Searching for New Polymorphs by Epitaxial Growth.

The formation of unknown polymorphs due to the crystallization at a substrate surface is frequently observed. This phenomenon is much less studied for epitaxially grown molecular crystals since the unambiguous proof of a new polymorph is a challenging task. The existence of multiple epitaxial alignments of the crystallites together with the simultaneous presence of different polymorphs does not allow simple phase identification. We present grazing incidence X-ray diffraction studies on conjugated molecules like perylenetetracarboxylic dianhydride (PTCDA), pentacene, dibenzopentacene (trans-DBPen), and dicyanovinylquater-thiophene (DCV4T-Et2) grown by physical vapor deposition on single crystalline surfaces like Ag(111), Cu(111), and graphene. A new method for indexing the observed Bragg peaks allows the determination of the crystallographic unit cells so that the type of crystallographic phase can be clearly identified. This approach even works when several polymorphs are simultaneously present within a single sample as shown for DCV4T-Et2 on Ag(111). Additionally, epitaxial relationships between the epitaxially grown crystallites and the single crystalline surfaces are determined. In a subsequent step, the experimental data are used for the crystal structure solution of an unknown polymorph, as shown for the example trans-DBPen grown on Cu(111).

Introduction

For molecular materials, the existence of different crystalline phases (polymorphism) is a widely observed phenomenon with huge technological importance.[1] Polymorph phases have a strong impact on application-relevant properties like solubility of pharmaceutics and charge transport of organic semiconductors.[2,3] Recently, the formation of polymorphs at surfaces became a focus of interest since the presence of a surface during the crystallization process can cause unknown types of polymorphs within thin films.[4,5] Polymorph formation at amorphous surfaces has been investigated in detail, and a strong preferred orientation of the crystals has been observed together with the appearance of multiple phases.[6−8] However, the polymorph formation of molecular crystals by epitaxial growth is much less studied.

Defined single crystalline surfaces can be used as templates for crystal formation. The initial growth scenario in terms of nucleation has been investigated in detail: the appearance of a stable (or metastable) structure depends on the balanced interaction of the organic adsorbate with the substrate in relation to the adsorbate–adsorbate interaction.[9,10] Weak adhesion is a key for the epitaxial film growth, and the arrangement of the molecules in crystal nuclei (or within the first monolayer) plays a crucial role in multilayer film growth.[11,12] Crystal growth studies starting from the initial stage of nucleation are of fundamental importance.[13] Even though a collection of epitaxial data of molecular crystals at surfaces exists,[14] a detailed identification of the underlying mechanisms, which cause the epitaxial crystallization, is still a topic of intense scientific research. Rearrangements of the molecules frequently occur at the interface so that deviations from the known crystallographic packing of the molecules appear. Successful explanations of organic epitaxy are based on lattice mismatch calculations[15−18] and ledge-directed or angle-directed crystallization.[19,20] A classification of epitaxial types, including both rigid and flexible lattices, was recently published.[21]

The discovery of unknown polymorphs through epitaxy is reported for several cases.[22−28] A number of experimental methods can be used to prove the presence of a new phase; spectroscopic techniques and diffraction methods are used.[29−31] However, the presence of several different phases is a frequently observed case within epitaxially oriented crystallites at surfaces.[27,32,33] To overcome this difficulty, selected crystals are removed from the surface and investigation by microscopy techniques can be performed.[34] However, a detailed crystal structure analysis of an unknown polymorph prepared by epitaxial growth is a challenging task since a crystal size in the sub-μm range does not allow the use of routine methods for crystal structure determination, e.g., single-crystal X-ray diffraction.[35]

Grazing incidence X-ray diffraction (GIXD) is a widely used technique for the crystallographic characterization of thin films. Recently, the method was extended by rotation of the sample during the GIXD measurement and collecting a diffraction pattern for each rotation angle.[36,37] Large volumes of the reciprocal space can be scanned so that even without any preknowledge of the diffraction fingerprint, an unknown polymorph can be recorded. However, the symmetry of the substrate surface causes several azimuthal alignments of the epitaxially grown crystals, which causes serious difficulties in the assignment of the individual diffraction peaks to the corresponding phase. Moreover, multiple crystal orientations of the same crystal phase can appear, and different polymorphs within a single sample can be present.[38,39] In our previous work, we have shown the theoretical concept of the assignment of diffraction peaks to individually oriented crystallites.[40] In this paper, we will apply this methodology to a number of examples with known and unknown bulk polymorphs. By indexing the complete diffraction patterns, we can identify the known phases that are present within the films. Unknown polymorphs are discovered, even if several phases are present within the epitaxially grown films.

