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Journal of Materials Science

, Volume 48, Issue 2, pp 785–796 | Cite as

Nanoscale plastic deformation mechanism in single crystal aragonite

  • Ning Zhang
  • Youping Chen
Article

Abstract

Molecular dynamics simulations have been performed to study the dynamic behaviors of single crystal aragonite under indentation, tension, and compression. The elastic modulus and hardness of single crystalline aragonite measured in our simulations are found in good agreement with experimentally measured values. Our simulation results show that the mechanical properties of aragonite crystal, including the elastic modulus, hardness, strength, and toughness, strongly depend on the crystallographic orientations and loading conditions. We have identified that this dependence is resulted from different deformation mechanisms, i.e., phase transformation, amorphous phase formation, dislocation, and twining. This work is an attempt to identify the deformation mechanisms in aragonite and to establish the relationship between the dominant deformation mechanisms and its crystallographic orientations and loading conditions.

Keywords

Aragonite Radial Distribution Function Stress Plateau Dislocation Nucleation Plastic Deformation Mechanism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Introduction

Calcium carbonate (CaCO3) minerals are the most abundant biominerals both in terms of the quantities produced and their widespread distribution. Aragonite is one of the polymorphs of calcium carbonate crystal. During the past few decades, aragonite has attracted considerable interest due to its significant role played in complex organic/mineral biogenic composites. Of all the many organisms, mollusk shell is one of the most extraordinary examples, in which calcium carbonate, in the form of calcite or aragonite, composes 95–99% of the shell weight [1].

Considering the wide distribution in nature and its mechanical function, the mechanical properties of aragonite is no doubt a critical dominance of its corresponding geological and biological materials. It exists at ambient conditions with a density of 2.56 g/cm [2]. Theoretical and experimental studies of aragonite have mainly concentrated on the high-pressure phase transition behavior, ranging from the pioneer work of Bridgman [3] to many static and dynamic experimental studies [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], and to recent atomistic simulations [16, 17, 18, 19, 20], with which the atomic-scale details of the phase transition processes of CaCO3 has been observed and studied.

Beside the phase transition behavior of aragonite, Han et al. [21] had measured the Knoop microhardness on different planes of single-crystal aragonite in 1991. Thereafter, the elasticity of aragonite is examined using Brillouin spectroscopy [22]. Kearney et al. [23] studied the nanoscale anisotropic elastic–plastic behavior and the hardness of single crystal aragonite using both atomic force microscopy (AFM) and finite element method (FEM). Load plateaus were observed in the obtained force-depth curves, which were believed to be related to dislocation nucleation events. Also, preferential pileup lobes were presented after indentation, indicating anisotropic plastic behavior. Through finite element simulation, Kearney et al. [23] proposed that the pileup zones might result from slip activities on {110} 〈001〉 systems.

It is generally accepted that the material hardness is related to the elastic moduli and the slip systems of crystals. In terms of aragonite structure, the (001) plane is parallel to the planar, trigonal CO3 2− groups, while the Ca2+ ions lie approximately in positions resembling hexagonal packing [21], as shown in Fig. 1. Experimental observation has demonstrated that the polar (110) face is stable and each ionic layer in this direction consists of either carbonate or Ca ions [24]. In other words, (110) plane is an imperfect cleavage plane [25]. Very recently, Huang et al. [26] studied the fracture mechanism of nacre under high-strain-rate compression. They believe that the emission of partial dislocation and the onset of deformation twinning are responsible for the fracture toughness of nacre according to their high-resolution transmission electron microscopy (HRTEM) observation.
Fig. 1

The orthorhombic unit cell of aragonite

Although some mechanical properties of aragonite have been measured and many interesting deformation mechanisms have been proposed based on experimental observations, the actual deformation mechanisms of aragonite are very complex and have not been well understood. Therefore, as an alternative approach that allows observation of the deformation processes on atomic scale, molecular dynamics (MD) simulation may be employed to investigate the underlying deformation mechanism of aragonite.

