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== Introduction  ==
== Introduction  ==


Much of our cultural heritage is constituted  by porous inorganic materials such as stone, brick, mortars and renders. Salts will enter these porous materials, e.g., from rising damp, and their crystallization in the pores will lead to their deterioration; a process that depends on the relative humidity (RH) and temperature. When the RH decreases, water from the salt solution will be released into the atmosphere until the deliquescence relative humidity (DRH) of the salt in question is reached. At this point, all the salt will be crystallized. If the RH increases, surpassing the DRH, the salt will absorb water vapor from the air and tend to form a saturated solution and, if the RH continues to increase, it will be further diluted. This shows that changes in RH around the DRH of the salt will lead to alternating crystallization and deliquescence cycles. This changes are responsible for the deterioration induced by these cycles that can be attributed to crystallization pressure; repeated cycling inducing more damage. One of the critical factors in developing an effective crystallization pressure is the formation of a supersaturated solution  <bib id="Steiger:2005"/>. Crystallization from a supersaturated solution will not occur when reaching the saturation concentration or temperature, where a saturated solution should be formed, but at a lower RH or temperature. Supersaturated solutions form through water vapor evaporation, if for example, the RH drops, or by lowering temperature (note did not include oder nach Flüssigwassereintrag because it does not make sense to me).  Dissolution of a metastable phase can result in a supersaturated solution, which will be discussed a following section <bib id="Steiger.etal:2008"/>.
Much of our cultural heritage is constituted  by porous inorganic materials such as stone, brick, mortars and renders. Salts will enter these porous materials, e.g., from rising damp, and their crystallization in the pores will lead to the materials' deterioration; a process that depends on the relative humidity (RH) and temperature. When the RH decreases, water from the salt solution will be released into the atmosphere until the deliquescence relative humidity (DRH) of the salt in question is reached, at this point a saturated solution will result; while below it the salt will crystallize. If the RH increases, exceeding the DRH, the salt will absorb water vapor from the air and tend to form a saturated solution and, if the RH continues to increase, it will be further diluted. This shows that changes in RH around the DRH of the salt will lead to alternating crystallization and deliquescence cycles. The cycling around the DRH is responsible for the deterioration induced and that can be attributed to crystallization pressure; repeated cycling inducing more damage. One of the critical factors in developing an effective crystallization pressure is the formation of a supersaturated solution  <bib id="Steiger:2005"/>. Crystallization from a supersaturated solution will only occur at a lower RH or temperature than those required for forming saturated solutions. Supersaturated solutions form through water vapor evaporation, if for example, the RH drops, or by lower temperatures.  Dissolution of a metastable phase can result in a supersaturated solution, which will be discussed a following section <bib id="Steiger.etal:2008"/>. Whether the presence of salts will result in a deterioration process depends on the nature of the salt, or salt-mixture, and its properties, but mainly by the environmental conditions, including the amount of water vapor available. These mechanisms, based on theoretical models, are only applicable for porous inorganic materials.
 
Whether the presence of salts will result in a deterioration process depends on the nature of the salt, or saltmixture, and its properties, but mainly by the environmental condition including the amount of water vapor available. These mechanisms, based on theoretical models, are only applicable for porous inorganic materials.


==Crystallization within a pore==
==Crystallization within a pore==


The concentration of a salt solution within a pore will depend on environmental factors such as relative humidity (RH) and temperature (T). In the RH drops, the concentration will increase as water vapor will be released from the solution; if the amount evaporated is such that the solubility of the salt in question is attained, then crystallization of the salt will occur. This RH is known as the deliquescence RH (DRH). Capillary transportation of the solution to the material's surface, where the main evaporation occurs, will increase the evaporation rate. As drying continues, the evaporation front will move into the interior of the porous material, as the evaporated moisture will move faster than the capillary movement to the evaporation front <bib id="Hall.etal:1984"/>. Therefore, salts transported by the solution can crystallize both on the material's surface, i.e., efflorescence, as well as in the area below the surface as a subflorescence. Where crystallization will actually occur depends on the drying conditions, the composition of the salt solution in question, its concentration and the material's properties <bib id="Espinosa-Marzal.etal:2010"/>.
The concentration of a salt solution within a pore will depend on environmental factors such as relative humidity (RH) and temperature (T). When the RH drops, the concentration will increase as water vapor will be released from the solution; if the amount evaporated is such that the solubility of the salt in question is attained, then crystallization of the salt will occur. This RH is known as the deliquescence RH (DRH). Capillary transportation of the solution to the material's surface, where the main evaporation occurs, will increase the evaporation rate. As drying continues, the evaporation front will move into the interior of the porous material, as the evaporated moisture will move faster than the capillary movement to the evaporation front <bib id="Hall.etal:1984"/>. Therefore, salts transported by the solution can crystallize both on the material's surface, i.e., efflorescence, as well as in the area below the surface as subflorescence. Where crystallization will actually occur depends on the drying conditions, the composition of the salt solution in question, its concentration and the material's properties <bib id="Espinosa-Marzal.etal:2010"/>.


==Historical Background==
==Historical Background==


Currently, our understanding of the models to explain the deterioration of porous materials and crystallization pressure from salts resulted in some controversial discussions since the 20th century. The growth of a crystal in the presence of obstacles was understood as a linear crystallization pressure (u.a. <bib id="Becker.etal:1916"/>, <bib id="Taber:1916"/>, <bib id="Correns.etal:1939"/>, <bib id="Duttlinger.etal:1993"/>). A growing crystal, when it crystallizes from a supersaturated solution, can generate a maximum pressure when it grows along a crystal surface and reaches an obstacle. A film solution should be present between the crystal surface and the obstacle to allow its ongoing growth <bib id="Taber:1916"/>. Important studies have been carried out by  <bib id="Correns:1926"/>, who classified the crystallization pressure as a function of the volume increase of the crystal (hydrostatic crystallization pressure), hydration pressure as well as those referred to as linear crystallization pressure.
Currently, our understanding of the models to explain the deterioration of porous materials and crystallization pressure from salts resulted from controversial discussions since the 20th century. The growth of a crystal in the presence of obstacles was referred to as linear crystallization pressure (e.g., <bib id="Becker.etal:1916"/>, <bib id="Taber:1916"/>, <bib id="Correns.etal:1939"/>, <bib id="Duttlinger.etal:1993"/>). A growing crystal, when it crystallizes from a supersaturated solution, can generate a maximum pressure when growing in one direction and reaching an obstacle; a film solution is present between the crystal surface and the obstacle to allow its ongoing growth <bib id="Taber:1916"/>. Important studies have been carried out by  <bib id="Correns:1926"/>, who classified the crystallization pressure as a function of the volume increase of the crystal (hydrostatic crystallization pressure), hydration pressure as well as those referred to as linear crystallization pressure.


However, others (<bib id="Taber:1916"/>), pointed out the influence of the interfacial energy that should have a given value so that the crystallization could take place. He pointed out that a growing crystal is not attached to the surface, there being a solution film between it and the surface, to allow for an ion exchange to  take place, and that can be attributed to the inter-facial energy between crystal and pore-wall (<bib id="Correns:1926"/>, <bib id="Bruhns.etal:1913"/>, <bib id="Weyl:1959"/>.
However, others (<bib id="Taber:1916"/>), pointed out the influence of the inter-facial energy that should reach a given value so that the crystallization could take place. He pointed out that a growing crystal is not attached to the surface, there being a solution film between it and the surface, to allow for an ion exchange to  take place, and that can be attributed to the inter-facial energy between crystal and pore-wall (<bib id="Correns:1926"/>, <bib id="Bruhns.etal:1913"/>, <bib id="Weyl:1959"/>.


Some experiments, where both a loaded and an unloaded alum crystal in a saturated solution, showed that only the unloaded crystal grew thus requiring a re-examination of the linear crystallization pressure, and that furthermore the pressure developed could be correlated better with a volume increase rather than the pressure of the crystal. This could also be applied to the hydration pressure, since an anhydrous or a low hydrated phase would have a smaller volume than the fully hydrated one (<bib id="Bruhns.etal:1913"/>). The hydrostatic pressure is given by the increased volume resulting from the crystallization of the salt, since the volume of salt and saturated solution is greater than that of the supersaturated solution. Relevant contributions regarding the hydration pressure can be found <bib id="Mortensen:1933"/>, who found that the hydration pressure of an unhydrous crystal could be calculated as follows;
Some experiments, where both a loaded and an unloaded alum crystal in a saturated solution were grown, showed that only the unloaded crystal grew thus requiring a re-examination of the linear crystallization pressure, and that furthermore the pressure developed could be correlated better with a volume increase rather than the pressure of the crystal. This could also be applied to the hydration pressure, since an anhydrous or a low hydrated phase would have a smaller volume than the fully hydrated one (<bib id="Bruhns.etal:1913"/>). The hydro-static pressure is given by the increased volume resulting from the crystallization of the salt, since the volume of salt and saturated solution is greater than that of the supersaturated solution. Relevant contributions regarding the hydration pressure can be found in <bib id="Mortensen:1933"/>, who realized that the hydration pressure of an anhydrate crystal could be calculated as follows;


Δ<i>p</i><sub>hydr</sub>=(Δ<i>nRT</i>/Δ<i>V</i><sub>m</sub>)∙ln(RH/RH<sub>eq</sub>)  (Eq.1)
Δ<i>p</i><sub>hydr</sub>=(Δ<i>nRT</i>/Δ<i>V</i><sub>m</sub>)∙ln(RH/RH<sub>eq</sub>)  (Eq.1)


where Δ<i>n</i> is the difference in water molecules per moles of salt of the lower hydrate <i>n</i><sub>1</sub> with the higher hydrate <i>n</i><sub>2</sub>; Δ<i>V</i><sub>m</sub> is the difference between the molar volume of both phases; RH the relative humidity at which the hydration reaction occurs, and RH<sub>eq</sub> the equilbrium moisture at the temperature <i>T</i> corresponding to the hydration-dehydration equilibriumt. The hydration pressure corresponds to the maximum developed pressure that a growing crystal of the higher hydration can exert on the pore wall, since at a higher pressure, dehydration would result <bib id="Mortensen:1933"/>, <bib id="Steiger.etal:2014"/>.
where Δ<i>n</i> is the difference in water molecules per mole of salt of the lower hydrate <i>n</i><sub>1</sub> with the higher hydrate <i>n</i><sub>2</sub>; Δ<i>V</i><sub>m</sub> is the difference between the molar volume of both phases; RH the relative humidity at which the hydration reaction occurs, and RH<sub>eq</sub> the equilibrium moisture at the temperature <i>T</i> corresponding to the hydration-dehydration equilibrium. The hydration pressure corresponds to the maximum developed pressure that a growing crystal at higher hydration can exert on the pore wall, since at a higher pressure, dehydration would result <bib id="Mortensen:1933"/>, <bib id="Steiger.etal:2014"/>.


