Synthesis and Photophysical Characterization of New Azaphthalocyanines and Azanaphthalocyanines for Semiconductor Interface Design

The aim of this work, which was carried out within the SFB1083, was the synthesis and characterisation of phthalocyanines (Pc), pyrazinoporphyrazines (Ppz), their hybrid compounds, the so called azaphthalocyanines (Pz, Nx-[Pc*M] with M = central metal or 2 H) and larger homologues, the naphthalocyanines (Nc). The focus was, besides their optoelectronic application in dye sensitized solar cells (DSSCs), the systematic investigation of selected compounds, frontier MOs using electronic absorption spectroscopy and in cyclic voltammetry. In addition, photophysical properties of these compounds were investigated, in particular their ability to form singlet oxygen; their fluorescence quantum yields and the fluorescence lifetimes were also determined. Organic precursors. Firstly, the literature known compounds PDN* 1, PyzDN* 2 and NDN* 3 were reproduced; the series was then completed by the synthesis of compounds NpzDN* 4, NqnDN* 5 and NppzDN* 6. Besides their synthesis and characterisations discussed in section 4.1, compound 3-6 are a novel series of C2v-symmetrical naphthalonitriles bearing alkyl groups in the peripheral position, while [-CH=] building blocks are systematically exchanged by [-N=] units. In comparison to the commercially available PDNtBu, the advantages of these 2,2,5,5-tetramethylcyclohexane annulated compounds are the increased solubility in common organic solvents due to the reduced aggregation of the Pc caused by sterically demanding alkyl groups. Furthermore, in cyclotetramerisation of C2v-symmetrical phthalonitriles no mixture of 4 regioisomers is obtained, in contrast to [PctBuM]. Owing to the symmetry of the A4-type molecules resulting from a cyclisation of 1-6, the analysis in NMR spectroscopy is simplified, crystallisation of these compounds is favoured, and, therefore, an X-ray analysis is possible. The key-step in the synthesis of PDN* 1 is the oxidation of the tetraline system to a dicarboxylic acid. The synthesis of PDN* 1 was firstly reported by MIKHALENKO. Up to now, the overall yield of ~30% over seven steps was limited due to the chosen conditions in the oxidation step. As oxidant potassium permanganate was used in excess in aq. pyridine. Following famous industrial processes, such as the aerobic oxidation of p-xylene to terephthalic acid, the side chain oxidation of tetraline was optimized in a catalytic procedure, increasing the yield up to 97%. Azaphthalocyanines (of Nx-[Pc*M] type with M = 2 H, Zn) were synthesised in a cocyclisation of two dinitriles PDN* 1 and PyzDN* 2, followed by metalation of chromatographically separated Nx-Pc*H2 using [Zn(hmds)2] or [Zn(OAc)2], respectively. Azaphthalocyanines Nx-[Pc*M] with x = 0, 2, 4, 6, or 8 are discussed and described in section 4.2. All Nx-[Pc*M] were characterized by using NMR, UV-Vis, FS spectroscopy, cyclic voltammetry, mass spectrometry and photophysical experiments. First synthesised ABAB N4-[Pc*M] with M = 2 H, Zn completed the up-to-now unfulfilled series. Both structural isomers ABAB and A2B2 could be clearly identified by using 1H NMR spectroscopy and UV-Vis spectroscopy. Besides the cocyclisation, A2B2 N4-Pc*H2 and AB3 N6-Pc*H2 could be synthesised in a KOBAYASHI ring expansion of an AB2 N4-[Spc*BCl] or [Sppz*BCl], respectively, using the isoindoline of PDN* 1. The values obtained by UV-Vis spectroscopy and CV were compared to TD-DFT calculations in cooperation with the TONNER group (Department of Chemistry of the Philipps-Universität Marburg). In both experimental data and theoretical calculations, a non-perfect linear trend of