Evolution of Strain in Heteroepitaxial Cadmium Carbonate

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Evolution of strain in heteroepitaxial cadmium carbonate overgrowths on dolomite Erika Callagon LaPlante, Peter J Eng, Sang Soo Lee, Neil C. Sturchio, Kathryn L. Nagy, and Paul Fenter Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.7b01716 • Publication Date (Web): 09 Apr 2018 Downloaded from http://pubs.acs.org on April 9, 2018

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Crystal Growth & Design

Evolution of strain in heteroepitaxial cadmium carbonate overgrowths on dolomite Erika Callagon La Plantea,§, Peter J. Engb, Sang Soo Leec, Neil C. Sturchiod, Kathryn L. Nagya, and Paul Fenterc,* a

Department of Earth and Environmental Sciences, University of Illinois at Chicago, Chicago, IL 60607 Center for Advanced Radiation Sources, University of Chicago, Chicago, IL 60637 c Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, IL 60439 d Department of Geological Sciences, University of Delaware, Newark, DE 19716 § Current address: Department of Civil and Environmental Engineering, University of California, Los Angeles, Los Angeles, CA 90095

b

Abstract The evolution and accommodation of lattice strain in an epitaxial mineral film grown on an isostructural substrate were observed as a function of film thickness. Cadmium carbonate films (approximately CdCO3 (otavite) in composition) were grown on the (104) surface of CaMg(CO3)2 (dolomite) from aqueous solutions that were supersaturated with respect to both pure otavite and Cd-rich (Cd1Specular and non-specular X-ray xCax)CO3. reflectivity (XR) revealed that the structure and strain of the otavite overgrowths evolved in a manner that is fully consistent with a Stranski-Krastanov growth mode. Otavite films initially grew as coherently strained films, up to an average thickness of ~15 Å, with lateral compressive strains and an expansion of the vertical film lattice spacing resulting in a unit cell volume consistent with pure otavite. Thicker films (>15 Å) became incommensurate with the substrate, having lattice parameters that are indistinguishable from pure otavite. These results indicate that the evolution of these mineral films is controlled by epitaxy and are consistent with the growth of essentially pure otavite films. These results provide a foundation for understanding the stability of thin-film overgrowths in the natural environment. *Corresponding author. Paul Fenter, Chemical Sciences and Engineering Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL, 60439 USA, Phone: 630-252-7053; E-mail: [email protected], Website: http://www.anl.gov/cse/group/interfacial-processes

1 ACS Paragon Plus Environment

Crystal Growth & Design 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Evolution of strain in heteroepitaxial cadmium carbonate overgrowths on dolomite Erika Callagon La Plantea,§, Peter J. Engb, Sang Soo Leec, Neil C. Sturchiod, Kathryn L. Nagya, and Paul Fenterc,* a

Department of Earth and Environmental Sciences, University of Illinois at Chicago, Chicago, IL 60607

b

Center for Advanced Radiation Sources, University of Chicago, Chicago, IL 60637

c

Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, IL 60439

d

Department of Geological Sciences, University of Delaware, Newark, DE 19716

*Corresponding author. E-mail: [email protected] §

Current address: Department of Civil and Environmental Engineering, University of California, Los

Angeles, Los Angeles, CA 90095

Abstract The evolution and accommodation of lattice strain in an epitaxial mineral film grown on an isostructural substrate were observed as a function of film thickness. Cadmium carbonate films (approximately CdCO3 (otavite) in composition) were grown on the (104) surface of CaMg(CO3)2 (dolomite) from aqueous solutions that were supersaturated with respect to both pure otavite and Cd-rich (Cd1-xCax)CO3. Specular and non-specular X-ray reflectivity (XR) revealed that the structure and strain of the otavite overgrowths evolved in a manner that is fully consistent with a Stranski-Krastanov growth mode. Otavite films initially grew as coherently strained films, up to an average thickness of ~15 Å, with lateral compressive strains and an expansion of the vertical film lattice spacing resulting in a unit cell volume consistent with pure otavite. Thicker films (>15 Å) became incommensurate with the substrate, having lattice parameters that are indistinguishable from pure otavite. These results indicate that the evolution of these mineral films is controlled by epitaxy and are consistent with the growth of essentially pure otavite films.

These results provide a foundation for understanding the stability of thin-film

overgrowths in the natural environment.


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1. Introduction The role of strain in mineral growth is relevant to the natural processes by which carbonate minerals form in supersaturated solutions, either at Earth’s surface or in the subsurface. Such behavior is important in two general contexts. First, it is important for understanding the initial steps by which carbonate films nucleate and grow heterogeneously on isostructural carbonate minerals. This process is relevant, for example, to carbon sequestration by the large-scale injection of supercritical CO2 gas from fossil fuel combustion into subsurface geological formations. Divalent metals such as Ca or Mg released by dissolution of silicate rocks combine with abundant aqueous carbonate to precipitate carbonate minerals.1 The rate at which CO2 transforms to carbonate solids is important to control for process safety and efficacy, and heterogeneous precipitation on existing minerals is a critical factor to consider. Second, the thermodynamic stability of carbonate overgrowth films is related to their longevity. This knowledge is especially needed for toxic heavy metals (e.g., Cd, Pb) that are sequestered in carbonate overgrowths to understand their long-term effectiveness to immobilize these contaminants in the environment. There has been a substantial amount of work on heteroepitaxial growth of mineral films, especially for carbonate phases. The epitaxial growth of calcite on dolomite and kutnahorite (MnCa(CO3)2) surfaces from calcite-supersaturated solutions has been investigated using atomic force microscopy (AFM), revealing the effect of lattice misfit on the morphology and the minimum solution supersaturation required for epitaxial growth.2 Similarly, the growth of oriented Mn0.5Ca0.5CO3 islands of nearly uniform dimensions has been observed on calcite surfaces reacted with Mn-containing solutions.3 Furthermore, the uptake of Cd on calcite surfaces has been previously investigated by several workers, revealing various mechanisms by which Cd is incorporated into the calcite surface, including incorporation at growing step edges and surface precipitation of a Cd-containing carbonate phase.4–15 The occurrence of an amorphous precursor phase prior to epitaxial crystalline growth has been proposed,15 and various morphologies of the otavite overgrowths have also been shown to form depending on the experimental condition, particularly the solution saturation state.14



