so dissolution takes place at higher, deposition at lower

The transport direction results only from the reaction enthalpy which is why the conclusion of all three investigated transport systems of WO2 is clear: The reaction enthalpy is positive in each case – a transport to the cooler zone results. The total amount of the reaction enthalpy does not affect the decision if a transport is carried out. If the reaction enthalpy is close to zero one has to check the accuracy of the used data as they can contain errors of 10 to 20 kJ mol−1.

**The rate of mass transport**. The substance transport via gas motion between dissolution and deposition site takes place by diffusion or convection. If the ampoule lies horizontally and if the total pressure is between 10–3 bar and 3 bar, the substance transport is affected by diffusion [1, 28]. In most cases, the diffusion is the velocity determining step, as it is much slower than the heterogeneous reaction of the solid with the transport agent. Using pressures above 3 bar,

The term "*transport rate*" expresses the amount of deposited substance per time in the sink. For transports which run by only *one* reaction, one can describe the transport rate by Schäfer's transport equation (45) under the precondition that the chemical transport is solely deter‐ minedbydiffusion1) [1, 15].HighvaluesofΔ*p* resultinahightransportrate.Alarge cross section effects the transportratepositivelyasdoes a shorttransportdistance.Accordingtothe transport equation a high average temperature is formally advantageous for the transport rate; howev‐ er, the influence of the temperature on the equilibrium constant, and thus Δ*p* is more essential.

*R* (42)

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243

0 0; ~ 1 / *r T H d lnK d T p* D < (43)

0 0; ~ *r T H d lnK dT p* D > (44)

dln*K p* d 1 *T*

temperatures. Now, the transport proceeds to the cooler zone (*T*2→*T*1).

on relation (42):

zone (*T*1→*T*2).

convection becomes dominating [28].

Through differences in the temperatures of the source and sink side, the equilibrium position is brought towards the gaseous products when dissolving and shifted towards the solid when deposing. Calculations of the equilibrium constants were first made for an average tempera‐ ture of 1000 K. If the temperatures vary, one will get the typical courses of the curve (see Figure 11). If the temperature is decreased, the equilibrium position in the transport system with HgCl2 becomes less extreme. In contrast, the equilibrium position for the transport with HgI2 becomes more favorable when the temperature is increased above 1000 K. The optimum, average temperature resulting from the quotient of the reaction enthalpy and entropy for the transport with HgCl2 is at about 700 K respectively 400 °C; with HgBr2 at about 1100 K respectively 800 °C and with HgI2 1400 K (1100 °C, respectively). In this case, the calculation of the temperature on the basis of the standard values at 298 K as well as of the derived values for 1000 K lead to the same results; which means that an estimation is possible with simple calculations, (39 – 41).

$$\text{WO}\_2\text{(s)} + \text{HgCl}\_2\text{(g)} \xrightleftharpoons \text{WO}\_2\text{Cl}\_2\text{(g)} + \text{Hg(g)}\tag{39}$$

$$
\Delta\_r H^0\_{\,298} = 122.5 \, kJ \cdot mol^{-1}, \, \, \Delta\_r S^0\_{\,298} = 183.6 \, J \cdot mol^{-1} \cdot K^{-1}
$$

$$
T\_{opt} = 125500 \, J \cdot mol^{-1} / 183.6 \, J \cdot mol^{-1} \cdot K^{-1}
$$

$$
T\_{opt} \approx 700 \, K \, respectively \, 400 \, \, ^\circ C
$$

$$\text{NO}\_2\text{(s)} + \text{HgBr}\_2\text{(g)} \xrightleftharpoons \text{NO}\_2\text{Br}\_2\text{(g)} + \text{Hg}\text{(g)}\tag{40}$$

*ΔrH* 0 298 = 1881 *kJ* · *mol* –1 , *ΔrS* 0 298 = 170.0 *J* · *mol* –1 · *K* –1 *Topt* ≈ 1100 *K respectively* 800 °*C*

$$\text{WO}\_2\text{(s)} + \text{H}\_3\text{I}\_2\text{(g)} \xrightleftharpoons \text{WO}\_2\text{I}\_2\text{(g)} + \text{H}\_3\text{(g)}\tag{41}$$

*ΔrH* 0 298 = 238.4 *kJ* · *mol* –1 , *ΔrS* 0 298 = 165.4 *J* · *mol* –1 · *K* –1 *Topt* ≈ 1400 *K respectively* 1100 °*C*

**The transport direction.** If a transport operation can be described in good approximation by only *one* reaction, the direction of the transport results from the heat balance of the heteroge‐ neous equilibrium according to the van 't Hoff equation respectively to the Clausius–Clapeyr‐ on relation (42):

For the precondition of balanced equilibrium position at *K* = 1 (Δr*G*0

calculations, (39 – 41).

242 Advanced Topics on Crystal Growth

298 = 122.5 *kJ* · *mol* –1

*Topt* ≈ 700 *K respectively* 400 °*C*

298 = 1881 *kJ* · *mol* –1

*Topt* ≈ 1100 *K respectively* 800 °*C*

298 = 238.4 *kJ* · *mol* –1

*Topt* ≈ 1400 *K respectively* 1100 °*C*

*Topt* = 125500 *J* · *mol* –1 / 183.6 *J* · *mol* –1 · *K* –1

, *ΔrS* 0

, *ΔrS* 0

, *ΔrS* 0

*ΔrH* 0

*ΔrH* 0

*ΔrH* 0

*Topt* = ∆ *HT*

( ) ( ) ( ) ( ) *WO s HgCl g WO Cl g Hg g* 2 2 2 2 + ¬

298 = 183.6 *J* · *mol* –1 · *K* –1

( ) ( ) ( ) ( ) *WO s HgBr g WO Br g Hg g* 2 2 2 2 + ¬

298 = 170.0 *J* · *mol* –1 · *K* –1

( ) ( ) ( ) ( ) *WO s HgI g WO I g Hg g* 2 2 2 2 + ¬

298 = 165.4 *J* · *mol* –1 · *K* –1

0 *r* ∆ *ST* 0 *r*

Through differences in the temperatures of the source and sink side, the equilibrium position is brought towards the gaseous products when dissolving and shifted towards the solid when deposing. Calculations of the equilibrium constants were first made for an average tempera‐ ture of 1000 K. If the temperatures vary, one will get the typical courses of the curve (see Figure 11). If the temperature is decreased, the equilibrium position in the transport system with HgCl2 becomes less extreme. In contrast, the equilibrium position for the transport with HgI2 becomes more favorable when the temperature is increased above 1000 K. The optimum, average temperature resulting from the quotient of the reaction enthalpy and entropy for the transport with HgCl2 is at about 700 K respectively 400 °C; with HgBr2 at about 1100 K respectively 800 °C and with HgI2 1400 K (1100 °C, respectively). In this case, the calculation of the temperature on the basis of the standard values at 298 K as well as of the derived values for 1000 K lead to the same results; which means that an estimation is possible with simple

*T* = 0) results:

¾¾®¾¾ + (39)

¾¾®¾¾ + (40)

¾¾®¾¾ + (41)

(38)

$$\frac{\Delta \text{dh}K\_p}{\Delta \frac{1}{T}} = \text{h} \cdot \frac{\Delta\_r H\_T^{\text{(\%)}}}{R} \tag{42}$$