Both Correns and Steinborn (<bib id="Correns.etal:1939"/>) also studied the "crystallization pressure". For the case of the "linear growth pressure" they gave a formula for the chemical potentials for which the degree of supersaturation of the solution defined the intensity of the developed pressure, as follows:
Both Correns and Steinborn (<bib id="Correns.etal:1939"/>) also studied the "crystallization pressure". For the case of the "linear growth pressure" they gave a formula for the chemical potentials for which the degree of supersaturation of the solution defined the intensity of the developed pressure, as follows:
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Since their various experiments using different crystal surfaces always produced lower values than the theoretical ones, they attributed this to the different inter-facial energies. In subsequent equations, the crystallization pressure was also given as a function of the supersaturation, which allowed different ways of expressing them (e.g., <bib id="Goranson:1940"/>, <bib id="Buil:1983"/>).  
Since their various experiments using different crystal surfaces always produced lower values than the theoretical ones, they attributed this to the different inter-facial energies. In subsequent equations, the crystallization pressure was also given as a function of the supersaturation, which allowed different ways of expressing them (e.g., <bib id="Goranson:1940"/>, <bib id="Buil:1983"/>).  


Everett (<bib id="Everett:1961"/> considered the crystalization of ice and suggested a theory through which the crystallization pressure was the consequence of stability differences of the larger crystals. These stability differences result from differences in curvature of the interface between the solid and the liquid phases, which lead to different chemical potential for crystals with different sizes. However, he did not consider the supersaturation, his equation:
Everett (<bib id="Everett:1961"/>) considered the crystallization of ice and suggested a theory through which the crystallization pressure was the consequence of stability differences between the larger crystals. These differences result from the disparities in curvature at the interface between the solid and liquid phases, which lead to different chemical potential for crystals with different sizes. However, he did not consider the supersaturation, his equation:


∆<i>p</i>=<i>γ</i><sub>cl</sub>∙(d<i>A</i>/d<i>V</i>)  (Eq. 3)
∆<i>p</i>=<i>γ</i><sub>cl</sub>∙(d<i>A</i>/d<i>V</i>)  (Eq. 3)


describes the pressure differences between two crystals of different size; where <i>γ</i><sub>cl</sub> is the interfacial energy between the solid and the liquid phase, <i>A</i> is the surface, and <i>V</i> is the volume. For spherical crystals this can be rewritten   
describes the pressure differences between two crystals of different size; where <i>γ</i><sub>cl</sub> is the inter-facial energy between the solid and the liquid phase, <i>A</i> is the surface, and <i>V</i> is the volume. For spherical crystals this can be rewritten   


∆<i>p</i>=2<i>γ</i><sub>cl</sub>∙[(1/<i>r</i><sub>1</sub>)-(1/<i>r</i><sub>2</sub>)]  (Eq. 4)
∆<i>p</i>=2<i>γ</i><sub>cl</sub>∙[(1/<i>r</i><sub>1</sub>)-(1/<i>r</i><sub>2</sub>)]  (Eq. 4)


The pressure that develops through crystal growth in the larger pores with the radius <i>r</i><sub>2</sub> is appropriate, since crystal growth in the smaller pores is not thermodynamically favored. The crystal developing in larger pores will grow as long as the chemical potential of the crystal corresponds to that of a crystal in the smaller pore <i>r</i><sub>1</sub> (<bib id="Everett:1961"/>, <bib id="Steiger:2005"/>).
The pressure that develops through crystal growth in the larger pores with the radius <i>r</i><sub>2</sub> is appropriate, since crystal growth in smaller pores is not thermodynamically favored. The crystal developing in a larger pore will grow as long as the chemical potential of the crystal corresponds to that of a crystal in the smaller pore <i>r</i><sub>1</sub> (<bib id="Everett:1961"/>, <bib id="Steiger:2005"/>).


The two approaches of Correns and Everett were considered contradictory deterioration mechanisms for many years, since one considered supersaturation and the other the crystal curvature as responsible for the crystallization pressure developed. Both approaches were followed in parallel, and that of Correns was criticized by its very high supersaturation. In the case of the Everett theory, because data for the reliable pore sizes were available, which is not the case for the supesaturation
The two approaches of Correns and Everett were considered contradictory deterioration mechanisms for many years, since one considered supersaturation and the other the crystal curvature as responsible for the crystallization pressure developed. Both approaches were followed in parallel, and that of Correns was criticized by its very high supersaturation. In the case of the Everett theory, because data for the reliable pore sizes were available, it was reconsidered, which was not the case for the supersaturation <bib id="Steiger:2005"/>.
<bib id="Steiger:2005"/>.


==Crystallization Pressure==
==Crystallization Pressure==


Deterioration of a porous material from salt crystallization can only occure when the crystal(s) grows in a supersaturated solution against an obstacle, such as a pore wall (e.g. <bib id="Correns.etal:1939"/>). As the crystal grows further, a mechanical load, i.e., tension, is applied to the porous material. Another requirement for crystal growth against a wall is the presence of a solution film between the crystal and the wall <bib id="Weyl:1959"/> (a thickness of about 1 nm <bib id="Scherer:1999"/>) through which the ion transport can occur. The reason for the presence of this solution film are the repulsive forces between the crystal and the pore wall, otherwise there would be no further growth <bib id="Steiger:2005"/>. In tests where a crystal was clamped between two glass-plates to evaluate the developed force, the presence of the solution film between crystal and glass-plates could be visually observed and its relevance confirmed <bib id="Desarnaud.etal:2016"/>. The repulsive pressure between the two components defines the maximal crystallization pressure, since if this value is increased a direct contact between crystal and wall would result in ending the crystal growth. Since the repulsive pressure has a slight dependence on the wetting properties and the surface charge, this implies that different salts and porous materials will develop diverse crystallization pressures <bib id="Desarnaud.etal:2016"/>.
Deterioration of a porous material from salt crystallization can only occur when the crystal(s) grows in a supersaturated solution against an obstacle, such as a pore wall (e.g., <bib id="Correns.etal:1939"/>). As the crystal grows further, a mechanical load, i.e., strain, is applied to the porous material. Another requirement for crystal growth against a wall is the presence of a solution film between the crystal and the wall <bib id="Weyl:1959"/> (a thickness of about 1 nm <bib id="Scherer:1999"/>) through which the ion transport can occur. The reason for the presence of this solution film are the repulsive forces between the crystal and the pore wall, otherwise there would be no further growth <bib id="Steiger:2005"/>. In tests where a crystal was clamped between two glass-plates to evaluate the developed force, the presence of the solution film between crystal and glass-plates could be visually observed and its relevance confirmed <bib id="Desarnaud.etal:2016"/>. The repulsive pressure between the two components defines the maximal crystallization pressure, since if this value is increased a direct contact between crystal and wall would result thus ending the crystal growth. Since the repulsive pressure has a slight dependence on the wetting properties and the surface charge, this implies that different salts and porous materials will develop diverse crystallization pressures <bib id="Desarnaud.etal:2016"/>.


A crystal growing in a pore is exposed to an anisotropic pressure. Those faces/surfaces of the crystal which grow towards the pore-wall, are subjected to a higher pressure than the free surfaces in contact with the solution and subjected to its hydrostatic pressure. The difference between these two pressures is the crystallization pressure. Since crystal solubility is dependent on the applied pressure and increases with it, the free, unloaded surfaces/faces and those that are loaded, i.e., under pressure, will have different solubilities. This means, that comparing the concentration of the solution at the loaded face with that found by the free surface, the latter will be supersaturated <bib id="Steiger:2005"/>. The equation for the crystallization pressure can be given as:     
A crystal growing in a pore is exposed to anisotropic pressure. Those faces/surfaces of the crystal which grow towards the pore-wall, are subjected to a higher pressure than the free surfaces in contact with the solution and subjected to its hydrostatic pressure. The difference between these two pressures is the crystallization pressure. Since crystal solubility is dependent on the applied pressure and increases with it, the free, unloaded surfaces/faces and those that are loaded, i.e., under pressure, will have different solubilities. This means, that comparing the concentration of the solution at the loaded face with that found by the free surface, the latter will be supersaturated <bib id="Steiger:2005"/>. The equation for the crystallization pressure can be given as:     


∆<i>p</i>=(<i>RT</i>/<i>V</i><sub>m</sub>)∙ln(<i>a</i>/<i>a</i><sub>0</sub>) (Eq. 5).
∆<i>p</i>=(<i>RT</i>/<i>V</i><sub>m</sub>)∙ln(<i>a</i>/<i>a</i><sub>0</sub>) (Eq. 5).


where ∆<i>p</i> is the crystallization pressure, i.e., the difference between the pressure on a loaded face <i>p</i><sub>c</sub> and the hydrostatic pressure of the free faces <i>p</i><sub>l</sub>; <i>a</i> is the activity of the supersaturated solution and <i>a</i><sub>0</sub> that of the saturated solution. By using activities the non-ideal behaviour of the salt solutions is considered <bib id="Steiger:2005"/>.
where ∆<i>p</i> is the crystallization pressure, i.e., the difference between the pressure on a loaded face <i>p</i><sub>c</sub> and the hydrostatic pressure of the free faces <i>p</i><sub>l</sub>; <i>a</i> is the activity of the supersaturated solution, and <i>a</i><sub>0</sub> that of the saturated solution. By using activities the non-ideal behaviour of the salt solutions is taken into account <bib id="Steiger:2005"/>.