Experimental Details

Experimental Methods

Different organic semiconductors were selected for this study: well-known molecules like 3,4;9,10-perylenetetracarboxylic dianhydride (PTCDA) and pentacene were chosen, but also the less characterized molecules 1,2;8,9-dibenzopentacene (trans-DBPen) and dicyanovinylquater-thiophene (DCV4T-Et2) (cf. Chart ). The molecules have predominantly rigid character, but DCV4T-Et2 shows also some flexibility allowing changes of the molecular conformation. Thin films were prepared under UHV conditions on different substrates, the nominal thicknesses of the films were in the range from 10 to 30 nm. Details about the sample preparation are given in the Supporting Information (cf. Table S1).

Chart 1

Structural Formulas of the Molecules Epitaxially Grown on Single Crystalline Surfaces

Specular X-ray scans were performed on a PANalytical Empyrean system, equipped with a copper X-ray tube (wavelength λ = 1.5418 Å). On the primary side, an X-ray mirror for monochromatization and parallelization of the incident beam and a 1/8° slit were used. On the secondary side, the system contained an anti-scatter slit (8 mm), 0.02 rad Soller slits, and a Pixcel 3D detector operated in the scanning line mode, utilizing all 255 channels. For the scans, a step size of 0.0131° and an effective time per step of approximately 103 s were chosen.

Grazing incidence X-ray diffraction measurements were performed at the XRD1 beamline, synchrotron Elettra, Trieste, Italy, using a wavelength of 1.4 Å and a stationary Pilatus 2M detector. The sample-detector distance was varied between 150 and 200 mm allowing the collection of the diffraction pattern for all samples with sufficient resolution and over the region of interest. The incident angle was decided individually for each sample, based on the number and sharpness of the observed diffraction peaks. Samples were rotated around their surface normal (ϕsample rotation) during the GIXD measurements, with integrations over Δϕsample of 0.5 or 1°, i.e., recording 720 or 360 images for the full rotation, respectively. Table S1 gives an overview of the exact experimental parameters for each individual sample.

Extraction of peak positions was performed manually as already described in the literature.[39] In short, peak positions were determined in the 360° integrated pixel image first. Then, the intensity around this position was monitored as a function of the sample rotation, resulting in a curve showing the intensity I(ϕ). From this data, the specific file where a certain peak occurred was determined, and the peak was fitted by a two-dimensional Gaussian function in this data file. Together with the information of the I(ϕ) curve, the fit result was converted into reciprocal space resulting in three-dimensional peak positions q = (q, q, q)T. Due to the large detector, data from the left-hand side (LHS) and the right-hand side (RHS) of the reciprocal space map (−q and +q, respectively, q = (q2 + q2)1/2), could be evaluated. Note that the information of a single detector side is sufficient for complete monitoring of the accessible reciprocal space. However, recording both sides allows us to independently perform the same evaluation on two datasets and to get better error estimates.

The determination of molecular packing motifs for the case of trans-DBPen requires a combined approach, utilizing the experimental GIXD data together with a computational packing, based on molecular dynamics (MD) simulations with the LAMMPS software package[41] and the CHARMM general force field version 3.0.1.[42] The indexed unit cell is thereby taken as a starting point for the MD simulation by placing randomly oriented trans-DBPen molecules into an enlarged (∼120%) unit cell and thus generating several thousand trial structures. During a simulation run of 80 ps with 1 fs time steps, the unit cell is shrunk down continuously to the experimentally determined size, while letting the molecules relax to find possible packing motifs. The calculated structures are then clustered based on their packing similarities, and the resulting structure factors can be compared to experimental peak intensities.

Indexing Algorithm

If multiple epitaxial orientations of the crystals relative to the substrate surface and/or different crystallographic phases are present, it is necessary to assign the measured reflections to the corresponding unit cells. Our procedure for indexing an unknown crystalline system has been described in detail in a previous paper.[40] In the following, we summarize the relevant steps.

