Anomalous Isomorphism and Mixed Crystals in the Systems NH4Cl

Oct 1, 2012 - 7/9, 199034 Saint-Petersburg, Russia ... amount of different guest phases is primarily dictated by the NH4Cl/MeCl2 ratios in mother liqu...
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Anomalous Isomorphism and Mixed Crystals in the Systems NH4Cl:(Cu,Mn) Lyubov’ A. Pyankova, Alexander G. Shtukenberg,*,† and Yurii O. Punin Saint-Petersburg State University, Universitetskaya emb. 7/9, 199034 Saint-Petersburg, Russia ABSTRACT: Anomalous mixed crystals are metastable objects consisting of randomly stacked blocks of several crystalline phases in mutual epitaxial relationships. This article reports the first systematic characterization of crystal growth, phase composition, epitaxial relationships, and imperfections of mixed host/guest NH4Cl:Me crystals forming in the two similar systems NH4Cl−MeCl2−H2O−CONH3 (Me = Cu, Mn) with a wide range of NH4Cl/MeCl2 ratios. The normal growth rates of {100} faces of cubic NH4Cl:Me crystals can be described by Bliznakov’s kink-blocking model in which lateral interactions between impurity particles is taken into account by using the Fowler−Guggenheim adsorption isotherm. Copper and manganese are incorporated into the crystal structure of ammonium chloride host crystals in significant amounts (up to 7 wt %) in the form of epitaxially oriented intergrowths of (NH4)2MeCl4·2H2O, MeCl2·2CONH3, and CuCl2·2H2O guest phases. The presence of guest phases in the host crystal is controlled by epitaxial matching not only in the growth plane {100} but also in the perpendicular direction. The relative amount of different guest phases is primarily dictated by the NH4Cl/MeCl2 ratios in mother liquor. The coherent phase matching in the crystals produces strong mismatch stress that shows up via stress birefringence and relaxes by means of brittle and plastic deformations.

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INTRODUCTION Crystallization from the multicomponent media simultaneously supersaturated with respect to several phases is very common in nature as well as in laboratory experiments and industrial processes. If cocrystallizing components are well miscible, they form solid solutions. In the opposite case of absolutely immiscible compounds, different phases crystallize simultaneously but independently of each other. However, between these relatively well studied limiting cases, there is a world of mixed crystals composed of nanometer to micrometer size blocks of different phases related to each other by crystallographic relationships. Pioneer work was done on mixtures of simple salts like ammonium chloride and transition metal chloride cocrystallizing from aqueous solutions.1−3 Later, salts and molecular crystals were found to form mixed crystals with big dye molecules.4,5 Independently, complex intergrowth of several phases were found among oxides, ferrites, hightemperature superconductors,6,7 and various minerals including biopyriboles, carbonates, and sheet silicates.7−9 Additionally, to direct crystallization, anomalous mixed crystals can form by means of solid state reactions.8,9 Nowadays, increasing attention is paid to different crystal-complex organic molecules and crystal-polymer composites,10,11 which are of high importance for biomineralization. Because of their diverse origin, mixed crystals earned different names including fragmentary crystals, composite crystals, anomalous isomorphic crystals, mixed crystals, mesocrystals, and polysomatic crystals, among some others. These terms are not strict synonyms; they can relate to different objects and highlight different aspects of mixed crystals. However, clear and transparent terminology has not been formulated. Likewise, general growth mechanisms and © 2012 American Chemical Society

principles that control formation of mixed crystals are not understood and need to be established. This article reports the first systematic study of mixed crystals forming in two similar and classic systems NH4Cl−MeCl2− H2O−CONH3 (Me = Cu, Mn), where the Me2+ bearing guest phases are incorporated into the host ammonium chloride crystal. Although these and similar systems were paid significant attention in the past,1−3,12−20 most of the studies were based only on measurements of total impurity concentration in a crystal and were carried out without application of X-ray diffraction methods and microscopic techniques like AFM and SEM. As a result, little is known about forms of impurity incorporation, sizes of impurity domains, mutual orientations between host and guest phases, growth mechanisms, and crystallization kinetics. In addition, the previous studies did not consider crystal optical properties and formation of defects. Our goal here is to address all these issues and to track the evolution of crystal organization, kinetics, micromorphology, crystal optics, and imperfections as a function of impurity concentration. Some of these issues have already been covered in our earlier publications.21−27 Here, we summarize all these findings and add new data on phase identification, epitaxial relationships, and anomalous birefringence.