the hypsochromic shift of the Q-band was found when the HOMO-LUMO gap is increased with the increasing number of substitution of [-CH=] by [-N=] in the non-peripheral position. The reason for the HOMO-LUMO gap increase is the stronger decrease of the HOMO level relative to the one of the LUMO with increasing number of [-N=] units in Nx-[Pc*M]. In addition, photophysical properties were investigated. Singlet oxygen quantum yields , fluorescence quantum yields and fluorescence lifetimes were determined for both series of Nx-[Spc*BCl] and Nx-[Pc*M] in cooperation with ZIMČÍK and NOVÁKOVÁ (Department of Pharmacy of the Charles-University in Prague). The highest value for singlet oxygen quantum yield was observed for ABAB N4-[Pc*Zn]. The sum of values is for both Nx-[Pc*Zn] and Nx-[Spc*BCl] ~0.9. In comparison, a trend, not yet described in literature, was found for Nx-Pc*H2, which shows a significant decrease of both values with increasing number of [-N=] units. For the first time, an asymmetrical 2,2,5,5-tetramethylcyclohexane substituted aza-phthalocyanine N2-Pc*H2 was analysed by X-ray diffraction. In contrast to the herringbone pattern of unsubstituted Pcs, N2-Pc*H2 units are twisted almost 90° in their lattice structure. Similar to other obtained structures, such as A2B2 N4-[Pc*Zn], substituted [-CH=] and [-N=] units cannot be differentiated by X-ray analysis. In both structures, a characteristic statistical disorder is observed, in which the [-CH=] units are partly occupied by [-N=], to 25%, or 50%, respectively. Within the bachelor thesis of LANGE, the isoindoline units of the azaphthalocyanine series Nx-Pc*H2 were annulated with a benzene unit. These Nx-Npz*H2 are discussed in section 4.2.6. The series was also completed with the ABAB N4-Npz*H2 and differentiated from its A2B2 isomer by using 1H NMR and UV-Vis spectroscopy. Azanaphthalocyanines (Nx,y-[Nc*M(NR)Cl] with M = Mo, W and R = tBu, Mes) were synthesised using 2,2,5,5-tetramethylcyclohexane annulated dinitriles 3-6 and group 6 metal precursors ([M(NR)2Cl2∙solv] with M = Mo, W, R = tBu, Mes and solv = py or dme). This is the first described series of azanaphthalocyanines (section 4.2.9) bearing alkyl groups in the peripheral position. The compounds were analysed using at least UV-Vis and IR spectroscopy, elemental analysis and mass spectrometric methods, such as MALDI-ToF or LIFDI. The Q-bands of the compounds N0,0-[Nc*Mo(NtBu)Cl], N0,8-[Nc*Mo(NtBu)Cl], N8,0-[Nc*Mo(NtBu)Cl] and N8,8-[Nc*Mo(NtBu)Cl] show a hypsochromic shift from 900 nm to 700 nm with increasing substitution of [-CH=] units by [-N=] and proximity to the central [-MN4-] unit. The Q-band is uncommonly strongly shifted by a substitution of the axial ligand of N0,0-[Nc*Mo(NR)Cl] with R = tBu or Mes: for N0,0-[Nc*Mo(NtBu)Cl] and N0,0-[Nc*Mo(NMes)Cl] a shift of 27 nm was observed. Both compounds, N0,0-[Nc*Mo(NtBu)Cl] and N0,0-[Nc*Mo(NMes)Cl], were analysed by EPR spectroscopy. In EPR measurements, the structural differences between the orthorhombic N0,0-[Nc*Mo(NMes)Cl], contrary to the axially symmetric N0,0-[Nc*Mo(NtBu)Cl], is clearly visible. Calculations of orbital interaction with our cooperation partner BERGER (Department of Chemistry of the Philipps-Universität Marburg) are in progress. Besides the synthesis of group 6 d1-metal naphthalocyanine complexes, the access to metal-free Nx,y-Nc*H2 ligands was attempted in a final stage of this work. N0,0-Nc*H2 and N0,8-Nc*H2 as well as their Zn-complexes, N0,0-[Nc*Zn] and N0,8-[Nc*Zn], were synthesised according to literature known methods (section 4.2.10). N8,0-[Nc*Zn] was obtained in 29% yield from compound 5 and [ZnCl2] in quinoline after 12 h at 230 °C. In first attempts to