Nanocrystalline thin films : microstructure, stability and properties

Stuttgart

Nanocrystalline thin films:

Microstructure, stability and properties

Silke J. B. Kurz

Dissertation

an der

Universität Stuttgart

Bericht Nr. 247

März 2014

NANOCRYSTALLINE THIN FILMS:

MICROSTRUCTURE, STABILITY AND PROPERTIES

Von der Fakultät Chemie der Universität Stuttgart zur Erlangung der

Würde eines Doktors der Naturwissenschaften (Dr. rer. nat.)

genehmigte Abhandlung

Vorgelegt von

Silke J. B. Kurz

aus Bietigheim-Bissingen

Hauptberichter

Prof. Dr. Ir. E. J. Mittemeijer

Mitberichter

Prof. Dr. J. Bill

Prüfungsvorsitzender

Prof. Dr. T. Schleid

Tag der Einreichung

17.01.2014

Tag der mündlichen Prüfung

03.03.2014

M

AX

-P

LANCK

-I

NSTITUT FÜR

I

NTELLIGENTE

S

YSTEME

(

EHEMALS

M

AX

-P

LANCK

-I

NSTITUT FÜR

M

ETALLFORSCHUNG

)

I

NSTITUT FÜR

M

ATERIALWISSENSCHAFT DER

U

NIVERSITÄT

S

TUTTGART

Contents

1 Introduction ... 9

1.1 The microstructure and properties of thin metallic films ... 9

1.1.1 Thin films ... 9

1.1.2 Nanocrystalline materials ... 10

1.1.3 Nanotwinned fcc metals ... 11

1.1.4 Ni-W films in literature ... 12

1.1.5 Ni-Mo films in literature ... 12

1.2 Diffraction analysis of the microstructure of materials ... 14

1.2.1 General remarks ... 14

1.2.2 Stress analysis by X-ray diffraction ... 16

1.2.3 Planar-fault analysis by X-ray diffraction ... 18

1.3 Outline of the thesis ... 20

2 Diffraction-stress analysis of highly planar-faulted, macroscopically elastically anisotropic thin films and application to tensilely loaded nanocrystalline Ni and Ni(W) ... 21

2.1 Introduction... 22

2.2 Theoretical background ... 23

2.2.1 Stress analysis by (X-ray) diffraction ... 23

2.2.1.1 Macroscopically elastically anisotropic specimens; use of the X-ray stress factors... 23

2.2.1.2 Macroscopically elastically anisotropic, strongly and sharply textured specimens; use of the crystallite-group method ... 24

2.2.2 Influence of planar faults on Bragg reflections ... 26

2.3 Experimental ... 26

2.3.1 Film deposition and chemical analysis ... 26

2.3.2 Transmission electron microscopy ... 27

2.4 Microstructural investigation ... 30

2.5 Residual stress analysis: The as-deposited state ... 33

2.5.1 Films on wafer substrates ... 33

2.5.2 Films on Kapton® substrates ... 37

2.6 Stress analysis during tensile loading ... 39

2.7 Conclusions ... 42

3 _{The thermal stability of Ni-Mo and Ni-W thin films:  Solute segregation and} planar faults ... 43

4 Discovery of a thermally persistent hcp solid-solution phase in the Ni-W system ... 53

4.1 Introduction... 54

4.2 Experimental procedures ... 55

4.2.1 Ni-W film growth and analysis ... 55

4.2.2 Microstructural characterization ... 55

4.3 Methodology of first-principles calculations ... 56

4.4 Results ... 57

4.4.1 The as-deposited phase and microstructure: fcc-like and hcp-like Ni(W) . 57 4.4.2 Thermal evolution of fcc-like and hcp-like Ni(W) ... 61

4.4.3 Calculations of phase stability in the Ni-W system ... 62

4.5 General discussion ... 64

4.5.1 Phase stabilities in the Ni-W system ... 64

4.5.2 Twin-fault stability of Ni(W) thin films at elevated temperatures ... 66

4.6 Conclusions ... 68

5 Anomalously high density and thermal stability of nanotwins in Ni(W) thin films: Quantitative analysis by X-ray diffraction ... 71