The classical view of epitaxy was developed in the context of crystal growth for electronics and other technological applications where smooth and continuous films are desired.16–21 This concept includes three classical epitaxial film growth modes that are often distinguished by the evolving film morphology: (1) Frank-van der Merwe growth (F-M), or layer-by-layer growth, where a continuous and uniform film forms;22 (2) Stranski-Krastanov growth (S-K), where growth initially occurs through an epitaxial film followed by growth of three-dimensional nuclei,23 and (3) Volmer-Weber growth (V-W) where growth nuclei form clusters directly on the bare substrate (3D island growth).24 A primary driver for the different growth modes is the lattice mismatch, or ‘misfit’, between the film and substrate structures (i.e., the fractional difference between the film and substrate lattice parameters). The strain in a coherently grown film25 from lattice mismatch is associated with an energy cost that is proportional to the thickness of the coherently strained film, leading to S-K and V-W growth modes for small and large misfits, respectively. In particular, the S-K growth mode26,27 is characterized by a ‘critical thickness’28, which separates growth of a commensurate (i.e., coherently strained) film from growth of an incommensurate strain-relieved film that typically develops through the introduction of discrete dislocations. The critical thickness can be predicted from a combination of the misfit magnitude and material properties.22,29–31 The coherently strained material, as well as the defects caused by strain relief, influences the physical properties of the film through its interaction with the substrate.32,33 We have previously characterized the morphological evolution of heteroepitaxial Cd-rich carbonate films (Cd–Ca carbonate solid solution, nearly pure otavite (CdCO3) in composition) on the CaMg(CO3)2 (dolomite) (104) surface from aqueous solutions by X-ray reflectivity (XR) and AFM.34 The films were observed to grow via the S-K growth mode up to several nanometers thick depending on the initial saturation state of the solution with respect to the otavite–calcite solid solution. Specular XR results revealed an expansion of +1.7% in the surface normal direction to d104 = 3.00 Å,34 consistent with observations by Chiarello and Sturchio.6 Despite the large body of work on the morphologies and rates of the epitaxial growth of otavite on carbonate surfaces, the influence of lattice misfit and film thickness on the evolution of strain and crystallographic structure of this overgrowth has not yet been clarified. Such


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information will have implications in the stability of the precipitated otavite phase and the Cd atoms contained therein. Here, we provide new direct observations on the evolution of strain of epitaxial cadmium carbonate films as a function of average film thickness. Both in situ and ex situ measurements of specular and nonspecular XR reveal the evolution of lattice structure and strain in otavite films on dolomite. We demonstrate that thin epitaxial Cd-carbonate films are initially coherently strained to match the dolomite lattice for average thicknesses of 15 Å) are incommensurate with the substrate, having lattice spacings that are indistinguishable from those of pure otavite. These strain changes are then related to overgrowth morphologies previously observed with AFM, and the experimentally determined critical thickness is compared with theoretical predictions.

2. Materials and Methods 2.1 Sample preparation and experimental conditions Experiments were designed to explore the structural variation at the dolomite (104)–otavite overgrowth interface as a function of film thickness. The film thickness was controlled through a combination of the saturation state of the growth solution and the growth time which we have previously shown to produce consistent growth behavior.34 Solutions prepared by dissolving ACS reagent grade CdCl2, CaCl2, and NaHCO3 salts in deionized water (DIW) were reacted with freshly-cleaved dolomite (104) surfaces; NaHCO3 was added a few seconds to a few minutes prior to the introduction of the dolomite sample to minimize the precipitation of Cd-carbonate in solution. Dolomite used in the experiment was cleaved from a gem quality specimen from Brazil. The experimental conditions are given in Table 1. Calculated pH values were between 7.4 and 8.1, and reaction durations ranged from ~2 hours to ~5 days. All experiments were carried out at ambient temperature (~22 ºC). For ex situ experiments, dolomite was reacted with 30 mL of solution for specified periods of time, and then dried with a brief burst of nitrogen gas. In one case, for Experiment D-6, an additional step of reaction with calcite-



saturated solution for 22.5 h was employed, before drying with nitrogen gas as in the other ex situ experiments. We have found that this reaction step does not change the structure or thickness of the overgrowth films, and this result is included because it demonstrates the initiation of strain relief in thicker films. Additional details on sample preparation and calculations of speciation and evolution of the solution composition with reaction progress were described previously.34 Thermodynamic calculations predict that all reaction solutions were supersaturated with respect to Cd-rich solid solution (Cd1-xCaxCO3)36 and pure otavite (CdCO3), and undersaturated with respect to calcite (Table 1). The most stable phase was a Cd-rich Cd–Ca carbonate solid solution,34 whose composition is nearly that of otavite. The unit cell structures of the dolomite substrate and the overgrowth film are schematically shown in Fig. 1. The dolomite (104) surface can be described by a monoclinic unit cell having lattice parameters, a = 7.706 Å, b = 4.812 Å, and c = 6.020 Å, where a and b define the twodimensional surface lattice, c describes the stacking of these layers, and β = 73.6° is the angle between a and c axes (Fig. 1A).37 Otavite lattice is described by a′ = 7.861 Å, b′ = 4.920 Å, and c′ = 6.130 Å, and β′ = 73.9° (Fig. 1B).38 This unit cell structure can be described equivalently using the lateral and vertical offsets between adjacent (104) planes, where is the lateral offset of the unit cell, and d104 = c sin(β)/2 is the vertical interlayer spacing, as also shown in Fig. 1.