In a reaction with negative reaction enthalpy (exothermic dissolving reaction), the equilibrium constant *Kp* increases with decreasing temperatures – thus dissolution takes place at low, deposition at high temperatures. To put it in other words: The transport is directed to the hotter zone (*T*1→*T*2).

$$
\Delta\_r H^0\_{\,\,T} < 0; \, d \, \ln K\_p \sim \, d1/T \tag{43}
$$

In a reaction with positive reaction enthalpy (endothermic dissolving reaction), *Kp* increases with increasing temperatures – so dissolution takes place at higher, deposition at lower temperatures. Now, the transport proceeds to the cooler zone (*T*2→*T*1).

$$
\Delta\_r H^0\_{\,\,T} > 0; \, d \, \ln K\_p \sim \, dT \tag{44}
$$

The transport direction results only from the reaction enthalpy which is why the conclusion of all three investigated transport systems of WO2 is clear: The reaction enthalpy is positive in each case – a transport to the cooler zone results. The total amount of the reaction enthalpy does not affect the decision if a transport is carried out. If the reaction enthalpy is close to zero one has to check the accuracy of the used data as they can contain errors of 10 to 20 kJ mol−1.

**The rate of mass transport**. The substance transport via gas motion between dissolution and deposition site takes place by diffusion or convection. If the ampoule lies horizontally and if the total pressure is between 10–3 bar and 3 bar, the substance transport is affected by diffusion [1, 28]. In most cases, the diffusion is the velocity determining step, as it is much slower than the heterogeneous reaction of the solid with the transport agent. Using pressures above 3 bar, convection becomes dominating [28].

The term "*transport rate*" expresses the amount of deposited substance per time in the sink. For transports which run by only *one* reaction, one can describe the transport rate by Schäfer's transport equation (45) under the precondition that the chemical transport is solely deter‐ minedbydiffusion1) [1, 15].HighvaluesofΔ*p* resultinahightransportrate.Alarge cross section effects the transportratepositivelyasdoes a shorttransportdistance.Accordingtothe transport equation a high average temperature is formally advantageous for the transport rate; howev‐ er, the influence of the temperature on the equilibrium constant, and thus Δ*p* is more essential.

$$\min(A) = \frac{n(A)}{t} = \frac{i}{\gamma} \cdot \frac{\Delta \cdot p}{\sum p} \cdot \frac{T^{0.75} \cdot q}{s} \cdot 0.6 \cdot 10^{-4} \left(mol \cdot l \cdot ^{1} \right) \tag{45}$$

rates of up to 15 mg h–1 can be achieved, Figure 13. The transport rate decreases drastically with falling temperatures. With an average temperature of 640 °C the rate is even lower than 1 mg h–1. Transport experiments with HgCl2 show worst results as far as the transport rate is concerned: According to the calculation, lower temperatures are principally more favorable, however, in the range from 500 to 700 °C the transport rates are only in the range of 1 mg h–1.

**Figure 12.** Progression of theoretical transport rates during the transport of WO2 with Hg*X*2 (*X* = Cl, Br, I) according to

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**Figure 13.** Experimental transport rates during the transport of WO2 with Hg*X*2 (*X* = Cl, Br, I) according to [2].

One can come to a completely different evaluation if the quality of the crystals instead of the transport rate is given prominence. Relatively high transport rates cause uncontrolled nucleation and crystal growth. As a consequence, one gets highly epitaxial and rose-shaped crystal agglomerations for transports with HgBr2. Frequently *one* compact solid of these epitaxial crystallites of WO2 is found in the sink. Using average temperatures of approx. 800 °C in the transport system with HgI2, one gets isolated, rod-shaped crystals of up to 1 mm edge length, Figure 14. The preparation of mono-crystals for crystal structure analysis is possible from these approaches, even though not every crystal is suitable. The low transport rate of 1

The transport almost grinds to a halt at higher temperatures.

[29, 30].

*n*˙(*A*): Transport rate /mol h−1

*i,j,k* stoichiometric coefficients in transport equation: *i A*(s)+*k B*(g) = *j C*(g)+…

Δ*p*: partial pressure difference of the *transport effective* species *C* /bar

Σ*p*: total pressure /bar

*T*¯ average temperature along the diffusion path /K (practically *T*¯ results as an average of *T*1 and *T*2)

*q*: cross-section of the diffusion path /cm2

*s*: length of the diffusion path /cm

*t*' duration of the transport experiment /h

In most cases instead of the diffusion factor 0.6 10−4 a value of 1.8 10−4 is given which found entrance to the literature [1]. According to recent findings the factor 0.6 10−4 results in a smaller numerical value of the diffusion coefficient and corrects a mathematical error.

The calculation of transport rates for WO2 by Schornstein and Gruehn [29, 30] at first show a clear dominance of transports with HgBr2 in the average temperature range: The expected transport rates are ten times higher than for transports with HgCl2 and HgI2. Due to the balanced position of the equilibrium, high differences of partial pressures occur between the source and the sink. This way, the driving force for diffusion of the gas particles is high and thus for the substance transport as well. For the transport with HgCl2 the transport rate decreases with increasing temperatures. As we have already seen, the equilibrium position, which is far to the right side, is responsible for it. Only if the temperature decreases, the equilibrium position can move to the left. The resulting, higher differences of partial pressures between dissolution and deposition side cause increasing transport rates at low temperatures. Using mercury iodide as transport agent, the equilibrium position is on the side of the source material at low temperatures. By increasing the temperature the equilibrium position is shifted to the side of the reaction products, the transport rate increases, Figure 12.

Corresponding to the simple estimation of the transport behavior of WO2 with mercury halides, one gets the best results with the addition of HgBr2. The chemical vapor transport of mercury bromide is possible in a wide temperature range. Transport rates above 30 mg h–1 are achievable, Figure 13. Temperatures of the source side of about 800 °C and of the sink side of 720 °C prove optimum. This result confirms the estimations of the optimum transport temperature. Due to the shift of the equilibrium position, the transport rate decreases at both, rising temperatures (880 → 800 °C respectively 960 → 880 °C; and falling temperatures (720 → 640 °C) [2]. Transports with HgCl2 and HgI2 clearly show smaller transport rates. Experiments with mercury iodides must be realized with higher temperatures according to the estimation. Temperatures up to 1000 °C are practicable; above, the silica glass ampoule will be heavily damaged by re-crystallization. Using an average transport temperature of 940 °C, transport

*n*˙(*A*)= *n*(*A*)

*q*: cross-section of the diffusion path /cm2

*t*' duration of the transport experiment /h

*s*: length of the diffusion path /cm

*n*˙(*A*): Transport rate /mol h−1

244 Advanced Topics on Crystal Growth

Σ*p*: total pressure /bar

and *T*2)

*t* ' = *i*

*j* ⋅ ∆ *p*

*i,j,k* stoichiometric coefficients in transport equation: *i A*(s)+*k B*(g) = *j C*(g)+…

Δ*p*: partial pressure difference of the *transport effective* species *C* /bar

∑ *p* ⋅ *T*¯ 0.75 ⋅ *q*

*T*¯ average temperature along the diffusion path /K (practically *T*¯ results as an average of *T*1