5.1 Introduction... 72

5.3 Evaluation of experimental data ... 75

5.3.1 (HR)TEM evaluation ... 75

5.3.2 XRD evaluation ... 77

5.3.2.1 fcc-like Ni(W) films ... 78

5.3.2.2 fcc+hcp Ni(W) films ... 80

5.4 Results of the quantitative fault analysis ... 83

5.4.1 Planar-fault density in the as-deposited state ... 83

5.4.2 Thermal stability of the planar-fault density ... 83

5.5 Discussion ... 86

5.5.1 Validation of the XRD analysis ... 86

5.5.2 Degree of hexagonality ... 87

5.5.3 Twin- and stacking-fault probabilities ... 88

5.5.4 Two-phase nature of Ni(W) films with W content > 15 at.% ... 90

5.5.5 Thermal stability of nanotwins ... 91

5.6 Conclusions ... 92

6 Summary ... 95

6.1 Summary in English ... 95

6.2 Zusammenfassung auf Deutsch ... 101

Introduction

1

Introduction

Different kinds of thin films are widely used in industry having specific mechanical, elec-trical, magnetic, optical and / or chemical properties. In particular, chromium hard coat-ings are typically produced for protective and decorative applications. However, the pro-duction process of galvanic chromium deposition involves the use of an electrolyte solu-tion containing toxic Cr(VI) ions. In the last decades many attempts were made to find an alternative for chromium hard coatings with even improved properties. This work focuses on the investigation of binary Ni-based thin films which were alloyed with refractory metals (W and Mo) to produce films with desired properties, thus enabling their applica-tion as coatings to replace the ecologically harmful chromium coatings. The properties are highly influenced by the microstructure of the films, including residual stress which strongly affects the performance of the film. Besides these more industrial issues, the in-vestigated films offer peculiar diffraction effects and astonishing features which are of scientific interest. Some useful background information about the properties of thin films exhibiting an outstanding microstructure and about diffraction principles is given in the following sections.

1.1

The microstructure and properties of thin metallic films

1.1.1 Thin films

The technological progress during the last decades was highly dependent on the minia-turization of microelectronic devices, micro-electromechanical systems (MEMS) and nano-electro-mechanical systems (NEMS). This fact demonstrates that the understanding of the microstructure-property relationship of (such) thin films is of crucial importance to enable tuning and optimization of their performance in, e.g. protective, functional and decorative applications.

Different film-deposition concepts and resulting microstructures are thoroughly dis-cussed in Ref. [1]. Very thin films are typically produced by physical vapour deposition (PVD). The PVD method used in the present thesis is sputtering: An inert gas, commonly argon, is ionized by glow discharge between the target, consisting of the pure metal to which the argon ions are accelerated by the imposed electrical field, and the substrate. Besides other processes, the argon ions remove metal atoms by momentum transfer. These metal atoms propagate to the substrate and, upon deposition, build up the thin film. The argon pressure, the substrate temperature and the surface roughness of the substrate are the main factors influencing the atom mobility on the surface of the substrate and, therefore, these factors determine the developing microstructure. A variation of the sput-ter-deposition process is magnetron sputtering: A magnet is located behind the target to enhance the sputter rate by forcing the electrons on a cycloidal path, which increases the ionization rate, and to shield the substrate to some extent from the plasma. For

co-deposition, two pure metal targets are used, which can be operated at different powers to adjust the respective deposition rates and, thereby, the alloy composition of the film.

The properties of thin films differ significantly from those of their bulk counterparts due to the dimensional constraints imposed by the film thickness and / or grain size. The dependence of hardness and strength, which are defined by the resistance against plastic deformation, on the film thickness is schematically illustrated in Figure 1.1: With de-creasing film thickness, the dislocation motion is more pronouncedly confined which leads to an increase of the film strength. An overview of mechanical properties of thin films is given in Ref. [2].

Figure 1.1: Illustration of a confined dislocation in a thin film. With decreasing film thickness, the film strength increases.

1.1.2 Nanocrystalline materials

The dimensions of a material can be further confined by introducing additional inter-faces, as grain boundaries, to enhance the strength and hardness of the material (neglect-ing the controversially discussed breakdown of the Hall-Petch behaviour for very small grain sizes, e.g. [3]). Materials with grain sizes smaller than 100 nm are defined as nano-crystalline and can be produced by e.g. ball milling, high-pressure torsion, electrodeposi-tion or sputtering. More than one half of their volume can be composed of grain bounda-ries which are in a glassy state (without long-range order, see Figure 1.2a) with a density reduced by 15 – 30 % compared to the crystalline state. Consequently, extraordinary prop-erties occur which were already found more than 20 years ago [4]; as an example for ex-traordinary intrinsic properties, a non-monotonic dependence of the lattice parameter on the grain size was reported [5]. Special attention was paid to the mechanical properties of nanocrystalline materials, which were reviewed recently [6]. However, nanocrystalline microstructures tend to grain growth even at room temperature, so-called self-annealing [7], to lower the overall energy of the material which can destroy desired properties. Grain-boundary segregation was found to act as efficient grain-boundary stabilizer in many systems [8-10] by (i) lowering the grain-boundary energy and, thereby, the driving force for grain growth and (ii) slowing down the kinetics by drag forces and / or an in-crease of activation energy of the grain-boundary mobility.