synthesise N8,0-Nc*H2 and N8,8-Nc*H2, similar to the synthesis of Ppz*H2, a higher tendency to form meso-Cnoctyl-substituted complexes Ppz*H2noctyl or N8,0-Nc*H2noctyl was observed. The mechanism, as well as the isolation of the pure N8,0-Nc*H2noctyl, has to be carried out in future studies. N8,0-Nc*H2 could be isolated by preparative TLC and was analysed by using mass spectrometry and UV-Vis spectroscopy. In the synthesis of N8,8-[Nc*Zn], no pure product could be isolated, but a cyclotetramerisation was proven by mass-spectrometry and UV-Vis spectroscopy. Subphthalocyanines (Spc) and Subpyrazinporphyrazines (Sppz) bearing the annulated 2,2,5,5-tetramethylcyclohexane ring could be reproduced and axially substituted with halogen atoms. A series of these smaller, ring contracted, "umbrella-like", distorted Pc homologues [Spc*BR] and the first series of [Sppz*BR] with R = F, Cl, Br and OH were synthesised and characterized. Spcs (N0-[Spc*BCl]) absorb light in the higher energetic area at about 580 nm and electron deficient Sppzs (N6-[Spc*BCl]) at 534 nm. On the right side, cuvettes of a new Nx-[Spc*BCl] series with X = 0, 2, 4 and 6 are shown (FS, illuminated at λ = 365 nm). Visible to the unaided eye is the change of the absorbance and emission behaviour, by exchanging [-CH=] by [-N=] building blocks. The structure of [Spc*BCl] is one example for the rare, substituted Spcs that was analysed by X-ray diffraction. In addition, first attempts were carried out to synthesise surrounded metal-complexes of [Me2M(-OBSpc)]2 type with M = Al, Ga using [MMe3] as metal precursor and [SpcBOH]. The synthesis of these compounds was monitored by 1H NMR spectroscopy and the resulting [Me2M(-OBSpc)]2 characterised by using UV-Vis, FS and IR spectroscopy. According to mass spectrometric results from MALDI-ToF, a dinuclear structure is proposed. Compared to axial substitution of phthalocyanines, the UV-Vis spectra of subphthalocyanine complexes [Me2M(-OBSpc)]2 with M = Al, Ga show a slight shift of the Q-band of about 1 nm in comparison to [SpcBOH]. In following experiments, the synthesis of numerous borato coordinated metal complexes was attempted, whereby [(SpcBO)4Ti] as well as [(SpcBO)3B] were observed and characterised. These metal complexes show a weak broadening of the Q-band in UV-Vis spectroscopy, because the -systems are forced into physical proximity. Application as Photosensitizer in Dye Sensitized Solar Cells (DSSCs) was carried out for equatorially functionalised compounds. Their synthesis is discussed in section 4.3. Unsubstituted Pc, [PcZn]FG, with different anchors were synthesised (FG = vinylphosphonic acid, phosphonic acid, vinylcarboxylic acid, or catechol) using a KOBAYASHI ring-expansion. In addition, 2,2,5,5-tetramethylcyclohexane annulated Pcs ([Pc*M]OH with M = 2 H, Zn) with a catechol anchor were synthesised in yields of up to 10% in a cocyclisation. All compounds were successfully bonded to ZnO semiconductor surfaces. Current-voltage characteristic (I-U curve) and IPCE measurements were carried out in collaboration with AG SCHLETTWEIN (Department of Physics of the Justus-Liebig-Universität Gießen). The most promising anchor moiety appears to be the phosphonic acid of [PcZn]vPA ( = 0.5%), followed by the carboxylic acid [PcZn]vCA ( = <0.2%) and the catechol [PcZn]OH ( ~ 0.001%), when correct solvent and conditions for the deposition are chosen. In comparison to the unsubstituted compound [PcZn]OH, the alkyl substituted [Pc*Zn]OH shows a higher efficiency in DSSCs by a factor 10, and with this, a better electron transfer to the semiconductor. This clearly shows how the electron donating and sterically demanding alkyl groups decrease aggregation