This equation shows a significant similarity to that suggested by Correns and Steinborn (<bib id="Correns.etal:1939"/>), however, we are considering the non-ideal behaviour of salt solutions by using the activity instead of concentrations. Furthermore, Correns neglected the anisotropic pressure to which the crystal is subjected.
This equation shows a significant similarity to that suggested by Correns and Steinborn (<bib id="Correns.etal:1939"/>), however, we are considering the non-ideal behaviour of salt solutions by using the activity instead of concentrations. Furthermore, Correns neglected the anisotropic pressure to which the crystal is subjected.


A pressure develops on the pore structure when the unloaded crystal face is in contact with the supersaturated solution, since the supersaturation will be decreased by the crystal growth of the unloaded crystal face (as long as they are available). This reduces the supersaturation and the pressure on the loaded face cannot be sustained. Since the original solution was saturated with regards to the loaded face, it will fall below saturation which will result in the dissolution of the loaded face thus reducing the pressure to maintain the equilibrium. Both these effects lead to short-term high crystallization pressures that only can operate under supersaturated conditions. Therefore, the pressure build-up through crystallization does not occur under equilibrium conditions; it depends on a kinetic and dynamic process that is subjected to diffusion and crystal growth rate of unloaded crystal faces (<bib id="Steiger:2009"/>, <bib id="Scherer:2004"/>).
A pressure develops on the pore structure when the unloaded crystal face is in contact with the supersaturated solution, since the supersaturation will be decreased by the crystal growth of the unloaded crystal face (as long as they are available). This reduces the supersaturation and the pressure on the loaded face cannot be sustained. Since the original solution was saturated with regards to the loaded face, it will fall below saturation which will result in the dissolution of the loaded face thus reducing the pressure to maintain equilibrium. Both these effects lead to short-term high crystallization pressures that can only operate under supersaturated conditions. Therefore, the pressure build-up through crystallization does not occur under equilibrium conditions; it depends on a kinetic and dynamic process that is subjected to diffusion and crystal growth rate of unloaded crystal faces (<bib id="Steiger:2009"/>, <bib id="Scherer:2004"/>).


==Expansion==
==Clarification==


When a salt dissolves, the following equation applies:
When a salt dissolves, the following equation applies:
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The activity of the dissolved salt is <i>a</i>=<i>a</i><sub>M</sub><sup><i>ν</i><sub>M</sub></sup>∙<i>a</i><sub>X</sub><sup><i>ν</i><sub>X</sub></sup>∙<i>a</i><sub>w</sub><sup><i>ν</i><sub>0</sub></sup>, the ion activity product, where <i>a</i><sub>w</sub> is the water activity.
The activity of the dissolved salt is <i>a</i>=<i>a</i><sub>M</sub><sup><i>ν</i><sub>M</sub></sup>∙<i>a</i><sub>X</sub><sup><i>ν</i><sub>X</sub></sup>∙<i>a</i><sub>w</sub><sup><i>ν</i><sub>0</sub></sup>, the ion activity product, where <i>a</i><sub>w</sub> is the water activity.


Expressing the activity as the activity coefficient and the molality <i>a</i><sub>i</sub>=<i>γ</i><sub>i</sub>∙(<i>m</i><sub>i</sub>/m<sup>0</sup>)
Expressing the activity as the activity coefficient and the molality as <i>a</i><sub>i</sub>=<i>γ</i><sub>i</sub>∙(<i>m</i><sub>i</sub>/m<sup>0</sup>), where <i>a</i><sub>i</sub> corresponds to the ion activity; <i>γ</i><sub>i</sub> the activity coefficient of the ions; <i>m</i><sub>i</sub> the molality of the ions in the solution, and where <i>m</i><sup>0</sup>=1 mol/kg, then the crystallization pressure of a crystal in contact with the solution can be calculated, as long as the activity coefficients and the water activity are known. 


where <i>a</i><sub>i</sub> corresponds to the ion activity; <i>γ</i><sub>i</sub> the acitivity coefficient of the ions; <i>m</i><sub>i</sub> the molaliry of the ions in the solution, and, where <i>m</i><sup>0</sup>=1 mol/kg, then the crystallization pressure of a crystal in contact with the solution can be calculated, as long as the activity coefficients and the water activity are known. 
It follows then that a more detailed equation for Δ<i>p</i> can be found. In case of a single salt, it is possible to introduce an average activity coefficient   
Δ<i>p</i>
<i>γ</i><sup>±</sup>=(<i>γ</i><sub>M</sub><sup><i>ν</i><sub>M</sub></sup><i>γ</i><sub>X</sub><sup><i>ν</i><sub>X</sub></sup>)<sup>(1/<i>ν</i>)</sup> but taking into consideration the simplification <i>m</i><sub>i</sub>=<i>ν</i><sub>i</sub>∙<i>m</i>. This then corresponds to the activity <i>a</i>=(<i>ν</i><sub>M</sub><sup><i>ν</i><sub>M</sub></sup><i>ν</i><sub>X</sub><sup><i>ν</i><sub>X</sub></sup>)∙(<i>mγ</i><sub>±</sub>)<sup>ν</sup>∙<i>a</i><sub>w</sub><sup><i>ν</i><sub>0</sub></sup>
It follows then that a more then a more detailed equation for Δ<i>p</i>. In case of a single salt, it is possible to introduce an average activity coefficient   
where <i>ν</i> corresponds to the number of ions that result from the salt dissolution. From this the following equation results:
<i>γ</i><sup>±</sup>=(<i>γ</i><sub>M</sub><sup><i>ν</i><sub>M</sub></sup><i>γ</i><sub>X</sub><sup><i>ν</i><sub>X</sub></sup>)<sup>(1/<i>ν</i>)</sup> but taking into consideration the simplifciation <i>m</i><sub>i</sub>=<i>ν</i><sub>i</sub>∙<i>m</i>. This then corresponds to the activity <i>a</i>=(<i>ν</i><sub>M</sub><sup><i>ν</i><sub>M</sub></sup><i>ν</i><sub>X</sub><sup><i>ν</i><sub>X</sub></sup>)∙(<i>mγ</i><sub>±</sub>)<sup>ν</sup>∙<i>a</i><sub>w</sub><sup><i>ν</i><sub>0</sub></sup>
where <i>ν</i> corresponds to the number of ions that result from the salt dissolution. From this results the following equation:


Δ<i>p</i>=<i>νRT</i>/<i>V</i><sub>m</sub>∙[ln(<i>m</i>/<i>m</i><sub>0</sub>)+ln(<i>γ</i><sub>±</sub>/<i>γ</i><sub>±,0</sub>)+(<i>ν</i><sub>0</sub>/<i>ν</i>)∙ln(<i>a</i><sub>w</sub>/<i>a</i><sub>w,0</sub>)]    (Eq. 7)
Δ<i>p</i>=<i>νRT</i>/<i>V</i><sub>m</sub>∙[ln(<i>m</i>/<i>m</i><sub>0</sub>)+ln(<i>γ</i><sub>±</sub>/<i>γ</i><sub>±,0</sub>)+(<i>ν</i><sub>0</sub>/<i>ν</i>)∙ln(<i>a</i><sub>w</sub>/<i>a</i><sub>w,0</sub>)]    (Eq. 7)


Next the influencing factors and the individual terms of the equation will be considered in more detail. The first term in brackets is the supersaturation express as concentration. The second and third term in brackets consider the non-ideal behaviour of the concentrated salt solution(s). If one considers an ideal behaviour, the second term is not required, since the average activity coefficient would be 1, however, the third term will remain. The water activity decreases with increasing molality and is always smaller in salt solutions than in pure water. However, since <i>ν</i><sub>0</sub>, i.e., the number of water molecules is relevant, it will not contribute in the case of anhydrate salts. Next to <i>ν</i><sub>0</sub> in the equation, is the composition of the salt with various components (such as ions and the mentioned water molecules). If the crystallization water is discarded, and with it the term that includes the water activity, the calculated crystallization pressure will not be too large (<bib id="Steiger:2005b"/>). However, if the influence of the ions is also discarded the calculated crystallization pressure will be significantly influenced, since <i>ν</i> also appears in the term before the brackets. Hence, the number of ions is directly proportional to the crystallization pressure, and if this is not taken into account, the calculation will be considerably lower, about a factor of 2 or more (<bib id="Steiger:2005b"/>, <bib id="Flatt.etal:2007"/>, <bib id="Coussy:2006"/>). If the non-ideal behaviour is neglected, the influence on the crystallization pressure will depend on the salt and can be greater or smaller. With increasing supersaturation, the activity coefficient increase and with it the pressure, and vice-versa. Considering a hydrated salt, the term with the water activity will decrease the calculated pressure, so that a pressure increase from the activity coefficients will be compensated (<bib id="Steiger:2005b"/>). On the other hand, the molar volume of the salt is inversely proportional to the crystallization pressure. This means, that salts with a low molar volume by equivalent supersaturation will develop higher pressures than those with larger molar volumes. To be considered is that sombe salts cannot reach high supersaturations <bib id="Steiger:2005"/>.
Next, the influencing factors and the individual terms of the equation will be considered in more detail. The first term in brackets is the supersaturation expressed as concentration. The second and third term in brackets consider the non-ideal behaviour of the concentrated salt solution(s). If one considers an ideal behaviour, the second term is not required, since the average activity coefficient would be 1, however, the third term will remain. The water activity decreases with increasing molality and is always smaller in salt solutions than in pure water. However, since <i>ν</i><sub>0</sub>, i.e., the number of water molecules is relevant, it will not contribute in the case of anhydrous salts. Next to <i>ν</i><sub>0</sub> in the equation, is the composition of the salt with various components (such as ions and the mentioned water molecules). If the crystallization water is discarded, and with it the term that includes the water activity, the calculated crystallization pressure will not be too large (<bib id="Steiger:2005b"/>). However, if the influence of the ions is also discarded the calculated crystallization pressure will be significantly influenced, since <i>ν</i> also appears in the term before the brackets. Hence, the number of ions is directly proportional to the crystallization pressure, and if this is not taken into account, the calculation will be considerably lower, about a factor of 2 or more (<bib id="Steiger:2005b"/>, <bib id="Flatt.etal:2007"/>, <bib id="Coussy:2006"/>). If the non-ideal behaviour is neglected, the influence on the crystallization pressure will depend on the salt and can be greater or smaller. With increasing supersaturation, the activity coefficient increases and with it the pressure, and vice-versa. Considering an hydrated salt, the term with the water activity will decrease the calculated pressure, so that a pressure increase from the activity coefficients will be compensated (<bib id="Steiger:2005b"/>). On the other hand, the molar volume of the salt is inversely proportional to the crystallization pressure. This means, that salts with a low molar volume at equivalent supersaturation will develop higher pressures than those with larger molar volumes. To be considered is that some salts cannot reach high supersaturations <bib id="Steiger:2005"/>.


