A commented translation of the paper by C.W. Correns and W. Steinborn on crystallization pressure

Abstract

Crystallization of salts is recognized to be a major factor of the degradation of porous materials such as stone and concrete. On the theoretical side, there is now general acceptance about the thermodynamic origin of this phenomenon. However, on the experimental side, there are only scarce quantitative data. In this respect, the reference work par excellence is that of Correns (Discuss Faraday Soc 5:267–271, 1949) who shows a good correlation between calculated and measured crystallization pressures. However, concerns about both the thermodynamic derivation and the experimental conditions raise the question about why Correns could have obtained such a good correlation. This issue is discussed extensively in this paper which is organized as a commented translation of a former paper by Correns, co-authored by Steinborn, and that is much richer in experimental details.

Appendix: Experiments for the measurement and explanation of the so-called force of crystallization (translation of: "Experimente zur Messung und Erklärung der sogenannten kristallisationskraft")

Correns and Steinborn (1939) (from the Mineralogical-Petrographical Institute of Rostock University).

Preface

Again and again in different contexts an undefined force of crystallization is mentioned in the literature. It has been repeatedly pointed to that this can only concern processes that are quantifiable by chemical and physical relations. In this context, it is appropriate to distinguish between two completely different kinds of such effects: volumetric action and linear effect.

The volumetric action in crystallization is generally known as bursting pressure of freezing water. The dependence of the resulting pressure on the temperature has long been experimentally investigated. A similar effect can also develop, if salts crystallize from supersaturated solution. This volumetric action was questioned. In what follows, it is quantitatively investigated. The volumetric action of hydration was included in this context as well, although strictly speaking, it does not belong there. In contrast to the volumetric action, we also considered the “linear” growth pressure exerted by an individual crystal. Most of this work is dedicated to the measurement of these pressures.

The supersaturated solutions used in these investigations were prepared as follows. They were first saturated in the heat and in the presence of excess solids. They were passed, hot, through a hardened filter and slowly cooled down. To avoid the presence of dust, the crystallization dishes were covered by glass plates and cardboard boxes.

Refractive index was used to determine solution concentrations. Values for potash alum at 15, 19, 20 and 25°C are given in Table 1,³ while the diagram in Fig. 4 gives values for 15 and 25°C. The refractive indices are given on the ordinate and the concentrations of KAl(SO₄)₂·12H₂O in gram per 100 cm³ of solution on the abscissa. From the alum solubility values from Landolt-Boernstein reported by Berkeley and Mulder, the saturation points were determined at 15, 19, 20 and 25°C and are also reported in Table 1. In Fig. 4, their data are used to plot a phase boundary.

Table 1 Refractive indices and concentrations of alum solutions at 15–25°C

Fig. 4

Saturation indices and concentration of alum solutions at 15–25°C. The thick line is the saturation curve

In what follows concentration level is defined as the ratio c/c _s, where c is the measured concentration and c _s the concentration at saturation, so that c/c _s can increase from 0 (pure water) to 1 (exactly saturated solution) and above (supersaturated solution).

As an example: dissolving 18.74 g alum while heating in 100 cm³ water, the subsequently cooled solution contains the same amount at 15°C, while the saturated solution should only contain 9.37 g at this temperature, hence, the supersaturation is $c \mathord{\left/ {\vphantom {c {c_{s} }}} \right. \kern-\nulldelimiterspace} {c_{s} } = {18.74} \mathord{\left/ {\vphantom {{18.74} {9.37}}} \right. \kern-\nulldelimiterspace} {9.37} = 2.0$, i.e. 200%. For concentrations c/c _s > 1.7, it was very difficult to determine the refractive indices since the crystallization of the salt from the solution droplet placed on the refractometer was too fast to determine the refractive index.

For the sodium chlorate solutions, the values from Landolt-Boernstein were used and complemented by own measurements.

Bursting action by crystallization from supersaturated solutions

Correns (1926) expressed his suspicion that during the precipitation of crystals from supersaturated solutions, the volume of the supersaturated solution could be smaller than the sum of the perfectly saturated solution and the precipitated crystals. He considers that, in cavities, a bursting force could result from this volume increase upon cooling or evaporating a supersaturated solution.