In this study, we use MD simulations to investigate the mechanical properties of aragonite under various loading conditions, including nanoindentation, uniaxial tension, and compression. Thereafter, we will elucidate the underlying deformation mechanisms of aragonite with atomic-scale details. This paper is organized as follows: “Computation and modeling” briefly describes the simulation setup and the force field model used in this study. In “Results and discussion” section, we perform simulations of nanoindentation, uniaxial tension and compression, and we analyze and discuss the simulated results. Then in “Conclusions” section, we summarize the major findings of this work.

Computation and modeling

The computer model

The crystal structure of aragonite that identified by De Villiers [27] is used to build the computer model in this work. A primitive unit cell of aragonite contains 20 atoms and is shown in Fig. 1. Aragonite has an orthorhombic crystal structure with the Pmcn space group. The lattice parameters are: a = 4.960 Å, b = 7.964 Å, c = 5.738 Å with α = β = γ = 90° [27]. The computer models of indentation, tension and compression simulations are composed of 100,800, 105,400 and 118,560 unit cells, respectively. The three-dimensional atomic-level computer models will be introduced in the following sections.

Constant volume and temperature (NVT) MD simulations are performed throughout this work. The Verlet–Leapfrog algorithm with a time step of 1 fs is used to integrate the equations of motion. We use the Nose-Hoover thermostat with relaxation constant of 0.1 ps to control the temperature at a constant value (298 K). The simulations performed in this study employ the general purpose MD simulation package DLPOLY 2.19 [28].

Interatomic potential

To select a suitable interatomic potential is a crucial step in MD simulations of materials behavior. Generally speaking, there are two kinds of interatomic potential models for ionic materials, i.e., the rigid ion model (RIM) and the shell model (SM). In the RIM, all ions are considered to have a frozen spherical electron density, which may be represented by a point charge. To accurately describe the polarization property of anions, O2− in particular, the SM has been developed by dividing the anion into two particles, known as the core and the shell [29]. However, one of the important consequences of the SM is that the simulation time and convergence rate are enhanced through all the information on coupling of coordinates with the polarization being utilized [30]. For aragonite, a number of potential models have been developed since 1992, including both RIMs [31, 32, 33, 34, 35, 36, 37] and SMs [31, 34, 38, 39, 40].

Table 1 lists some of the interatomic potential models and their parameters for aragonite. It can be seen that the major differences between different potential models reside in the C–O interaction. Although SMs that allow polarization of the –CO3 group can reproduce the bulk properties more accurate [38, 39], the addition of core and shell function of oxygen atoms significantly reduces the computer efficiency. Consequently, the simulation systems employing SM will have to be small systems. In contrast, the RIM for CaCO3 can be extended to larger size with higher computer efficiency. Through simulation and comparing the RIMs listed in Table 1, we have found that the potential model developed by Dove et al. [32] by fitting to the structure and properties of both aragonite and calcite predicts material properties in better agreement with experimental measured properties. Therefore, the empirical potential of aragonite derived by Dove et al. [32] is employed in this study.
Table 1

A summary of the potential parameters of different models for aragonite

References

Pavese et al. [31] RIM

Dove et al. [32] RIM

Jackson et al. [33] RIM

Pavese et al. [38] SM

Braybrook et al. [37] RIM

Ca–O

 Buck A (eV)

2,043.19

3,943.5977

8,839.3

1,550.0

8,839.3

 Buck ρ (Å)

0.2886

0.251570

0.23813

0.2970

0.23813

O–O

 Buck A (eV)

1,563,461

2,879.1262

3,6010.8

16,372.0

36,010.8

 Buck ρ (Å)

0.1366

0.252525

0.19756

0.2130

0.19756

 Buck C (eV Å−6)

3.47

0.0

0.0

0.0

0.0

C–O

 Buck A (eV)

14,460.95 × 107

1.7411 × 1013

3,088.4

 Buck ρ (Å)