Triplets (g, g, g) of any three measured noncollinear reciprocal vectors are combined to a matrix [g, g, g]. If a triplet corresponds to a unit cell, the determinant of the corresponding matrix is indirectly proportional to the volume of this unit cell, or, if the matrix of the corresponding Laue indices has a determinant greater than one, to some integer fraction of it. If the crystallites are characterized by the same unit cell and differ only in their rotational arrangement in the xy-plane, three reciprocal vectors are chosen from different subgroups with identical pairs of g = (g2 + g2)1/2 and g.

If the reciprocal-space vectors in the matrix belong to the same system, the inverse matrix –1 multiplied with the vectors of the corresponding Laue indices will result in the vectors of the unit cell. This can be accomplished by multiplying –1 with vectors 2π(m1, m2, m3)T containing systematically varied integers m. Then, the vectors are sorted according to their lengths, and the shortest vectors that are not coplanar are chosen. The criteria for excluding false vector triplets are the scalar product criteria[43] and the expected upper and lower limits of the cell parameters or the unit cell volume. If a contact plane, i.e., a defined crystallographic plane parallel to the substrate surface exists, and the specular scan qspec can be measured, the triplets whose z-components are integer multiples of 2π/qspec can be assigned as possible solutions.

The tentative unit cell vectors are multiplied with all experimentally determined reciprocal space vectors. If the scalar products yield integers (i.e., the corresponding Laue indices), these vectors belong to the same system. A high number of compatible reciprocal vectors with a small overall error (i.e., deviations from integers) indicate a good solution.

In Table , the formulas of such obtained unit cell vectors are summarized (cf. eqs S1–S18 in the Supporting Information). The following points are emphasized:

Table 1

Expressions for the Unit Cell Vectors a, b, and c with the Parameters a = |a|, b = |b|, c = |c|, α, β, γ, and the Respective Vector z-Elements a, b, and c in the Nonrotated and the Rotated Casea

a·b = ab cos γ	a·c = ac cos β	b·c = bc cos α
Nonrotated Case (az = bz = 0)
Rotated Case

For a contact plane with the Miller indices u, v, and w, and the specular diffraction peak at position gspec: a = u2π/g, b= v2π/g, and c = w2π/g.

In the orientation matrix of the unit cell, i.e., the general three-dimensional rotation matrix (ϕ, ψ, φ), the two rotation angles ψ and φ can be expressed as functions of the lattice parameters and the Miller indices u, v, and w of the contact plane. Therefore, if a specular scan can be measured, in addition to the rotation angle φ in the xy-plane, the Miller indices can be assigned as the orientation parameters of the unit cell. In general, this information is contained in the z-components of the unit cell vectors.

As the azimuthal rotation angle φ can be independently calculated from the lattice vectors a, b, and c, the accuracy of the result can be checked and a mean value of φ can be determined. In our cases, the errors were smaller than 0.1%.

Considering experimental inaccuracies, the unit cell parameters can be optimized using various methods.[40]

Results and Discussion

The selected molecules together with their single crystalline substrates present a variety of systems for epitaxial growth from well-known molecule/substrate combinations to less-studied systems. Numerous scientific investigations on the thin film structure, morphology, and the electronic and vibronic properties have been performed for PTCDA on Ag(111),[44,45] and this system can be used to verify the proposed indexing strategy. The polymorphism of the molecule pentacene has been investigated quite intensively: polymorph I[46,47] and polymorph II[48,49] are the two known bulk phases, while polymorph III is a substrate-induced phase.[50] Here, we present its epitaxial growth on Cu(111) and clearly identify the phase by our indexing algorithm. The bulk structure of trans-DBPen has only been studied theoretically in terms of crystal structure prediction;[51] we use our indexing procedure to confirm the theoretically predicted molecular packing. The crystallographic properties of the molecule DCV4T-Et2 have not been studied so far;[52] here, the lattice constants of numerous polymorphs are found and compared with each other.