In order to observe such volume changes in crystallizing solutions, the instrument illustrated in Fig. 5 was used. It consists of a 100-cm³ container in which a thermometer and a tube with a precisely etched graduation are inserted. The connecting frits were covered with a thin layer of vacuum grease, in order to avoid crystallization within the pores. In this container, the hot nuclei-free supersaturated solution was cooled down to room temperature. After adding a nucleation seed through the insertion tube, a droplet of coloured oil was added with a capillary to cover the solution meniscus, avoiding evaporation and facilitating the determination of the meniscus position. Highly supersaturated solutions crystallized immediately after introducing the nuclei; with weakly supersaturated solutions, the seed grew slowly. The experiments were not interrupted until saturation seemed to be reached. For higher accuracy, the refractive index of the solution was determined at the end of each experiment and checked with respect to Fig. 5 to ensure that the solution was no longer supersaturated. The measurements were carried out in a cellar with a roughly constant temperature, of which the maximum fluctuations were 2°C, but on average rarely greater than 0.5°C over a 24-h period.

Fig. 5

Measuring device for observation of the volume change during crystallization of supersaturated solutions

In these experiments, one must also take into account dissipation of the crystallization heat, which can cause an expansion. Experiments must therefore only be interrupted once the thermometer indicates once again the starting temperature. For alum solutions, the thermal volumetric effect was only very small, in comparison it was much stronger for sodium chlorate solutions (for concentrations c/c _s > 1.7, the temperature rose up to 10°C).

Volumetric increase from crystallization out of supersaturated solution was observed for alum, soda and CaCl₂·6H₂O, while contraction was found with sodium chlorate. One can assume that salts that contract during dissolution, like alum, will exhibit expansion when crystallizing from a supersaturated solution, while salts such as NaClO₃, that cause a volume increase during dissolution, will show a contraction when crystallizing from a supersaturated solution.

In order to calculate the pressure caused by crystallization, the formula for compressibility coefficient was used.

$$ \beta _{t} = \frac{1} {{V_{1} }}\frac{{V_{1} - V}} {{p - p_{1} }}, $$

(4)

where

β _t :

compressibility coefficient at t°C in atm⁻¹

V ₁ :

liquid volume at pressure p = 1 atm (the volume to be compressed)

V :

liquid volume at pressure p (the volume to be achieved)

The pressure p is obtained by solving the above equation for p:

$$ p = \frac{1} {{V_{1} }}\frac{{V_{1} - V}} {{\beta _{1} }} + p_{1} . $$

(5)

In the case of experiment 30 in Table 2, we have, e.g.

V ₁ :

100.863 cm³

V :

100 cm³ = volume of the measuring instrument

p ₁ :

1 atm

β _t :

43.4 × 10⁻⁶ atm^–1

p :

198.1 atm = 204.7 kg/cm²

For β _t , in the absence of appropriate values for alum solutions, values for water found by Amagat from Landolt-Boernstein (valid at 20°C from 1 to 500 atm) were used instead. Values for other concentrated salt solutions are of the same order of magnitude.

Table 2 Supersaturation, volume increase during crystallization and growth pressure in alum solutions

The observed volumetric increases and the associated pressures are listed in Table 2. In addition, Fig. 6 shows graphically the relation between supersaturation and pressure.

Fig. 6

Dependence of growth pressure of crystallizing alum solutions on the degree of supersaturation. • Translation note: the two points that lie slightly out of regression at c/c _s 1.73 and 1.89 correspond to data in Table 2, although values in the original graph line up in the original plot

In a similar way to the freezing of water, in order for the bursting action to develop from the volume change of the supersaturated solution, crystallization must take place in a cavity, of which the outlets are clogged by ongoing crystallization. The bursting effect of supersaturated alum solutions can be demonstrated using thin-walled glass balls that one can easily produce oneself. After filling the ball to about 90% with hot, supersaturated alum solution. The ball neck is heated and pulled in such a way as to make a long capillary tube. The solution in the ball is heated. The ball is then placed in cold water and the end of the capillary in a hot, supersaturated alum solution. This solution is readily sucked up into the slightly evacuated ball. This procedure is repeated until the glass ball and the entire capillary are filled with solution. After cooling to room temperature, the capillary is broken and through the produced opening a tiny crystallization seed is introduced into the solution. Shortly after, the capillary is clogged to such an extent with crystals that the glass ball is practically closed. If the solution is not too weakly supersaturated, the ball is broken apart. The same results are also obtained with soda and calcium chloride solutions.

