ARTICLE pubs.acs.org/crystal
Nanoindentation Method To Study Slip Planes in Molecular Crystals in a Systematic Manner Yuanyuan Jing,† Yan Zhang,‡ John Blendell,† Marisol Koslowski,*,§ and M. T. Carvajal*,‡,|| †
)
School of Materials Engineering, Neil Armstrong Hall of Engineering, Purdue University, 701 West Stadium Avenue, West Lafayette, Indiana 47907-2045, United States ‡ Industrial and Physical Pharmacy, Purdue University, 575 Stadium Mall Drive, West Lafayette, Indiana 47907-2091, United States § Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, Indiana 47907-2088, United States Agricultural and Biological Engineering, Purdue University, 225 South University Street, West Lafayette, Indiana 47907-2093, United States ABSTRACT:
A rotating sample method has been developed to study the slip planes of succinic acid by atomic force microscopy (AFM) nanoindentation. A nonaxisymmetric cube corner indenter was utilized to generate an inhomogeneous stress field, which selectively activates different slip systems simply by rotating the sample. The slip planes identified were repeatable and frequently observed for different indentations of the single crystals using four sample rotations. By applying this rotating sample method to both (001) and (010) crystal faces, the repeatedly observed major slip planes were identified as (010) and (111) planes; these agree with the theoretical prediction. Many higher index operative slip planes were identified that were not reported previously. The rotating sample method presented herein is pragmatic and suggests that the anisotropic slip properties of single pharmaceutical crystals can be studied in a systematic manner.
’ INTRODUCTION Reduction of particle size by milling is a common process in the manufacturing of pharmaceutical dosage forms. Powders with higher surface area increase dissolution and, consequently, significantly improve bioavailability of a drug product.13 In addition, small particle size promotes adhesion between activeexcipient powders during mixing.4 These benefits are offset by the detrimental effects of milling such as the potential to cause significant chemical and physical instability. Of particular interest, milling induces small levels of disorder or amorphous material r 2011 American Chemical Society
predominantly at the surface of particles.57 Small organic molecular crystals, subjected to high pressure or high shear processing, become mechanically activated, undergoing transformations between the crystalline and the disordered states. This phenomenon has been observed in numerous materials including inorganic ceramics,812 alloys, intermetallics, semiconductors, Received: May 31, 2011 Revised: August 12, 2011 Published: August 17, 2011 5260
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Crystal Growth & Design and organic pharmaceuticals.13,14 It has been proposed that during milling a large number of dislocations nucleate, increasing the strain energy in excess of that of an amorphous phase.15 The crystalline to amorphous transformation takes place when molecules in the crystal are displaced into a metastable position or continuum regime.16 In this continuum, the material has stored energy due to the distortion of the bonds during milling and when reaching a critical level the system undergoes cooperative motions with the ability to cause a glass relaxation.17,18 It is clear that milling causes a dramatic disruption of the local arrangement of the molecules. This may include formation of cracks, dislocations, defects, and higher energy molecular conformations and the potential for partial or complete disordering as the result of grinding.5,19,20 This phenomenon is frequently observed but poorly understood. It is relevant to pharmaceutical processing with particular emphasis on the physicochemical behavior that will impact mechanical properties and functionality and performance of processed pharmaceutical materials.18 In the pharmaceutical industry, formation of disordered solids during high-pressure or high-shear processing14 is not uncommon; the three-dimensional periodic arrangement of molecules and nonbonded interactions may be effectively disrupted. Hence, at the crystal molecular level, identification of the slip systems and Burgers vectors, both of which are material-specific properties, defined by the crystal lattice, is required for potential predictive mechanistic models. Though multiple slip systems vectors are common for atomic crystals,21 the options in molecular organic crystals are often limited by steric interference imposed by the orientation of various functional groups.14 Therefore, there is clearly a need for experimental characterization of slip planes and Burgers vectors. The slip planes of inorganic materials15 have been studied to a great extent. This kind of crystallographic information for small organic crystals is scarce in the literature. Recently, AFM indentation has been used to study pharmaceutically relevant organic materials such as sucrose,2225 acetaminophen,26 lactose,24,27 ascorbic acid, and ibuprofen.24 The tool of choice in the majority of the reported studies on the crystallinity-disorder-amorphous scenario in molecular crystals is X-ray diffraction. In this work, AFM nanoindentation is