0.0458

0.03873

0.12635

 Morse D (eV)

4.71

 Morse β (Å−1)

3.80

 Morse r 0 (Å)

1.18

 Harmonic k (eV Å−2)

400.0

 Harmonic r 0 (Å)

1.29

Ion charges

 q Ca/|e|

+2.000

+1.64203

+2.000

+2.000

+2.000

 q C/|e|

+0.817

+1.04085

+0.99805

+1.134

+0.99805

 q O/|e|

−0.939

−0.894293

−0.99935

−1.045

−0.99935

 q Os/|e|

−1.632

Spring constants

 k b(O–C–O) (eV rad−2)

4.0397

3.69441

9.3179

1.69

9.3179

 k t (eV)

0.1562

0.125125

1.1392

0.1129

1.1392

 k cs(O) (eV Å−2)

507.4

The Dove potential function comprises both bonded and non-bonded parts. For the non-bonded part, Coulomb interactions are included using the Ewald sum. The short-range repulsive interactions between Ca–O, O–O, and C–O are treated by the Born-Mayer potential,
$$ V(r) = A\exp ( - r/p) $$
(1)
The bond bending terms of O–C–O are implemented by using the following intermolecular harmonic function,
$$ V(\theta ) = \frac{1}{2}k_{\theta } \left( {\theta - \theta_{0} } \right)^{2} $$
(2)
where \( k_{\theta } \) is the bond bending force constant, \( \theta_{0} \) is the equilibrium bond angle, and \( \theta \) is the bond angle between the O–C–O atoms. The out-of-plane potential for –CO3 group is implemented using a four-body or a torsional term,
$$ V\left( \varphi \right) = k_{t} \left[ {1 - \cos \left( {2\varphi } \right)} \right] $$
(3)
where \( k_{t} \) is the out-of-plane force constant, \( \varphi \) is the angle between two O–C–O planes in a single molecular ion. The potential parameters of this model can be found in Table 1.

Results and discussion

Nanoindentation

Figure 2 presents the computer model for nanoindentation of single crystal aragonite. The simulated system consists of an aragonite substrate and a rigid spherical indenter with the indenter tip radius of 50 Å. To test the effect of periodic boundary condition and loading rate on the simulation results, we first use a smaller model containing 1.6 million atoms, labeled as sample 1 in Table 2. To study the effect of crystal orientation on mechanical behavior of aragonite, simulations of indentations along two crystallographic orientations, namely a-axis and c-axis, are performed. These two substrates, labeled samples 2 and 3 in Table 2, have similar sizes and contain about 2 million atoms, respectively. The contact forces between the substrate atoms and the indenter are modeled as repulsive forces. At the beginning of the simulations, the indenter is positioned 10 Å above the center of the surface, and moves at a constant velocity. In both cases, the computer models have free surfaces in the indent direction. To restrict the rigid-body motion of the substrate, three layers of atoms on the bottom of the substrate are absolutely fixed. Periodic boundary conditions are applied along the directions perpendicular to the indent axis.
Fig. 2

An MD indentation model of aragonite

Table 2

A summary of the computer models of nanoindentation

Samples

L a  × L b  × L c (nm)

Number of atoms

Indentation direction

1

40.0 × 40.0 × 11.5

1,600,000

c-axis

2

45.0 × 45.0 × 11.5

2,016,000

c-axis

3

12.0 × 45.0 × 45.0

2,096,640

a-axis

L a , L b and L c represent the length of samples along a-, b- and c-axis, respectively

The effect of periodic boundary condition

To ensure that the sample sizes are large enough to avoid spurious effect of the periodic boundary conditions on simulation results, preliminary indentation simulations of sample 1 with finite size and periodic boundary conditions are performed, respectively. The obtained load–displacement (PH) relations are compared in Fig. 3, from which it is seen that the PH curves with the two different boundary conditions almost overlap with each other. This implies that the current computer models are large enough and can be considered to be independent of the boundary conditions. Therefore, in the following indentation simulations, periodic boundary conditions are applied to simulate bulk properties of aragonite.
Fig. 3