PTCDA on Ag(111)

Two monoclinic polymorphs of PTCDA are known, denoted as the α-phase (a = 3.74 Å, b = 11.96 Å, c = 17.34 Å, β = 98.8°) and the β-phase (a = 3.87 Å, b = 19.30 Å, c = 10.77 Å, β = 83.6°).[32,45] The epitaxy of thin films of PTCDA grown on Ag(111) has been studied using various methods. Using GIXD measurements, Krause et al. obtained evidence for the coexistence of α and β-like polymorphs, slightly modified by epitaxial strain (α1: b = 11.96 Å, α2: b = 19.91 Å, β1: b = 12.45 Å, β2: b = 19.30 Å). Using powder and single-crystal XRD investigations, Levin et al. determined the following lattice parameters, which could be regarded as a reference for α-PTCDA: a = 3.73283(4) Å, b = 12.0328(6) Å, c = 17.3998(4) Å, and β = 98.689(2)° (monoclinic).[53]

In our XRD experiments, the specular X-ray diffraction pattern showed a clear diffraction peak that can be assigned to PTCDA crystals (compare Figure a). In our notation, the position of this peak is denoted as qspec = q = 1.947 Å–1. The GIXD experiments gave 180 and 149 reciprocal lattice vectors with three components q, q, and q for the RHS and LHS, respectively. The different number is due to some peaks falling into the detector gaps at one detector side only.

Figure 1

Specular diffraction peaks (q = qspec) of the analyzed samples indicated by black arrows. (a) PTCDA/Ag(111) (black curve) and DCV4T-Et2/Ag(111) (red curve). (b) DCV4T-Et2/G/SiC(0001). (c) Pentacene/Cu(111) (blue curve) and trans-DBPen (green curve). Additionally, the specular X-ray diffraction patterns show features of the Ag(111) (a), graphene/SiC(0001) (b), and Cu(111) (c) substrate, respectively.

The indexing procedure on this data resulted in 12 solutions with individual lattice vectors a, b, and c (from which the lattice constants can be determined). Additionally, the contact planes (uvw = (1 0 3) and (−1 0 −3), each six times) and the 12 azimuthal rotation angles φ of the solutions were obtained. Two groups of azimuthal alignments, each with a 60°-symmetry and a difference between the two groups of Δφ = 16.5(7)° were found. This clearly reflects the symmetry of the Ag(111) surface. Due to their small differences, the lattice parameters were determined by averaging over all sets of lattice constants of the 12 individual solutions (Table ). An evaluation of the data from the LHS and RHS of the detector revealed no significant differences (see Supporting Information, Table S2). The expected peak positions of the determined solution are plotted together with the two-dimensional reciprocal space map in Figure . Assuming a monoclinic lattice and accordingly fitting the parameters result in a = 3.743(5) Å, b = 12.116(62) Å, c = 17.064(36) Å, β = 94.69(17)° with the contact planes (1 0 −3) and (−1 0 3). In Figure , the q/q and q/q positions of the extracted diffraction peaks and the corresponding calculated values from the indexing result are shown.

Table 2

Unit Cell Parameters a, b, c, α, β, and γ, the Volume V, and the Miller Indices of the Contact Planes (uvw) for PTCDA/Ag(111), Pentacene/Cu(111), Trans-DBPen/Cu(111), DCV4T-Et2/G/SiC(0001), and DCV4T/Ag(111)a

PTCDA/Ag(111)
(1 0 3)	3.737(7)	12.206(102)	17.013(90)	89.87(12)	84.93(28)	89.93(6)	773.0(28)	139	12
(−1 0 −3)
Pentacene/Cu(111)
(0 2 0)	6.226(11)	7.726(31)	14.630(59)	76.51(58)	89.33(35)	83.60(28)	679.4(29)	80	6
(0 −2 0)								73	6
Trans-DBPen/Cu(111)
(0 2 0)	6.751(8)	7.566(4)	18.529(41)	89.88(8)	86.71(25)	89.84(12)	944.8(13)	141	6
(0 −2 0)								143	6
DCV4T-Et2/G/SiC(0001)
(1 −2 2)	8.431(17)	9.050(11)	10.374(16)	104.97(15)	109.61(13)	105.20(15)	665.3(10)	87	6
(−1 2 −2)								95	6
DCV4T-Et2/Ag(111)
(1 −2 2)	8.408(17)	9.070(14)	10.370(12)	104.79(10)	109.91(6)	105.43(8)	662.5(14)	59	6
(−1 2 −2)								61	6
(2 −1 1)	8.083(19)	8.401(18)	9.860(49)	97.74(36)	93.57(36)	92.49(27)	661.1(36)	46	6
(−2 1 −1)								44	6
(0 2 0)	6.115 (9)	7.290(9)	16.095 (13)	83.44(20)	89.52(17)	71.53(13)	673.5(13)	34	6
(0 −2 0)								32	6

nrefl is the number of associated reflections and nφ is the number of different azimuthal alignments.