used to collect information about the slip plane activity of small organic molecular crystals. Slip occurs along specific crystallographic planes and by dislocation glide as the result of stresses applied to the material that has been subjected to mechanical milling. The most active slip planes will be the source of disorder or defects during deformation. Slip planes in molecular crystals have been identified using methods such as attachment energy data,29 cleavage planes, and inferred data based on hydrogen bonding. The approach in this study is a modification of a previous study reported by Finnie et al. (2001) for paracetamol22 and by Ramos et al. (2009) for RDX.28 The information extracted from the indentation impressions, such as the slip direction, is used to determine the slip systems in succinic acid. This compound was used as a model drug as it is widely used in the pharmaceutical and food industries. More recently, succinic acid has been used for crystal engineering to form cocrystals30,31 with other compounds where the process may involve milling. To this end, it is expected to adapt the method developed herein to collect data on the experimental identification of organic crystals slip planes for which such fundamental material properties are not readily determinable. The information will help for potential further investigations on the underlying physical and mechanical processes taking place upon milling, since currently a series of
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Figure 1. Succinic acid formula and crystal structure.
assumptions and approximations is used to adapt models for prediction purposes including plastic deformation of molecular crystals to applied stress.32
’ MATERIALS AND METHODS The crystal structure and molecular formula for succinic acid (C4H6O4) are shown in Figure 1. Succinic acid is a monoclinic crystal with a cell angle of β = 91.53° and cell lengths of a = 5.098(2) nm, b = 8.879(2) nm, and c = 5.5201(9) nm. The space group is P21/a. There are four molecules per unit cell. Crystal Growth. Succinic acid crystals were grown by slow cooling a saturated solution. The saturated succinic acid solution was made by dissolving succinic acid (Sigma-Aldrich) in ethanol (KOPTEC, 200 proof pure) at 40 °C and stirred for 4 h. The solution was filtered and allowed to cool slowly to room temperature to induce crystallization. After 48 h, crystal growth was observed. The large crystals observed by optical microscopy were isolated from the solution and dried prior to being analyzed. Single-crystal X-ray diffraction (XRD) and nanoindentation were performed on the succinic acid crystals. Nanoindentation Procedure. The exemplary plate-like singlecrystal habit is shown in Figure 2. Nanoindentation was conducted on different faces of the succinic acid single crystal similar to those experiments carried out on paracetamol21 and RDX.28 The orientation of each of the indentation faces was determined by XRD (Bruker D8 Focus, Billerica, USA). One reference direction on each indentation face was identified to allow the slip planes determination from the indent impression topography. The reference direction was chosen as the edges of the indentation face, the orientations of which were determined by XRD. Nanoindentation and imaging of the indent impression topography were performed using atomic force microscopy (Veeco Dimension 5000, Plainview, USA). The nanoindentation probe was a diamond cube corner (Veeco DNISP probe). The tip has a radius of around 40 nm, with a spring constant of 220 N/m and a resonant frequency of 63 kHz. Since the indentation created by the probe is an equilateral triangle, rotation of the sample results in different load distributions relative to the crystal lattice and may activate different slip planes. Compared to the commonly used axis-symmetric sphere and cone indenters, the cube corner indenter concentrates much higher stress fields around the sharp corners and can potentially activate slip planes that are inactive under a small isotropic stress field. Sample Preparation. The experiment was conducted on a 3 mm succinic acid single crystal. The normal and transverse crystal orientations of two different indentation faces were determined using singlecrystal X-ray diffraction. With the transverse reference direction aligned parallel to the nanoindenter cantilever, the sample is indented and the indent impression imaged. The slip traces in the indent impression topography were identified, and their angles relative to the reference edge are used to calculate the orientation of the observed slip traces in the crystal coordinates. To activate as many slip planes as possible and also systematically study the anisotropic plastic deformation by slip, the sample was rotated 30°, 60°, and 90° using a high-precision rotation stage and indented again. On each indentation face and for each sample rotation angle at least three repetitions 10 μm apart were conducted. 5261
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Figure 2. (a) SEM image of a succinic acid crystal with two unknown faces labeled “face a” and “face b” in the sketch. (b) XRD patterns of the crystal “face a”, “face b”, and powder sample, identifying “face a” as (001) and “face b” as (010).