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EXPERIMENTAL SECTION

Synthesis. The ammonium chloride crystals were grown from water−formamide solutions in Petri dishes by the temperature lowering. The growth temperature varied from 20 to 45 °C; Received: June 23, 2012 Revised: September 11, 2012 Published: October 1, 2012 5283

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supercooling varied from 2 to 10 °C. The water to formamide mass ratio was always equal to 1:1 except in several experiments where crystallization was performed from pure water. Depending on the NH4Cl and MeCl2 salt concentrations, different crystalline phases can precipitate.28 The increasing of the MeCl2 to NH4Cl ratio is accompanied by replacement of NH4Cl:Me crystals with double salts (NH 4 ) 2 MeCl 4 ·2H 2 O and then with the MeCl2·2CONH3 compounds. Growth Kinetics and Surface Micromorphology. The normal growth rates of NH4Cl {100} faces were measured with a light microscope in a microcrystallization cell29 in solutions saturated at 31.5−35 °C and supercooled at ΔT = 1, 3, and 5 °C. Although strictly isothermal crystallization conditions were not achieved, the effect of temperature on the growth rate is much weaker than the effect of impurity concentration and can be neglected. For each supercooling, the growth face advancements were measured for 3 to 6 time intervals (each of them took at least 10 min and corresponded to the face advancement of at least several micrometers) and averaged. The mean squared deviation determined for any seed crystal did not exceed 3%, whereas the growth rate variations measured for different crystals attained 8% due to variability of their imperfections. The surface micromorphology of the growing crystal was observed in situ in a microcrystallization cell (copper and manganese system) and with an atomic force microscope (AFM) NTEGRA Prima (NT-MDT) (manganese system). AFM measurements were performed at room temperature in a fluid cell in tapping mode and ex situ in contact mode.30 Chemical Composition. The copper and manganese concentrations in ammonium chloride crystals were measured with X-ray fluorescence microscope RAM-30μ. The crystals were crushed in powder with mortar and pestle and pressed into tablets. Additionally, the local element mapping of single crystals was carried out in regimes of pointwise and continuous scanning (spots of 50 μm in diameters; scanning step of 50 μm; measurement time of 0.5 s/point). Concentration of copper was also determined colorimetrically. The crystals were dissolved in water, and the absorbance of light going through solution was converted into copper concentrations using a series of standard samples. Phase Identification. Syntactic intergrowths of copper bearing phases in ammonium chloride were detected using X-ray powder diffractometer DRON-2.0 (CoKα radiation, Bragg−Brentano focusing scheme). For the manganese system, X-ray diffractometer DIFREY equipped with a position sensitive detector was used (CrKα radiation, Zeeman−Bolin focusing scheme). The same diffractometer was used for the mapping of the phase distribution (step 0.5 mm) over the (100) growth surface. The presence of manganese bearing phases on the surfaces of ammonium chloride crystals was detected using AFM NTEGRA Prima (NT-MDT) in tapping mode. The areas with different composition and structure can be visualized due to the phase lag of the cantilever oscillation with respect to the excitation force. The phase lag is generated due to the differences in adhesion, capillary, and other forces.30 The value of birefringence was measured with a polarized light microscope equipped with a Berek compensator. For comparison of calculated and observed birefringence, approximately ten crack-free crystals grown in the same batch were analyzed. Table 2 and Figure 9 show the maximum value of the birefringence detected (degree of stress relaxation is supposed to be minimal).