These considerations clarity that Correns and Steinborn (<bib id="Correns.etal:1939"/>) did not consider in their study the non-ideal behaviour of the salt, but more relevantly, they neglected the composition of the salt, since the influence of the number of ions was not considered the calculated crystallization pressures were too low (<bib id="Steiger:2005b"/>, <bib id="Flatt.etal:2007"/>, <bib id="Coussy:2006"/>).
These considerations make it clear that Correns and Steinborn (<bib id="Correns.etal:1939"/>)in their study did not consider the non-ideal behaviour of the salt, but more relevantly, they neglected the composition of the salt, since the influence of the ion number was not considered and therefore the calculated crystallization pressures were too low (<bib id="Steiger:2005b"/>, <bib id="Flatt.etal:2007"/>, <bib id="Coussy:2006"/>).


==Crystallization in small pores==
==Crystallization in small pores==


Bei kleinen Porengrößen muss auch der Einfluss der Kristallgröße auf ihre Löslichkeit berücksichtigt werden. Je kleiner die Kristallgröße, desto höher ist die Löslichkeit, so dass bei Kristallen in kleine Poren höhere Konzentrationen für ein Kristallwachstum erforderlich sind. Der Einfluss der Kristallgröße sphärischer Kristalle auf die Löslichkeit kann mit der folgenden Gleichung angegeben werden (Ostwald-Freundlich-Gleichung):
In the case of small pores the effect of the crystal size on their solubility has to be considered. The smaller the crystal size, the higher the solubility, so that crystals in small pores require higher concentrations for their growth. The influence of the size of spherical crystals on their solubility can be calculated by the following equation (Ostwald-Freundlich equation):
 
ln<i>a</i><sub>0</sub>/<i>a</i><sub>∞</sub>=(2<i>γ</i><sub>cl</sub><i>V</i><sub>m</sub>)/<i>rRT</i> (Gl. 8).


Darin sind <i>a</i><sub>0</sub> und <i>a</i><sub>∞</sub> die thermodynamischen Löslichkeitsprodukte des kleinen beziehungsweise eines unendlich großen Kristalls, <i>γ</i><sub>cl</sub> die Grenzflächenenergie zwischen dem Kristall und der Lösung und <i>r</i> der Radius des Kristalls. <bib id="Steiger:2005b"/>
ln<i>a</i><sub>0</sub>/<i>a</i><sub>∞</sub>=(2<i>γ</i><sub>cl</sub><i>V</i><sub>m</sub>)/<i>rRT</i> (Eq. 8)


Wird eine kugelförmige Pore mit kleinen zylindrischen Poreneingängen betrachtet, ergibt sich ein Modell für zwei verschieden große benachbarte Poren. Ist eine Lösung in Bezug auf den kleineren Kristall mit <i>r</i><sub>1</sub> (im Poreneingang) gesättigt, so ist sie in Bezug auf den größeren Kristall mit <i>r</i><sub>2</sub> (in der kugelförmigen Pore) übersättigt. Damit kann der größere Kristall weiterwachsen und Druck auf die Porenwand ausüben, bis das Gleichgewicht wieder erreicht ist. Da die für das Wachstum benötigte Konzentration an der freien Fläche (der kleine Kristall) größer ist als die am großen Kristall, ist das Wachstum nur unter Druckaufbau gegen die Porenwand möglich. Unter Anwendung der Gleichung für den Kristallisationsdruck mit der Sättigungsaktivität des großen Kristalls (anstelle der Aktivität der gesättigten Lösung) und der des kleinen Kristalls im Poreneingang (anstelle der Lösungsaktivität) und der zuletzt genannten Gleichung für die Löslichkeitsabhängigkeit, kann der folgende Ausdruck für die Berechnung des Kristallisationsdrucks erhalten werden:
where <i>a</i><sub>0</sub> and <i>a</i><sub>∞</sub> are the thermodynamic solubility products of the smaller crystal with regards to an infinitely large crystal; 
<i>γ</i><sub>cl</sub> is the interfacial energy between the crystal and the solution, and <i>r</i> the radius of the crystal <bib id="Steiger:2005b"/>.


∆<i>p</i>=2<i>γ</i><sub>cl</sub>∙[(1/<i>r</i><sub>1</sub>)-(1/<i>r</i><sub>2</sub>)] (Gl. 4).
In the case of a round pore having a small cylindrical entrance, a model for two dissimilar sized pores is required. If the solution is saturated with regards to the smaller crystal at the pore entry <i>r</i><sub>1</sub>, then it will be supersaturated with regards to the larger crystal in the spherical pore <i>r</i><sub>2</sub>. Therefore the larger crystal will continue its growth and apply pressure to the pore wall, until equilibrium is reached. Since the required concentration at the free surface (the small crystal) is greater than for the large crystal, then growth can only proceed under pressure against the pore-wall. Applying the crystallization equation for pressure using the saturation activity of the larger crystal (instead of the activity of the saturated solution), with that of the smaller crystal at the pore entry (instead of the solution activity), and the last equation for solubility dependence, the following equation for calculating the crystallization pressure is obtained: 
∆<i>p</i>=2<i>γ</i><sub>cl</sub>∙[(1/<i>r</i><sub>1</sub>)-(1/<i>r</i><sub>2</sub>)] (Eq. 4)


Es ergibt sich die Gleichung von <bib id="Everett:1961"/>. Everetts Gleichung ist also ein Sonderfall für eine bestimmte Geometrie, er bezieht sich aber auch auf einen Druckaufbau infolge von Übersättigung. Somit sind die Gleichungen von Correns und Everett ineinander überführbar und beschreiben im Falle der beschriebenen Geometrien den gleichen Schadensmechanismus und sind somit keineswegs widersprüchlich <bib id="Steiger:2005"/>. Im Falle der angegebenen Geometrie erhöht sich die Übersättigung mit abnehmendem Durchmesser des Poreneingangs. Für andere Geometrien können weitere Ausdrücke für den Kristallisationsdruck hergeleitet werden (<bib id="Steiger:2005"/>, <bib id="Scherer:1999"/>, <bib id="Flatt:2002"/>, <bib id="Steiger:2006"/>.
The equation corresponds to that of <bib id="Everett:1961"/>; it is a special case for a given geometry based on a pressure build-up following supersaturation. Thus, the equations of Correns and Everett are interconvertible, i.e., exchangeable, and describe the same deterioration mechanism for specific geometries, and therefore are not contradictory <bib id="Steiger:2005"/>. In the case of the described geometry, the supersaturation will increase with respect to a decreasing pore entry. For other geometries, other equations for the crystallization pressure can be developed (<bib id="Steiger:2005"/>, <bib id="Scherer:1999"/>, <bib id="Flatt:2002"/>, <bib id="Steiger:2006"/>.


Auch bei kleinen Poren gilt, dass Druck nur aufgebaut werden kann, wenn die Porenlösung in Bezug auf die freie Fläche beziehungsweise auf die relevante Fläche in unbelastetem Zustand übersättigt ist. Bei den kleinen Poren ist das die Konsequenz der unterschiedlichen Löslichkeiten durch die Krümmungen der Flächen. Je stärker die Krümmung, desto höher die Löslichkeit und desto höher die Übersättigungen an den anderen weniger gekrümmten Flächen, an denen Kristallwachstum stattfindet. In diesem Fall sind die Übersättigung und damit auch der Kristallisationsdruck ein Gleichgewichtszustand, so dass er auch über längere Zeiträume wirken kann. Dringend zu berücksichtigen ist aber, dass der Einfluss der Kristallgröße auf die Löslichkeit erst bei Radien <0.1 µm (<bib id="Steiger:2005"/>) deutlich wird und für ausreichend hohe Drücke unter diesen Bedingungen Porendurchmesser <10-50 nm (<bib id="Steiger:2009"/>) vorliegen müssen, was nur bei den wenigsten Baustoffen der Fall ist. Im Falle von größeren Poren ist der Kristallisationsdruck kein Gleichgewichtszustand (s. oben). Dann ist es vorstellbar, dass bei langsamer werdender Verdunstung nur noch hochkonzentrierte Lösungen verbleiben, die nicht mit allen Kristallflächen in Kontakt stehen. Liegt nicht ausreichend Kontakt zu freien Flächen vor, so können Übersättigungen gegebenenfalls lange wirken, und Drücke länger aufrechterhalten werden (<bib id="Steiger:2005b"/>). Auch durch schnelle Verdunstung können hohe Übersättigungen aufgebaut werden. Wird die Ionendiffusion durch die Lösung im porösen System unterbrochen, kann das Wachstum an den belasteten Flächen die Folge sein, wenn die freien Flächen nicht mehr mit Lösung in Kontakt stehen (<bib id="Flatt:2002"/>).
Also for smaller pores, the pressure will only develop when the pore solution is supersaturated with respect to free surfaces, i.e., an unloaded surface. For smaller pores this is the consequence of the different solubility presented by the curving of surfaces. The higher the curvature, the higher will the solubility be and therefore the supersaturation with respect to the less curved faces where crystal growth occurs. In this case, the supersaturation and the crystallization pressure will be in equilibrium, so that they can operate for longer periods. Nonetheless, it is critical to take into account that the influence of crystal size on its solubility will only be relevant for radius <0.1 µm (<bib id="Steiger:2005"/>) and to attain higher pressures a pore diameter of <10-50 nm (<bib id="Steiger:2009"/>) is required, and this occurrence happens only for some construction materials. For larger pores the crystallization pressure is not in equilibrium (see above). In this case, the slow evaporation will result in highly concentrated solutions when they are not in contact with all crystal faces. If there is no sufficient contact with a free surface, the supersaturation can work for longer time, and the pressures maintained (<bib id="Steiger:2005b"/>). High supersaturation can be achieved through fast evaporation. If the diffusion of ions in the solution is interrupted, this may result in growth at loaded faces, when free faces are no longer in contact with the solution (<bib id="Flatt:2002"/>).