Figure 3. (a) Schematic of nanoindentation on the (001) crystal face of a succinic acid crystal using AFM. (b) Samples were rotated to 0°, 30°, 60°, and 90° to systematically study the slip planes.
Attachment Energy Calculations. Potential slip planes for succinic acid were determined by calculating the attachment energy magnitude of various predicted crystallographic planes using commercial molecular simulation software (Materials Studio 4.0, Accelrys, San Diego, CA). Succinic acid is formed by the layers of the acid molecules interacting with each other by strong hydrogen bonding. Attachment energies of different crystallographic planes were calculated using the force field of COMPASS. The slip planes were predicted by the fact that the plane with a relatively low attachment energy could serve as slip plane systems.
’ RESULTS AND DISCUSSION Single-crystal X-ray diffraction clearly indicated the dominant (001) plane bounded by a (010) face. Miller indices are used as the standard notation herein to describe crystal planes and directions. The crystal direction Bv is represented with a square bracket [hkl]: Bv = h 3 B a + k 3B b + l 3 B, c where B a , B, b and B c are the unit cell axes. The orientations of planes are represented by a round bracket (hkl), where 1/h, 1/k, and 1/l are intercepts of the plane with the three lattice axes. The set of equivalent planes by the lattice symmetry is represented by a curly bracket {hkl}. Figure 2a shows the morphology of a succinic acid single crystal;
indentation plane was identified by XRD (Figure 2b) as the (001) crystal plane, and the adjacent planes were identified as the (010) plane. The intersection of the two planes, the [100] direction, was used as a reference direction. The experimental setup is shown in Figure 3a, where the indentation load is determined from the vertical bending of the cantilever, detected by a deflected laser and a photodetector. The impression left after an indentation is shown by the dark triangle that has a fixed orientation relative to the cantilever direction. Using the sample rotation strategy, four sets of indentions were conducted on the (001) face as shown in Figure 3b. The corresponding sample rotations angles are 0°, 30°, 60°, and 90°. The 0° rotation aligned with the crystal [100] reference direction. A sample rotation angle of 120° is equivalent to the rotation of 0° due to the 3-fold symmetry of the indenter. From the indentation impressions, the trace angle Θtrace (the angle between an observed trace and the reference direction) was experimentally measured. This observed Θtrace was matched with calculated values of the trace angles, giving the Miller indices of the corresponding slip plane. To calculate Θtrace for a specific crystal plane, the plane normals were calculated for both the indentation plane and the given crystal plane using the lattice 5262
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Table 1. Calculated Θtrace of (h,k,l) on the Succinic Acid (001) Face (reference direction [100]) (“l” can be any integer; it cannot be unambiguously determined from indentation on (001)) h\k
3
2
1
0
1
2
3
3
60
69
79
90
79
69
60
2
49
60
74
90
74
60
49
1
30
41
60
90
60
41
30
0
0
0
0
x
0
0
0
1
150
139
120
90
120
139
150
2
131
120
106
90
106
120
131
3
120
111
101
90
101
111
120
Table 2. Calculated Θtrace of (h,k,l) on the Succinic Acid (010) Face (reference direction [100]) (“k” can be any integer; it cannot be unambiguously determined from indentation on (010)) h\l
3
2
1
0
1
2
3
3
46
57
71
92
74
59
48
2
35
46
64
92
66
48
36
1
20
28
46
92
48
29
20
0
0
0
0
X
0
0
0
1
160
151
132
92
134
152
160
2 3
144 132
132 120
114 106
92 92
116 109
134 123
145 134
parameters of succinic acid in an orthogonal coordinate system a ¼ 5:098 3 ½ 1 B
0
0
B b ¼ 8:879 3 ½ 0
1
0
c ¼ 5:52 3 ½ 0:0267 B
0
0:9996
The reference direction can be calculated from the cross product of the normal vectors of the indentation plane and the neighboring plane. Similarly, the orientations of the slip traces can be calculated by the cross product of the normal vectors of the indentation face and the slip planes. The Θtrace between a specific slip trace and the reference trace can be obtained by the dot product of these two vectors. Using (001) as the indentation plane and [100] as the reference direction, Θtrace for all low-index crystal planes |h|, |k|, and |l| smaller than 3 are listed in Table 1. The same calculation was conducted with (010) as the indentation plane and [100] as the reference direction, and the results are listed in Table 2. Specially grown large crystals are often required to accommodate indentation; this poses a limitation of the microindentation technique. In the event that large crystals are not possible and only small crystals are feasible, it is worth mentioning that the fundamental limitation with smaller crystals is the resolution of the diffraction technique (identifies thr indentation plane) and the geometry of the nanoindenter (determines indent size). The slip planes of crystals as small as a few hundred micrometers should be identifiable routinely using the proposed methods. However, as the crystal becomes smaller, determining the phase and crystal planes by X-ray would become more difficult. Mounting