Admixture of formamide is known to stabilize cubic flat-faced morphology of ammonium chloride crystals. The crystals grown in the presence of copper or manganese from water− formamide mixtures (supercooling 2 to 8 °C) are also characterized by cubic morphology. Thus, in this ternary system, the morphology is primarily dictated by the adsorption of formamide. Divalent ions adsorb on the surface already modified by formamide. Impurities of copper and manganese strongly reduce normal growth rates of {100} NH4Cl faces. For the copper bearing system, growth rate decreases monotonically as concentration of impurity, C, increases (Figure 1a). For the manganese

Figure 1. Normal growth rate, V, of the (100) ammonium chloride growth face as a function of impurity concentration, C. Different symbols correspond to different supercoolings, ΔT, whose values (°C) are shown near the curves. Curves are guides to the eye. (a) Impurity of CuCl2; saturation temperature Tsat = 35 °C.23 (b) Impurity of MnCl2; Tsat = 31.5−35 °C.27 Error bars are not shown if their sizes are smaller than the point sizes. Reproduced with permission from refs 23 and 27. Copyright 2007/2012 Springer.

bearing system, the monotonous decreasing of growth rate is observed if CMnCl2 < 6 g/100 g of solvent. At higher impurity concentrations (CMnCl2 = 6−11 g/100 g of solvent), growth rate increases again, forming a broad maximum (Figure 1b). The shape of kinetic curves as well as the absence of the dead zone suggest that the decreasing growth rate in the copper bearing system and for low impurity concentrations in the manganese bearing system cannot be explained by the Cabrera−Vermilyea step pinning mechanism,32,33 but rather by the Bliznakov kink blocking mechanism.32,33 According to the latter model, the step velocity is

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RESULTS AND DISCUSSION Growth Kinetics. The theoretical equilibrium shape of ammonium chloride crystals is rhombododecahedron.31 However, crystallized from aqueous solution, it forms strongly branched skeletal crystals with the branches elongated along [100]. Admixture of copper partially suppresses skeletal growth, whereas admixture of manganese completely suppresses skeletal growth leading to crystals of rhombododecahedral morphology with flat faces. 5284

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(1)

where θ is the surface coverage by impurity, and V0 and V∞ are step velocities in the absence of impurity and in the presence of high impurity concentration, for which θ = 1. In the case of Langmuir adsorption isotherms, the surface coverage is θ = C /(kL + C)

(2)

where 1/kL is the impurity adsorption constant. By combining eqs 1 and 2, one can obtain a linear relationship between 1/(V0 − V) and 1/C: 1/(V0 − V ) = 1/(V0 − V∞) + kL /((V0 − V∞)C)

(3)

Indeed, the kinetic data for the copper bearing system and for the manganese bearing system for CMnCl2 < 6 g/100 g of solvent can be linearized if plotted in accordance with eq 3. However, application of eq 2 contradicts the impurity incorporation mechanism. The Langmuir adsorption isotherm was developed for monolayer adsorption of noninteracting impurity molecules. This assumption is wrong. According to Xray data, impurities aggregate as oriented individual crystallites in the bulk of ammonium chloride single crystal.22,26 Formation of such a crystal requires strong lateral interaction between adsorbed molecules that can be described in the simplest way using the Fowler−Guggenheim adsorption isotherm:34 C = [k 2Fθ /(1 − θ)]exp[−k1Fθ /RT ]

(4)

where the first parameter, k2F, characterizes adsorbate− adsorbent interactions and corresponds to kL in the Langmuir isotherm; R is the universal gas constant, and T is the absolute temperature. The second parameter k1F characterizes intermolecular adsorbate−adsorbate interactions. Varying k1F, k2F, and V∞ and assuming that the rate of ammonium chloride attachment on the surface already covered by impurity does not depend on the impurity coverage, θ, eq 4 fits the experimental data very well (Figure 2). The best agreement can be achieved with k1F = 3.0 kJ/mol and k2F = 0.12 g/100g of solvent for the copper bearing system and with k1F = 0.4 kJ/mol and k2F = 0.5 g/100g of solvent for the manganese bearing system. For the manganese bearing system, at CMnCl2 = 6 g/100 g of solvent, growth rate starts increasing (Figure 1b); that can be explained by modification of the adsorption mechanisms and adsorbing species. In situ optical and ex situ AFM observations show significant changes in the crystal surface micromorphology near the same threshold concentration. As it will be shown below, the same concentration separates regions with different phase composition of impurity domains. Surface Micromorphology. In the copper bearing system ammonium chloride, {100} faces are featured with conical vicinal hillocks. As copper concentration increases and growth rate monotonously decreases, intensity of steps coalescence, and step heights and roughness gradually increase (Figure 3a), which confirms strong adsorption of the impurity. In the manganese bearing system at CMnCl2 = 6 g/100 g of solvent, the surface micromorphology changes significantly. At low impurity concentrations, the {100} face grows by means of flat round (6 to 16 μm in diameter) vicinal hillocks, bound by thick (120−240 nm) macrosteps (Figure 3b). The upper hillock surface is not absolutely flat but slightly convex with a slope of about 0.2° that corresponds to an equidistant