In most cases instead of the diffusion factor 0.6 10−4 a value of 1.8 10−4 is given which found entrance to the literature [1]. According to recent findings the factor 0.6 10−4 results in a smaller

The calculation of transport rates for WO2 by Schornstein and Gruehn [29, 30] at first show a clear dominance of transports with HgBr2 in the average temperature range: The expected transport rates are ten times higher than for transports with HgCl2 and HgI2. Due to the balanced position of the equilibrium, high differences of partial pressures occur between the source and the sink. This way, the driving force for diffusion of the gas particles is high and thus for the substance transport as well. For the transport with HgCl2 the transport rate decreases with increasing temperatures. As we have already seen, the equilibrium position, which is far to the right side, is responsible for it. Only if the temperature decreases, the equilibrium position can move to the left. The resulting, higher differences of partial pressures between dissolution and deposition side cause increasing transport rates at low temperatures. Using mercury iodide as transport agent, the equilibrium position is on the side of the source material at low temperatures. By increasing the temperature the equilibrium position is shifted

Corresponding to the simple estimation of the transport behavior of WO2 with mercury halides, one gets the best results with the addition of HgBr2. The chemical vapor transport of mercury bromide is possible in a wide temperature range. Transport rates above 30 mg h–1 are achievable, Figure 13. Temperatures of the source side of about 800 °C and of the sink side of 720 °C prove optimum. This result confirms the estimations of the optimum transport temperature. Due to the shift of the equilibrium position, the transport rate decreases at both, rising temperatures (880 → 800 °C respectively 960 → 880 °C; and falling temperatures (720 → 640 °C) [2]. Transports with HgCl2 and HgI2 clearly show smaller transport rates. Experiments with mercury iodides must be realized with higher temperatures according to the estimation. Temperatures up to 1000 °C are practicable; above, the silica glass ampoule will be heavily damaged by re-crystallization. Using an average transport temperature of 940 °C, transport

numerical value of the diffusion coefficient and corrects a mathematical error.

to the side of the reaction products, the transport rate increases, Figure 12.

*s* ⋅0.6⋅10-4(*mol* ⋅ *l* -1) (45)

**Figure 12.** Progression of theoretical transport rates during the transport of WO2 with Hg*X*2 (*X* = Cl, Br, I) according to [29, 30].

rates of up to 15 mg h–1 can be achieved, Figure 13. The transport rate decreases drastically with falling temperatures. With an average temperature of 640 °C the rate is even lower than 1 mg h–1. Transport experiments with HgCl2 show worst results as far as the transport rate is concerned: According to the calculation, lower temperatures are principally more favorable, however, in the range from 500 to 700 °C the transport rates are only in the range of 1 mg h–1. The transport almost grinds to a halt at higher temperatures.

**Figure 13.** Experimental transport rates during the transport of WO2 with Hg*X*2 (*X* = Cl, Br, I) according to [2].

One can come to a completely different evaluation if the quality of the crystals instead of the transport rate is given prominence. Relatively high transport rates cause uncontrolled nucleation and crystal growth. As a consequence, one gets highly epitaxial and rose-shaped crystal agglomerations for transports with HgBr2. Frequently *one* compact solid of these epitaxial crystallites of WO2 is found in the sink. Using average temperatures of approx. 800 °C in the transport system with HgI2, one gets isolated, rod-shaped crystals of up to 1 mm edge length, Figure 14. The preparation of mono-crystals for crystal structure analysis is possible from these approaches, even though not every crystal is suitable. The low transport rate of 1 to 2 mg h–1 makes an undisturbed nucleation and crystal growth possible in this case. In the process, smaller, highly defected crystallites are dissolved in favor of other individuals.

halogens and halogen compounds are qualified. Some elements, hydrogen compounds, and

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**Halogen compounds**. Due to its volatility, metal halides and non-metal halides play a central role for chemical transport reactions. Thus, halogens and many halogen compounds are

**Halogens and halogen compounds as transport agents**. The elemental halogens chlorine, bromine and iodine are used frequently as transport agent. Fluorine, in contrast, is not suited due to extreme equilibrium position of formation of fluorides in most cases. Besides, there are material problems because fluorine reacts with the ampoule materials if silica glass is used. Under the pertinent transport conditions, chlorine, bromine, and iodine react with solids of different substance classes, e.g. with metal, intermetallic compounds, semi-metals, metal oxides, sulfides, selenides, tellurides, nitrides, phosphides, arsenides, antimonides, silicides, germanides, some metal halogens and more. In the process, gaseous metal halides respectively semi-metal halides and the respective non-metal are formed as a rule. In some cases, non-metal halides are formed. Thus, during a reaction of metal phosphides with a halogen or a halogen compound, not only metal halides but also phosphoric halides can occur. Due to the fact that halides show oxidizing characteristics, metal halides or oxide halides are often formed as transport effective species in which the metal has a higher oxidation level than in the solid as shown for the transport of chromium(III) chloride with chlorine (46) or tungsten(IV) oxide

Hydrogen halides are versatile transport agents. The oxidation levels of the metal in the solid and in the transport effective gas species are generally equal because hydrogen halides do not have an oxidizing effect. Hydrogen halides are often used during the transport of oxides. Here, the gaseousmetal halide and water vapor are formed. Halogen compounds, such asTeCl4,PCl5, NbCl5 or TaCl5 are also useful transport agents, especially for metal oxides. Reactions of the mentioned chlorides lead on the one hand to the formation of gaseous metal chloride or metal oxide chloride, on the other hand oxygen is fixed in form of volatile oxides (TeO2, P4O6, P4O10) or oxide chlorides (TeOCl2, POCl3, NbOCl3, TaOCl3). Oppermann was able to show that tellurium(IV) chloride is aparticularversatile transport agent[31].Accordingto thebasicworks of Schäfer, gaseous metal respectively semi-metal halides are formed as transport effective species during the reaction of different solids with halogens or halogen compounds [1].

( ) ( ) ( ) 32 4 *CrCl s Cl g CrCl g* + 1/ 2 ¬¾¾ ¾ ®¾ (46)

( ) ( ) ( ) *WO s I g WO I g* 2 2 2 2 + ¬¾¾ ¾¾® (47)

( ) ( ) ( ) *Co s I g CoI g* 2 2 + ¬¾¾ ¾¾® (48)

oxygen compounds are suitable as transportable species, too.

effective and often used transport agents.

with iodine (47).

**Figure 14.** Typical crystal morphology of single crystallites formed during the transport of WO2 with HgI2.

Finally, in selecting the transport agent, the temperature, and the temperature gradient, respectively, one should consider the aim of the transport. A high transport rate is undoubtedly advantageous for the synthesis of a compound or the purification of it. If crystals are to be grown, keep in mind the crystal quality and therefore rather choose a smaller transport rate.