Load–displacement (PH) curves for sample 1 with finite size and the periodic boundary conditions, respectively

The effect of loading rate

The effect of the indenter loading rate on hardness of single crystal aragonite is also investigated through indentation on sample 1. In Fig. 4, we compare the simulated load–displacement (PH) curves with loading rates of 0.1 and 0.3 Å/ps. It is seen that the two curves with loading rates of 0.1 and 0.3 Å/ps are very similar and there are very small difference in the load values. This suggests that the loading rate is low enough and will not significantly affect the mechanical behavior of aragonite in simulations. Therefore, in the following simulations, the lower loading rate of 0.1 Å/ps is applied.
Fig. 4

Load–displacement (PH) curves of sample 1 with loading rates of 0.1 and 0.3 Å/ps, respectively

The crystallographic orientation-dependent properties

In this section, the crystallographic orientation-dependent properties of aragonite are studied through indentation along two crystallographic orientations, a-axis and c-axis, respectively. Figure 5 presents the measured load–displacement curves in the simulations of the indentation on different orientated crystal surfaces. It can be seen from Fig. 5 that in both cases the load–displacement curves are linear at small displacement but becomes increasingly non-linear at larger displacement.
Fig. 5

Load–displacement (PH) curves of indentation along a-axis and c-axis

In spite of some similarities in the pattern of the curves, there are several differences between them. First, the slope of load–displacement (PH) curve shown in Fig. 5 for the case of indenting along c-axis is larger than that along a-axis. The displacement at which plastic flow first occurs is 1.2 nm in the case of indentation along c-axis, while 2.2 nm in the case of indentation along a-axis. Using the common definition of the hardness of a material as its resistance to local plastic deformation, the hardness of aragonite, H, is determined as the maximum elastic indentation load P max being divided by the projected contact area A, i.e., \( H = P_{\max } /A \). Accordingly, for indentation along c-axis with maximum elastic load of 300 nN and a contact area of 33.18 nm2, we obtain a hardness H [001] of 9.04 GPa. This result is in good agreement with the experimental measurement value, 8.6 ± 0.36 GPa [23]. With the same formula, we determine the hardness of aragonite along a-axis is 7.96 Gpa. This means that aragonite hardness is significantly affected by the crystal orientation. The result that the hardness along c-axis is larger than that along a-axis is consistent with the experimental finding [21] that the (001) plane is harder than any other planes in aragonite.

The other difference resides in the plastic regime that a series of load plateaus are observed in the case of indentation along c-axis, while load drops are seen in the case of indentation along a-axis. This phenomenon implies that the plastic behaviors of indentation on different crystallographic orientation surfaces may be dominated by different deformation mechanisms.

To further study the deformation processes, in Fig. 6 we plot the atomic configurations at indentation displacement of 3.5 nm in the cases of indentation along c-axis and a-axis, respectively. It is noticed that in Fig. 6a, a surrounding pileup zone is observed when indenting along c-axis. The observation of such a pileup zone is consistent with a previous reported experimental observation on aragonite [23]. In contrast, such pileup phenomenon is not clearly observed in the case of indentation along a-axis, as shown in Fig. 6b. This phenomenon can be further studied through comparing the side cross-sectional views of the deformed structures for the two cases in Fig. 7a, b. It is observed that in the case of indentation along c-axis the aragonite atoms beneath the contacted surface has transformed into the amorphous phase, while the atoms that are several layers away from the indenter maintained the initial aragonite crystal structure; no dislocations or cracks are observed. In the case of the indentation along a-axis, other than small amount of atoms transformed into amorphous phase, another regularly arranged new phase is observed and extends in the normal direction to the contact surface.
Fig. 6

Deformed structures at a displacement of 3.5 nm for indentation along a c-axis and b a-axis, respectively