and recombination processes. However, in accordance with the Nx-[Pc*M] series with M = 2 H, Zn, lower efficiencies were measured for Pc*H2OH compared to [Pc*Zn]OH, which is caused by increased "quenching" processes taking place when the central metal atom is removed. Currently, photoluminescence measurements are being carried out for constructed cells. A fast electron transfer to the semiconductor was observed, but also a fast recombination process, which might explain the low electron transfer to the semiconductor and the low cell efficiencies. However, a favoured electron transfer from the dye to a semiconductor by using an equatorial anchor in comparison to previously described axial anchor moieties was proven. In future work, the described structure-property correlation obtained from previous sections can be used to design and modify equatorially functionalised Pcs. The readily accessible [Pc*Zn]OH can be converted into a vinylphosphonic acid substituted A3B type Pc, such as [Pc*Zn]vPA or [Pc*Zn]vCA. Furthermore, the complexes should be tested with additives such as cheno or axially coordinating moieties such as guanidine; meso-CFG Pc and derivatives could also be investigated. Phthalocyanine Sandwich-Complexes of a [Pc*2MRE] and [Nc*2MRE] type were synthesised for MRE = Eu, Tb, Ce and Nd. The main focus was on the rare earth metals Eu3+ and Tb3+, because of their different spin of +/- ½ in comparison to the quite well investigated f7-Gd3+ phthalocyanine complexes, of a [Pc2Gd] type. In this work, the easiest synthetic access to [Pc*2MRE] and [Nc*2MRE] was found to be the reaction of the free ligand Pc*H2 and Nc*H2 in presence of the respective [MRE(hmds)3]. For a complete formation to the [(Pc)- (Pc’)2- MRE, 3+]0 complex reaction times of up to 7 d at 110 °C in toluene were necessary. The obtained sandwich complexes show a split of the B-band in the UV-Vis spectrum at 323-331 nm and at 341-352 nm. In addition, both naphthalocyanine and phthalocyanine complexes show, with a decreasing radius of the central metal ion MRE, 3+, an increasing hypsochromic shift of the Q-band from 800 nm ([Nc*2Ce]) to 778 nm ([Nc*2Eu]) and from the metal free ligand at 711 nm (Pc*H2) over 694 nm ([Pc*2Eu]) to 692 nm ([Pc*2Tb]). Furthermore, typical v(C=N) valence vibrations in the IR spectrum of [Nc*2Ce] were observed at 1362 cm-1 and 1314 cm-1. The presented work displayed multi-faceted chemistry of phthalocyanines, naphthalocyanines and their aza-analogue complexes. Within a set of selected examples, the prediction of optoelectronic properties using structure-property correlations has been demonstrated

1D HERMITE ELEMENTS FOR C1-CONTINUOUS SOLUTIONS IN SECOND GRADIENT ELASTICITY

We present a modified strain gradient theory of elasticity for linear isotropic materials in order to account for the so-called size effect. Additional material length scale parameters are introduced and the problem of static beam bending is analyzed. A numerical solution is derived by means of a finite element approach. A global C1-continuous displacement field is applied in finite element solutions because the higher-order strain energy density additionally depends on second gradients of displacements. So-called Hermite finite elements are used that allow for merging gradients between elements. The element stiffness matrix as well as the global stiffness matrix of the problem is developed. Convergence, C1-continuity and the size effect in the numerical solution is shown. Experiments on bending stiffnesses of different sized micro beams made of the polymer SU-8 are performed by using an atomic force microscope and the results are compared to the numerical solution