**Conclusion**. Chemical vapor transport reactions are predictable. Simple estimations concern‐ ing the feasibility and the course of transport reactions are already possible with a basic understanding of the method and its thermodynamic backgrounds. It is worth the effort in every case – one avoids unnecessary experiments using "trial and error" procedure. Conclu‐ sions by analogy between similar transport systems are helpful as a first guide. However, the factual favorable parameter for a transport system should be estimated carefully in advance

### **3. Chemical vapor transport reactions – applications**

### **3.1. Transport agents and gas species**

It is of prime interest for preparative working chemists whether a certain solid can be prepared by chemical transport reactions, which transport agents are suitable and under which condi‐ tions a transport can be expected. If one wants to use transport reactions only in a preparative way – without the purpose of understanding the course of the reaction in detail – often it is sufficing to check on an empiric basis which solid can be transported by using what kind of transport agent. A further, quantitative description of the transport reaction requires knowl‐ edge of the thermodynamic data of the condensed phases and gaseous molecules that are involved. In this section, we will provide a short overview of the different kinds of gaseous inorganic molecule that can occur during chemical vapor transport reactions. Under the precondition of formation of only gaseous species, transport agents and transport effective species share the property of high volatility under experimental conditions. Thus, especially halogens and halogen compounds are qualified. Some elements, hydrogen compounds, and oxygen compounds are suitable as transportable species, too.

to 2 mg h–1 makes an undisturbed nucleation and crystal growth possible in this case. In the process, smaller, highly defected crystallites are dissolved in favor of other individuals.

**Figure 14.** Typical crystal morphology of single crystallites formed during the transport of WO2 with HgI2.

**3. Chemical vapor transport reactions – applications**

**3.1. Transport agents and gas species**

246 Advanced Topics on Crystal Growth

Finally, in selecting the transport agent, the temperature, and the temperature gradient, respectively, one should consider the aim of the transport. A high transport rate is undoubtedly advantageous for the synthesis of a compound or the purification of it. If crystals are to be grown, keep in mind the crystal quality and therefore rather choose a smaller transport rate.

**Conclusion**. Chemical vapor transport reactions are predictable. Simple estimations concern‐ ing the feasibility and the course of transport reactions are already possible with a basic understanding of the method and its thermodynamic backgrounds. It is worth the effort in every case – one avoids unnecessary experiments using "trial and error" procedure. Conclu‐ sions by analogy between similar transport systems are helpful as a first guide. However, the factual favorable parameter for a transport system should be estimated carefully in advance

It is of prime interest for preparative working chemists whether a certain solid can be prepared by chemical transport reactions, which transport agents are suitable and under which condi‐ tions a transport can be expected. If one wants to use transport reactions only in a preparative way – without the purpose of understanding the course of the reaction in detail – often it is sufficing to check on an empiric basis which solid can be transported by using what kind of transport agent. A further, quantitative description of the transport reaction requires knowl‐ edge of the thermodynamic data of the condensed phases and gaseous molecules that are involved. In this section, we will provide a short overview of the different kinds of gaseous inorganic molecule that can occur during chemical vapor transport reactions. Under the precondition of formation of only gaseous species, transport agents and transport effective species share the property of high volatility under experimental conditions. Thus, especially

**Halogen compounds**. Due to its volatility, metal halides and non-metal halides play a central role for chemical transport reactions. Thus, halogens and many halogen compounds are effective and often used transport agents.

**Halogens and halogen compounds as transport agents**. The elemental halogens chlorine, bromine and iodine are used frequently as transport agent. Fluorine, in contrast, is not suited due to extreme equilibrium position of formation of fluorides in most cases. Besides, there are material problems because fluorine reacts with the ampoule materials if silica glass is used. Under the pertinent transport conditions, chlorine, bromine, and iodine react with solids of different substance classes, e.g. with metal, intermetallic compounds, semi-metals, metal oxides, sulfides, selenides, tellurides, nitrides, phosphides, arsenides, antimonides, silicides, germanides, some metal halogens and more. In the process, gaseous metal halides respectively semi-metal halides and the respective non-metal are formed as a rule. In some cases, non-metal halides are formed. Thus, during a reaction of metal phosphides with a halogen or a halogen compound, not only metal halides but also phosphoric halides can occur. Due to the fact that halides show oxidizing characteristics, metal halides or oxide halides are often formed as transport effective species in which the metal has a higher oxidation level than in the solid as shown for the transport of chromium(III) chloride with chlorine (46) or tungsten(IV) oxide with iodine (47).

$$\text{CrCl}\_3\text{(s)} + 1/2\text{ Cl}\_2\text{(g)} \xrightleftharpoons \text{CrCl}\_4\text{(g)}\tag{46}$$

$$\text{WO}\_2\text{(s)} + I\_2\text{(g)} \xrightleftharpoons \text{WO}\_2I\_2\text{(g)}\tag{47}$$

Hydrogen halides are versatile transport agents. The oxidation levels of the metal in the solid and in the transport effective gas species are generally equal because hydrogen halides do not have an oxidizing effect. Hydrogen halides are often used during the transport of oxides. Here, the gaseousmetal halide and water vapor are formed. Halogen compounds, such asTeCl4,PCl5, NbCl5 or TaCl5 are also useful transport agents, especially for metal oxides. Reactions of the mentioned chlorides lead on the one hand to the formation of gaseous metal chloride or metal oxide chloride, on the other hand oxygen is fixed in form of volatile oxides (TeO2, P4O6, P4O10) or oxide chlorides (TeOCl2, POCl3, NbOCl3, TaOCl3). Oppermann was able to show that tellurium(IV) chloride is aparticularversatile transport agent[31].Accordingto thebasicworks of Schäfer, gaseous metal respectively semi-metal halides are formed as transport effective species during the reaction of different solids with halogens or halogen compounds [1].

$$\text{Co}(\text{s}) + I\_2\text{(g)} \xrightleftharpoons \text{CoI}\_2\text{(g)}\tag{48}$$

$$\text{Si}(s) + \text{SiI}\_4(\text{g}) \xrightleftharpoons \text{2 SiI}\_2(\text{g})\tag{49}$$

Some gaseous oxide halides are known of main group metals. Elements of group 13 form oxide halides, such as AlOCl, at very high temperatures around 2000 °C. Phosphorus forms several oxide chlorides and -bromides that are stable at high temperatures: PO*X*3, PO2*X*, and PO*X* (*X* = Cl, Br) [42]. For arsenic and antimony AsOCl and SbOCl are stable at high temperatures, however, oxide halides with the metal in the oxidation stage V are not known [42]. TeOCl2 is the most important oxide halide of the main group elements. This gas species plays an important role during the transport of numerous oxides with tellurium(IV) chloride [31].

**Elements in gaseous state**. The importance of elemental halogens for chemical vapor transport reactions was already mentioned. Other elements also often occur in gaseous state during transport reactions, especially gaseous non-metals. Gaseous species of elements of groups 15 and 16 are formed during the transport of pnictides or chalcogenides with halogens (56) or halogen compounds in many cases. In contrast, metal gas species play a role in only a few reactions. In particular, this behavior occurs, if the transport agent reacts with the non-metal instead of the metal atoms and the metal is sufficient volatile (57). The formation of an unsaturated metal vapor during transport reactions can only be expected if the boiling temperature of the metal is below approx. 1200 °C. This only applies to the following metals: Na (881 °C), K (763 °C), Rb (697 °C), Cs (657 °C), Mg (1093 °C), Zn (906 °C), Cd (766 °C), Hg