Fig. 7

Side cross-sectional views of the deformed structure in Fig. 6, indentation along a c-axis and b a-axis

We use both radial distribution function (RDF) and coordination number in this study to identify the new phase. The side views of atomic structure of aragonite and the transformed phase induced by indentation along a-axis are shown in Fig. 8a, b. It is noticed in Fig. 8 that the carbonate ions in the initial aragonite structure tend to rotate and move, which accordingly lead the correlated calcium atoms to deviate from their original positions. Consequently, the geometry distribution o f calcium atoms changes from the initial zigzag shape to approximately straight lines. Figure 9 summarizes the RDFs of key atoms pair separations for aragonite and the transformed phase induced by indentation, tension, and compression, which will be discussed in the following sections. RDF of aragonite and new transformed phase induced by indentation along a-axis are labeled as “ARA” and “IND-x”, respectively. It appears that the radius of the nearest Ca–Ca neighbor of transformed phase is smaller than that of aragonite, which indicates a density increase and a volume reduction. Lacking detailed phase structures of CaCO3 from experimental studies, we propose this new phase based on our MD simulation results.
Fig. 8

Comparison of atomic structure diagrams, viewed along c-axis of a aragonite and bd transformed phases induced by indentation, tension and compression along a-axis, respectively

Fig. 9

Radial distribution functions of a calcium–carbon, b calcium–calcium, c calcium–oxygen, and d carbon–carbon for aragonite and transformed phase induced by indentation, tension and compression, respectively

To identify the distribution of the new phase formed in the indented region, the surrounding environments of each atom are considered and the number of nearest neighbor atoms, namely coordination number, is adopted to trace and investigate the history of phase transformation. According to the difference in the radius of nearest Ca–Ca neighbors for aragonite and the new phase observed in the indentation simulations described above, here we adopt the coordination number of calcium atoms to identify phase transformation region. Aragonite has two nearest calcium neighbors at a distance of 3.89 Å, while the new phase is detected to have two nearest calcium neighbors at a distance of 3.33 Å. Hence, a cutoff radius of 3.4 Å, which is between 3.33 and 3.89 Å, is chosen to calculate the coordinate number. Within the radius of 3.4 Å, there are no atoms in the aragonite phase while there are two atoms in the new phase.

Figure 10 shows cross-sectional views of the distribution of the transformed phase induced by indentation along a-axis at different deformation stages. The atoms are colored according to the coordination number of calcium atoms. The blue atoms represent the original undeformed aragonite crystalline structure, the yellow and green atoms represent the ordered new phase and the amorphous phase that have been completely transformed into after indented, respectively. It can be seen from Fig. 10 that the phase transformations occur and propagate anisotropically, resulting in a symmetry petal pattern.
Fig. 10

Side cross-sectional views of the transformed region induced by indentation along a-axis at the penetration depth of a 2.6 nm, b 3.0 nm, and c 3.5 nm. The atoms are colored by coordination number. Blue atoms are the original aragonite. Yellow and green atoms are the transformed ordered crystalline phase and the amorphous phase, respectively (Color figure online)

Looking back at the load–displacement relationship in Fig. 5, it may be concluded that the observed load plateaus in the load–displacement (PH) curve of indentation along c-axis is attributed to the pileup zone formation, which leads to sudden energy release and accordingly results in the decrease of the overall slope, i.e., load plateaus. However, in the case of indentation along a-axis, the plastic load-drops in load–displacement (PH) curve in Fig. 5 may be induced by the phase transformation. As indicated in Fig. 10, this new phase nucleates beneath the contact surface and grows under higher loads. As the volume is reduced due to phase transformation, the resistivity of aragonite rapidly decrease, which consequently results in plastic flow and load drops in load–displacement curve.