Photogrammetrische Verfahren zur Risserkennung und -analyse im bautechnischen Versuchswesen

Photogrammetrische Methoden gewinnen zunehmend an Bedeutung im bau­tech­nischen Versuchswesen. Die Auswertung von Bildsequenzen ermöglicht eine kontakt­lose, flächenhafte, hochaufgelöste und hochgenaue Veränderungs­detek­tion von Ober­flächen in der Materialprüfung und Bauwerksüberwachung. Diese Arbeit behan­delt einige Aspekte der Deformationsanalyse auf Basis von Bild­sequenzen mit Hilfe triangulierter Verschiebungsfelder. Zunächst wird auf Unter­suchungen zu Defor­ma­tionen ebener Objektoberflächen, die mit mono­kularen Bild­sequenzen beo­bachtet wurden, eingegangen. Im weiteren Verlauf wird auf Stereobildsequenzen über­ge­gangen, die Deformations­mes­sungen für beliebige Ober­flächen erlauben. Im ersten Teil der Arbeit wird gezeigt, wie Verschiebungsfelder in monokularen Bild­sequenzen bestimmt werden können. Die Bildpunkte, an welche die Verschie­bungen geknüpft sind, werden zu einem Dreiecksnetz trianguliert. Jedes einzelne Dreieck wird auf Änderungen zu der Referenzepoche, die als die erste Epoche ohne jegliche Defor­mation definiert ist, untersucht. Ein gängiges Verfahren zur Analyse solcher Verän­derungen ist die Berechnung von Haupt­dehnungen für jedes Dreieck. Schwell­werte können zur Erkennung deformierter Bereiche und die farbkodierte Darstellung der Hauptdehnungen für eine visuelle Betrachtung genutzt werden. In den räumlich verteilten Hauptdehnungen sowie im zeitlichen Ablauf treten Rausch­effekte auf. Deshalb werden verschiedene Filtermethoden zur Rausch­unter­drückung untersucht. Dabei kommt ein Filter zum Einsatz, der gleichzeitig in der räumlichen sowie der zeitlichen Dimension filtert. Es werden aber auch Filter unter­sucht, die in beiden Dimensionen getrennt filtern. Aus den Hauptdehnungen können nicht direkt Rissbreiten abgeleitet werden. Diese spielen für die Materialprüfung im Bauwesen allerdings eine wichtige Rolle, wes­wegen sich diese Arbeit auch mit der Berechnung von Riss­breiten in Dreiecks­netzen befasst. Als deformierte Dreiecke werden diejenigen detektiert, deren Hauptdehnung einen Schwellwert überschreiten. Für diese Kandidaten werden im Folgenden Rissbreiten bestimmt. Drei verschiedene Verfahren für die Ermittlung von Rissbreiten werden vorgestellt und verglichen. Die Dehnbarkeit faserbewehrter Komposite, die unter anderem zur Verstärkung von Mauern und anderen Bauwerken verwendet werden, wird bei Belastung durch die Bildung multipler Rissstrukturen gewährleistet. Auf Grund dessen widmet sich ein weiterer Teil der Dissertation der Auswertung multipler Riss­strukturen. Hierzu werden dichte Verschiebungsfelder berechnet. Dann wird zunächst eine Auswahl der verfolgten Punkte genutzt, um ein grobes Dreiecks­netz zu generieren. Deformierte Dreiecke der ausgedünnten triangu­lierten Punktmenge werden mit dem Betrag des relativen Trans­lations­vektors, der als Deformations­maß eingeführt wird, detektiert. Eine iterative Verdichtung des Dreiecknetzes in defor­mierten Bereichen ermöglicht die Auswertung enger Riss­muster. Zudem erlaubt eine Ausgleichung, dass nicht-triangulierte Punkte des dichten Verschie­bungs­feldes in die Rissbreiten­berechnung einbe­zogen werden können. Ein weiterer Bestandteil der Arbeit ist die Betrachtung unebener Oberflächen, die mit Stereokamerasystemen beobachtet werden. Dazu werden die Algorithmen für die zweidimensionale Auswertung entsprechend übertragen und erweitert. Auf Basis von Verschiebungsfeldern dreidimensionaler Punkte wird auch hier ein Dreiecksnetz zur Änderungsdetektion genutzt. So wird am Beispiel von dynamischen Dehnungstests an zylindrischen Probe­körpern ein Algorithmus zur Rissbreitenmessung auf nicht