Experimental demonstration of the bursting effect of hydration

With a similar experimental set-up, the bursting effect of hydrate formation can also be demonstrated. Mortensen (1933) calculated the pressures that can arise under natural conditions.

Glass balls were filled with finely powdered thenardite, others with anhydrous calcium chloride or anhydrous sodium carbonate. After making a capillary out of the ball neck, the glass balls were placed in a desiccator of which the bottom was filled with water. The desiccator was then closed. The glass ball filled with thenardite took up so much water within 3 days that the volume increase caused the glass ball to break. With calcium chloride, it took only 2 days, with sodium carbonate 5 days, respectively. Breaking took place considerably earlier if the opening of the glass ball was directly placed in water, or in the presence of a stream of water vapour.

The examples mentioned only concern apparent volume increases since 53 cm³ thenardite and 180 cm³ water form only 221 cm³ mirabilite; 50 cm³ CaCl₂ and 108 cm³ water form only 133 cm³ CaCl₂· 6H₂O; 42 cm³ Na₂CO₃ and 180 cm³ water form only 191 cm³ soda. In the above-mentioned experiments, the necessary conditions to allow hydration to cause the bursting are achieved. These are namely that the reaction product must be a coarse, solid material and should not form in the capillary, which only serves for the transport of water to the reaction site (Correns 1926).

Measurement of linear growth pressure

The experiments presented by Correns (1926) about growth pressure and its dependence on the interfacial tension between crystal, solution and cover or support, have been continued. It should be stated here that Correns (1926), in contrast to a statement of Schubnikow (1934), had made no “measurement” of growth pressure, but only gave loads used in his experiments in order to show the role of interfacial tension. In the following, the pressures were now really measured. It is shown that values are obtained, which are much larger than the loads that were used in 1926.

The growth pressure not only depends on the interfacial tension, but also on the degree of supersaturation. It must in fact be so according to the Riecke principle, and it is only surprising that this dependence was not discovered earlier. A crystal under pressure is slightly more soluble than one that is not pressed; it is thus in equilibrium with a supersaturated solution, and the larger the pressure the more supersaturated the solution must be. The relationship between pressure and supersaturation can be derived from thermodynamics as follows.⁴

If a solution of concentration c _s (saturation concentration) at pressure p is in equilibrium with a crystal at the same pressure, then the chemical potential of the solution μ _L and the crystal $\mu _{{K{\left( p \right)}}}$ are equal, we have

$$ \mu _{L} = \mu _{{k(p)}} . $$

(6)

Also, the following is generally valid:

$$ \mu _{L} = \mu + RT\,{\text{ln}}(c). $$

(7)

Thus in our case,

$$ \mu _{L} = \mu + RT\,\ln {\left( {c_{S} } \right)}. $$

(8)

From this, we find

$$ \mu _{{K{\left( p \right)}}} = \mu + RT\,\ln {\left( {c_{{\text{s}}} } \right)}. $$

(9)

Now, if a solution of concentration c at pressure p is in equilibrium with a crystal at pressure p + P, then similarly we have

$$ \mu _{L} = \mu _{{K{\left( {p + P} \right)}}} . $$

(10)

Now, however,

$$ \mu _{L} = \mu + RT\,\ln {\left( c \right)} $$

(11)

and

$$ \mu _{{K{\left( {p + P} \right)}}} = \mu _{{K{\left( p \right)}}} + {\int\limits_p^{p + P} {\frac{{\partial \mu _{K} }} {{\partial p}}} }. $$

(12)

It follows that

$$ \mu + RT\,\ln {\left( c \right)} = \mu _{{K{\left( p \right)}}} + {\int\limits_p^{p + P} {\frac{{\partial \mu _{K} }} {{\partial p}}} } $$

(13)

and

$$ \mu + RT\,\ln {\left( c \right)} = \mu + RT\,\ln {\left( {c_{S} } \right)} + {\int\limits_p^{p + P} {\frac{{\partial \mu _{K} }} {{\partial p}}} }, $$

(14)

respectively. Also,

$$ RT\,\ln {\left( {\frac{c} {{c_{{\text{S}}} }}} \right)} = {\int\limits_p^{p + P} {\frac{{\partial \mu _{K} }} {{\partial p}}} }\,{\text{d}}p. $$

(15)

By definition $\partial G = \mu \partial n$, where G = Gibbs energy, n = number of moles, i.e. $\mu = \frac{{\partial G}} {{\partial n}}$.