Figure 2

PTCDA on Ag(111). Integrated reciprocal-space map, overlaid on the right-hand side (RHS) with the indices and calculated peak positions of the determined crystal structure; the strong diffraction peaks from the Ag(111) substrate was shadowed by metal plates. For q = 0, the specular scan is indicated (the corresponding Laue indices are the Miller indices of the contact plane (1 0 3)).

Figure 3

Positions of experimentally determined X-ray diffraction peaks (black) of PTCDA crystals grown on Ag(111), obtained from rotating GIXD experiments. q/q position of the diffraction peaks (a) and q/q positions of the diffraction peaks (b). Indexing (red) of epitaxially oriented crystals grown with the ±(1 0 3) plane parallel to the substrate surface.

In a previous study for α-PTCDA, the following lattice parameters were found: a = 3.7328 Å, b = 12.033 Å, c = 17.4 Å, β = 98.69° assuming the contact plane (1 0 2). Note that this unit cell can be linearly transformed to the equivalent unit cell with the parameters a = 3.7328 Å, b = 12.033 Å, c = 17.2356 Å, β = 93.672°, and the contact plane (1 0 −3), but only the second unit cell, which is reduced,[54] fulfills the Niggli criterion for a, c, and β (cf. Supporting Information).

In a subsequent step, we considered the relationships between the main axes in the xy-plane of the sample (PTCDA) and the substrate Ag(111). The following epitaxial description could be derived: (111)Ag || ±(1 0 3)PTCDA; the b-axis [010] of PTCDA in ±(1 0 3) orientation is rotated by about −22° (i.e., clockwise) and by +22° (i.e., counter-clockwise) with respect to the ⟨11̅0⟩Ag direction (cf. Figure a). In this particular case, the conditions v = 0 and α = γ = 90° are fulfilled, and it follows that the lattice vectors a, b, and c for the contact planes (uvw) and (−u–v–w) are collinear (a → −a, b → b, c → −c; cf. eqs S17 and S18 in the Supporting Information). Therefore, an unambiguous assignment of the rotation angles φ to either the contact plane (uvw) or (−u–v–w) is not possible. However, when comparing with the other sample examples (cf. Table ), it may be supposed that the (1 0 3) and (−1 0 −3) orientations are rotated clockwise and counter-clockwise, respectively.

Figure 6

In-plane angles Δφ between the main crystallographic axes of the sample and the substrate. PTCDA crystals are grown on Ag(111). [010] axis of epitaxially oriented PTCDA crystals, grown with the ±(1 0 3) plane parallel to the substrate surface, relative to the [1–10] axis of Ag (a). Trans-DBPen crystals grown on Cu(111). [100] axis of epitaxially oriented trans-DBPen crystals, grown with the (0 2 0) and (0 −2 0) plane parallel to the substrate surface, relative to the [1–10] axis of Cu (b).

Table 3

In-Plane Angles Δφ between the Main Axes of the Molecular Crystal and the Substrate Depending on the Contact Plane for PTCDA/Ag(111), Pentacene/Cu(111), Trans-DBPen/Cu(111), DCV4T-Et2/G/SiC(0001), and DCV4T/Ag(111)

	substrate		molecule
	orientation	main axis	contact plane	main axis	Δφ (°)	symmetry (°)
PTCDA/Ag	(1 1 1)	[1 −1 0]	±(1 0 3)	[1 0 0]	–21.9(6)	60
					+21.7(8)
pentacene/Cu	(1 1 1)	[1 −1 0]	(0 2 0)	[1 0 0]	–6.7(2)	60
			(0 −2 0)		+6.6(2)
trans-DBPen/Cu	(1 1 1)	[1 −1 0]	(0 2 0)	[1 0 0]	–3.7(2)	60
			(0 −2 0)		+3.5(2)
DCV4T-Et2/G/SiC	(0 0 0 1)	[1 0 0]	(1 −2 2)	[2 1 0]	+22.7(2)	60
			(−1 2 −2)		–22.9(3)
DCV4T-Et2/Ag	(1 1 1)	[1 −1 0]	(1 −2 2)	[2 1 0]	–25.7(1)	60
			(−1 2 −2)		+25.7(1)
	(1 1 1)	[1 −1 0]	(2 −1 1)	[1 2 0]	–7.6(2)	60
			(−2 1 −1)		+7.8(2)
	(1 1 1)	[1 −1 0]	(0 2 0)	[1 0 0]	–7.7(4)	60
			(0 −2 0)		+7.9(3)