and leveling the indentation face becomes more challenging as well. Indentation on the Crystal (001) Face. AFM indentation impression images are displayed in Figure 3ad. Four representative indentations at 0°, 30°, 60°, and 90° sample rotations are shown. Using the crystal [100] direction as the reference direction, the relative angle Θtrace between the slip traces and the reference direction was measured. Table 3 shows the various rotations and the respective sets of traces observed with respect to the reference direction in Figure 3ad. Matching the experimentally measured trace angles with the calculation from Table 1, the possible slip planes at each sample rotation are identified and shown in the last column of Table 3. When indenting on the (001) face, the third miller index {l} cannot be identified because the slip trace angle is only determined by the first two indices. Comparing these four sets of indentations, it is noteworthy that different combinations of slip planes were observed in different sample rotations. This may be attributed to the inhomogeneous stress distribution of the indenter. To initiate slip on a specific slip plane, the resolved shear stress should exceed a critical level in the slip direction. As the stress distribution under a cube corner indenter is not homogeneous, the largest resolved shear stress on a given slip plane changes as the sample is rotated. Thus, different slip plane combinations are present at different sample rotations. While many slip planes such as (10n) only appeared at one sample rotation angle, there are slip planes such as (31n) that are present repeatedly at various sample rotation angles. These slip planes are identified as those that need relatively less energy to activate. Because these planes are relatively easier to be activated, they also have relatively large areas, as more slip will take place on these planes. As a result, the main slip planes can be identified by counting the number of parallel slip traces. It is apparent in the images of Figure 4a and 4c that the slip planes {01n} at 0° with respect to the reference trace appeared more frequently than others. From the images of Figure 4b and 4d, the most frequently observed slip traces were {11n} at angles (62° away from the reference trace. Although with the current data the value of the third index was not possible to determine, the results agree quite well with the main slip planes, (020) and (111), predicted by the attachment energy calculation. On the basis of the attachment energy calculation, the most likely slip planes are ranked as shown in Table 4. In our experiment, the observed slip planes were ranked by the number of parallel lines for each set of slip planes observed in the experiment. Clearly, in the first four sets of slip planes, the experiments and prediction have excellent agreement. Indentation on the Crystal (010) Face. The same set of experiments was conducted on a different crystal plane, the (010) plane with [100] being the reference direction. The indentation impressions are shown in Figure 5. The experimentally measured trace angles, listed in Table 5, are correlated to specific planes using data in Table 2. One significant difference between the indentation impressions on the (010) plane and on the (001) plane is the amount of the ‘pile up’. On the (001) plane, the impressions are relatively flat and there was no noticeable material piling up around the indentation, whereas a significant pile up around the impressions on the (010) plane is observed. The facets in the pile ups are believed to be slip planes. The slip traces are the intersection of the facet and the indentation face. By identifying the orientation of the slip traces and their corresponding trace angles from the experimental results, the observed slip planes are as listed in 5263