It follows

$$ \frac{{\partial \mu _{K} }} {{\partial p}} = \frac{\partial } {{\partial p}}\frac{{\partial G}} {{\partial n}} = \frac{\partial } {{\partial n}}{\left( {\frac{{\partial G}} {{\partial p}}} \right)} = \frac{\partial } {{\partial n}}V = v, $$

(16)

i.e. we get

$$ RT\,\ln {\left( {\frac{c} {{c_{S} }}} \right)} = {\int\limits_p^{p + P} v }\,{\text{d}}p. $$

(17)

Taking v as a constant over the pressure range from p to p + P, we find

$$ RT\,\ln {\left( {\frac{c} {{c_{S} }}} \right)} = vP, $$

(18)

where

R :

gas constant

T :

absolute temperature

c :

given concentration

c _s :

saturation concentration

v :

molar volume of the crystalline solid

The maximum work needed to transfer 1 mol of substance from a solution at concentration c to a solution at concentration c _s and in equilibrium with a crystal at the same pressure is similarly $RT\,\ln {\left( {c \mathord{\left/ {\vphantom {c {c_{{\text{s}}} }}} \right. \kern-\nulldelimiterspace} {c_{{\text{s}}} }} \right)}$. If the crystal is under a positive pressure P, then the transfer of 1 mol of substance requires an additional work of Pv to be provided. Thus, the maximum positive pressure up to which a crystal can still grow, is given by

$$ P = \frac{{RT}} {v}\ln {\left( {\frac{c} {{c_{{\text{s}}} }}} \right)}. $$

(19)

• Translation note: as described in the discussion, Eq. 19 is only valid for ideal solutions of molecular solutes (monomolecular crystals, such as sugar).

Conversely, the maximum pressure P depends on supersaturation and is directly proportional to the natural logarithm of concentration.

For T = 293.19 (t = 20°C), c/c _s = 2.0 and R = 0.08203 L atm K^–1, we have as an example for alum ${\left( {v = {474.38} \mathord{\left/ {\vphantom {{474.38} {1.751}}} \right. \kern-\nulldelimiterspace} {1.751} = 270.91} \right)}$:

$$ P = \frac{{82.03 \times 293.91}} {{270.91}}2.30259 \times 0.3010, $$

$$ P = 61.506\,{\text{atm}} = 63.544\,{\text{kg}}\,{\text{cm}}^{{ - 2}} . $$

For a part of the pressure measurements, a simple pushrod was used that fed through a guide and that could be loaded with weights. The lower part of the pushrod was in a glass tube the end of which was stuck to a smooth glass plate to avoid contact of the solution with metal. The buoyancy of the part of the pushrod in the solution was deducted when calculating the pressure. The growth experiments were carried out in part in a bowl with a mirror base and in part with a glass plate below the crystal.

Another part of the experiments was carried out with a pressure gauge, which was built by Correns (1926) and whose details are shown in Fig. 7. It allows continuous observation of whether the crystal continues to grow. The mirror set-up resulted in a reading of 15 mm for 1 μm of growth. The pressure p was determined from the following equation:

Fig. 7

Pressure gauge for the continuous observation of growth pressure. Schematic illustration. P _l tungsten spot light, S ₁ rotatable mirror, S ₂ fixed mirror, S _k scale, D pin that rotates the mirror, C suspension of the scale G, K crystal, A notch, Al aluminium pushrod, B edge, H thread for height adjustment

$$ {\text{load }}G \times {\text{load lever BC}} = p \times {\text{pressure lever AC}} $$

(20)

determined taking into account the buoyancy of the aluminium rod, which as for the pushrod tip was plugged into a glass shoe.