Uniaxial tension

In this section, we investigate the structural and mechanical properties of aragonite subjected to uniaxial tensile loading along a-axis. This simulation is motivated by the experimental tension study of nacre tablets [41]. Figure 11 shows the three-dimensional computer model of aragonite plate. The system size is set as 50.0 nm × 50.0 nm × 10.0 nm and it includes 2,108,000 atoms in total. The simulation is carried out at room temperature with a loading rate of 0.1 Å/ps.
Fig. 11

The MD computer model of aragonite for uniaxial tension simulation

The obtained stress–strain relation is plotted in Fig. 12. It is seen that the simulated Young’s modulus is 142 GPa, which is in good agreement with the experimental measured value of 144 GPa of single crystal aragonite [42]. Moreover, the elastic shoulder is followed by a sudden stress drop, which indicates the beginning of plastic flow. To further reveal the underlying plastic deformation mechanism, in Fig. 13a, b we present the atomic configurations at strains of 0.052 and 0.056, respectively. We see that in Fig. 13a dislocations nucleate and propagate along {110} slip plane, which is also one of the cleavage planes [25]. Voids are observed at the dislocation tips marked with black arrows in Fig. 13b. We believe that it is dislocation nucleation that results in the sudden stress drop in stress–strain curve in Fig. 12. In addition, as two dislocations meet, it is observed that the atomic arrangement in some areas is changed, which indicates possible occurrence of phase transformation.
Fig. 12

Stress–strain relation for single crystal aragonite under tensile loading along a-axis

Fig. 13

Side cross-sectional views of aragonite under uniaxial tensile loading along a-axis at the strain of a 0.052, b 0.056. The black arrows indicate the voids formed during dislocation propagation

To further investigate the nature of the dislocation slip and phase transformation in aragonite during uniaxial tension, we analyze the dislocation migration path and the phase diagram. Firstly, we zoom in the deformed structure to track the motion of atoms along dislocation line. The dislocation nucleation and propagation process is schematically illustrated in Fig. 14. As displayed in Fig. 1, the primitive unit cell of aragonite contains four CaCO3 units. It can be seen from Fig. 14 that dislocation onsets is attribute to the relative motion of CaCO3 units in primitive unit cell other than the movement of atoms within a CaCO3 unit. This may be understood because the ionic attractive interaction between Ca2+ and CO3 2− within a single molecule is much stronger than the interaction between CaCO3 molecules. Hence, when atoms are forced to slip under tensile loading the Ca2+ and CO3 2− in a single molecule will be bonded together and move as a group. As reported by a theoretical study [25], the cleavage plane of crystal aragonite tends to occur to rupture the weaker bonds in preference to the stronger bonds. Similarly, dislocations prefer to be triggered by relative movement between CaCO3 units.
Fig. 14

A schematic of dislocation nucleation and migration process. a Initial perfect aragonite structure, b atoms moving one Burgers vector along [110] slip plane, c atomic arrangements after the dislocation move out to sample surface

Secondly, the atomic structure of aragonite and the transformed phase induced by uniaxial tension are compared in Fig. 8a, c. Also, RDF is employed again to evaluate the phase transformation. RDF information of the aragonite phase and the new phase induced by tensile loading are labeled in Fig. 9 as “ARA” and “TEN-x”, respectively. Through comparison it is evident that different from aragonite structure, the transformed phase induced by tension is a new ordered phase.

Uniaxial compression

In this section, we present numerical simulations of aragonite under uniaxial compression along a-axis and c-axis. The computer model consists of 2,371,200 atoms in total with a size of 30.0 nm × 30.0 nm × 30.0 nm. Figure 15 shows the atomic configuration of the aragonite cube adopted in our compression simulations. It is a finite size sample and no periodic boundary condition is applied. The compressive loading is applied to the atoms within four layers at the two ends along the compression axis. The strain rate is controlled at 3.33 × 108 s−1.
Fig. 15