( ) ( ) ( ) ( ) *ZnO s H g Zn g H O g* 2 2 + ¬

In some cases, gaseous elements can work as transport agents. Hence, oxygen can cause the transport of some platinum metals [40]. Sulfur can transport a series of transition metal sulfides [43]. Here, gaseous polysulfides, such as TaS3, are assumed transport effective species. There are similar observations for the chemical transport of some selenides. Sulfur is an effective transport agent for tellurium as well [44]. Compounds in which tellurium atoms were integrated in the different ring-shaped sulfur molecules were detected as transport effective species. Phosphorus can transport gallium phosphide, GaP, and indium phosphide, InP, probably via GaP5 respectively InP5 as transport effective species [45]. With the help of arsenic, the transport of gallium arsenide, GaAs, and indium arsenide, InAs, succeeded in a similar

Metal vapors predominantly consist of the atoms. The fraction of bi- or polyatomic molecules in the saturated vapor is between 10−5 and 10 % [47]. In contrast, the vapors of non-metals, apart from noble gases, consist of very stable polyatomic molecules which appear in the gas phase in great amounts, atoms appear only subordinated: N2, P4, P2, As4, As2, Sb4, Sb2, O2, S2, S3 … S7, S8, Se2, Se3 … Se7, Se8, Te2, Cl2, Br2, and I2. The ratio of different molecular species in the vapors of non-metals depends on the temperature and the pressure. Higher temperature

and lower pressures abet the formation of small molecules respectively atoms.

( ) ( ) ( ) ( ) 22 4 4 *ZrAs s I g ZrI g As g* + + 2 1/ 2 ¬¾¾ ¾¾® (56)

¾¾®¾¾ + (57)

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(356 °C), Yb (1194 °C) and Te (989 °C).

way [46].

$$\text{TiO}\_2\text{(s)} + 4\text{ HCl(g)} \xrightleftharpoons \text{TiCl}\_4\text{(g)} + 2\text{ H}\_2\text{O}\text{(g)}\tag{50}$$

$$\text{CrCl}\_3\text{(s)} + 1/2\text{ Cl}\_2\text{(g)} \xrightleftharpoons \text{CrCl}\_4\text{(g)}\tag{51}$$

$$\text{2 InP} \text{(s)} + \text{InI}\_3 \text{(g)} \xleftrightarrow{\text{2} InI} \text{(g)} + \text{1/2 P}\_4 \text{(g)}\tag{52}$$

The vapor of metal halides can consist of monomeric, dimeric and/or oligomeric molecules. With *M* = Al, Ga, In, Fe, Sc, Y, *Ln* (*Ln* = lanthanoides), one can observe particular large amounts of dimers *M*2*X*6. Trimers occur with copper(I) halides and silver halides. Metal halides of different components *A* and *B* can react in the gaseous state under the formation of *gas complexes* [32]. Such gas complexes are also formed during heterogeneous reactions between solid and gaseous halides. For example, gaseous aluminum(III) chloride reacts with a number of heavy volatile, solid metal chlorides under the formation of gas complexes. This way, their volatility is massively increased, often by orders of magnitude. These reactions can be used in vapor transport experiments [33]. This way, cobalt chloride can be transported with alumi‐ num(III) chloride (53) far below the boiling temperature (e.g. 400 → 350 °C) [34]. To date, numerous of these examples are known [34 - 37]. Thermodynamic data were determined for a considerable number of gas complexes [38] and empirical rules which can help estimating the thermodynamic data of gas complexes are laid down [36, 38].

$$\text{CoCl}\_2\text{(s)} + \text{Al}\_2\text{Cl}\_6\text{(g)} \xrightleftharpoons \text{CoAl}\_2\text{Cl}\_8\text{(g)}\tag{53}$$

**Oxide halides**. Gaseous oxide halides are known of few metals only, in particular of transition elements [39]. These molecules appear in particular in case of metals with high oxidation numbers. VO*X*3, NbO*X*3, TaO*X*3 (*X* = F…I), CrO2*X*2 (*X* = F…Br), MoO2*X*2, WO2*X*2 (*X* = F…I), MoO*X*4, WO*X*4 (*X* = F…Br), ReOCl4, OsO2Cl2, OsOCl4, RuOCl, ReO3*X* (*X* = F…I). Gaseous oxide halides can play an important part as transport effective species during the transport of oxides [40].

$$\text{SiC}\_2\text{(s)} + 2\text{ }\text{TaCl}\_5\text{(g)} \xrightleftharpoons \text{SiCl}\_4\text{(g)} + 2\text{ }\text{TaOCl}\_3\text{(g)}\tag{54}$$

$$\text{MoO}\_3\text{(s)} + \text{I}\_2\text{(g)} \xrightleftharpoons \text{MoO}\_2\text{I}\_2\text{(g)} + \text{1/2 O}\_2\text{(g)}\tag{55}$$

Some gaseous oxide halides are known of main group metals. Elements of group 13 form oxide halides, such as AlOCl, at very high temperatures around 2000 °C. Phosphorus forms several oxide chlorides and -bromides that are stable at high temperatures: PO*X*3, PO2*X*, and PO*X* (*X* = Cl, Br) [42]. For arsenic and antimony AsOCl and SbOCl are stable at high temperatures, however, oxide halides with the metal in the oxidation stage V are not known [42]. TeOCl2 is the most important oxide halide of the main group elements. This gas species plays an important role during the transport of numerous oxides with tellurium(IV) chloride [31].

( ) ( ) ( ) 4 2 *Si s SiI g SiI g* + ¬¾¾ ¾¾®2 (49)

( ) ( ) ( ) 32 4 *CrCl s Cl g CrCl g* + 1/ 2 ¬¾¾ ¾ ®¾ (51)

( ) ( ) ( ) ( ) 3 4 2*InP s InI g InI g P g* + + ¬¾¾ ¾¾®3 1 / 2 (52)

( ) ( ) ( ) *CoCl s Al Cl g CoAl Cl g* 2 26 2 8 + ¬¾¾ ¾¾® (53)

( ) ( ) ( ) ( ) 25 4 3 *SiO s TaCl g SiCl g TaOCl g* + + 2 2 ¬¾¾ ¾¾® (54)

¾¾®¾¾ + 1/ 2 (55)

¾¾®¾¾ + (50)

( ) ( ) ( ) ( ) 2 4 2 *TiO s HCl g TiCl g H O g* + 4 2 ¬

The vapor of metal halides can consist of monomeric, dimeric and/or oligomeric molecules. With *M* = Al, Ga, In, Fe, Sc, Y, *Ln* (*Ln* = lanthanoides), one can observe particular large amounts of dimers *M*2*X*6. Trimers occur with copper(I) halides and silver halides. Metal halides of different components *A* and *B* can react in the gaseous state under the formation of *gas complexes* [32]. Such gas complexes are also formed during heterogeneous reactions between solid and gaseous halides. For example, gaseous aluminum(III) chloride reacts with a number of heavy volatile, solid metal chlorides under the formation of gas complexes. This way, their volatility is massively increased, often by orders of magnitude. These reactions can be used in vapor transport experiments [33]. This way, cobalt chloride can be transported with alumi‐ num(III) chloride (53) far below the boiling temperature (e.g. 400 → 350 °C) [34]. To date, numerous of these examples are known [34 - 37]. Thermodynamic data were determined for a considerable number of gas complexes [38] and empirical rules which can help estimating

**Oxide halides**. Gaseous oxide halides are known of few metals only, in particular of transition elements [39]. These molecules appear in particular in case of metals with high oxidation numbers. VO*X*3, NbO*X*3, TaO*X*3 (*X* = F…I), CrO2*X*2 (*X* = F…Br), MoO2*X*2, WO2*X*2 (*X* = F…I), MoO*X*4, WO*X*4 (*X* = F…Br), ReOCl4, OsO2Cl2, OsOCl4, RuOCl, ReO3*X* (*X* = F…I). Gaseous oxide halides can play an important part as transport effective species during the transport of oxides

( ) ( ) ( ) ( ) 3 2 2 2 2 *MoO s I g MoO I g O g* + ¬

the thermodynamic data of gas complexes are laid down [36, 38].