ebenen Ober­flächen vorge­stellt. Dabei wird angenommen, dass die Defor­mationen ausschließlich tangential zur Oberfläche auftreten. Dies erlaubt die Transformation (Kongruenz­abbildung) der Dreiecke in einen zwei­dimen­sionalen Raum und auch eine zwei­dimensionale Auswertung. Außerdem wird eine Methode zur Berechnung des dreidimensionalen Riss­öffnungs­vektors präsentiert. Dieses Verfahren ist eine Erweiterung zum vorher­gehenden Algorithmus und erlaubt zudem die Vermessung vertikaler Defor­ma­tionen. Defor­mierte Dreiecke im trian­gulierten dreidimensionalen Verschie­bungs­feld werden mit Hilfe des zwei­dimen­sionalen Relativ­translations­vektor­betrags der in den zwei­dimen­sionalen Raum transformierten Dreiecke detek­tiert. Anschließend folgt für alle defor­mierten Dreiecke durch Hinzunahme min­des­tens eines undeformierten Nachbar­dreiecks die Berechnung eines drei­dimen­sionalen relativen Trans­lations­vektors, mit Hilfe dessen die Komponenten des Riss­öffnungsvektors ermittelt werden.:Kurzfassung iii Abstract v 1. Einführung 1 1.1. Struktur der Arbeit 1 1.2. Motivation 2 1.3. Verwandte Arbeiten 4 1.4. Ziele der Arbeit 7 2. Photogrammetrische Deformationsmessung in monokularen Bildsequenzen 8 2.1. Filtermethoden in Dreiecksnetzen 9 2.2. Rissbreitenberechnung mit Hilfe von Dreiecksnetzen 19 2.3. Strategie zur Rissbreitenmessung für multiple Rissstrukturen 29 3. Photogrammetrische Deformationsmessung in Stereobildsequenzen 50 3.1. Rissbreitenberechnung für tangentiale Deformationen auf nicht ebenen Oberflächen mit gegebenem 3D-Verschiebungsfeld 51 3.2. Berechnung des dreidimensionalen Rissöffnungsvektors bei gegebenem 3D-Verschiebungsfeld 59 4. Diskussion 70 5. Ausblick 77 5.1. Bestimmung der Anzahl der Risse 77 5.2. Rissspitzenbestimmung und -verfolgung 78 5.3. Anwendung der entwickelten Algorithmen auf Voxeldaten 78 5.4. Modellerweiterung durch Relativrotation 82 5.5. Genauigkeitssteigerungen für die Rissposition 82 5.6 Verbesserung der Rissnormalenschätzung 82 Literaturverzeichnis 83 Abkürzungsverzeichnis 89 Tabellenverzeichnis 90 Abbildungsverzeichnis 90Photogrammetric methods are gaining importance in civil engineering material testing and structural health monitoring. The analysis of image sequences ensures an extensive change detection of surfaces with a high spatial resolution and a high accuracy. This thesis deals with some aspects of deformation analysis based on image sequences and triangulated displacement fields. At the beginning, the examination of planar surfaces of specimens observed with monocular image sequences is considered. Later, a transition to stereo image sequences is given because they allow a deformation measurement of arbitrary surfaces. The first part of the thesis shows how to derive displacement fields from monocular image sequences. The matching points corresponding to the displace­ments are triangulated into a mesh. Each triangle is compared to the reference epoch which is defined as the first time epoch under zero load without any deformation. As a current method, principal strains are used to detect deformations. Thresholds can be used to find deformed areas. In addition, color-coded maps of the principal strains are helpful for a visual detection. In the field of the principal strains, noise effects appear in the spatial as well as in the temporal domain. Therefore, different filter methods are applied to reduce noise. In addition to filter techniques that are applied independently in the time and the spatial domain, a combined spatio-temporal filter is tested. Crack widths cannot be derived directly from principal strains but crack widths are an important issue in civil engineering material testing. For