The 3D MD model for single crystal aragonite under compression

Figure 16 presents the stress–strain curves obtained from the compression simulations along a- and c-axis, respectively. As can be seen from Fig. 16, the measured Young’s modulus along c-axis in the simulation is about 80 GPa, which is consistent with the experimental measurement of 82 GPa [42]. However, the Young modulus along a-axis is slightly smaller than the one along c-axis, i.e., 67 versus 80 GPa. The other significant difference between the curves is the yield stress. For the case of compression along a-axis, plastic deformation starts at the strain of 0.02 corresponding to a yield stress of 120 MPa. A stress plateau is observed after the yield point, which implies possible structural change and atomic rearrangement. Thereafter, the stress increases dramatically and the material fails. If we define the fracture toughness as the energy required to fail the material, which can be calculated through area under the stress–strain curves, we find that the fracture toughness of aragonite is also highly crystallographic orientation dependent.
Fig. 16

Stress–strain curves for single crystal aragonite under uniaxial compression along a-axis and c-axis, respectively

In order to identify the plastic deformation mechanism, snapshots of the deformed structure at different plastic stage are presented in Fig. 17. It is seen that voids, marked with black arrows, are formed due to the propagation of dislocations along [110] direction. A more detailed study of dynamic process indicates that the nucleation and propagation of dislocations follow the same path as schematically explained in Fig. 14.
Fig. 17

Snapshots of aragonite under compression along a-axis at different strain stages: a ε = 0.03, b ε = 0.06, c ε = 0.1. The black arrows label the voids formed due to dislocation propagation

In addition, it is observed in Fig. 17a–c that the new arrangement of atoms in the compressed region differs considerably from the initial structure. The crystal structure before and after deformation is plotted in Fig. 8a, d, respectively. We find that the atoms in transformed phase still maintain a long-range crystalline order. This suggests that a phase transformation of aragonite has occurred. Using the RDF, it is found that this phase is very similar to the transformed new phase induced by indentation along a-axis. Note that in Fig. 9b this new phase has two nearest Ca neighbors at a shorter distance of 3.33 Å than that of aragonite (3.89 Å). Hence a cutoff radius of 3.6 Å, which is between 3.33 and 3.89 Å, is chosen to calculate the coordinate number of Ca. Figure 18b presents the new phase distribution at a strain of 0.12. The atoms are colored according to coordination number with red for the new phase, blue for aragonite and other colors for amorphous phase. It is worth emphasizing that different from the dislocation propagation observed in the tension simulation, dislocations triggered by compressive loading cannot propagate to the free surface of the computer model due to the obstacle of newly transformed phase.
Fig. 18

Cross-sectional view of atomic arrangement a before and b after compression along a-axis at a strain of 0.12. The atoms in b are colored by coordinate number. c The twined structure after compression, whose region before compression is squared in a (Color figure online)

Furthermore, it is surprising to note from Fig. 18b that the newly formed phase twinned together, which is especially clear in the lower half region of model specimen. The twinning boundaries that marked by blue or yellow atoms between red regions can be clearly identified. To further investigate the nature of the twinning structure, we pick the lower half region of the specimen before and after compression to trace the deformation process and compare them in Fig. 18a, c. It is seen that the transformed phase is symmetry to twin boundary (TB) planes with an inclination angle of 68.2°, which is comparable to the experiment observation of 63.8° that reported by Huang et al. [26]. However, no phase transformation was reported in their study. Very recently, it is reported that a well-defined twinning structure could highly promote material strength [43, 44, 45]. Recalling the stress–strain curve in Fig. 16, there is no doubt that the gradual stress increasing after plateau region is attributed to the deformation resistance from twinned structure.

As for the case of compression along c-axis, Fig. 16 shows that the material yields at a larger strain of 0.09 with a yield stress of 600 MPa that is higher than the counterparts of compression along a-axis. This result again confirms with the experimental observation that (001) plane is harder than (100) plane [21]. From this viewpoint we can, to some extent, explain why nacre develops a “brick-and-mortar” tablet arrangement with the c-axis of aragonite perpendicular to the surface to protect itself from a harsh predatory penetrating attack. The oscillations in the stress–strain curve in elastic region are believed to be induced by thermal fluctuation of atoms in the room temperature environment employed in this study. A short stress plateau region is observed after yield point. Different from the case of compression along a-axis, stress–strain curve shows a sudden drop after the stress plateau.