Pentacene on Cu(111)

The specular X-ray diffraction peak of pentacene could be determined as qspec = q = 1.693 Å–1 (see Figure c). The GIXD experiments gave 141 and 137 reciprocal lattice vectors for the RHS and LHS, respectively. Twelve different in-plane alignments of the crystallites could be found; six for the contact plane (0 2 0) and another six for the contact plane (0 −2 0), respectively, each with a 60° symmetry. The obtained lattice constants (from the RHS) are listed in Table . In a previous study, the following unit cell of a pentacene crystal was found by single-crystal diffraction: a = 6.266(8) Å, b = 7.775(10) Å, c = 14.5300(19) Å, α = 76.475(2)°, β = 87.682(2)°, and γ = 84.684(2)°.[49] From our data, we can conclude that we obtained the Holmes phase.

The following epitaxial relationships were determined: (1 1 1)Cu || ±(0 2 0)pentacene; the a-axis [100] of pentacene in (0 2 0) orientation is rotated by about −6.5° (i.e., clockwise) and the a-axis [100] of pentacene in (0 −2 0) orientation is rotated by about by +6.5° (i.e., counter-clockwise) with respect to the ⟨11̅0⟩Cu direction, respectively.

Trans-DBPen on Cu(111)

The specular X-ray diffraction peak of trans-DBPen crystals could be observed at qspec = q = 1.660 Å–1 (see Figure c). The GIXD experiments gave 275 and 332 reciprocal lattice vectors for the RHS and LHS, respectively. Twelve different in-plane alignments of the crystallites could be found; six for the contact plane (0 2 0) and another six for the contact plane (0 −2 0), respectively, each with a 60° symmetry. The following epitaxial relationships were found: (1 1 1)Cu || ±(0 2 0); the a-axis [100] of trans-DBPen in (0 2 0) orientation is rotated by about −3.5° (i.e., clockwise) and the a-axis [100] of trans-DBPen in (0 −2 0) orientation is rotated by about by +3.5° (i.e., counter-clockwise) with respect to the ⟨11̅0⟩Cu direction, respectively (cf. Figure b). The obtained lattice constants (from the RHS) are summarized in Table . Assuming a monoclinic lattice and accordingly fitting the parameters result in a = 6.748(9) Å, b = 7.564(4) Å, c = 18.533(39) Å, and β = 93.42(7)°.

In a previous study, using first-principles density functional theory (DFT) with van der Waals correction, the following unit cell was found: a = 6.745 Å, b = 7.613 Å, c = 18.495 Å, α = 90°, β = 97.13°, γ = 90°, and volume V = 942.5 Å3.[51] With the exception of β, these lattice parameters match ours.

After extraction of peak intensities and performing MD simulations as described previously, a comparison of the simulated structure factors and the experimental peak intensities is attempted. Theoretical peak positions for crystals with a (0 2 0) and (0 −2 0) contact plane, respectively, and six different in-plane alignments each, together with their respective structure factors are calculated. Slices through planes of constant q are evaluated, and for each experimentally observed peak, the corresponding squared structure factors are compared to the calculated peak intensities, repeating this for several possible packing motifs. The procedure is performed for both the left- and right-hand-side data searching for the overall best agreement between experimental and simulated data. The best match is achieved for a herringbone structure (herringbone angle, 23.3°), the molecular packing within the herringbone layer is depicted in Figure d. To visualize the agreement of calculated and measured intensity properly for peaks with small structure factors, the intensity is shown in Figure a–c as circles, with their radii proportional to the logarithm of the calculated intensity and squared structure factor, respectively. The CIF of the crystal structure solution is available in the Supporting Information.