• Translation note: as described in the discussion, Eq. 20 is not correct in terms of units and also because AC should read AB. It is unclear if this was just a typing mistake.

The results for alum crystals, which were constrained above and below by octahedral surfaces, are given in Table 3, selecting only the values necessary for constructing the boundary curve b in Fig. 8. Table 4 gives values for alum crystals in stirred solution, constrained above and below by rhombododecahedral surfaces and placed between glass plates. Figure 8 gives measured and thermodynamically computed values for both surfaces.

Table 3 Growth pressure and supersaturation in alum, {111}, stirred solution

Fig. 8

Dependence of growth pressure on supersaturation. Alum at 20°C, stirred solution. a Calculated curve, b observed curve for {111} (open triangle no growth, filled triangle growth), and c observed curve for {110} (open circle no growth, filled circle growth)

Table 4 Growth pressure and supersaturation in alum, {110}, stirred solution

The crystal was weighed before and after the experiments in order to make sure that it had continued to grow even in the cases where no lifting of the weight and therefore no height change was observed.

The experiments must be performed in stirred solutions. If not, one has a considerable concentration gradient between bottom and top of the solution. In one case, values of c/c _s were observed to be 1.601 at the bottom, 1.596 above the crystal and 1.525 at the upper surface of the solution. With this downward gradient, the crystal practically only grows at its underside, as is to be observed from the slight overgrowth of chrome alum crystals by potassium alum. Under those conditions, material supply to the edges takes place so fast that the well-known step-like cavities develop on the lower surface of the crystals. In stirred solutions, the surfaces are smooth or almost smooth.

The experiments basically show that there is a connection between supersaturation and growth pressure. However, the values for {111} do not reach the thermodynamically calculated values, remaining below them. Values for {110} lie even further below. If one tries to let cubes grow between glass plates, they do not grow at all. There is therefore something more than just supersaturation at play. It is the relative values of interfacial tensions. This possibility was already referred to in earlier work and already Correns (1926) showed that octahedral alum crystals can grow between glasses but not between mica plates. We continued these investigations. It turns out that alum with {110} and {100} as bearing surfaces does not grow either between mica plates. With {111} as bearing surface, it grows between cleaved gypsum plates along {010}, but not, if {110} and {100} are the bearing surfaces. Cubic sodium chlorate crystals grew neither between glass, mica nor gypsum plates.

The result of Schubnikow (1934), who found much smaller pressures with alum than Correns (1926), can thus be explained firstly because other supersaturations were used and secondly because Schubnikow (1934) used for the upper pressurizing surface a ball as load for which different crystal surfaces were active. If one puts a small glass ball on an alum crystal in a supersaturated solution, it gets incorporated. However, glass plates that are smaller than the crystal surface can be lifted by the octahedral surface of alum and are not incorporated at small supersaturation. If the supersaturation is large, the crystal grows around the glass because growth on the free surface is faster than under the glass. For the same reason, balls that only affect the surface on one point are always incorporated.

Finally our experiments indicate that incorporation also takes place in cases where the supersaturation is not large enough with respect to the pressure needed to push away the foreign body. This might for instance be the reason, why one usually finds clear gypsum in clays, while they tend to include sand. The “self-cleaning ability” of crystals is thus based on a synergy of different circumstances.

Following an initial attempt by Des Coudres, Correns (1926) attempted to explain the relationship between interfacial tension and growth pressure: If the crystal is to grow, then liquid must be pulled in between it and the supporting and the loading surface, respectively. In what follows, we only consider the supporting surface: If the crystal a, which is surrounded on its sides by the solution b and rests on the support c, is removed from the latter, work must be carried out. An interface of size ϖ and interfacial tension σ _ac disappears in this process. At the same time, two new equally sized interfaces are created, which have the interfacial tensions σ _bc and σ _ab.

If the crystal lifts its own and the added weight during growth, then the work required is

$$ A = \varpi {\left( {\sigma _{{ac}} - \sigma _{{ab}} - \sigma _{{bc}} } \right)}. $$

(21)

• Translation note: this work actually defines the maximum work that can be exerted by the crystal against an applied load while maintaining a liquid film between itself and the surfaces exerting that load. The presence of this film allows growth against load. Its disappearance thus defines a maximum in crystallization pressure (Scherer 1999).