this reason, this thesis also gives attention to the computation of crack widths in triangle meshes. The principal strains of the triangles are tested for exceeding a threshold to detect deformed triangles. For the deformed triangles, crack widths are computed. Three different methods for the crack width determination are presented and compared. Multiple cracking ensures the ductility of loaded fiber-reinforced composites used to strengthen walls among other things. Therefore, another part of the dissertation deals with the photogrammetric analysis of multiple crack patterns. Herein, dense displacement fields are computed. Then, a thinned-out set of points is triangulated into a mesh. For each triangle, the norm of the relative translations vector defined as a new quantity to detect deformations is deter­mined and used to find cracked triangles. The mesh is densified iteratively in deformed areas to ensure an analysis of narrow crack structures. In addition, a least squares algorithm is presented which allows that points of the displace­ment field, that are not part of the mesh, can be included in the crack width computation. A further part of the dissertation deals with non-planar surfaces observed with stereo camera systems. The algorithms of the two dimensional analysis are adapted and extended to use them for these applications. These methods are based on three dimensional displacement fields and also use triangle meshes to detect deformed areas. One algorithm concentrates on the crack width measurement of non-planar surfaces with deformations that are only tangential to the surface. The method is applied on a cylindrical specimen in a dynamic tension test. The assumption that deformations are tangential to the surface allows the transformation of the triangles in the two dimensional space and also a two dimensional analysis. In addition, an algorithm for the computation of the three dimensional crack opening vectors is presented. This method is an extension to the foregoing algorithm and is capable of measuring vertical deformations. To find deformed triangles in the triangulated three dimensional displacement field, the triangles are transformed in the two dimensional space in a first step. In a second step, the norm of the two dimensional relative translation vector is determined and tested if it exceeds a threshold. In the following, for each deformed triangle, the three dimensional relative translation vector is computed using a undeformed neighbor triangle. At the end, the three dimensional relative translation vectors can be transformed to the crack opening vectors.:Kurzfassung iii Abstract v 1. Einführung 1 1.1. Struktur der Arbeit 1 1.2. Motivation 2 1.3. Verwandte Arbeiten 4 1.4. Ziele der Arbeit 7 2. Photogrammetrische Deformationsmessung in monokularen Bildsequenzen 8 2.1. Filtermethoden in Dreiecksnetzen 9 2.2. Rissbreitenberechnung mit Hilfe von Dreiecksnetzen 19 2.3. Strategie zur Rissbreitenmessung für multiple Rissstrukturen 29 3. Photogrammetrische Deformationsmessung in Stereobildsequenzen 50 3.1. Rissbreitenberechnung für tangentiale Deformationen auf nicht ebenen Oberflächen mit gegebenem 3D-Verschiebungsfeld 51 3.2. Berechnung des dreidimensionalen Rissöffnungsvektors bei gegebenem 3D-Verschiebungsfeld 59 4. Diskussion 70 5. Ausblick 77 5.1. Bestimmung der Anzahl der Risse 77 5.2. Rissspitzenbestimmung und -verfolgung 78 5.3. Anwendung der entwickelten Algorithmen auf Voxeldaten 78 5.4. Modellerweiterung durch Relativrotation 82 5.5. Genauigkeitssteigerungen für die Rissposition 82 5.6 Verbesserung der Rissnormalenschätzung 82 Literaturverzeichnis 83 Abkürzungsverzeichnis 89 Tabellenverzeichnis 90 Abbildungsverzeichnis 9