Table 1. Experimental conditions for specular and non-specular X-ray reflectivity measurements. Sample Initial solution pHa Saturation Indices, SI Reaction number concentrations (mM) time (h) [Cd] [Ca] [CO3] SI CaCO3b SI CdCO3c log d D-1# 0.005 0.4 0.4 7.71 -1.12 0.46 0.47 126.45 # D-2 0.01 1 1 8.09 -0.02 1.42 1.43 124.67 D-3# 0.2 0.2 0.2 7.41 -2.02 1.47 1.47 12.00 D-4# 0.2 1 1 8.08 -0.05 2.68 2.68 3.00 D-5a* 0.2 0.2 0.2 7.41 -2.02 1.47 1.47 1.87 D-5b* 1 1 1 8.03 -0.15 3.25 3.25 12.85 D-6 0.2 0.2 0.2 7.41 -2.02 1.47 1.47 12.00 # previously reported in 34 *in situ experiment a calculated pH from PHREEQC39 with minteq.v4 database b

= log

,


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c

d

= log =

,

" #" ! ! $ !

% &'()*

#"

& )"

Figure 1. Top view (above) and side view (below) of the (A) dolomite, and (B) otavite (104) surfaces. The unit cell parameters (a, b, c, α, β, γ for the substrate, and a′, b′, and c′, α′, β′, γ′ for the overgrowth, where γ and γ′ are 90°) are indicated. Also shown are the parameters the lattice offset, , and vertical layer spacing, d104. Crystallographic radii40 are used to represent relative sizes of atoms.

2.2 Specular and Non-Specular X-ray Reflectivity X-ray reflectivity measurements were conducted at GSECARS beamline 13-ID-C of the Advanced Photon Source using an X-ray beam energy, E = 16 keV, corresponding to a wavelength, + = 0.775 Å. A PILATUS area detector41 was used for data acquisition. The X-ray reflectivity signal, R(Q), which is defined as the ratio between reflected and incident X-ray fluxes, was measured as a function of momentum transfer, Q, defined as , = -. / -0 , where ki and kr are incident and reflected X-ray wave vectors. The magnitude of Q is related to the scattering angle (2θ) by |,| = &43⁄+)567 &29⁄2). The reflectivity from a crystalline surface is in the form of a crystal truncation rod (CTR), which is a set of weak rods of reflected intensity that are oriented normal to the surface in reciprocal space, connecting the crystalline substrate Bragg peaks.42 The reciprocal space coordinates for each measurement are indexed in



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CD

CD

reciprocal lattice units, :; , >? , >@ A = B% * :, % E * ;, %

CD #FG

* ? , and >@ (Fig. 3A). The broadening of the film Bragg peak in >@ is a consequence of the finite thickness of the film as described by the Scherrer equation.47 For films that have lattice spacings (a′, b′, d′) that are all larger than those of substrate (a, b, d), two representative cases are possible. In the first, the film is laterally strained and fully commensurate with the substrate (Fig. 3B). Consequently, a′ = a and b′ = b, and the film and substrate Bragg peaks are coincident in > (and H) and >? (and K) (Fig. 3B, bottom). The film Bragg peaks in the vertical direction are shifted to a lower >@ with respect to the substrate Bragg peaks (Fig. 3B, middle) in a position CD

determined by the film vertical lattice parameter, d′, according to Bragg’s law, >@ = % * , >? , and >@ positions (middle, bottom), corresponding to larger film lattice spacings, a′, b′, and d′ (top). The RSMs collected in our experimental conditions are described in detail below to demonstrate strain evolution with film thickness.



Figure 3. Schematic of (A) matched, (B) mismatched strained, and (C) mismatched unstrained epitaxial films in real space (top) and reciprocal space (middle, bottom). The mismatched films have lattice parameters, a´, b´, and d´, that are larger compared to those of the substrate. > , >? , and >@ are related to a, b, and d, as illustrated. In (A) and (B), the film is commensurate with the substrate, i.e., film and substrate a and b are equal. The shifts in film Bragg peaks relative to the substrate Bragg peaks correspond to the relative sizes of the film and substrate unit cells.

2.4 Quantification of Cd Coverage by XR The total coverage, distribution, and thickness of the film were determined from the best-fit model in comparison with the measured specular XR data for each sample.43 Given the relatively narrow range of data in Qz, the variation in the coverage of individual film layers as a function of height, 9M , above the substrate surface was modeled as an error function profile given by:


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'

9M = N C B1 / PQR %

@S (@F

*H,

(1)

√C |UF |

where VM = ∆ + 7&'YZ ), which is characterized by a substrate-film separation, ∆, a film thickness, V[ , a film roughness, \[ , a film vertical layer spacing, 'YZ , and a first layer occupancy factor, N.34 The dolomite substrate surface was assumed to be atomically flat.48 Each film layer was modeled using the internal coordinates of the bulk otavite unit cell structure. The total surface Cd coverage is given by ∑ 9M , and the average thickness of the film, < V >, is calculated by < V >= 'YZ

∑ `S @S . ∑ `S

The quality of fit was assessed by a C and R-factor, which are given by the following equations: C

a C = &1⁄b) ∑c= c / c,ded !⁄fc A and g = &1⁄b) ∑ch c / c,ded !⁄ c h , where N is the number of data points, and c , c,ded , and fc are the measured intensity, calculated intensity, and measured uncertainty of the ith data point. The results of analyses around the (104) film Bragg peak (Q = 1.5 to 2.5 Å-1) are presented in the following discussion. The in situ data were analyzed using the same model (Eq. 1). The parameters according to Eq. 1 of the best-fit models (Fig. S3), and total Cd occupancies for different areas on multiple samples, are given in Table 3 for ex situ samples, and Table 4 for in situ samples.