A positive A, i.e. elevation, is only possible if the condition

$$ \sigma _{{ac}} > \sigma _{{ab}} + \sigma _{{bc}} $$

(22)

is fulfilled. Nothing is known about σ _ac. Concerning σ _bc, there is a value for gypsum and pure water based on solubility measurements (1,050 dyn/cm²) which is associated with large uncertainties.

From our experiments, one can conclude that σ _ac and σ _ab are different on the different crystal surfaces. This demonstrates that interfacial tensions of different crystalline planes can be different. One can further conclude that not only the solid/solid interfacial tension, σ _ac, but also the solid/liquid interfacial tension σ _ab, changes according to surface orientation. If one assumes that different solid/liquid interfacial tensions also mean different solubilities, one reaches the statement that the solubility of different surfaces can be different, which has been rejected since the work of Valeton (1939). It cannot be the purpose of this presentation of our experimental results to discuss in detail the old question about the dependence of the solubility on the crystalline face, which have been settled since the work of Valeton (1939). Only the following is pointed out: Valeton (1939) proved experimentally that at saturation there is no difference of solubility and he supported this theoretically. Figure 8 shows that deviations of the rhombododecahedral and octahedral contact surfaces from the thermodynamic curve are only observed for pressures above about 20 kg/cm² and supersaturations c/c _s = 1.2. Thereby differences between the two surfaces are then also seen. Exactly at saturation c/c _s = 1, there should be no deviation in the case of a cube either, the curve of which in Fig. 8 follows the abscissa.

The different interfacial tensions of the surfaces surely arise from different structures of these surfaces, and one might think of a crystal intergrowth. However, we found no intergrowth, if we let seeds of alum grow on mica or gypsum. Growth or no growth under load was independent of the orientation of the crystal against support. Alum crystals, which grew with the cubic surface on glass, generally adhere in such a way that one must use noticeable force in order to remove it, while they remain completely loose on octahedral surfaces. Surfaces {111} on mica and {110} as well as {100} on gypsum behave similarly as {100} on glass. Covering an octahedral alum crystal, which grew firmly on a mica plate, with a gypsum plate, and leaving it grow further in supersaturated solution, then it lifts up the load. An alum crystal with {110} firmly grown onto a gypsum plate, and which is covered with a mica plate, does not lift the latter. A discussion of the structural reasons for this kind of growth requires further investigations.

Summary

The crystallization from supersaturated solutions of alum, soda and calcium chloride is accompanied by a volume increase. It was measured and the resulting pressure was calculated.

Experiments demonstrating this volume effect as well as the bursting effect resulting from hydration are presented.

The linear growth pressure is driven by supersaturation. It would be directly proportional to it, if the effect of the interfacial forces did not come into play. The dependence of growth pressure on the crystalline plane of the growing crystal and of the supporting surface and load are given in Table 5, in which + indicates growth, and − no growth under pressure.

From these experiments it follows that the interfacial tensions of {111}, {110}, {100} with respect to solution are different for alum.

Table 5  

• Translation note: in these experiments the crystals are placed between two surfaces of the materials listed in the first column of Table 5. The orientation of the alum crystals was such that different crystal faces were in contact with these surfaces.

References

Correns CW (1926) Über die Erklärung der sogenannten Kristallisationskraft. Sitz.-Ber. D. Preuß. Akad. d. Wiss. 11:81ff

Landolt-Börnstein, Physikalisch-Chemische Tabellen. 5. Aufl

Miers HA (1904) Untersuchung über die Variation der an Krystallen beobachteten Winkel, speziell von Kalium- und Ammoniumalaun. Z Kristallogr 39:220–278

Mortensen H (1933) “Die Salzsprengung” und ihre Bedeutung für die regiona1klimatische Gliederung der Wüsten. Petermanns Geogr. Mitt. 5/6:130–135

Schubnikow A (1934) Vorläufige Mitteilung über die Messung der sogenannten Kristallisationskraft. Z Kristallogr 88:466–469

Ulrich U (1930) Chem Themodyn

Valeton JPP (1939) Kristallform und Löslichkeit. Ber. über die Verhandl. d. kgl. Sächs. Ges. d. Wiss. zu Leipzig 67/68(1915/16):1–59