Figure 2. Fitting of kinetic data (triangles) shown in Figure 1 ((a) Impurity of CuCl2, ΔT = 5 °C; (b) impurity of MnCl2, ΔT = 5 °C; reproduced with permission from ref 27. Copyright 2012 Springer) with the Bliznakov eq 1. Solid and dashed lines correspond to the fitting with Fowler−Guggenheim and Langmuir adsorption isotherms, respectively.

elementary step train with step spacing of about 100 nm. The measured step heights are 0.31−14 nm (elementary step height on NH4Cl {100} face is a = 0.39 nm), and step density is 1−2 to 15 steps/μm. The average step heights increase with time, and the height distribution broadens due to the step bunching process. The size of hillocks increases as well. However, this process slows down as hillocks get bigger and higher. At CMnCl2 > 6 g/100 g of solvent flat growth hillocks are replaced by conical hillocks (Figure 3c) similar to the hillocks observed for the copper bearing system (Figure 3a). They are characterized by a broad distribution of step heights ranging from elementary steps (a = 0.39 nm) to macrosteps (>100 nm). The height of hillocks ranges from 75 to 800 nm, and their average slope varies between 0.9° and 2.9°. The shape of hillocks is often asymmetric and the difference in step velocity can be as high as two times. The surface micromorphology is mainly controlled by manganese concentration and, to a lesser extent, by supercooling. Crystal dissolution is opposite to growth; dissolution of flat hillocks starts with formation of flat-bottomed pits, whereas dissolution of conical hillocks starts with formation of conical pits confirming formation of hillocks around dislocation outcrops. The elementary step velocity is v = V/p = aV/d, where p is the slope of the hillock and d is the elementary step spacing. 5285

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Figure 3. Growth micromorphology of ammonium chloride {100} faces. (a) Copper system, CCuCl2 = 1.39 g/100 g of solvent, ΔT = 5 °C, in situ micrograph.23 (b,c) Manganese system, AFM ex situ images recorded in tapping mode, ΔT = 6 °C.27 (b) CMnCl2 = 1.7 g/100 g of solvent, (c) CMnCl2 = 10.8 g/100 g. Reproduced with permission from refs 23 and 27. Copyright 2007/2012 Springer.

For low and high impurity concentrations (CMnCl2 = 1.7 and 10.6 g/100 g of solvent, respectively) and supercooling ΔT = 5 °C (that corresponds to supersaturation σ = Δc/ceq = 8 × 10−2), the average vicinal hillock slopes are 0.2° and 2.0°, respectively. Using normal growth rates from Figure 1, one can estimate average step velocities as 3 × 10−6 and 2 × 10−7 m/s, respectively, and then calculate the kinetic coefficient β = v/ (ωceqσ),33,35 where ω ≈ 6 × 10−29 m−3 is the molecular volume and ceq ≈ 3 × 1027 m−3 is the saturation concentration. This gives β = 2.0 × 10−4 and 1.3 × 10−5 m/s for low and high concentrations of MnCl2 in solution, respectively. Since the normal growth rates are very similar, the almost 10-fold difference in kinetic coefficients is compensated for by the same 10-fold difference in the step densities. Rapid decreasing of the kinetic coefficient, β, in the narrow range of impurity concentrations can be explained by strong increasing of adsorption strength due to the changes in composition of adsorbing complexes. Rapid decreasing of the step spacing, d, is hardly associated with very strong increasing of the power of dislocation sources. More likely, it is caused by decreasing of the step specific free energy due to the impurity adsorption. Heterophase Entrapment of Impurities. Direct measurements of the crystal composition show that ammonium chloride can incorporate as much as 7 wt % of Cu and Mn (Figure 4) with anomalously high distribution coefficients, which attain 0.5−4 for the copper bearing system and 0.2−0.4 for the manganese bearing one. If crystals are grown from pure water, the impurity concentration is limited by 3 wt %; at higher concentrations, impurity phases start crystallizing instead of ammonium chloride. Such significant amounts of impurities cannot be incorporated in the crystal structure of ammonium chloride isomorphically. Instead, as shown by X-ray diffraction method, the partially coherent syntactic intergrowths of ammonium chloride host and Me bearing crystalline guest phases are formed. In NH4Cl:Cu crystals, low copper concentrations are accompanied by intergrowths with the double salt (NH4)2CuCl4·2H2O. At higher copper concentrations, double salt is replaced by phases of copper chloride CuCl2·2H2O and the copper−formamide compound CuCl2·2CONH3 (Figure 5a). Likewise, in NH4Cl:Mn crystals, intergrowths with the double salt (NH4)2MnCl4·2H2O at low manganese concentrations are replaced by intergrowths with manganese− formamide compound MnCl2·2CONH3 at higher manganese