==Special case of hydration pressure==
==Special case of hydration pressure==


Einige Salze können in unterschiedlichen Hydratphasen vorliegen, beispielsweise verschiedene Phasen des Magnesiumsulfats (MgSO<sub>4</sub>∙<i>n</i>H<sub>2</sub>O). Durch den unterschiedlichen Wassergehalt in den Phasen ergibt sich ein für die jeweils höher hydratisierte Phase höheres molares Volumen, was lange Zeit für die Druckausübung auf das Porengefüge verantwortlich gemacht wurde (z.B.<bib id="Correns:1926"/>). Inzwischen werden zwei unterschiedliche Arten der Hydratationsreaktion unterschieden.
Some salts can crystallize with different degrees of hydration, for example, magnesium sulfate (MgSO<sub>4</sub>∙<i>n</i>H<sub>2</sub>O), where n ranges from 1,4-7. The different hydration number results in that the higher hydrated phases have a larger molecular volume, which were held responsible for exerting pressure on the pore structure for a long time(e.g.,<bib id="Correns:1926"/>). Two different type of hydration reactions can be established.


Zum einen kann eine Hydratation über Wasserdampf, also über die relative Luftfeuchte der Umgebung, erfolgen. Liegt der Wert der RH dabei unterhalb der Deliqueszenzfeuchte des geringeren Hydrats beziehungsweise der wasserfreien Phase, so geschieht die Hydratation über eine Festphasenreaktion. Für den dabei maximal durch das Wachstum eines Kristalls der hydratisierten Phase wirkenden Druck gegen die Porenwand kann die Gleichung für den Hydratationsdruck nach Mortensen <bib id="Mortensen:1933"/> verwendet werden (s.o.). Während bei der Kristallisation aus einer Lösung die Übersättigung der Lösung Triebkraft für den ausgeübten Druck ist, ist es bei der Hydratation über Wasserdampf (RH<DRH des niedrigeren Hydrats) die Übersättigung des Wasserdampfs der Umgebungsluft gegenüber des Gleichgewichtsdampfdrucks der Hydratphase bei der gegebenen Temperatur. Im Falle einer solchen Hydratation und der Verwendung der Gleichung nach Mortensen muss beachtet werden, dass es eine maximale relative Luftfeuchtigkeit gibt, oberhalb derer die Anwendung der Gleichung nicht mehr legitim ist. Überschreitet die relative Luftfeuchtigkeit die Deliqueszenzfeuchte der höheren Hydratphase, liegt nur noch eine Lösung vor, wodurch auch kein Hydratationsdruck wirken kann. <bib id="Steiger.etal:2014"/>
One corresponds to the hydration via water vapor, which is dependent on the air moisture in the environment. If the RH value is below the deliquescence moisture of the lower hydrate, or the anhydrous phase, then the hydration occurs as a solid phase reaction. In this case, the maximum pressure that the hydrating crystal can induce on the pore wall can be calculated with the equation for hydration pressure given by Mortensen <bib id="Mortensen:1933"/> (see Historical Background section). During crystallization, the supersaturation of the solution is the driving force for the exerted pressure, while during hydration via water vapor (RH<DRH of the lower hydrate) it corresponds to the supersaturation of the water vapor in the environment in relation to the equilibrium water vapor pressure of the hydrated phase at the given temperature. In this case, if the equation of Mortensen is used, it has to be considered that there is a maximal RH above which the equation is no longer valid. If the moisture in the air is above the deliquescence moisture of the higher hydrated phase, then no hydration pressure can develop <bib id="Steiger.etal:2014"/>. 


Liegt die RH bei der Befeuchtung oberhalb der Deliqueszenzfeuchte der niedriger hydratisierten Phase, so erfolgt die Hydratation über einen anderen Mechanismus. Das geringere Hydrat bildet eine (gesättigte) Lösung, aus welcher die höher hydratisierte Phase auskristallisiert (Auflösungs- und Rekristallisationsvorgang). Auch hierbei ist nicht die Volumenzunahme Grund für den Druckaufbau im porösen Gefüge, sondern die Kristallisation der Hydratphase aus einer ihr gegenüber übersättigten Lösung. Somit stellt dieser Mechanismus einen Sonderfall des Kristallisationsdrucks in Folge der Kristallisation aus übersättigten Lösungen dar. Ebenfalls dieser Mechanismus ist bei einer Flüssigwasserbefeuchtung eines porösen Systems mit einer wasserfreien oder geringer hydratisierten Phase für den Druckaufbau verantwortlich. <bib id="Steiger:2003b"/>
If the RH during moisture absorption is above the DHR of the lower hydrated phase, then hydration will continue via other mechanisms. The lower hydrate forms a saturated solution, out of which a higher hydrate will crystallize out (dissolution and recrystallization process). Also in this case the volume increase is not the reason for the pressure increase on the porous structure, but the crystallization of the higher hydrate phase from a supersaturated solution. Thus, this mechanism is a special case of the crystallization pressure as a result of crystallization from supersaturated solutions. And this mechanism is also responsible for the pressure developed through moisture absorption of liquid water in a porous system where an anhydrous or lower hydrated phase is present <bib id="Steiger:2003b"/>.


Beispielhaft lässt sich dies gut anhand des Systems [[Natriumsulfat]]-Wasser zeigen. Wird ein poröser Prüfkörper mit [[Thenardit]] im Porenraum bei Raumtemperatur getränkt, so bildet sich eine in Bezug auf [[Thenardit]] gesättigte Lösung. Ein Blick auf das Phasendiagramm des Systems zeigt jedoch, dass diese Lösung in Bezug auf [[Mirabilit]] übersättigt ist und der Grad der Übersättigung mit sinkender Temperatur zunimmt. Bei der Kristallisation von [[Mirabilit]] aus einer stark übersättigten Lösung können bei ausreichend gefüllten Poren hohe Drücke auf das Porengefüge wirken. Dies kann nicht nur bei der Flüssigwasserbefeuchtung beobachtet werden, sondern auch bei der Befeuchtung der wasserfreien bzw geringer hydratisierten Phase bei relativen Luftfeuchtigkeiten bis zur oder oberhalb der Deliqueszenzfeuchte, wobei die hydratisierte Phase dann aus dieser in Bezug auf sie übersättigten Lösung gebildet wird. Verallgemeinert ausgedrückt, kommt es durch das Auflösen einer metastabilen Phase zur Bildung einer in Hinblick auf die stabile Phase übersättigten Lösung, so dass während der Kristallisation der stabilen Phase hohe Drücke wirken können. <bib id="Steiger.etal:2008"/>
For instance, the system [[sodium sulfate]]-water is a good example. If a porous material is moistened with a solution of [[thenardite]] at room temperature, then a saturated solution with regards to [[thenardite]] will form. Looking at the phase diagram of the system, it is evident that the solution will be saturated with regards to [[mirabilite]], and that the supersaturation increases with lowering temperature. When [[mirabilite]] crystallizes out of a highly supersaturated solution then, if sufficient pores are filled, high pressures can develop in the porous structure. This can be observed during wetting, as well as during wetting of the anhydrous or lower hydrated phases at RH up to or above the DRH, where the hydrated phase can form a supersaturated solution. In general terms, this occurs through the dissolution of a metastable phase to allow the formation of a supersaturaed solution with regards to a more stable phase, so that during its crystallization high pressures can develop <bib id="Steiger.etal:2008"/>.


==Consideration of crystallization pressure within building deterioration==
==Consideration of crystallization pressure within building deterioration==


Schädigungen von realen Bauwerken aus porösem Material, hervorgerufen durch Salzkristallisation, werden häufig beobachtet. Die Salze beziehungsweise Salzlösungen in den porösen Materialien stehen im direkten Austausch mit der Umgebung. Somit können Schwankungen der relativen Luftfeuchtigkeit zu zyklischen Wechseln zwischen Kristallisation und Auflösung führen, wenn die Schwankungen in Bereichen ober- und unterhalb der Deliqueszenzfeuchte erfolgen. Auch der Eintrag von Regenwasser oder das Auftreten von Kondensation kann zur Befeuchtung oder Hydratation von vorliegenden Salzen führen. Einige Salze können auch bei alleinigen Temperaturschwankungen Phasenwechsel durchlaufen, wenn in dem Salzsystem Phasen vorliegen, die nur in einem bestimmten Temperaturbereich stabil sind (beispielsweise [[Mirabilit]]). An Bauwerken liegen aber in den meisten Fällen geringere Konzentrationen und weniger drastische Bedingungen vor als in den im Labor für die Untersuchung der Schädigungsmechanismen durchgeführten Experimenten.
Salt crystallization will induce damage and deterioration in porous inorganic materials. Salts, as well as their solution(s), are present in the buildings environment, e.g., rising damp, so that there is a direct interchange between them. Changes in RH will result in cycling between crystallization and dissolution, especially when they occur around the DRH. Rain, as well as condensation induced by temperature changes will also result in the introduction of water or hydration of the salts already present in the material. Some salts will change phases with only temperature variation, depending on their stability within the temperature range, for example, [[mirabilite]]. However, in buildings the concentration of salts seldom reaches those that were used in laboratory studies to understand the damage mechanism.