[40].

248 Advanced Topics on Crystal Growth

**Elements in gaseous state**. The importance of elemental halogens for chemical vapor transport reactions was already mentioned. Other elements also often occur in gaseous state during transport reactions, especially gaseous non-metals. Gaseous species of elements of groups 15 and 16 are formed during the transport of pnictides or chalcogenides with halogens (56) or halogen compounds in many cases. In contrast, metal gas species play a role in only a few reactions. In particular, this behavior occurs, if the transport agent reacts with the non-metal instead of the metal atoms and the metal is sufficient volatile (57). The formation of an unsaturated metal vapor during transport reactions can only be expected if the boiling temperature of the metal is below approx. 1200 °C. This only applies to the following metals: Na (881 °C), K (763 °C), Rb (697 °C), Cs (657 °C), Mg (1093 °C), Zn (906 °C), Cd (766 °C), Hg (356 °C), Yb (1194 °C) and Te (989 °C).

$$\text{ZrAs}\_2\text{(s)} + 2\text{ I}\_2\text{(g)} \xrightleftharpoons \text{ZrI}\_4\text{(g)} + 1/2\text{ As}\_4\text{(g)}\tag{56}$$

$$ZnO(s) + H\_2(g) \xrightleftharpoons Zn(g) + H\_2O(g)\tag{57}$$

In some cases, gaseous elements can work as transport agents. Hence, oxygen can cause the transport of some platinum metals [40]. Sulfur can transport a series of transition metal sulfides [43]. Here, gaseous polysulfides, such as TaS3, are assumed transport effective species. There are similar observations for the chemical transport of some selenides. Sulfur is an effective transport agent for tellurium as well [44]. Compounds in which tellurium atoms were integrated in the different ring-shaped sulfur molecules were detected as transport effective species. Phosphorus can transport gallium phosphide, GaP, and indium phosphide, InP, probably via GaP5 respectively InP5 as transport effective species [45]. With the help of arsenic, the transport of gallium arsenide, GaAs, and indium arsenide, InAs, succeeded in a similar way [46].

Metal vapors predominantly consist of the atoms. The fraction of bi- or polyatomic molecules in the saturated vapor is between 10−5 and 10 % [47]. In contrast, the vapors of non-metals, apart from noble gases, consist of very stable polyatomic molecules which appear in the gas phase in great amounts, atoms appear only subordinated: N2, P4, P2, As4, As2, Sb4, Sb2, O2, S2, S3 … S7, S8, Se2, Se3 … Se7, Se8, Te2, Cl2, Br2, and I2. The ratio of different molecular species in the vapors of non-metals depends on the temperature and the pressure. Higher temperature and lower pressures abet the formation of small molecules respectively atoms.

**Hydrogen compounds**. Hydrogen compounds of non-metals play an important role for chemical vapor transport reactions. Hydrogen halides, which are often used as transport agents, are particularly important; for example during the transport of metal oxides. The example (58) shows that water vapor becomes transport effective species. However, water can also function as transport agent as for the transport of molybdenum(VI) oxide (59) and the one of germanium (60). Additionally, water can lead to the formation of transport effective gaseous hydroxides (61):

$$\text{MgO} \text{(s)} + 2\text{ HCl} \text{(g)} \xrightleftharpoons \text{MgCl}\_2 \text{(g)} + \text{H}\_2\text{O} \text{(g)}\tag{58}$$

$$\text{MoO}\_3\text{(s)} + \text{H}\_2\text{O}\text{(g)} \xrightleftharpoons \text{H}\_2\text{MoO}\_4\text{(g)}\tag{59}$$

( ) ( ) ( ) 24 3 *OsO s OsO g OsO g* + ¬¾¾ ¾¾®2 (63)

The role of non-metals is more important. Carbon monoxide can function as transport agent

Non-metal oxides occur as *transport effective species* for the transport of oxides. Thus, sulfuric

During the chemical transport of metal oxides, tellurium(IV) chloride plays a particular role, it reacts under the formation of a metal chloride or a metal oxide chloride and binds oxygen

Further gaseous oxides that are important for the transport of oxide compounds are amongst

**Other substance groups**. During some transport reactions, gaseous sulfides, selenides, tellurides or sulfide halides are of particular importance. Thus, boron can be volatilized in presence of sulfur or selenium; In this context, the molecules BS2 [52] and BSe2 [53] were detected. Aluminum also forms gaseous sulfides and selenides at high temperatures: Al2S, AlS, Al2S2, Al2Se, AlSe, Al2Se2 [54]. Gaseous sulfides, selenides and tellurides of group 14 are also known: SiS, SiSe, SiTe, GeS, GeSe, GeTe, SnS, SnSe, SnTe, PbS, PbSe, PbTe [54]. These molecules form dimers to a minor degree. Disulfides respectively diselenides of these elements are less

( ) ( ) ( ) ( ) ( ) 22 2 2 2 *SnO s I g S g SnI g SO g* + + 1/ 2 ¬

( ) ( ) ( ) ( ) 24 42 *TiO s TeCl g TiCl g TeO g* + ¬

( ) ( ) ( ) ( ) 2 2 *SnO s CO g SnO g CO g* + ¬

vapor can cause in presence of iodine the transport of tin(IV) oxide [51].

in form of TeO2(g) or TeOCl2(g) at the same time [31].

others: B2O3, SiO, P4O6, P4O10, As4O6, Sb4O6, SeO2.

stable. The gaseous monosulfide, PS, of sulfur is described [55].

in different ways [50]:

( ) ( ) ( ) 2 2 *Pt s O g PtO g* + ¬¾¾ ¾¾® (64)

( ) ( ) ( ) ( ) 4 *Ni s CO g Ni CO g* + 4¬¾¾ ¾¾® (66)

¾¾®¾¾ + (65)

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¾¾¾¾® + (67)

¾¾®¾¾ + (68)

( ) ( ) ( ) ( ) *MoO s TeCl g MoO Cl g TeOCl g* 3 4 2 2 2 + ¬¾¾¾®¾ + (69)

$$\text{Ge}(s) + H\_2\text{O}(\text{g}) \xrightleftharpoons \text{GeO}(\text{g}) + H\_2\text{(g)}\tag{60}$$

$$\text{Li}\_2\text{O}(\text{s}) + \text{H}\_2\text{O}(\text{g}) \xrightleftharpoons 2\text{LiOH}(\text{g})\tag{61}$$

The transport reaction of tungsten with water and iodine is an important one in daily life. This reaction provides the basis of the operating mode of halogen lamps.

$$\text{WO}(\text{s}) + 2\,\,^2H\_2\text{O}(\text{g}) + 3\,\,^2I\_2\text{(g)} \xrightleftharpoons \text{WO}\_2I\_2\text{(g)} + 4\,\,^1H\text{(g)}\tag{62}$$

Traces of water, often from the wall of the silica glass tubes, which were used during the transport, can be important for transport effects [48]. Hydrogen sulfide and hydrogen selenide also appear during the transport of sulfides respectively selenides with hydrogen halides. Hydrogen telluride is too unstable to develop under transport conditions. Ammonium chloride is particularly important. It decomposes to ammonia and hydrogen chloride during sublimation. Thus, it is a hydrogen chloride source which is easy to handle and easy to dose. Ammonia decomposes to the elements at higher temperature and thus creates a reducing atmosphere which effects the equilibria involved in the transport in different ways.