To reveal the underlying deformation mechanism, in Fig. 19 we present the snapshots of the deformed structure at strains of 0.12 and 0.17, respectively. It is seen from Fig. 19a that the stress plateau in the stress–strain curve is corresponding to the process of the rearrangement of atoms. In Fig. 20 we compare the arrangements of atoms in the squared region in Fig. 19a before and after compression. From Fig. 20a, b it is seen that the initial overlapped -CO3 groups from side view tend to slip and rearrange to a straight line to resist the continuous compressive loading until the strain reaches about 0.15. Figure 20b shows that there is a significant increase in structure density. This can be explained through Fig. 9d that the new phase has a shorter nearest C–C neighbor radius of 0.26 nm than that of aragonite (0.30 nm). Thereafter, the structure fail finally through amorphous phase transition and propagation along {110} slip planes, as shown in Fig. 19b. This result demonstrates that the propagation of amorphous phase prefers to occur along {110} slip planes.
Fig. 19

Side cross-sectional views of deformed structure at strains of a 0.12 and b 0.17 when compressed along c-axis

Fig. 20

Comparison of a initial aragonite structure and b compressed structure that squared in Fig. 19a

Conclusions

In summary, room temperature MD simulations have been performed to study the mechanical properties and dynamic behaviors of single crystal aragonite under indentation, tension and compression. The measured elastic modulus and hardness of single crystalline aragonite in our simulations are in good agreement with experimentally measured values. Some observations that reported by previous experimental studies of aragonite crystals have been reproduced in our simulations, including the load plateau in the force-displacement curves and the presence of pileup zones when being indented along c-axis.

Through MD simulations we have found that when indented along different crystallographic orientations aragonite has different deformation patterns, different load–displacement curves, very different elastic modulus, strength, and hardness. The simulations have revealed that those differences are resulted from different deformation mechanisms, i.e., amorphous phase formation under indentation along c-axis and a new crystalline phase transformation under indentation along a-axis. We have also found that the material behavior differently under different loading conditions. Under uniaxial tension the plastic deformation is induced by both phase transformation and dislocations, while under compression along c-axis, the dominant plastic deformation mechanism is the phase transformation. However, in compression simulation along a-axis, we have not only observed phase transformation, dislocation nucleation and migration, but also twinning. As a result of the different deformation mechanisms, the yield strength and fracture toughness of aragonite in c-axis are significant higher than those in a-axis. The loading type and crystallographic orientation-dependent deformation mechanisms are summarized in Table 3.
Table 3

A summary of deformation mechanisms under indentation, tension and compression

Deformation mechanisms

Amorphous phase formation

New crystalline phase transformation

Dislocation

Crystal twinning

Indentation along c-axis

Yes

No

No

No

Indentation along a-axis

No

Yes

No

No

Tension along a-axis

No

Yes

Yes

No

Compression along c-axis

Yes

Yes

No

No

Compression along a-axis

No

Yes

Yes

Yes

This work is an attempt to identify the deformation mechanisms in single crystalline aragonite and to establish the relationship between the dominant deformation mechanisms and the crystallographic orientation and loading conditions, so as provide some insights on the formation and properties of nacre tablets. Simulation of a nacre tablet that consists of both the aragonite crystals and the organic proteins is our ongoing work, through which the dynamic behavior of single crystalline aragonite will be further investigated.

Notes

Acknowledgements

This work was supported by National Science Foundation under Award CMMI-0855795 and DARPA under Award Number N66001-10-1-4018. Simulations were performed at the High Performance Computing Center at the University of Florida.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of FloridaGainesvilleUSA

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