Zudem gelten in Bezug auf den Kristallisationsdruck die bereits im Abschnitt „Vertiefung“ erwähnten Punkte. Kleine Poren, die für einen Kristallisationsdruck als Gleichgewichtszustand notwendig sind, liegen in den meisten Baumaterialien nicht vor, sind aber in Zement möglich. Demnach ist der schädigende Kristallisationsdruck an realen Objekten in der Regel kein Gleichgewichtszustand, sondern ein dynamischer Prozess (<bib id="Steiger:2009"/>, <bib id="Scherer:2004"/>. Die hohen Übersättigungen liegen dann nur über kurze Zeiträume vor und werden durch die Kristallisation an freien Flächen abgebaut.
Furthermore, for the case of crystallization pressure the points discussed in the Clarification section are valid. Small pores, that are necessary for an equilibrium of the crystallization pressure, are not frequently found in most construction materials, but can be found in cement. Therefore, crystallization pressure in real buildings is not found in equilibrium, but rather as a dynamic process (<bib id="Steiger:2009"/>, <bib id="Scherer:2004"/>. The high supersaturation conditions occur only in short events and are reduced by the crystallization on free surfaces.


== Literature  ==
== Literature  ==

Latest revision as of 13:42, 24 November 2022

Autoren: Stahlbuhk, Amelie

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Abstract[edit]

The different salt crystallization processes that can lead to deterioration of porous inorganic materials are discussed.


Introduction[edit]

Much of our cultural heritage is constituted by porous inorganic materials such as stone, brick, mortars and renders. Salts will enter these porous materials, e.g., from rising damp, and their crystallization in the pores will lead to the materials' deterioration; a process that depends on the relative humidity (RH) and temperature. When the RH decreases, water from the salt solution will be released into the atmosphere until the deliquescence relative humidity (DRH) of the salt in question is reached, at this point a saturated solution will result; while below it the salt will crystallize. If the RH increases, exceeding the DRH, the salt will absorb water vapor from the air and tend to form a saturated solution and, if the RH continues to increase, it will be further diluted. This shows that changes in RH around the DRH of the salt will lead to alternating crystallization and deliquescence cycles. The cycling around the DRH is responsible for the deterioration induced and that can be attributed to crystallization pressure; repeated cycling inducing more damage. One of the critical factors in developing an effective crystallization pressure is the formation of a supersaturated solution [Steiger:2005]Title: Crystal growth in porous materials: I. The crystallization pressure of large crystals
Author: Steiger, Michael
Link to Google Scholar. Crystallization from a supersaturated solution will only occur at a lower RH or temperature than those required for forming saturated solutions. Supersaturated solutions form through water vapor evaporation, if for example, the RH drops, or by lower temperatures. Dissolution of a metastable phase can result in a supersaturated solution, which will be discussed a following section [Steiger.etal:2008]Title: Crystallization of sodium sulfate phases in porous materials: The phase diagram Na2SO4–H2O and the generation of stress
Author: Steiger, Michael; Asmussen, Sönke
Link to Google Scholar. Whether the presence of salts will result in a deterioration process depends on the nature of the salt, or salt-mixture, and its properties, but mainly by the environmental conditions, including the amount of water vapor available. These mechanisms, based on theoretical models, are only applicable for porous inorganic materials.

Crystallization within a pore[edit]

The concentration of a salt solution within a pore will depend on environmental factors such as relative humidity (RH) and temperature (T). When the RH drops, the concentration will increase as water vapor will be released from the solution; if the amount evaporated is such that the solubility of the salt in question is attained, then crystallization of the salt will occur. This RH is known as the deliquescence RH (DRH). Capillary transportation of the solution to the material's surface, where the main evaporation occurs, will increase the evaporation rate. As drying continues, the evaporation front will move into the interior of the porous material, as the evaporated moisture will move faster than the capillary movement to the evaporation front [Hall.etal:1984]The entry doesn't exist yet.. Therefore, salts transported by the solution can crystallize both on the material's surface, i.e., efflorescence, as well as in the area below the surface as subflorescence. Where crystallization will actually occur depends on the drying conditions, the composition of the salt solution in question, its concentration and the material's properties [Espinosa-Marzal.etal:2010]Title: Advances in Understanding Damage by Salt Crystallization
Author: Espinosa-Marzal, Rosa M.; Scherer, George W.
Link to Google Scholar.

Historical Background[edit]

Currently, our understanding of the models to explain the deterioration of porous materials and crystallization pressure from salts resulted from controversial discussions since the 20th century. The growth of a crystal in the presence of obstacles was referred to as linear crystallization pressure (e.g., [Becker.etal:1916]Title: Notes on the Linear Force of Growing Crystals
Author: Becker, G.F.; Day, A.L.
Link to Google Scholar, [Taber:1916]Title: The Growth of Crystals under External Pressure
Author: Taber, Stephen
Link to Google Scholar, [Correns.etal:1939]Title: Experimente zur Messung und Erklärung der sogenannten Kristallisationskraft
Author: Correns, Carl W.; Steinborn, W.
Link to Google Scholar, [Duttlinger.etal:1993]Title: Salzkristallisation und Salzschadensmechanismen
Author: Duttlinger, Werner; Knöfel, Dietbert
Link to Google Scholar). A growing crystal, when it crystallizes from a supersaturated solution, can generate a maximum pressure when growing in one direction and reaching an obstacle; a film solution is present between the crystal surface and the obstacle to allow its ongoing growth [Taber:1916]Title: The Growth of Crystals under External Pressure
Author: Taber, Stephen
Link to Google Scholar. Important studies have been carried out by [Correns:1926]Title: Über die Erklärung der sogenannten Kristallisationskraft
Author: Correns, Carl W.
Link to Google Scholar, who classified the crystallization pressure as a function of the volume increase of the crystal (hydrostatic crystallization pressure), hydration pressure as well as those referred to as linear crystallization pressure.

However, others ([Taber:1916]Title: The Growth of Crystals under External Pressure
Author: Taber, Stephen
Link to Google Scholar), pointed out the influence of the inter-facial energy that should reach a given value so that the crystallization could take place. He pointed out that a growing crystal is not attached to the surface, there being a solution film between it and the surface, to allow for an ion exchange to take place, and that can be attributed to the inter-facial energy between crystal and pore-wall ([Correns:1926]Title: Über die Erklärung der sogenannten Kristallisationskraft
Author: Correns, Carl W.
Link to Google Scholar, [Bruhns.etal:1913]Title: Über die sogenannte "Kristallisationskraft"
Author: Bruhns, W.; Mecklenburg, W.
Link to Google Scholar, [Weyl:1959]Title: Pressure Solution and the Force of Crystallisation - A Phenomenological Theory
Author: Weyl, Peter K.
Link to Google Scholar.

Some experiments, where both a loaded and an unloaded alum crystal in a saturated solution were grown, showed that only the unloaded crystal grew thus requiring a re-examination of the linear crystallization pressure, and that furthermore the pressure developed could be correlated better with a volume increase rather than the pressure of the crystal. This could also be applied to the hydration pressure, since an anhydrous or a low hydrated phase would have a smaller volume than the fully hydrated one ([Bruhns.etal:1913]Title: Über die sogenannte "Kristallisationskraft"
Author: Bruhns, W.; Mecklenburg, W.
Link to Google Scholar). The hydro-static pressure is given by the increased volume resulting from the crystallization of the salt, since the volume of salt and saturated solution is greater than that of the supersaturated solution. Relevant contributions regarding the hydration pressure can be found in [Mortensen:1933]Title: Die 'Salzprengung' und ihre Bedeutung für die regionalklimatische Gliederung der Wüsten
Author: Mortensen, Hans
Link to Google Scholar, who realized that the hydration pressure of an anhydrate crystal could be calculated as follows;

Δphydr=(ΔnRT/ΔVm)∙ln(RH/RHeq) (Eq.1)

where Δn is the difference in water molecules per mole of salt of the lower hydrate n1 with the higher hydrate n2; ΔVm is the difference between the molar volume of both phases; RH the relative humidity at which the hydration reaction occurs, and RHeq the equilibrium moisture at the temperature T corresponding to the hydration-dehydration equilibrium. The hydration pressure corresponds to the maximum developed pressure that a growing crystal at higher hydration can exert on the pore wall, since at a higher pressure, dehydration would result [Mortensen:1933]Title: Die 'Salzprengung' und ihre Bedeutung für die regionalklimatische Gliederung der Wüsten
Author: Mortensen, Hans
Link to Google Scholar, [Steiger.etal:2014]Title: Weathering and Deterioration
Author: Steiger, Michael; Charola A. Elena; Sterflinger, Katja
Link to Google Scholar.

Both Correns and Steinborn ([Correns.etal:1939]Title: Experimente zur Messung und Erklärung der sogenannten Kristallisationskraft
Author: Correns, Carl W.; Steinborn, W.
Link to Google Scholar) also studied the "crystallization pressure". For the case of the "linear growth pressure" they gave a formula for the chemical potentials for which the degree of supersaturation of the solution defined the intensity of the developed pressure, as follows:

∆p=(RT/Vm)∙lnS=(RT/Vm)∙ln(c/c0) (Eq. 2)

where ∆p is the crystallization pressure; R the gas constant; T the temperature; Vm the molecular volume of the salt; S the supersaturation; c the concentration of the supersaturated solution, and c0 the concentration of the saturated solution.

Since their various experiments using different crystal surfaces always produced lower values than the theoretical ones, they attributed this to the different inter-facial energies. In subsequent equations, the crystallization pressure was also given as a function of the supersaturation, which allowed different ways of expressing them (e.g., [Goranson:1940]The entry doesn't exist yet., [Buil:1983]Title: Thermodynamics and Experimental Study of the Crystallization Pressure of Water Soluble Salts
Author: Buil, Michel
Link to Google Scholar).