Figure 4. Concentration of Me ions in NH4Cl:Me crystals as a function of Me ions concentrations in a salt part of solutions. Circles, Me = Cu; growth from water−formamide solutions; solid and open circles correspond to data measured by X-ray fluorescence and colorimetry methods, respectively. Diamonds, Me = Cu; data from ref 19 for the crystals grown from aqueous solutions. Squares and triangles, Me = Mn; growth from water−formamide and aqueous solutions, respectively.

Figure 5. X-ray diffraction patterns of NH4Cl:Me crystals ((a) Me = Cu; (b) Me = Mn) showing strong 100 NH4Cl reflections accompanied by weak reflections of the guest phases. Numbers near each pattern denote concentration (wt %) of corresponding ion Me2+ in a crystal. DS, double salts; FC, metal−formamide compounds; CC, copper chloride.

concentrations (Figure 5b). The phase of manganese chloride, however, was not detected. 5286

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Figure 6. Epitaxial relationships between host NH4Cl (100) face (upper row) and guest phases (bottom row): (a) (NH4)2CuCl4·2H2O, projection on (001) face, [100] direction is vertical; (b) CuCl2·2CONH3, projection on (01̅2) face, [100] direction is vertical. Copper atoms are hidden below oxygen atoms.

With respect to the NH4Cl host crystal, the guest phases are oriented in the following ways: for metal−formamide compounds, FC, (01̅2)FC∥(100)NH4Cl; for double salts, DS, (001)DS∥(100)NH4Cl or (more rarely) (100)DS∥(100)NH4Cl; for copper chloride, CC, (010)CC∥(100)NH4Cl. Formation of oriented intergrowths can be explained by epitaxial relationships between crystal structures of host and guest phases, whose structure basis is provided by the structure similarity of complexes MeCl42− (which are present in crystal structures of all guest phases) and Cl44− squares on the NH4Cl (100) faces (Figure 6). The crystal structure similarity results in an epitaxial adsorption of impurity on NH4Cl (100) faces that leads to significant decreasing of growth rates, two-dimensional crystallization of impurity phases, and their entrapment by growing NH4Cl faces.36,37 The lattice constants turn out to be close not only in the growth plane but also in the perpendicular direction (Table 1). Moreover, the probability of finding some guest phase inside NH4Cl crystal decreases as lattice mismatch in the direction normal to the intergrowth plane increases (Table 1). This agrees with the idea that formation of mixed crystals requires matching of crystal lattices in all three dimensions.36,38 X-ray fluorescence and X-ray diffraction mapping26 show changes in the overall Me concentration and fractions of guest phases over the crystal face. This emphasizes mass transfer inhomogeneity in the diffusion boundary layer and its consequences: competition between different guest phases and enrichment of the face centers in phases with higher copper content. The presence of guest phases was detected with AFM images for the NH4Cl:Mn crystals with high manganese concentration (Figure 7). The crystal surface is featured with isolated ⟨110⟩ slightly elongated and identically oriented flat islands with sizes of 100−700 nm and heights of 30−50 nm of some manganese phase (presumably of the manganese−formamide compound). Some of the islands coalesce with formation of big (up to 2 μm) irregular aggregates and stripes. Anomalous Birefringence. Ammonium chloride crystals belong to the cubic system and are optically isotropic. Incorporation of the Me guest phases into ammonium chloride