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Table 3. Results of analysis of ex situ specular CTR Sample numbera D-1 (1)# D-1 (2)# D-2 (1)# D-3 (1)# D-3 (2)# D-3 (3)# D-4 (1)# D-6 (1) D-6 (2)

Scale factorb 0.10 0.10 0.0297 0.10 0.10 0.10 0.0234 0.10 0.10

N&f) 1* 1* 1* 1* 1* 1* 1* 1* 1*

V[ &f), Å

\[ &f), Å

∆ &f), Å

'YZ &f), Å

5.58 (0.04) 5.87 (0.05) 59.72 (5.20) 15.88 (0.59) 16.68 (1.19) 13.31 (0.40) 31.15 (3.12) 18.69 (1.28) 26.97 (0.83)

3.03 (0.05) 3.00 (0.05) 46.23 (5.96) 8.65 (0.27) 13.66 (2.61) 9.47 (0.24) 14.39 (1.86) 15.14 (2.76) 15.08 (1.39)

2.90 (0.003) 2.94 (0.004) 2.52 (0.02) 3.09 (0.02) 2.56 (0.04) 3.33 (0.01) 2.72 (0.02) 2.57 (0.05) 2.67 (0.01)

3* 3* 2.997 (0.003) 2.992 (0.003) 3.020 (0.021) 3.006 (0.003) 3.010 (0.007) 3.001 (0.017) 3.002 (0.006)

a

Σ9M &f), k, Å 4.57 4.67 46.12 11.22 13.83 10.92 19.58 15.33 18.26

a C (R) 1.3 (0.04) 2.0 (0.05) 42.1 (0.24) 34.2 (0.24) 25.9 (0.19) 11.9 (0.13) 73.0 (0.37) 25.7 (0.17) 19.4 (0.16)

The sample numbers are as in Table 1; numbers in parentheses denote the different areas on the surface where measurements were carried out. Details of CTR analysis are shown in Fig. S3. b used in the calibration of XR signal c 1 monolayer, ML = 1 Cd/(Auc/2), where Auc/2= 18.54255 Å2 # previously reported in 34 * fixed parameter in analysis


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Table 4. Results of analysis of in situ specular CTR Reaction stepa a (1) – 5a b (1) – 5a b (2) – 5a c (2) – 5a d (1) – 5b d (1) – 5b† d (2) – 5b d (2) – 5b† d (3) – 5b d (3) – 5b† e (1) – 5b† e (2) – 5b† e (3) – 5b† f (1) – 5b† f (2) – 5b† f (3) – 5b† g (1) – 5b† g (2) – 5b† g (3) – 5b† h (1) – 5b† h (2) – 5b† h (3) – 5b†

Time (h) 0.28 0.85 0.85 1.87 2.37 2.37 2.37 2.37 2.37 2.37 2.70 2.70 2.70 3.22 3.22 3.22 3.92 3.92 3.92 12.85 12.85 12.85

Scale factor 0.098 0.098 0.098 0.098 0.098 0.126 0.098 0.126 0.098 0.126 0.126 0.126 0.126 0.126 0.126 0.126 0.126 0.126 0.126 0.126 0.126 0.126

N&f) 0.34 (0.01) 0.51 (0.01) 0.62 (0.01) 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1* 1*

V[ &f), Å 3* 3* 3* 5.61 (0.06) 35.43 (1.50) 32.11 (0.91) 37.62 (1.26) 26.65 (0.82) 37.53 (1.09) 35.14 (0.53) 34.93 (2.98) 35.23 (2.68) 36.56 (1.77) 66.88 (2.16) 68.77 (1.98) 53.92 (2.14) 104.35 (2.55) 99.83 (2.12) 79.41 (2.13) 193.59 (2.17) 199.97 (2.35) 152.27 (2.65)

\[ &f), Å 0.001* 0.001* 0.001* 4.10 (0.09) 23.35 (1.27) 42.69 (1.87) 21.93 (1.34) 43.01 (1.61) 24.33 (1.20) 33.17 (1.04) 93.04 (5.85) 86.05 (5.30) 71.90 (3.81) 124.49 (5.13) 111.03 (4.81) 101.55 (4.94) 151.33 (5.98) 110.50 (4.99) 121.92 (5.30) 185.17 (5.37) 161.03 (5.36) 163.24 (7.07)

∆ &f), Å

'YZ &f), Å

Σ9M &f), k, Å

2.85 (0.00) 2.91 (0.00) 2.93 (0.01) 2.88 (0.00) 2.75 (0.01) 2.57 (0.02) 2.69 (0.01) 2.56 (0.02) 2.74 (0.01) 2.60 (0.02) 2.52 (0.05) 2.53 (0.05) 2.50 (0.03) 2.44 (0.03) 2.45 (0.03) 2.47 (0.04) 2.45 (0.04) 2.43 (0.04) 2.40 (0.03) 2.43 (0.03) 2.40 (0.03) 2.35 (0.03)

3* 3* 3* 3* 2.987 (0.002) 2.982 (0.002) 2.994 (0.003) 2.990 (0.002) 2.996 (0.002) 2.991 (0.002) 2.975 (0.001) 2.978 (0.001) 2.982 (0.001) 2.971 (0.001) 2.972 (0.001) 2.976 (0.001) 2.966 (0.000) 2.968 (0.001) 2.970 (0.001) 2.960 (0.000) 2.959 (0.000) 2.959 (0.000)

0.34 (0.01) 0.51 (0.01) 0.62 (0.01) 1.51 (0.02) 11.69 (0.50) 12.36 (0.23) 12.31 (0.42) 11.00 (0.18) 12.35 (0.36) 12.26 (0.16) 18.99 (0.50) 18.17 (0.48) 16.73 (0.37) 30.11 (0.53) 29.01 (0.53) 24.31 (0.50) 42.36 (0.73) 37.09 (0.69) 32.87 (0.60) 69.91 (0.82) 70.10 (0.87) 56.44 (0.96)