Figure 4

Comparison of experimental and calculated diffraction patterns of trans-DBPen crystals grown on a Cu(111) surface. The q/q positions of the Bragg peaks are given by the centers of the half-circles at different q heights with 0.83 Å–1 (a), 1.67 Å–1 (b), and 2.49 Å–1 (c). Black and red half-circles are for crystals with (0 2 0) and (0 −2 0) orientation, respectively; blue half-circles represent the calculated peak positions. Peak intensities are given by the areas of half-circles for experimental values (red, black) and for the calculated values (blue). Packing of trans-DBPen molecules within the solved crystal structure, the molecules are projected along their long molecular axes (d).

DCV4T-Et2

DCV4T-Et2 on Graphene (G/SiC(0001))

DCV4T is a prototypical donor material for small-molecule solar cells. Crystallographic studies were performed by Elschner et al.[55] For the ethyl side chain substituted DCV4T-Et2, no single-crystal structure is available. From their studies, Guskova et al. concluded that the molecules are oriented nearly flat-lying with tilt angles higher than 70° in the crystalline film regions.[52]

In our experiments, the specular X-ray diffraction peak of DCV4T-Et2 crystals grown on graphene could be determined at qspec = q = 1.858 Å–1 (see Figure b). The GIXD experiments gave 218 and 209 reciprocal lattice vectors on RHS and LHS, respectively. Twelve different in-plane alignments of the crystallites could be found; six for the contact plane (1 −2 2) and another six for the contact plane (−1 2 −2), respectively, each with a 60° symmetry. The obtained lattice constants (from RHS) are listed in Table . In Figure a,b the q/q and q/q positions of the measured diffraction peaks and the corresponding calculated values from the indexing results are shown.

Figure 5

Positions of experimentally determined X-ray diffraction peaks (black) of DCV4T-Et2 crystals grown on G/SiC(0001) (a, b) and on Ag(111) (c, d), obtained from rotating GIXD experiments. q/q position of the diffraction peaks (a, c); q/q positions of the diffraction peaks (b, d). Indexing of epitaxially oriented crystals grown with the (1 −2 2) plane (red circles), and with the (−1 2 −2) plane (red squares), respectively, parallel to the substrate surface (a, b). Indexing of three epitaxially oriented polymorphs grown with the (1 −2 2) and (−1 2 −2) plane (red), (2 −1 1) and (−2 1 −1) plane (blue) and (0 2 0) and (0 −2 0) plane (green), respectively, parallel to the substrate surface (c, d).

The following epitaxial relationships were found: (0001)G/SiC || ±(1 −2 2)DCV4T-Et2; the axis [210] of DCV4T-Et2 in (1 −2 2) orientation is rotated by about +23° (i.e., counter-clockwise) and the axis [210] of DCV4T-Et2 in (−1 2 −2) orientation is rotated by about by −23° (i.e., clockwise) with respect to the ⟨100⟩G/SiC direction, respectively.

DCV4T-Et2 on Ag(111)

Two specular X-ray diffraction peaks are observed at positions qspec = q = 1.828 Å–1 and qspec = q = 1.857 Å–1, respectively (see Figure a). The second peak was already observed when G/SiC(0001) was used as the substrate. The GIXD experiments gave 253 and 186 reciprocal lattice vectors at the RHS and LHS, respectively. Three polymorphs with different unit cell parameters and contact planes, ±(1 −2 2), ±(2 −1 1), and ±(0 2 0), could be assigned. For each of them, 12 different in-plane alignments of the crystallites could be found; six for the positive contact plane and another six for the negative contact plane, respectively, each with a 60° symmetry. The obtained lattice constants (from RHS) are listed in Table . In Figure c,d, the q/q and q/q positions of the obtained diffraction peaks and the corresponding calculated values from the indexing results for the three polymorphs are shown. Though some of the reflections of the ±(1 −2 2) and ±(2 −1 1) orientations overlap, most of the reflections of the three polymorphs are clearly distinguishable. The three crystal structure solutions seem to be reasonable since their unit cell volumes are comparable.

The epitaxial relationships are specified in Table . While the specular scan qspec = 1.857 Å–1 can be assigned to the unit cell in ±(1 −2 2) orientations, the specular scan qspec = 1.828 Å–1 is related to the unit cells in ±(2 −1 1) and ±(0 2 0) orientations. The lattice parameters of the unit cell with the contact planes ±(1 −2 2) are clearly the same for both the graphite and silver substrate.