**Oxygen compounds**. The large amount of metal oxides decomposes completely or partly while heating to high temperatures. Gingerich provides a compilation of gaseous metal oxides and their stability [47]. Some metal oxides vaporize congruently: CrO3, MoO3, WO3, Re2O7, IrO3, RuO3, RuO4, OsO4, GeO, SnO, and PbO. In the vapors of CrO3, MoO3 and WO3 trimeric molecules appear as *M*3O9. SnO and PbO form dimers and trimers. Nevertheless, gaseous metal oxides play a subordinated role for chemical vapor transport reactions [40, 49]:

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$$\text{OsO}\_2(s) + \text{OsO}\_4(g) \xrightleftharpoons 2\text{ OsO}\_3(g) \tag{63}$$

$$Pt\text{ }(s) + O\_2\text{ }(g) \xrightleftharpoons PtO\_2\text{ }(g)\tag{64}$$

The role of non-metals is more important. Carbon monoxide can function as transport agent in different ways [50]:

**Hydrogen compounds**. Hydrogen compounds of non-metals play an important role for chemical vapor transport reactions. Hydrogen halides, which are often used as transport agents, are particularly important; for example during the transport of metal oxides. The example (58) shows that water vapor becomes transport effective species. However, water can also function as transport agent as for the transport of molybdenum(VI) oxide (59) and the one of germanium (60). Additionally, water can lead to the formation of transport effective gaseous

( ) ( ) ( ) ( ) 2 2 *MgO s HCl g MgCl g H O g* + 2 ¬

( ) ( ) ( ) ( ) *Ge s H O g GeO g H g* 2 2 + ¬

reaction provides the basis of the operating mode of halogen lamps.

The transport reaction of tungsten with water and iodine is an important one in daily life. This

Traces of water, often from the wall of the silica glass tubes, which were used during the transport, can be important for transport effects [48]. Hydrogen sulfide and hydrogen selenide also appear during the transport of sulfides respectively selenides with hydrogen halides. Hydrogen telluride is too unstable to develop under transport conditions. Ammonium chloride is particularly important. It decomposes to ammonia and hydrogen chloride during sublimation. Thus, it is a hydrogen chloride source which is easy to handle and easy to dose. Ammonia decomposes to the elements at higher temperature and thus creates a reducing

**Oxygen compounds**. The large amount of metal oxides decomposes completely or partly while heating to high temperatures. Gingerich provides a compilation of gaseous metal oxides and their stability [47]. Some metal oxides vaporize congruently: CrO3, MoO3, WO3, Re2O7, IrO3, RuO3, RuO4, OsO4, GeO, SnO, and PbO. In the vapors of CrO3, MoO3 and WO3 trimeric molecules appear as *M*3O9. SnO and PbO form dimers and trimers. Nevertheless, gaseous metal

atmosphere which effects the equilibria involved in the transport in different ways.

oxides play a subordinated role for chemical vapor transport reactions [40, 49]:

¾¾®¾¾ + (58)

¾¾®¾¾ + (60)

( ) ( ) ( ) *MoO s H O g H MoO g* 3 2 24 + ¬¾¾ ¾¾® (59)

( ) ( ) ( ) 2 2 *Li O s H O g LiOH g* + ¬¾¾ ¾¾®2 (61)

( ) ( ) ( ) ( ) ( ) 2 2 2 2 *W s H O g I g WO I g HI g* + + 2 3 ¬¾¾ ¾¾® + 4 (62)

hydroxides (61):

250 Advanced Topics on Crystal Growth

$$\text{SnO}\_2\text{(s)} + \text{CO(g)} \xrightarrow{\text{(g)}} \text{SnO(g)} + \text{CO}\_2\text{(g)}\tag{65}$$

$$\text{Ni}(\text{s}) + 4\text{ CO}(\text{g}) \xrightleftharpoons \text{Ni}(\text{CO})\_4(\text{g})\tag{66}$$

Non-metal oxides occur as *transport effective species* for the transport of oxides. Thus, sulfuric vapor can cause in presence of iodine the transport of tin(IV) oxide [51].

$$\text{SnO}\_2\text{(s)} + \text{I}\_2\text{(g)} + \text{I} / 2 \text{ S}\_2\text{(g)} \rightleftharpoons \text{SnI}\_2\text{(g)} + \text{SO}\_2\text{(g)}\tag{67}$$

During the chemical transport of metal oxides, tellurium(IV) chloride plays a particular role, it reacts under the formation of a metal chloride or a metal oxide chloride and binds oxygen in form of TeO2(g) or TeOCl2(g) at the same time [31].

$$\text{TiO}\_2\text{(s)} + \text{TeCl}\_4\text{(g)} \xrightleftharpoons \text{TiCl}\_4\text{(g)} + \text{TeO}\_2\text{(g)}\tag{68}$$

$$\text{MoO}\_3\text{(s)} + \text{TeCl}\_4\text{(g)} \xrightleftharpoons \text{MoO}\_2\text{Cl}\_2\text{(g)} + \text{TeOCl}\_2\text{(g)}\tag{69}$$

Further gaseous oxides that are important for the transport of oxide compounds are amongst others: B2O3, SiO, P4O6, P4O10, As4O6, Sb4O6, SeO2.

**Other substance groups**. During some transport reactions, gaseous sulfides, selenides, tellurides or sulfide halides are of particular importance. Thus, boron can be volatilized in presence of sulfur or selenium; In this context, the molecules BS2 [52] and BSe2 [53] were detected. Aluminum also forms gaseous sulfides and selenides at high temperatures: Al2S, AlS, Al2S2, Al2Se, AlSe, Al2Se2 [54]. Gaseous sulfides, selenides and tellurides of group 14 are also known: SiS, SiSe, SiTe, GeS, GeSe, GeTe, SnS, SnSe, SnTe, PbS, PbSe, PbTe [54]. These molecules form dimers to a minor degree. Disulfides respectively diselenides of these elements are less stable. The gaseous monosulfide, PS, of sulfur is described [55].