1.1.3 Nanotwinned fcc metals

The influence of interfaces on material properties became already evident in the last two sections. Advanced material properties can be obtained by optimization of the amount and character of these interfaces in materials. To this end, materials exhibiting nano-scale twins, so-called nanotwinned materials as shown schematically in Figure 1.2b, are in the focus of current research. This special microstructure can be synthesized by phase transformation, by deformation or by growth. Growth twins are discussed in the present work, which are typically produced by electro- or sputter-deposition. Nano-twinned microstructures of several pure fcc metals exhibiting low stacking-fault energies as Cu, Ag and Ni as well as of austenitic stainless steel were successfully produced [11-14]. Extraordinarily, even Si nanowires exhibiting nanotwins were prepared by car-bothermal reduction [15]. A preliminary project of this work dealt with the production and investigation of nanotwinned Ni(W) films [16].

Nanotwinned microstructures can exhibit ultrahigh strength following the Hall-Petch law if the grain size D is substituted by the twin spacing L [14], i.e.

τ

∝_L−1 2_{. At the same}

time, nanotwinned metals can retain a certain degree of ductility and can show significant work hardening in contrast to nanocrystalline metals (cf. review article [17]). Further, the fracture toughness and fatigue properties of nanotwinned materials could be improved by increasing the twin density and maintaining a constant grain size [18]. Tensile testing of a Ni(W) film exhibiting nanotwins is performed in the course of this work and is presented in Chapter 2. For industrial application, not only the mechanical but also the thermal sta-bility of these structures is crucial. Unfavourably, distinct detwinning was observed dur-ing heat treatments in pure fcc metals [19,20], and several detwinndur-ing mechanisms were suggested [21]. A thorough investigation of the thermal stability of nanotwins in Ni-based films is presented in Chapters 3 – 5.

The sputter-deposited Ni(W) and Ni(Mo) films investigated in the present study exhibit columnar grains with nanotwins which are strictly aligned parallel to the film surface (cf. Figure 1.7a). Although those microstructures are known to be somewhat less mechanical-ly stable than the ultra-fine grained metals exhibiting arbitrarimechanical-ly oriented twins, they are of particular scientific interest due to their peculiar diffraction effects.

Figure 1.2: Schematic microstructures of (a) a nanocrystalline material with small grains (open cir-cles) and a large volume of grain boundaries (black circir-cles) and (b) a nanotwinned material consisting of hexagonally shaped grains exhibiting a high density of twin faults.

1.1.4 Ni-W films in literature

Since the present work is only concerned with nanocrystalline thin Ni-W films, the lit-erature about bulk Ni-W systems is omitted. Nevertheless, the existing phase diagram is shown in Figure 1.3a indicating a moderate solubility of W in Ni, the ordered Ni4W phase

and two further intermetallic phases whose existence is highly questioned [22].

An early work about amorphous and nanocrystalline Ni-W films was published in 1998 [23], indicating a Hall-Petch relation for the hardness of the electrodeposited films. In the following years a large amount of publications was addressed to electrodeposited Ni-W films. Besides the use of different deposition parameters and additives during the deposi-tion process, the influence of alloying was investigated: The grain size could be reduced by increasing the W content in the film [24]. The microstructure development was inves-tigated by Monte Carlo simulations [25]. Since Ni-W coatings are intended to replace Cr(VI) coatings, their properties are of crucial interest: Wear and corrosion studies [26-30] attested Ni-W films better performance compared to Cr(VI) coatings [27,26]. The hardness as a function of grain size was related to the Hall-Petch law [31] but also other strengthening mechanisms as an enhanced solid solution strengthening concept [32] and grain boundary relaxation strengthening [33] were discussed. Only a few studies are con-cerned with fatigue [34] and fracture toughness [35], demonstrating a moderate mechani-cal stability. The thermal stability of nanocrystalline Ni-W was found to be remarkably high [36,37] owing to grain boundary segregation which was confirmed by atom probe tomography [38] and atomistic computer simulations [39].