2.85 2.91 2.93 5.15 25.60 35.55 25.63 34.22 26.85 30.85 67.18 62.93 54.52 94.73 87.02 77.25 121.27 95.56 96.51 167.77 156.18 142.25

a

a C (R) 2.08 (0.05) 2.07 (0.05) 6.11 (0.09) 1.36 (0.04) 23.03 (0.18) 46.20 (0.24) 19.36 (0.16) 25.56 (0.17) 13.19 (0.14) 23.96 (0.29) 158.03 (0.23) 149.06 (0.25) 107.66 (0.42) 146.41 (0.49) 160.99 (0.51) 160.12 (0.58) 233.58 (0.52) 263.22 (0.71) 187.15 (0.84) 163.11 (0.57) 217.17 (0.74) 293.18 (1.01)

The sample numbers are as in Fig. 2; numbers in parentheses denote the different areas on the surface where measurements were carried out. Details of CTR analysis are shown in Fig. S3. b 1 monolayer, ML = 1 Cd/(Auc/2), where Auc/2= 18.54255 Å2 * fixed parameter in analysis † Cd occupancies derived from interpolated CTR



3. Results and Discussion 3.1 Evolution of lattice structure of thin overgrowths and initiation of strain relief The evolution of the vertical and lateral film structure in relation to the substrate was determined from RSMs of specular and non-specular CTRs near the film and substrate Bragg peak positions (Figs. 4-6, 8). The RSMs are slices through the 3D interpolated truncation rods, showing the X-ray intensities in the vicinity of the otavite film and dolomite substrate diffraction features. For the observed RSMs, a schematic of the reciprocal space structure in (H, K) and the location and orientation of the slice, are shown in white and red, respectively, for reference. Also included, superimposed on the RSMs, are dashed white lines that indicate the lateral location of the dolomite substrate truncation rods. For Samples D-1 and D-3 (i.e., 126 and 12 h at log = 0.47 and 1.47, respectively), the specular CTR near the (002) Bragg peak of the dolomite substrate shows an enhancement in intensity over a wide range of L values centered at L ~ 1.92 (RSMs for one area on each sample are shown in Figs. 4A and 4B). This enhancement in the CTR intensity resulted from the formation of overgrowth films on the dolomite (104) surface. The width of this film Bragg peak along the L direction indicates that the films were relatively thin. The data analyses (Table 3) reveal that these films were on average either 5 or 12 Å thick for the lower and higher log , respectively. It is noted that different areas on the sample may have varying coverages resulting from the pre-existing step density on the surface.34 Furthermore, these films had an average layer spacing, d104´ = 3.007 Å, that was larger than that of substrate (d104 = 2.888 Å), and that of otavite (d104 = 2.945 Å), the phase predicted by thermodynamic calculations to be most similar in composition to the overgrowth. Corresponding (02L) non-specular CTR data near the 024 substrate Bragg peak also showed a film Bragg peak at L = ~3.85 (=~1.922), consistent with the observations from the specular CTR. This film Bragg peak was superimposed on top of the non-specular CTR, indicating that overgrowth films were fully commensurate with the substrate (Figs. 5A and 5B), and therefore with compressive strain values of -2.1% and -2.3%, in the a and b directions, respectively. This threedimensional strain leads to a unit cell volume (as defined by a, b, and d104), of 111.0 Å3 for the film,


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compared to 113.9 Å3, the unit cell volume of bulk otavite. It is noted that the volume of the unit cell of calcite is 122.7 Å3; substitution of Ca in the otavite film would likely result in an increase in this volume, analogous to observations for a (Sr,Ba)CO3 solid solution.35 The specular CTR for Sample D-6 (i.e., 12 h at log = 1.47) revealed further enhancement in intensity at L ~1.92 (Figs. 4C and 4D). This increased film Bragg intensity resulted from increases in both film thickness (from average values of 5 and 12 Å for D-1 and D-3 to 17 Å for D-6) and Cd coverage (from average values of 1.5 and 4.8 ML for D-1 and D-3 to 7.4 ML for D-6) (Table 3). In addition, the lateral shift of the non-specular (02L) otavite film Bragg peak to smaller K indicated an increase of the b′ lattice spacing (Fig. 5D). This change is consistent with the result predicted from lateral relaxation of the thin film lattice from a coherently strained film, where b′ = bdolomite (4.81 Å), to a partially strain-relieved film, where bdolomite (4.81 Å) < b′ < botavite (4.92 Å). From these observations, we can estimate that the critical thickness of the film, i.e., the thickness at which strain was initially relieved, was between ~10 and 20 Å, with a corresponding Cd coverage of ~5–6 ML (Table 3).



Figure 4. Specular ex situ RSMs near the (00L) truncation rod for thin overgrowths, showing an enhancement in intensity (white arrows) shown as a logarithmic color map along the surface rod (dashed white lines), indicating the formation of a coherent otavite film. Sample numbers are indicated (where D6 (1) and D-6 (2) indicate two separate areas of sample D-6). A schematic (inset) shows the location of each scan and the orientation of each slice (red line) in reciprocal space. The dolomite Bragg peaks are located at L = 2. Cd coverages were (A) 1.5, (B) 4.8, (C) 6.2, and (D) 8.7 ML (Table 3).