Gaseous sulfide halides or selenide halides are known of only a few elements. For example, PS*X*3 and PS*X* (*X* = F, Cl, Br) [42] for phosphorus are described. Niobium forms the gaseous sulfide halides respectively selenide halides NbSCl3, NbSBr3, NbSeBr3 [56], for tantalum TaSCl3 and TaSeBr3 are known [56]; the transport effectiveness of MoSBr was mentioned [57]. Tungsten forms two volatile sulfide chlorides, WS2Cl2 [39] and WSCl4 [58]. The thermodynamic data of WS2*X*2 (*X* = Cl, Br, I) were determined [59]. The transport effectiveness of the hydrated oxide halides, Bi(OH)2*X* (*X* = Cl, Br, I), was reported [60]. Finally, Pt(CO)2Cl2 is a gaseous compound that becomes transport effective during the transport of platinum with carbon monoxide and chlorine [61].

halogenating and thus form gaseous halides with the transporting elements. Additionally, they stabilize them by forming gaseous complexes. Halogens such as fluorine, chlorine and bromine as well as the hydrogen halides, water, the chalcogens oxygen, sulfur, selenium, tellurium as well as carbon monoxide are other transport agents which can be used in individual cases. Although carbon monoxide can be used for the transport of nickel only, the industrial purifying process according to Mond and Langer found its way into chemistry textbooks, making carbon monoxide particularly prominent as a transport agent [66]. More details and references of CVT

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**Iodine as transport agent**. The exothermic transport of an element with iodine from *T*1 to *T*2 is the most frequently described transport reaction involving metals. This reaction type were studied and described extensively for titanium, zirconium, hafnium, and thorium (process of van Arkel and de Boer) [67 -70]. Further elements which can be transported this way are yttrium, vanadium, niobium, tantalum, chromium, iron, cobalt, nickel, copper, boron, silicon, germanium and tin as well as uranium and protactinium [63, 64, 71 - 75]. This kind of transport to the hotter zone shall be illustrated with the example of the transport of zirconium with iodine. The temperatures of the dissolving side *T*1 can vary between 200 and 650 °C. The most suitable temperature is between 350 and 400 °C. The temperatures of the decomposing side *T*2 can be between 1100 and 2000 °C; whereby temperatures around 1400 °C are usually applied. Often, a wire heated by current flow is the place of decomposition. The transport behavior is

() ( ) ( ) 2 4 *Zr s I g ZrI g* + 2¬¾¾ ¾¾® (70)

() ( ) ( ) *Zr s I g ZrI g* 2 2 + ¬¾¾ ¾¾® (71)

of the elements are presented in [2].

described by the equilibria (70 – 72), Figure 15.

**Figure 15.** Partial pressures of species in the transport system Zr/I.

### **3.2. Chemical vapor transport of elements and compounds**

To date the chemical vapor transport of almost all substance classes has been described. This chapter will show characteristic examples of different transport reactions. A comprehensive overview with more than 2000 references of CVT is not intended here. For more details and references of CVT of elements and compounds see [2]. The chemical vapor transport of elements has been studied and described in detail using metals and some semi-metals as examples; the transport of intermetallic phases principally follows the one of metals. The oxides are the largest group among all compounds which were crystallized by chemical transport reactions with more than 600 examples. The transport of chalcogenides clearly differs from the ones of the oxides. This is due to the higher thermodynamic stability of the metal oxides, compared to the sulfides, selenides, and tellurides. Finally, the chemical vapor transport provides a very good access to phosphides and arsenides, too.

#### *3.2.1. Chemical vapor transport of elements*

The chemical transport of elements has been studied and described in detail using metals and some semi-metals as examples. In the case of the typical non-metals phosphorus and sulfur, there is no need to increase their volatility in the sense of a chemical vapor transport reaction due to their high vapor pressures. This way, those metals and semi-metals which feature high vapor pressures can also easily be transferred into the gas phase through distillation or sublimation. The following elements belong to this group: Alkali and alkaline earth metals, zinc, cadmium, mercury, europium, ytterbium, arsenic, antimony, selenium and tellurium. Some metals' melting temperature is that low that they can be obtained in liquid form at the most. This, for example, applies for gallium, tin and lead. Thus, chemical vapor transports are relevant for high melting elements with low vapor pressures. These elements can be deposited from the gas phase in closed reaction vessels (ampoules), fluid systems, special reactors (hotwire process according to (Van Arkel und De Boer), or through CVD-processes [62]. All of these processes are based on the same thermodynamic basic principles. This way, more than 40 elements can be crystallized with chemical transport reactions, more than 25 with iodine as transport agent [63, 64].

In addition to iodine as most important transport agent for elements, compounds such as aluminum(III) chloride, gallium(III) chloride and iron(III) chloride as well as aluminum(III) iodide and indium(III) iodide are described as transport effective additive [65]. These can act halogenating and thus form gaseous halides with the transporting elements. Additionally, they stabilize them by forming gaseous complexes. Halogens such as fluorine, chlorine and bromine as well as the hydrogen halides, water, the chalcogens oxygen, sulfur, selenium, tellurium as well as carbon monoxide are other transport agents which can be used in individual cases. Although carbon monoxide can be used for the transport of nickel only, the industrial purifying process according to Mond and Langer found its way into chemistry textbooks, making carbon monoxide particularly prominent as a transport agent [66]. More details and references of CVT of the elements are presented in [2].

**Iodine as transport agent**. The exothermic transport of an element with iodine from *T*1 to *T*2 is the most frequently described transport reaction involving metals. This reaction type were studied and described extensively for titanium, zirconium, hafnium, and thorium (process of van Arkel and de Boer) [67 -70]. Further elements which can be transported this way are yttrium, vanadium, niobium, tantalum, chromium, iron, cobalt, nickel, copper, boron, silicon, germanium and tin as well as uranium and protactinium [63, 64, 71 - 75]. This kind of transport to the hotter zone shall be illustrated with the example of the transport of zirconium with iodine. The temperatures of the dissolving side *T*1 can vary between 200 and 650 °C. The most suitable temperature is between 350 and 400 °C. The temperatures of the decomposing side *T*2 can be between 1100 and 2000 °C; whereby temperatures around 1400 °C are usually applied. Often, a wire heated by current flow is the place of decomposition. The transport behavior is described by the equilibria (70 – 72), Figure 15.

**Figure 15.** Partial pressures of species in the transport system Zr/I.

Gaseous sulfide halides or selenide halides are known of only a few elements. For example, PS*X*3 and PS*X* (*X* = F, Cl, Br) [42] for phosphorus are described. Niobium forms the gaseous sulfide halides respectively selenide halides NbSCl3, NbSBr3, NbSeBr3 [56], for tantalum TaSCl3 and TaSeBr3 are known [56]; the transport effectiveness of MoSBr was mentioned [57]. Tungsten forms two volatile sulfide chlorides, WS2Cl2 [39] and WSCl4 [58]. The thermodynamic data of WS2*X*2 (*X* = Cl, Br, I) were determined [59]. The transport effectiveness of the hydrated oxide halides, Bi(OH)2*X* (*X* = Cl, Br, I), was reported [60]. Finally, Pt(CO)2Cl2 is a gaseous compound that becomes transport effective during the transport of platinum with carbon

To date the chemical vapor transport of almost all substance classes has been described. This chapter will show characteristic examples of different transport reactions. A comprehensive overview with more than 2000 references of CVT is not intended here. For more details and references of CVT of elements and compounds see [2]. The chemical vapor transport of elements has been studied and described in detail using metals and some semi-metals as examples; the transport of intermetallic phases principally follows the one of metals. The oxides are the largest group among all compounds which were crystallized by chemical transport reactions with more than 600 examples. The transport of chalcogenides clearly differs from the ones of the oxides. This is due to the higher thermodynamic stability of the metal oxides, compared to the sulfides, selenides, and tellurides. Finally, the chemical vapor