Table 1. Misfit between (100) Face of Ammonium Chloride (Space Group Pm3̅m, a = 3.878 Å) and Guest Me Bearing Phases in the Plane of Intergrowth and Perpendicular to That Plane guest phase, space group, lattice constants DS, (NH4)2CuCl4·2H2O, P42/mnm a = 7.595Å, c = 7.965 Å CC, CuCl2·2H2O, Pbmn a = 7.414Å, b = 8.089 Å, c = 3.746 Å FC, CuCl2·2CONH3, P1̅ a = 3.705Å, b = 7.049 Å, c = 7.375 Å α = 113.57°, β = 96.17°, γ = 94.85° DS, (NH4)2MnCl4·2H2O, P42/mnm a = 7.525 Å, c = 8.276 Å FC, MnCl2·2CONH3, P1̅ a = 3.685 Å, b = 7.136 Å, c = 7.779 Å α = 117.17°, β = 95.35°, γ = 92.23°

plane of intergrowth

in-plane misfit, %

System NH4Cl:Cu (001) along a and b +2.1

normal-to-plane misfit, % −2.7

(010)

along a +4.4 along c +3.4

−4.3

(01̅2)

along a +4.5 along [021] +15.8

+5.8

System NH4Cl:Mn (001) along a and b +3.0 (01̅2)

along a +5.0

−6.7

+0.5

along [021] +16.9

crystals causes strong anomalous birefringence distributed in accordance with the sector-zoning anatomy of the crystals (Figure 8). The optical indicatrix is uniaxial with the optic axis directed perpendicular to the growth direction [100] (Figure 8b). The optic sign is positive for both systems. The single exception is the NH4Cl:Cu crystals with CCu > 5.4 wt %, where extinction becomes oriented along diagonal ⟨110⟩ directions (Figure 8a). Simultaneously, the crystal color changes from blue to green, probably indicating formation of the copper chloride guest phase. In the NH4Cl:Mn crystals, a corresponding manganese chloride phase was not detected. The birefringence in NH4Cl:Cu crystals increases from 0.0001 to 0.0006 as copper concentration in the crystals increases from 2 to 7 wt %. For the lower impurity concentration, birefringence 5287

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Table 2. Total Me Concentration in a Crystal, CMe, Guest Phase Volume Fractions, f j, Total Strain, ε, and Calculated, Δncalc, and observed, Δnobs, Birefringence in Mixed Crystals NH4Cl:Me CMe, wt %

Figure 7. AFM deflection image of postgrowth (100) face of NH4Cl:Mn crystal (CMnCl2 = 10.8 g/100 g of solvent) showing isolated islands and aggregates of islands of some manganese phase.

f DS

f CC

0.13 0.7 3.8 6.6

0.01 0.025 0.07 0.1

2.5 3.1 3.5 3.7 5.5 7.0

0.087 0.11 0.1 0.07 0.04

0.02 0.06 0.08 0.2

f FC

ε

System NH4Cl:Mn −0.0003 0.005 −0.0003 0.05 −0.013 0.11 −0.017 System NH4Cl:Cu −0.0018 −0.0023 −0.004 −0.007 0.02 −0.014 0.05 −0.015

Δncalc

Δnobs

0.00006 0.001 0.003 0.004

0.0005 0.0009 0.0021 0.0035

0.0004 0.0005 0.0008 0.0014 0.0029 0.0032

0.0001 0.00015 0.00035 0.00035 0.00065 0.00075

Figure 9. Observed (circles) and calculated (triangles) values of birefringence in NH4Cl:Me crystals as a function of Me concentration in a crystal. (a) Me = Cu. (b) Me = Mn. Lines are guides for the eye.