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Figure 5. Non-specular ex situ RSMs near the (02L) truncation rod for thin overgrowths shown as a logarithmic color map (as indicated). Sample numbers are indicated (where D-6 (1) and D-6 (2) indicate two separate areas of sample D-6). Corresponding specular RSMs for the same samples are given in Figure 4. A schematic (inset) illustrates the location of each scan and the orientation of each slice (red line) in reciprocal space. The film Bragg peaks (white arrows) in (A) and (B) are located along the substrate truncation rod (dashed white lines), indicating that the film was commensurate with the substrate. The gradual shift of the film Bragg peak towards a smaller K in (C) and (D) signifies the development of a larger b lattice spacing and the initiation of strain relief (in addition to a residual strained film). The dolomite Bragg peaks are located at L = 4. Cd coverages were (A) 1.5, (B) 4.8, (C) 6.2, and (D) 8.7 ML (Table 3).



3.2 Lattice structure of thick bulk otavite-like overgrowths The lattice structure of thicker overgrowths is exemplified in RSMs of Sample D-4 (i.e., 3 h at log = 2.68) (Fig. 6). Images of selected non-specular rods that are laterally orthogonal, (01L) (Figs. 6A and 6B) and (20L) (Figs. 6C and 6D), illustrate the shift of the film Bragg peak to both smaller K for the (01L) rod (Fig. 6B) and smaller H in the (20L) rod (Fig. 6C). This shift signifies strain relief, and corresponds to the development of a larger two-dimensional otavite lattice parameters with respect to the substrate lattice. This departure from a commensurate structure, schematically shown in Fig. 7, leads to shifts in the positions of the film Bragg peaks relative to those of the substrate as seen in the RSMs sfor this sample. The strained component remained at the surface as evidenced by the persistence of the intensity enhancement along the non-specular rods (white dotted lines) in Figs. 6B and 6C. Specifically, the Bragg peaks corresponding to the strained film are marked with white arrows and are shown in Fig. 6D. The unstrained film Bragg peaks are marked with yellow arrows in Figs. 6B and 6C, and are also shown in Figs. 6G and 6H, which are slices at K = 0.97 near the (01L) truncation rod and H = 1.97 near the (20L) truncation rod, respectively. The thick overgrowth had both strained (white arrows in Fig. 6) and strain-relieved (yellow arrows in Fig. 6, Fig. 6G, Fig. 6H) components, which can be schematically represented as in Figs. 3B and 3C, respectively. The shift to smaller H and K was coupled with the evolution of the specular film Bragg peak position to L ~1.94 (Figs. 6E and 6F). This L was larger than that observed for the thin coherently strained film, at ~1.92, and corresponded to a smaller d104 in the strain-relieved film compared to the strained film. In addition, a lateral broadening of the film Bragg peak was observed, where the lateral width of the secondorder peak (at L = 3.88) was about twice that observed for the first-order Bragg peak (at L = 1.94) (Fig. S4). This indicates the presence of angular (i.e., mosaic) disorder in the strain-relieved overgrowth with respect to the substrate. Further strain relief was observed in RSMs of Sample D-2 (i.e., 125 h at log = 1.43), where a lateral shift of the film Bragg peak (in H) away from the specular CTR indicated a part


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of the film grew with a film (104) crystallographic orientation that was tilted with respect to the surface normal of dolomite (104) (Fig. S5).

Figure 6. Specular and non-specular ex situ CTR of thick overgrowth in Sample D-4 (i.e., 3 h at log = 2.68) as a logarithmic color map (as indicated). RSMs near the (A, B, G) (01L), (C, D, H) (20L), and (E, F) (00L) truncation rods are sliced along the H-L and K-L planes to show the relative positions of the film and substrate Bragg peaks. A schematic (inset) shows the location of each scan and the orientation of each slice (red line) in reciprocal space. (G) and (H) are slices at K = 0.97 and H = 1.97, respectively, showing the unstrained film Bragg peaks. The locations of the dolomite truncation rods are given by dashed white lines. The shift of the film Bragg peak towards smaller (B) K, (C) H, and (E, F) L values



signify the development of a larger film lattice in the thick unstrained film (yellow arrows) as compared to the thin coherently strained film (white arrows). The dolomite Bragg peaks are located at L = 1 (panels A, B, G), 2.44 (panels C, D, H), and 2 (panels E, F). Cd coverage of the coherently strained otavite is ~10 ML.

Figure 7. Schematic of the reciprocal space lattice of dolomite (solid black lines) and strain-relieved Cd carbonate overgrowth (dashed blue lines). The relative positions of the film Bragg peaks (blue circles) with respect to the substrate Bragg peaks (black circles) were derived from observations of RSMs of various truncation rods of Sample D-4 (i.e., 3 h at log = 2.68). H and K indices for dolomite are indicated.

3.3 In situ observations of the evolution of the film lattice structure The evolution of overgrowth structure with extent of reaction for the same areas on a sample was determined from in situ measurements. RSMs of the specular CTR (Fig. 8) are shown for reaction steps d to h (corresponding to reaction times (t) from 2.37 to 12.85 h (Fig. 2) and Cd coverages of 12 to 70 ML). These images reveal the evolution of the film structure during the range of reaction times where the overgrowth had both strained and unstrained components. The film remained largely coherent with the substrate lattice in the surface normal direction even after extensive growth (Fig. 8). The enhancement in intensity in the region around L ~ 1.92 (Fig. 8A) indicates growth of the Cd-carbonate phase with d104′ ~ 2.99 Å, similar to that observed for ex situ measurements, shown above. The otavite diffraction peak evolved to include a superposition with a vertically sharper (i.e., narrower range in H and K) component at L ~ 1.96 (Figs. 8B–E), corresponding to growth of the thicker films having a vertical lattice spacing, d104′ ~ 2.96 Å. The second peak was observed to be laterally broader in H and K than the initial coherently strained otavite Bragg peak, indicating that the thicker film had smaller lateral domains. This is consistent


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with previous AFM observations of the development of a three-dimensional island morphology for the thicker films.34 The specular XR analyses reveal that the overgrowth film had an average layer spacing of 2.987 l 0.002 Å at t = 2.37 h, which decreased gradually to 2.959 ± 0.000 Å at t = 12.85 h (Table 4).