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Table 5. When comparing the slip planes predicted by the attachment energy calculation from Table 4, {1n1} is seen to match with (111), (121), and (232). Comparing indentations of succinic acid on the (001) and (010) faces suggests that because of the anisotropic crystal structure nature, different combinations of slip planes are activated at different sample rotation angles and on different crystal faces. This approach demonstrates that the sample rotation method, developed herein, is a powerful tool and practical method to study the anisotropic properties of materials. For succinic acid the following was noticed. First, with identification of the slip planes and directions for this material, various higher index slip planes were observed in this organic crystal in addition to the low-symmetry {111} also observed in face-centered cubic (fcc) metals.33 This suggests that the lower symmetry of the monoclinic crystal structure must be taken into account when Table 3. Experimental Observed Slip Traces on (001) Figure 4
sample rotation
sets of traces
possible slip planes
a
0°
0°, 49°, 78°,
{01n}, {23n}, {31n},
90°, 138° b
30°
52°, 62°
{10n}, {12n}
analyzing the deformation, compared to a highly symmetric cubic structure. It seems that the limited amount of available low-index slip planes requires higher index slip planes to be activated for deformation in noncubic organic crystals. With fewer available slip planes the distinct facets in the impression pile ups are expected as the required combination of slip systems to produce uniform flow is much larger in noncubic systems. In contrast, the multiplicity of low-index systems in cubic systems leads to a much more uniform deformation. Second, the indentation impressions are more planar on the (001) face and have significant pile ups on the (010) face, indicating different deformation mechanisms. It is suggested34,35 that when the slip plane is perpendicular to the indentation plane, the dislocations generated by slip can cause work hardening of the indented crystal face and lead to a relatively stiffer surface and smaller indentation impression, as shown in Figure 6a.34In Figure 6b, however, the indented face (010) is parallel to the {010} slip planes. There is no significant work hardening effect, and the same Table 4. Slip Planes As Determined from Attachment Energy Calculations and from AFM Nanoindentation on the Crystal (001) Face (hkl)
{23n}, {11n}
1st
2nd
3rd
4th
5th
6th
c
60°
78°, 118°
{31n}, {11n}
attachment energy prediction (020) (111) (121) (232) (131) (201)
d
90°
0°, 40°, 132°
{01n}, {12n}, {23n}
experimental results on (001) {02n} {11n} {12n} {23n} {10n} {31n}
Figure 4. AFM topographic images of indentation on the crystal (001) face, with the (010) trace being the reference; image width is 10 μm. 5264
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Figure 5. AFM topographic images of indentation on the crystal (010) face, with the (001) trace being the reference; image width is 10 μm.
Table 5. Experimental Observed Slip Traces on (010) sample
sets of
possible slip
Figure 5
rotation
traces
planes
a b
0° 30°
0°, 34°, 90°, 160° 35°,58°, 113°, 130°
{0n1}, {2n3}, {1n0}, {1n3} {2n3}, {3n2}, {2n1}, {1n1}
c
60°
45°, 60°, 90°, 120°,
{1n1}, {3n2}, {1n0},
150°, 160° d
90°
60°, 70°, 172°
(1n2), (1n3) {3n2}, {3n1}, {0n1}
load results in a relatively larger indentation impression and more pile ups around the indentation. In summary, the difference in the indentation impression and stiffness of (001) and (010) planes, as shown in Figures 4 and 5, can be explained by the relative orientation of the available slip planes with respect to the indented plane. Third, cracks were also observed in all indentations performed on the (001) face but none on the (010) face under the same indentation loading. This may be related to the geometry of the impressions. The stress may be effectively released on the (010) face by pile-up formation through slipping, but it cannot be effectively released on the (001) face and leads to cracks. This was further supported by the average size of impressions on the (010) face, which is significantly larger than that of the (001)