between the NH4Cl host crystal and guest phases misoriented by 90° (the layer becomes stretched or compressed uniformly in all directions). Looking perpendicular to the growth [100] direction, the contribution of intrinsic birefringence should also be negligible. Crystallites of the guest phases are strongly flattened along the growth [100] direction and have small sizes in directions perpendicular to the light propagation. Such geometry should result in light scattering rather than in birefringence. On the contrary, the stress birefringence due to the lattice mismatch between ammonium chloride and the guest phases (Table 1) can be significant, and this contribution will be analyzed below. The volume fractions of the guest phases f j were roughly estimated from integral intensities of the X-ray diffraction maxima (Table 2). Since the guest phases form thin and flat crystallites, the total strain, ε, was calculated in the growth plane (100) as ε =Σj f jεj, where summation is performed over all phases j. εj = Δdj||/aNH4Cl corresponds to mismatch between host and guest phases in the growth plane (Table 1), and aNH4Cl is the lattice constant of ammonium chloride. The birefringence was calculated as Δn = |n03(π12 − π11)(c11 − c12)ε/2|,39 where πij are piezooptic constants (π11 − π12 = 3.3 × 10−12 24,40), cij are elastic stiffness constants (c11 − c12 = 29.5 GPa41), and n0 =

Figure 8. Schematic outlines and micrographs of anomalous birefringence in NH4Cl crystals with 6.2 wt % of Cu2+ (a) and 8.2 wt % of Mn2+ (b). White crosses show orientations of the crossed polarizers.

is very weak. In NH4Cl:Mn crystals, the birefringence is much higher. It increases from 0.001 to 0.035 as manganese concentration in the crystals changes from 0.7 to 9 wt % (Table 2, Figure 9). There are two possible reasons for anomalous birefringence in ammonium chloride: (1) intrinsic birefringence of the guest phase and (2) stress birefringence. Viewed between crossed polarizers, the cubic crystals of ammonium chloride expose growth sectors in two orientations: parallel and perpendicular to the growth direction [100]. In the first case, because of the presence of a 4-fold axis, the guest phases on the (100) face with equal probability will epitaxially grow in two equivalent orientations misoriented by 90°. As a result, intrinsic birefringence of some phase in one orientation is canceled by intrinsic birefringence produced by crystallites of the same phase misoriented by 90°. The same cancellation effect will apply to the stress birefringence formed by mismatch stress 5288

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internal stress is much clearer for the crack-free crystals (Figure 11).

1.639 is the refractive index of NH4Cl. In this geometry, the optical indicatrix is uniaxial with the optic axis parallel to the (100) face normal. The birefringence is assumed to be positive if the refractive index along the optic axis is larger than the refractive index in perpendicular directions. Table 2 and Figure 9 show that calculated and observed orientations of the optical indicatrix coincide with each other. The calculated and observed birefringence in the manganese bearing system and for small impurity concentrations in the copper bearing system are similar. However, in the copper bearing system with high concentrations of impurity, the observed birefringence is significantly smaller than the calculated one. Fractions of impurity phases, strain, and calculated birefringence are similar for both systems, whereas the observed birefringence is significantly smaller for the copper bearing system. A possible explanation for this discrepancy is a different degree of intergrowth coherency. The birefringence distribution in crystals with several discrete zones of different copper concentration provides a further confirmation of the relationship between anomalous birefringence and mismatch stress. At the zoning boundaries, orientation of the optical indicatrix rotates on 90° suggesting replacement of tensile stress with the compressive one. Because of the stress concentration, the birefringence strongly increases near the corners of the zoning boundaries. In general, the calculations show that the most part of the observed anomalous birefringence can be explained via mismatch stress between the host crystal and domains of the guest phases. This allows us to estimate values and distribution of internal stress from distribution of anomalous birefringence. The maximal shear stress calculated as 2τmax = 2Δn/[n03(π12 − π 11)] attains 0.25 GPa for the NH4Cl:Cu crystals and 1.6 GPa for the NH4Cl:Mn crystals. Autodeformation Defects. Brittle deformations are one of the consequences of strong internal stress in NH4Cl crystals. As follows from values of birefringence (Figure 9), increasing of Mn2+ concentration is accompanied by increasing of internal stress. As a result, the size of crack-free crystals decreases (Figure 10). Because of the partial stress relaxation on cracks, the correlation between Mn2+concentration and value of

Figure 11. Maximal shear stress calculated from value of anomalous birefringence in crack-free crystals (circles) and crystals with cracks (squares) as a function of Mn concentration in a crystal.