Figure 8. Specular in situ RSMs for thick overgrowths in reaction steps as in Table 4: (A) d (1) – 5b, (B) e (1) – 5b, (C) f (1) – 5b, (D) g (1) – 5b, (E) h (1) – 5b. The reaction times are indicated. Sections along the plane normal to (0.45 1 0) are taken, and then projected onto the H-L plane. The x-axis has both H and K components. The increase in intensity in the film Bragg peak (white arrows) with reaction extent is evident, as is the change in its position to higher L corresponding to 2.95 Å. Cd coverages were (A) 12.4, (B) 19.0, (C) 30.1, (D) 42.4, and (E) 70.0 ML (Table 4). Dashed yellow lines indicate the L values corresponding to c = 2.88 Å (dolomite), 2.95 Å (bulk otavite), and 3.00 Å (strained otavite). Dashed white lines mark the dolomite (104) surface rod. A schematic (inset) illustrates the location of each scan and the orientation of each slice (red line) in reciprocal space, and the logarithmic color map (bottom right).

We now examine the in situ changes in the lateral structure of the thick film at t = 12.85 h from RSM images that cut through the (02L) rod near L = 4 at an oblique angle, as illustrated in Figs. 9 and S1. These specific scans were chosen both to probe a wider range of reciprocal space and to acquire this information more rapidly than in the other non-specular RSM (e.g., Fig. 5). This faster imaging allowed



us to observe the evolution from strained to unstrained film structure and minimized any distortion of the RSMs due to changes in the structure during data collection.

Figure 9. (A) Non-specular RSM of the (02L) truncation rod sliced at H = 0, and (B) oblique slice of the (02L) truncation rod. The Bragg peaks corresponding to the dolomite substrate and the strained and unstrained Cd-carbonate film in the two slices are indicated by orange lines in (A) and (B). The ranges of the H, K, and L values for the oblique slice (B) are also shown in Fig. S1. The oblique slices projected onto the K-L (Fig. 10) and H-K (Fig. S6) planes revealed the evolution of the position and intensity of the film Bragg peak as a function of reaction time. The change in location of the film Bragg peak from L = 3.87 to L = 3.90 with increasing growth is evident in Fig. 10. The final L value corresponds to d104′ = 2.95 Å. At the same time, an apparent decrease in K from 1.975 to 1.96 with reaction extent indicated that the film unit cell had laterally expanded from 4.87 to 4.91 Å in the b


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direction. Both lattice parameters derived from this in situ measurement at t = 12.85 h are consistent with those derived for the thick film from the ex situ measurements and also match the values for bulk otavite. Rietveld structure refinement of five film Bragg reflections (02L, 0-2L, 20L, -20L, and 00L) was performed for reaction step h in the in situ experiment (Table 4) to determine the unit cell parameters for a thick otavite film (with the Cd coverage of ~70 ML). These results led to observed film lattice spacings: a′ = 7.833 Å, b′ = 4.933 Å, and d104′ = 2.954 Å, which can be compared with those of the known otavite structure given above38 (Table 5). The values are consistent within experimental error, showing that the thick strain-relieved film had a structure that was indistinguishable from bulk-like otavite. For reference, the substrate has unit cell parameters consistent with dolomite, as expected (Table 5). These results suggest that the thicker otavite films had negligible Ca content, as expected from the thermodynamic analysis.34



Page 26 of 34

Figure 10. Oblique slices along the (02L) rod projected onto the K-L plane. (A) Ex situ experiment D-6 (2) (i.e., 12 h at log = 1.47), in which strain relief was initiated. (B-E) In situ experiment 5b, corresponding to reaction steps (d) to (h) in Fig. 2 (reaction times are indicated). Dashed red lines indicate H = 0, and the parts of the images above and below the line have positive and negative H values, respectively (Fig. 9). Diffuse scattering from the dolomite Bragg peak and film Bragg peak are marked in (B). The surface rods are located at the intersection of the dashed red line (H = 0) and K = 2, and are marked with white arrows. Cd coverages were (A) 8.7, (B) 12.4, (C) 19.0, (D) 30.1, (E) 42.4, and (F) 70 ML (Tables 3, 4). Table 5. Lattice parameters a, b, and c (Å), and angles m, , and n (°), and corresponding offset parameter, (Å), and layer spacing, d104 (Å), from analysis of Bragg diffraction peaks of the dolomite substrate and the strain-relieved otavite film structures for in situ reaction step h (using the surface lattice indexing, as described in Table 2). Parameter

Dolomite substrate

Bulk dolomite37

Parameter

Thick otavite film

Bulk otavite38

a

7.699 Å

7.706 Å

a′

7.833 Å

7.861 Å

b

4.809 Å

4.812 Å

b′

4.933 Å

4.920 Å

c

6.019 Å

6.020 Å

c′

6.153 Å

6.130 Å

m

90°

90°

m′

89.990°

90°

73.630°

73.6°

′

73.740°

73.9°

n

90°

90°

n′

89.947°

90°

1.697 Å

1.700 Å

′

1.723 Å

1.700 Å

d104

2.888 Å

2.888 Å

d104′

2.954 Å

2.945 Å

3.4 Film critical thickness and strain-relief mechanisms The CTR data revealed that the strain relief of the film began when the total surface coverage of Cd was about 5 – 6 ML, equivalent to an average film thickness of ~10 – 20 Å (Table 3; Fig. S3). This observation can be compared with calculations of the critical thickness using the traditional model of dislocation development in strained films. Several expressions for critical thickness from the literature were summarized by Wagner et al.49 The widely used Matthews and Blakeslee50 expression for critical q

w

thickness is given by the recursive relation, ℎd = Bln % qx * + 1H, where b is the Burgers vector, rDs&'tu) which is assumed to be equal to the lattice parameters of dolomite a = 7.70 Å or b = 4.81 Å, R =