In the case of the polymorph in ±(0 2 0) orientation, 66 reflections could be assigned to the corresponding triples of unit cell vectors differing in their azimuthal alignments. This relation between available reciprocal lattice vectors and corresponding unit cell vectors may define the lower limit for our indexing method. At least three linearly independent reciprocal lattice vectors are necessary to determine the lattice parameters and orientation of the underlying unit cell; in this particular case, we used on average 5.5 reflections for the indexing procedure.

Summary and Discussion

Including our previous study of 6,13-pentacenequinone (PQ) on Ag(111),[40] the following general crystallographic features of epitaxially grown films could be observed:

The crystallites grow with defined crystallographic planes parallel to the substrate surface (i.e., contact planes), which can be observed by specular X-ray diffraction. The specular diffraction peak comprises the information on the Miller indices of the contact plane. Including this information in the mathematical formalism is of considerable help in indexing of conventional and rotated GIXD data.[40,56,57] In all our test cases, we found positive and negative orientations of the contact planes, i.e., the planes with the Miller indices (uvw) and (−u–v–w). In the particular case of PTCDA, where v = 0 and α = γ = 90°, indexing the reflections does not allow an unambiguous assignment to either one of these two systems. In the case of DCV4T-Et2 on Ag(111), we observed three polymorphs with both different crystallographic unit cells as well as contact planes. In comparison, for the system sexithiophene grown on KCl(100), Schwabegger et al. found various contact planes for the same crystalline phase.[39]

The crystallites additionally show distinct alignments in the xy-plane. When Ag(111), Cu(111), and graphene/SiC(0001) were used as substrates, for each contact plane two groups of 60°-symmetry were observed, one for the positive (uvw) and one for the negative (−u–v–w) orientation. This is reflected in the angles between the main crystallographic axes of the organic crystals and the corresponding substrates (see Table ). The respective two main axes of the organic crystals are aligned symmetrically, mostly anticlockwise and clockwise, around the main axes of the substrates (see Figure ). The inaccuracy of the obtained results was within 1°. For each system, 12 different azimuthal alignments could be observed. In the case of DCV4T-Et2 on Ag(111), where three different polymorphs could be found, our method allowed a clear assignment of the reflections to the respective unit cells on the basis of about 200 reciprocal lattice vectors.

As each unit cell is represented several times, mean values and standard deviations of the cell parameters can be calculated. Analyzing the reflections of the detector RHS, the obtained data are specified in Table . The inaccuracies are always below 1%, in most cases a few per mill. The results for the LHS can be found in the Supporting Information (cf. Table S2). In general, we did not find significant differences between the parameters obtained for the two detector sides. In the case of PTCDA and pentacene, our results clearly correspond to well-known phases, and our lattice parameters are in good agreement with previously published data. Our results on trans-DBPen also show a close match with the literature. Differences must be attributed to the fact that the literature reports the crystal structure solution from simulations at 0 K, whereas our measurements are performed at room temperature. For the very flexible molecule DCV4T-Et2 on graphene/SiC, a single solution is found. Interestingly, the same solution is obtained for DCV4T-Et2 on Ag(111). However, there are two different crystal structures obtained in addition. The present results clearly show that the proposed algorithm can be applied on a wide variety of systems, independent of the substrate type, the molecule’s flexibility and shape, and the coexistence of several crystalline phases on the same substrate.

Conclusions

Applying a previously described algorithm for indexing rotated GIXD diffraction patterns, we analyzed well-known (PTCDA, pentacene) as well as crystallographically less-characterized samples (trans-DBPen, DCV4T-Et2) on various substrates. In all cases, we obtained crystallographic unit cells exhibiting specific contact planes with the substrate. Additionally, distinct 60° symmetries for the positive and negative orientations of the contact plane were found, without an a priori assumption of any symmetry of the substrate for the indexing procedure. Our results for the unit cell parameters of PTCDA and pentacene are in good agreement with previous data; in both cases, we found an already characterized polymorph. In the case of trans-DBPen grown on Cu(111), our experimental data are used for the crystal structure solution of a previously unknown polymorph, which was performed on the basis of molecular dynamics simulations. In the particular case of DCV4T-Et2 grown on Ag(111), we found three new polymorphs with different contact planes and cell parameters; when using graphene/SiC(0001) as a substrate, however, only one of these polymorphs could be observed. This work shows that indexing is possible even when different alignments of crystals occur within a thin film and also in the presence of several polymorphs.