face. It is interesting to note that at the same applied load on the (001) primary face cracks were formed around the indents. However, when the indentation is done on the face (010), cracks do not appear as readily. This clearly shows the anisotropy of the material. Data of similar properties for other materials are reported the literature.36 Nanoindentation of pharmaceutical materials depends on the deformation and fracture properties of the material. Thus, indentation of brittle and semibrittle materials can often lead to cracking around the indent impression. Cracking may occur before yield (plastic deformation), and the crack would be along crystal directions and the orientation of the stress field. More cracks are expected for a more brittle material, but some slip traces are expected as well, due to the inhomogeneous stress field from the cube corner indenter and the anisotropic properties of the materials. In addition, the hydrastatic stress generated by the nanoindenter can suppress crack formation and facilitate plastic deformation. The applied loads would have to be lower and the slip traces smaller but still resolvable by AFM. Attachment Energy. Lastly, the slip planes calculated using the attachment energy29 method were in agreement with our experiments in predicting the first and second most likely slip planes in the case of succinic acid. However, the calculation method could not predict other slip planes, which exist in lowsymmetry organic crystals. Thus, it is critical to experimentally 5265
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Figure 6. (a) Indentation on the (001) face, where the material flow is accommodated mostly by the slip along {010} planes, leading to a work hardening effect and a relatively shallow impression. (b) Indentation on the (010) face, where no significant work hardening occurs, leading to a deeper impression and pile up at the surface.
method such as the one developed herein, the information may be attainable for anisotropic materials like succinic acid. The defined plasticity of materials depends on the identified number of slip planes.22 On the basis of the data in Tables 4 and 5 represented in Figure 7a and 7b and direct observation of the AFM images (Figures 4 and 5), the succinic acid crystals show some discrete dislocation events.
Figure 7. (a and b) Crystallographic structure of succinic acid on (001) and (010) faces with the various possible slip planes, respectively.
confirm the actual slip planes in order to be able to accurately predict the material’s mechanic behavior. The diagrams in Figure 7a and 7b show a representation of the most favorable activated slip systems as presented in Tables 4 and 5 for nanoindentation on (001) and (010) faces, respectively. As pointed out previously, it is important to assess the mechanical response of molecular crystals in order to understand the dislocation activity due to the indentation, i.e., the degree of development of the plastic region around the indentation. The process of dislocation motion is complex; the equivalent slip planes are not easier to obtain for organic materials, but using a systematic
’ CONCLUSIONS In this study, we have shown that AFM nanoindentation of succinic acid, a soft molecular crystal, seems to generate plastic deformation. The slip planes of a model molecular crystal, succinic acid, were identified. The major slip planes for succinic acid were found to be (010) and (111), which agrees with calculations based on the attachment energy. Many other slip systems detected with the experiment are not predicted by the attachment energy calculation or reported in the literature. It is clear from the images that higher index slip planes are repeatable and systematically observed at the various indentations with different sample rotations, although they have lower activity. In addition, indentation impressions on the (001) and (010) faces clearly show that different crystal planes have different plastic deformation mechanisms in response to mechanical loading. This study has shown that the sample rotating method developed herein provides an approach to systematically study the anisotropic slip properties of pharmaceutical single crystals. Identification of the slip planes warrants investigation, since it is anticipated that this experimental approach could serve as an important development tool to fundamentally understand the milling ability of compounds as well as the consequences of milling (including resulting active surface, inadvertent and uncontrolled formation of disorder) during the pharmaceutical processing and manufacturing activities. ’ AUTHOR INFORMATION Corresponding Author
*Phone: (765) 496-6438 (M.T.C.); (765) 496-1045 (M.K.). Fax: (765) 496-1356 (M.T.C.). E-mail:
[email protected] (M.T.C.);
[email protected] (M.K.)
’ ACKNOWLEDGMENT We are grateful for the support of the Materials and Surface Engineering Division of the NSF under grant NSF-CMMI-0825994 5266
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Crystal Growth & Design and Hoffman la Roche. For helpful discussions, Drs. Harpreet Sandhu and Navnit Shah from Hoffmann-LaRoche and Dr. Calvin Sun from the University of Minnesota are thanked. We thank an anonymous reviewer for helpful suggestions.
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