Everett ([Everett:1961]Title: The thermodynamics of frost damage to porous solids
Author: Everett, D.H.
Link to Google Scholar) considered the crystallization of ice and suggested a theory through which the crystallization pressure was the consequence of stability differences between the larger crystals. These differences result from the disparities in curvature at the interface between the solid and liquid phases, which lead to different chemical potential for crystals with different sizes. However, he did not consider the supersaturation, his equation:

∆p=γcl∙(dA/dV) (Eq. 3)

describes the pressure differences between two crystals of different size; where γcl is the inter-facial energy between the solid and the liquid phase, A is the surface, and V is the volume. For spherical crystals this can be rewritten

∆p=2γcl∙[(1/r1)-(1/r2)] (Eq. 4)

The pressure that develops through crystal growth in the larger pores with the radius r2 is appropriate, since crystal growth in smaller pores is not thermodynamically favored. The crystal developing in a larger pore will grow as long as the chemical potential of the crystal corresponds to that of a crystal in the smaller pore r1 ([Everett:1961]Title: The thermodynamics of frost damage to porous solids
Author: Everett, D.H.
Link to Google Scholar, [Steiger:2005]Title: Crystal growth in porous materials: I. The crystallization pressure of large crystals
Author: Steiger, Michael
Link to Google Scholar).

The two approaches of Correns and Everett were considered contradictory deterioration mechanisms for many years, since one considered supersaturation and the other the crystal curvature as responsible for the crystallization pressure developed. Both approaches were followed in parallel, and that of Correns was criticized by its very high supersaturation. In the case of the Everett theory, because data for the reliable pore sizes were available, it was reconsidered, which was not the case for the supersaturation [Steiger:2005]Title: Crystal growth in porous materials: I. The crystallization pressure of large crystals
Author: Steiger, Michael
Link to Google Scholar.

Crystallization Pressure[edit]

Deterioration of a porous material from salt crystallization can only occur when the crystal(s) grows in a supersaturated solution against an obstacle, such as a pore wall (e.g., [Correns.etal:1939]Title: Experimente zur Messung und Erklärung der sogenannten Kristallisationskraft
Author: Correns, Carl W.; Steinborn, W.
Link to Google Scholar). As the crystal grows further, a mechanical load, i.e., strain, is applied to the porous material. Another requirement for crystal growth against a wall is the presence of a solution film between the crystal and the wall [Weyl:1959]Title: Pressure Solution and the Force of Crystallisation - A Phenomenological Theory
Author: Weyl, Peter K.
Link to Google Scholar (a thickness of about 1 nm [Scherer:1999]Title: Crystallization in pores
Author: Scherer, George W.
Link to Google Scholar) through which the ion transport can occur. The reason for the presence of this solution film are the repulsive forces between the crystal and the pore wall, otherwise there would be no further growth [Steiger:2005]Title: Crystal growth in porous materials: I. The crystallization pressure of large crystals
Author: Steiger, Michael
Link to Google Scholar. In tests where a crystal was clamped between two glass-plates to evaluate the developed force, the presence of the solution film between crystal and glass-plates could be visually observed and its relevance confirmed [Desarnaud.etal:2016]The entry doesn't exist yet.. The repulsive pressure between the two components defines the maximal crystallization pressure, since if this value is increased a direct contact between crystal and wall would result thus ending the crystal growth. Since the repulsive pressure has a slight dependence on the wetting properties and the surface charge, this implies that different salts and porous materials will develop diverse crystallization pressures [Desarnaud.etal:2016]The entry doesn't exist yet..

A crystal growing in a pore is exposed to anisotropic pressure. Those faces/surfaces of the crystal which grow towards the pore-wall, are subjected to a higher pressure than the free surfaces in contact with the solution and subjected to its hydrostatic pressure. The difference between these two pressures is the crystallization pressure. Since crystal solubility is dependent on the applied pressure and increases with it, the free, unloaded surfaces/faces and those that are loaded, i.e., under pressure, will have different solubilities. This means, that comparing the concentration of the solution at the loaded face with that found by the free surface, the latter will be supersaturated [Steiger:2005]Title: Crystal growth in porous materials: I. The crystallization pressure of large crystals
Author: Steiger, Michael
Link to Google Scholar. The equation for the crystallization pressure can be given as:

∆p=(RT/Vm)∙ln(a/a0) (Eq. 5).

where ∆p is the crystallization pressure, i.e., the difference between the pressure on a loaded face pc and the hydrostatic pressure of the free faces pl; a is the activity of the supersaturated solution, and a0 that of the saturated solution. By using activities the non-ideal behaviour of the salt solutions is taken into account [Steiger:2005]Title: Crystal growth in porous materials: I. The crystallization pressure of large crystals
Author: Steiger, Michael
Link to Google Scholar.

This equation shows a significant similarity to that suggested by Correns and Steinborn ([Correns.etal:1939]Title: Experimente zur Messung und Erklärung der sogenannten Kristallisationskraft
Author: Correns, Carl W.; Steinborn, W.
Link to Google Scholar), however, we are considering the non-ideal behaviour of salt solutions by using the activity instead of concentrations. Furthermore, Correns neglected the anisotropic pressure to which the crystal is subjected.

A pressure develops on the pore structure when the unloaded crystal face is in contact with the supersaturated solution, since the supersaturation will be decreased by the crystal growth of the unloaded crystal face (as long as they are available). This reduces the supersaturation and the pressure on the loaded face cannot be sustained. Since the original solution was saturated with regards to the loaded face, it will fall below saturation which will result in the dissolution of the loaded face thus reducing the pressure to maintain equilibrium. Both these effects lead to short-term high crystallization pressures that can only operate under supersaturated conditions. Therefore, the pressure build-up through crystallization does not occur under equilibrium conditions; it depends on a kinetic and dynamic process that is subjected to diffusion and crystal growth rate of unloaded crystal faces ([Steiger:2009]Title: Mechanismus der Schädigung durch Salzkristallisation
Author: Steiger, Michael
Link to Google Scholar, [Scherer:2004]Title: Stress from crystallization of salt
Author: Scherer, George W.
Link to Google Scholar).

Clarification[edit]

When a salt dissolves, the following equation applies:

MνMXνX∙ν0H2O⇌νMMzM++νXXzX-+ν0 H2O (Eq. 6)

where M are the cations; X the anions, ν the number of ions M and X; z the charge of the corresponding ions and ν0 the number of water molecules.

The activity of the dissolved salt is a=aMνM∙aXνX∙awν0, the ion activity product, where aw is the water activity.

Expressing the activity as the activity coefficient and the molality as ai=γi∙(mi/m0), where ai corresponds to the ion activity; γi the activity coefficient of the ions; mi the molality of the ions in the solution, and where m0=1 mol/kg, then the crystallization pressure of a crystal in contact with the solution can be calculated, as long as the activity coefficients and the water activity are known.

It follows then that a more detailed equation for Δp can be found. In case of a single salt, it is possible to introduce an average activity coefficient γ±=(γMνMγXνX)(1/ν) but taking into consideration the simplification mi=νi∙m. This then corresponds to the activity a=(νMνMνXνX)∙(mγ±)ν∙awν0 where ν corresponds to the number of ions that result from the salt dissolution. From this the following equation results:

Δp=νRT/Vm∙[ln(m/m0)+ln(γ±/γ±,0)+(ν0/ν)∙ln(aw/aw,0)] (Eq. 7)

Next, the influencing factors and the individual terms of the equation will be considered in more detail. The first term in brackets is the supersaturation expressed as concentration. The second and third term in brackets consider the non-ideal behaviour of the concentrated salt solution(s). If one considers an ideal behaviour, the second term is not required, since the average activity coefficient would be 1, however, the third term will remain. The water activity decreases with increasing molality and is always smaller in salt solutions than in pure water. However, since ν0, i.e., the number of water molecules is relevant, it will not contribute in the case of anhydrous salts. Next to ν0 in the equation, is the composition of the salt with various components (such as ions and the mentioned water molecules). If the crystallization water is discarded, and with it the term that includes the water activity, the calculated crystallization pressure will not be too large ([Steiger:2005b]Title: Crystal growth in porous materials: II. The influence of crystal size
Author: Steiger, Michael
Link to Google Scholar). However, if the influence of the ions is also discarded the calculated crystallization pressure will be significantly influenced, since ν also appears in the term before the brackets. Hence, the number of ions is directly proportional to the crystallization pressure, and if this is not taken into account, the calculation will be considerably lower, about a factor of 2 or more ([Steiger:2005b]Title: Crystal growth in porous materials: II. The influence of crystal size
Author: Steiger, Michael
Link to Google Scholar, [Flatt.etal:2007]Title: A commented translation of the paper by C.W. Correns and W. Steinborn on crystallization pressure
Author: Flatt, Robert J.; Steiger, Michael; Scherer, George W.
Link to Google Scholar, [Coussy:2006]The entry doesn't exist yet.). If the non-ideal behaviour is neglected, the influence on the crystallization pressure will depend on the salt and can be greater or smaller. With increasing supersaturation, the activity coefficient increases and with it the pressure, and vice-versa. Considering an hydrated salt, the term with the water activity will decrease the calculated pressure, so that a pressure increase from the activity coefficients will be compensated ([Steiger:2005b]Title: Crystal growth in porous materials: II. The influence of crystal size
Author: Steiger, Michael
Link to Google Scholar). On the other hand, the molar volume of the salt is inversely proportional to the crystallization pressure. This means, that salts with a low molar volume at equivalent supersaturation will develop higher pressures than those with larger molar volumes. To be considered is that some salts cannot reach high supersaturations [Steiger:2005]Title: Crystal growth in porous materials: I. The crystallization pressure of large crystals
Author: Steiger, Michael
Link to Google Scholar.