Internal stress in NH4Cl crystals can also relax by means of plastic deformations: twinning and noncrystallographic branching.42 The intensity of branching is close for both systems, and it increases as Me concentration increases (Figure 12).

Figure 12. (a,b) Macroblocks on the surface of NH4Cl:Me crystals. (c,d) Average number (each point is averaging over ten crystals) of macroblocks, N, for one crystal as a function of Me concentration in a crystal. (a,c) Me = Cu. (b,d) Me = Mn.

Twinning according to the spinel law is typical for NH4Cl:Mn crystals and, to a significantly lesser extent, for NH4Cl:Cu crystals. The twinning frequency changes with impurity concentration nonmonotonously, but with a maximum (Figure 13). The presence of a maximum can be explained by the wellknown competition of the twinning and branching processes.42

Figure 10. Maximal size of visually perfect defect-free NH4Cl:Mn crystals as a function of Mn2+ concentration in the salt part of the solution. Reproduced with permission from ref 24. Copyright 2009 Springer. Curves 1 and 2, growth from water−formamide mixtures; supersaturation σ1 > σ2. Curve 3, growth from aqueous solutions. 5289

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AUTHOR INFORMATION

Corresponding Author

*Tel: +1 (212) 9929815. Fax: +1 (212) 9953884. E-mail: [email protected]. Present Address †

Department of Chemistry, New York University, 100 Washington Square East, 10th floor, New York, New York 10003, United States.

Notes

The authors declare no competing financial interest.

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Figure 13. Fraction of twins, f tw, as a function of Mn concentration in a salt part of the solution. Curves 1 and 2 correspond to different supersaturations, σ1 < σ2. Inset shows micrograph of a twin.

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REFERENCES

CONCLUSIONS

Ammonium chloride crystals growing from water−formamide solutions can incorporate a significant amount (up to 6−7 wt %) of the divalent metals, copper and manganese. Such large amounts cannot be present in the NH4Cl crystal structure in the form of an isomorphic impurity. Instead, ammonium chloride forms oriented syntactic intergrowths with the guest phases of (NH4)2MeCl4·2H2O, MeCl2·2CONH3 (Me = Cu, Mn), and CuCl2·2H2O. These intergrowths can form due to the small lattice mismatch in the growth plane of ammonium chloride (100) as well as in the perpendicular direction (quasi three-dimensional similarity) that agrees well with the epitaxial criteria proposed for the mixed crystals.36,38 Divalent cations Me2+ strongly reduce growth rate of ammonium chloride (100) faces. The growth kinetics agree with the Bliznakov kink blocking model modified to take into account lateral interaction between impurity particles and epitaxial adsorption of the guest phases. For the manganese bearing system, at some critical concentration (CMnCl2 = 6 g/ 100 g of solvent), growth kinetics and face micromorphology change rapidly. This transition accompanies changes in composition of the guest phases, highlighting solid relationships between speciation in mother liquor and crystal growth processes. The guest phases crystallize outside their stability fields but in the field of stability of ammonium chloride. However, for both guest phases inside NH4Cl and bulk guest phases precipitating from solutions, increasing Me concentration is accompanied by replacement of (NH4)2MeCl4·2H2O with MeCl2·2CONH3. The epitaxial mode of crystallization stabilizes the guest Me bearing phases and shifts concentration ranges of their stability. Epitaxial growth also stabilizes the phase of copper chloride, which does not form in the ternary NH4Cl− CuCl2−H2O−CONH3 system but crystallizes in the simpler NH4Cl−CuCl2−H2O system. The lattice mismatch between the NH4Cl host crystal and lamellae of guest phases induces internal stress that produces strong anomalous birefringence and later partially relaxes with formation of cracks and plastic defects such as noncrystallographic branching and twinning. 5290

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