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eyz{| (e}~ ! e}~

, where l is a lattice parameter; f is ~0.02 in the a and b directions, and ν is the Poisson’s

ratio of the film.51,52 Using a value of 0.3 to 0.35 for carbonate minerals,13 the critical thickness is estimated to be ~15 – 25 Å, which is in agreement with the value observed in our experiments. This picture implicitly assumes that strain relief is achieved by the formation of dislocation networks and that the coherently strained film is pure otavite. Previous studies have suggested Ca incorporation in the film.53 This would have the effect of increasing the misfit in the coherent film leading to smaller critical thicknesses. This was not observed implying that Ca incorporation was minimal, as expected from thermodynamic considerations,34 and as further evidenced by the agreement in the unit cell volumes of the strained otavite film and bulk otavite. We do not directly observe the presence of dislocations in the film, although the development of the observed angular disorder in the overgrowth, evidenced by the lateral broadening of the unstrained film (00L) Bragg peak, is fully consistent with the presence of dislocations in our system. Such dislocations have been observed in a related MnCO3/CaCO3 system.53 The evolution of the film overgrowth morphology has been previously elucidated, and was consistent with a S-K epitaxial film growth mode, where initial layer-by-layer growth is followed by the development of island formation.34 Atomic force microscopy revealed fan-shaped islands that are about 3 nanometers high nucleating at seemingly random areas on the sample surface and growing concurrently with the film that grows layer by layer (Fig. 11). Although these features start to form at film thicknesses less than 10 Å, they were more dominant during the advanced stages of growth and may be a manifestation of the film undergoing strain relief. These observations can be compared to previous studies of magnesian calcite epitaxial growth on calcite substrate, where strain in the overgrowth caused the formation of ridges, which were interpreted as being due to defect networks.54 Comparable to our results, the epitaxial magnesian calcite initially grew by spreading of monolayers and then by formation of separate crystal segments that are crystallographically and morphologically aligned on the calcite substrate.54



Figure 11. Ex situ atomic force microscopy (A) height and (B) phase images of otavite overgrowths (gray in B) on dolomite (black in B). Features that were several otavite layers thick (e.g., yellow box) formed on the surface together with continuous thin overgrowth layers (white arrows). The sample was reacted with a growth solution that had [Cd] = 0.5, [Ca] = 0.76, and [CO3] = 0.738 mM, and log = 2.82, for 1 hour.

4. Conclusions The combination of specular and non-specular X-ray reflectivity measurements revealed the evolution of the vertical and lateral structure of Cd-carbonate overgrowths on dolomite. We have correlated the lattice structures of the overgrowths of various thicknesses, obtained from specular and non-specular XR, to Cd coverages and film thicknesses from analysis of specular XR data. Because of the film–substrate misfit of ~2% in a and b directions, the film overgrowth was initially compressed laterally to match the dolomite substrate, and consequently extended vertically. As the Cd coverage increased to 5 – 6 ML, which corresponds to a film thickness of ~10 – 20 Å, the film started to relax and gradually adopted a structure that is indistinguishable from bulk otavite. The unstrained overgrowth occurred as 3-D islands that were angularly disordered with respect to the dolomite (104) surface. The manner of epitaxial growth for mismatching structures observed in this work follows the expectation from epitaxial growth theory, and the observed critical thickness was consistent with theoretical predictions. This film growth behavior is further supported by previous AFM observations. Furthermore, no evidence was found for intermixing or incorporation of Ca in the Cd-rich overgrowth, unlike that observed for otavite on calcite15, and the measured volume of the unit cell matches reasonably that of otavite.


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This study provides a well-defined foundation on which to further assess the relationship between the strain in a heteroepitaxial overgrowth and its stability to dissolution.

With this molecular-scale

understanding of the evolution of the film structure, the likelihood that metals incorporated into metal carbonate films may be re-released in the environment can be better assessed. In particular, we expect that this behavior will be important for predicting sequestration of heavy metals such as Cd having concentrations in the natural environment that are typically low, but that may form heteroepitaxial thin films having solubilities distinct from those of bulk carbonate phases.

Acknowledgments This material is based on work supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences (Geosciences Research Program) through Argonne National Laboratory. Argonne is a U.S. Department of Energy laboratory managed by UChicago Argonne, LLC, under contract DE-AC02-06CH11357. X-ray-based measurements were performed at GeoSoilEnviroCARS beamline 13-ID-C of the Advanced Photon Source at Argonne National Laboratory. GeoSoilEnviroCARS is supported by the National Science Foundation – Earth Sciences (EAR-1128799) and DOE – Geosciences (DE-FG02-94ER14466). This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC0206CH11357. The authors thank Christian M. Schlepütz for help with the RSMap3D software, and Joanne Stubbs for beamline support at APS.

Supporting Information. Image of the oblique scan cutting through the (02L) truncation rod shown also in Fig. 9, RSMs near the (00L) for the in situ experiments, details of analysis of ex situ and in situ specular CTRs, analysis of >∥ of specular CTR for Sample D-4, ex situ RSMs near (00L) for Sample D-2, and oblique slices along (02L) rod projected onto the H-K plane.



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For Table of Contents Use Only

Evolution of strain in heteroepitaxial cadmium carbonate overgrowths on dolomite Erika Callagon La Plante, Peter J. Eng, Sang Soo Lee, Neil C. Sturchio, Kathryn L. Nagy, and Paul Fenter

The accommodation of lattice strain in epitaxial cadmium carbonate (CdCO3) films grown on an isostructural CaMg(CO3)2 (dolomite) substrate was investigated using synchrotron X-ray reflectivity, revealing that the overgrowth lattice parameters and morphology evolved as a function of the thickness of the film from a strained to a strain-relieved structure.


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Evolution of Strain in Heteroepitaxial Cadmium Carbonate

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