These considerations make it clear that Correns and Steinborn ([Correns.etal:1939]Title: Experimente zur Messung und Erklärung der sogenannten Kristallisationskraft
Author: Correns, Carl W.; Steinborn, W.
Link to Google Scholar)in their study did not consider the non-ideal behaviour of the salt, but more relevantly, they neglected the composition of the salt, since the influence of the ion number was not considered and therefore the calculated crystallization pressures were too low ([Steiger:2005b]Title: Crystal growth in porous materials: II. The influence of crystal size
Author: Steiger, Michael
Link to Google Scholar, [Flatt.etal:2007]Title: A commented translation of the paper by C.W. Correns and W. Steinborn on crystallization pressure
Author: Flatt, Robert J.; Steiger, Michael; Scherer, George W.
Link to Google Scholar, [Coussy:2006]The entry doesn't exist yet.).

Crystallization in small pores[edit]

In the case of small pores the effect of the crystal size on their solubility has to be considered. The smaller the crystal size, the higher the solubility, so that crystals in small pores require higher concentrations for their growth. The influence of the size of spherical crystals on their solubility can be calculated by the following equation (Ostwald-Freundlich equation):

lna0/a∞=(2γclVm)/rRT (Eq. 8)

where a0 and a∞ are the thermodynamic solubility products of the smaller crystal with regards to an infinitely large crystal; γcl is the interfacial energy between the crystal and the solution, and r the radius of the crystal [Steiger:2005b]Title: Crystal growth in porous materials: II. The influence of crystal size
Author: Steiger, Michael
Link to Google Scholar.

In the case of a round pore having a small cylindrical entrance, a model for two dissimilar sized pores is required. If the solution is saturated with regards to the smaller crystal at the pore entry r1, then it will be supersaturated with regards to the larger crystal in the spherical pore r2. Therefore the larger crystal will continue its growth and apply pressure to the pore wall, until equilibrium is reached. Since the required concentration at the free surface (the small crystal) is greater than for the large crystal, then growth can only proceed under pressure against the pore-wall. Applying the crystallization equation for pressure using the saturation activity of the larger crystal (instead of the activity of the saturated solution), with that of the smaller crystal at the pore entry (instead of the solution activity), and the last equation for solubility dependence, the following equation for calculating the crystallization pressure is obtained:

∆p=2γcl∙[(1/r1)-(1/r2)] (Eq. 4)

The equation corresponds to that of [Everett:1961]Title: The thermodynamics of frost damage to porous solids
Author: Everett, D.H.
Link to Google Scholar; it is a special case for a given geometry based on a pressure build-up following supersaturation. Thus, the equations of Correns and Everett are interconvertible, i.e., exchangeable, and describe the same deterioration mechanism for specific geometries, and therefore are not contradictory [Steiger:2005]Title: Crystal growth in porous materials: I. The crystallization pressure of large crystals
Author: Steiger, Michael
Link to Google Scholar. In the case of the described geometry, the supersaturation will increase with respect to a decreasing pore entry. For other geometries, other equations for the crystallization pressure can be developed ([Steiger:2005]Title: Crystal growth in porous materials: I. The crystallization pressure of large crystals
Author: Steiger, Michael
Link to Google Scholar, [Scherer:1999]Title: Crystallization in pores
Author: Scherer, George W.
Link to Google Scholar, [Flatt:2002]Title: Salt damage in porous materials: how high supersaturations are generated
Author: Flatt, Robert J.
Link to Google Scholar, [Steiger:2006]Title: Crystal growth in porous materials: Influence of supersaturation and crystal size
Author: Steiger, Michael
Link to Google Scholar.

Also for smaller pores, the pressure will only develop when the pore solution is supersaturated with respect to free surfaces, i.e., an unloaded surface. For smaller pores this is the consequence of the different solubility presented by the curving of surfaces. The higher the curvature, the higher will the solubility be and therefore the supersaturation with respect to the less curved faces where crystal growth occurs. In this case, the supersaturation and the crystallization pressure will be in equilibrium, so that they can operate for longer periods. Nonetheless, it is critical to take into account that the influence of crystal size on its solubility will only be relevant for radius <0.1 µm ([Steiger:2005]Title: Crystal growth in porous materials: I. The crystallization pressure of large crystals
Author: Steiger, Michael
Link to Google Scholar) and to attain higher pressures a pore diameter of <10-50 nm ([Steiger:2009]Title: Mechanismus der Schädigung durch Salzkristallisation
Author: Steiger, Michael
Link to Google Scholar) is required, and this occurrence happens only for some construction materials. For larger pores the crystallization pressure is not in equilibrium (see above). In this case, the slow evaporation will result in highly concentrated solutions when they are not in contact with all crystal faces. If there is no sufficient contact with a free surface, the supersaturation can work for longer time, and the pressures maintained ([Steiger:2005b]Title: Crystal growth in porous materials: II. The influence of crystal size
Author: Steiger, Michael
Link to Google Scholar). High supersaturation can be achieved through fast evaporation. If the diffusion of ions in the solution is interrupted, this may result in growth at loaded faces, when free faces are no longer in contact with the solution ([Flatt:2002]Title: Salt damage in porous materials: how high supersaturations are generated
Author: Flatt, Robert J.
Link to Google Scholar).

Special case of hydration pressure[edit]

Some salts can crystallize with different degrees of hydration, for example, magnesium sulfate (MgSO4∙nH2O), where n ranges from 1,4-7. The different hydration number results in that the higher hydrated phases have a larger molecular volume, which were held responsible for exerting pressure on the pore structure for a long time(e.g.,[Correns:1926]Title: Über die Erklärung der sogenannten Kristallisationskraft
Author: Correns, Carl W.
Link to Google Scholar). Two different type of hydration reactions can be established.

One corresponds to the hydration via water vapor, which is dependent on the air moisture in the environment. If the RH value is below the deliquescence moisture of the lower hydrate, or the anhydrous phase, then the hydration occurs as a solid phase reaction. In this case, the maximum pressure that the hydrating crystal can induce on the pore wall can be calculated with the equation for hydration pressure given by Mortensen [Mortensen:1933]Title: Die 'Salzprengung' und ihre Bedeutung für die regionalklimatische Gliederung der Wüsten
Author: Mortensen, Hans
Link to Google Scholar (see Historical Background section). During crystallization, the supersaturation of the solution is the driving force for the exerted pressure, while during hydration via water vapor (RH<DRH of the lower hydrate) it corresponds to the supersaturation of the water vapor in the environment in relation to the equilibrium water vapor pressure of the hydrated phase at the given temperature. In this case, if the equation of Mortensen is used, it has to be considered that there is a maximal RH above which the equation is no longer valid. If the moisture in the air is above the deliquescence moisture of the higher hydrated phase, then no hydration pressure can develop [Steiger.etal:2014]Title: Weathering and Deterioration
Author: Steiger, Michael; Charola A. Elena; Sterflinger, Katja
Link to Google Scholar.

If the RH during moisture absorption is above the DHR of the lower hydrated phase, then hydration will continue via other mechanisms. The lower hydrate forms a saturated solution, out of which a higher hydrate will crystallize out (dissolution and recrystallization process). Also in this case the volume increase is not the reason for the pressure increase on the porous structure, but the crystallization of the higher hydrate phase from a supersaturated solution. Thus, this mechanism is a special case of the crystallization pressure as a result of crystallization from supersaturated solutions. And this mechanism is also responsible for the pressure developed through moisture absorption of liquid water in a porous system where an anhydrous or lower hydrated phase is present [Steiger:2003b]Title: Salts and Crusts
Author: Steiger, Michael
Link to Google Scholar.

For instance, the system sodium sulfate-water is a good example. If a porous material is moistened with a solution of thenardite at room temperature, then a saturated solution with regards to thenardite will form. Looking at the phase diagram of the system, it is evident that the solution will be saturated with regards to mirabilite, and that the supersaturation increases with lowering temperature. When mirabilite crystallizes out of a highly supersaturated solution then, if sufficient pores are filled, high pressures can develop in the porous structure. This can be observed during wetting, as well as during wetting of the anhydrous or lower hydrated phases at RH up to or above the DRH, where the hydrated phase can form a supersaturated solution. In general terms, this occurs through the dissolution of a metastable phase to allow the formation of a supersaturaed solution with regards to a more stable phase, so that during its crystallization high pressures can develop [Steiger.etal:2008]Title: Crystallization of sodium sulfate phases in porous materials: The phase diagram Na2SO4–H2O and the generation of stress
Author: Steiger, Michael; Asmussen, Sönke
Link to Google Scholar.

Consideration of crystallization pressure within building deterioration[edit]

Salt crystallization will induce damage and deterioration in porous inorganic materials. Salts, as well as their solution(s), are present in the buildings environment, e.g., rising damp, so that there is a direct interchange between them. Changes in RH will result in cycling between crystallization and dissolution, especially when they occur around the DRH. Rain, as well as condensation induced by temperature changes will also result in the introduction of water or hydration of the salts already present in the material. Some salts will change phases with only temperature variation, depending on their stability within the temperature range, for example, mirabilite. However, in buildings the concentration of salts seldom reaches those that were used in laboratory studies to understand the damage mechanism.

Furthermore, for the case of crystallization pressure the points discussed in the Clarification section are valid. Small pores, that are necessary for an equilibrium of the crystallization pressure, are not frequently found in most construction materials, but can be found in cement. Therefore, crystallization pressure in real buildings is not found in equilibrium, but rather as a dynamic process ([Steiger:2009]Title: Mechanismus der Schädigung durch Salzkristallisation
Author: Steiger, Michael
Link to Google Scholar, [Scherer:2004]Title: Stress from crystallization of salt
Author: Scherer, George W.
Link to Google Scholar. The high supersaturation conditions occur only in short events and are reduced by the crystallization on free surfaces.

Literature[edit]

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relative humidity

Deliquescence Relativ Humidity

crystallization of a dissolved salt

concentration given as amount of substance (mol) of the dissolved substance per kilogram solvent; unit: mol•kg-1.

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