In contrast to the well investigated properties and microstructures of electrodeposited Ni-W films, only a limited number of publications is concerned with the investigation of mechanically alloyed [40], sintered [41] and sputter-deposited [16,32,42,43] Ni-W films. The method of sputter deposition is utilized in this study. Not all mentioned publications do explicitly indicate the microstructure of the Ni-W films, but (at least) Welzel et al. [16] observed the occurrence of nanotwinning perpendicular to the growth direction in {111}fcc fibre-textured Ni-W films. These microstructural features have to be thoroughly

investigated and included in the discussion of properties. This is the objective of the pre-sent thesis.

1.1.5 Ni-Mo films in literature

The production of nanocrystalline Ni-Mo films was promoted by the hope to find an al-ternative for Cr(VI) coatings, similar to Ni-W films. The choice of Mo instead of W is straightforward, since those two refractory metals belong to the same group in the period-ic table of elements and are expected to behave chemperiod-ically quite similarly. The phase diagram of Ni-Mo is indeed related to the one of Ni-W (cf. Figure 1.3), except for the additional intermetallic phases Ni3Mo and NiMo. In the field of application of hydrogen

as energy carrier, Ni-Mo can act successfully as electrode in the hydrogen evolution reac-tion [44]. Nanocrystalline Ni-Mo was often prepared by mechanical alloying and only in the last decade Ni-Mo films were electrodeposited using various deposition parameters. Hardness, wear resistance and corrosion resistance were investigated [45-47] and

com-pared with Cr(VI) coatings, revealing no improved properties comcom-pared to Cr(VI) at room temperature [48].

Sputter-deposited Ni-Mo films were very rarely reported in literature. Besides research concerning hydrogen production [49], Ni-Mo thin films for MEMS and NEMS devices were fabricated [50]. In the latter case, a very high indentation hardness and a low surface roughness could be achieved, maintaining metallic conductivity.

Figure 1.3: Phase diagrams of (a) Ni-W and (b) Ni-Mo having similar features (modified from [51,52]).

1.2

Diffraction analysis of the microstructure of materials

1.2.1 General remarks

Diffraction techniques are the main tools for experimental investigation in the present work, emphasizing on X-ray diffraction (XRD). XRD is a powerful, non-destructive technique to characterize crystal structures, phase contents, strains, crystallographic and morphological textures, microstructural features, layer thicknesses etc. probing a certain specimen volume (for overview see e.g. [53]) and enabling in-situ analysis. In principle, X-rays are diffracted at periodic atomic arrangements, i.e. crystals, and constructive inter-ference occurs for a constant wavelength and a certain atomic plane distance at a specific diffraction angle 2

θ

as given by Bragg’s law. However, one further, geometrical require-ment has to be satisfied: the diffraction vector has to be oriented perpendicular to the atomic lattice planes to be analysed which can be a challenge especially for highly tex-tured materials. Therefore, the use and definition of further angles in the specimen frame of reference is necessary as visualized in Figure 1.6a (these angles are defined in various ways in literature): the tilt angle

ψ

indicates the angle between diffraction vector and sur-face normal of the specimen and the rotation angle

ϕ

the rotation around the surface nor-mal of the specimen. Depending on the issue of interest, the diffraction patterns are eval-uated by means of reflection positions, reflection intensities, reflection shapes and / or diffuse intensity. In many cases these four measures are influenced by numerous different sources leading to an ambiguity of the results which can only be solved by additional, e.g. microscopic, investigations. Besides the commonly used laboratory X-ray sources, sever-al investigations require the use of e.g. a higher X-ray flux and seversever-al different wave-lengths. For these investigations, synchrotron sources are available which produce a large spectrum of electromagnetic waves by deflection of accelerated electrons.

In the course of the present work, XRD is used for advanced methods, besides classical phase and texture analysis: namely stress analysis and planar-fault analysis which are introduced in detail in Sections 1.2.2 and 1.2.3. To this end, two different synchrotron sources are utilized: the Surface Diffraction Beamline at ANKA in Karlsruhe, Germany (see Figure 1.4a), and the Rossendorf Beamline BM20 at ESRF in Grenoble, France (see Figure 1.5). Thereby, two types of in-situ investigations become feasible: (i) in-situ ten-sile loading of thin films on Kapton® substrates using a tenten-sile-testing machine of Kammrath & Weiss (Dortmund, Germany, see Figure 1.4b), and (ii) in-situ heating exper-iments of thin films on Si wafer substrates in a DHS 900 heating chamber of Anton Paar (Graz, Austria, see Figure 1.4c) applying a reductive gas atmosphere.

Figure 1.4: (a) Setup of the Surface Diffraction Beamline at ANKA in Karlsruhe, Germany, showing the path of the radiation, the Eulerian cradle where the specimen stage is mounted and the secondary optics consisting of a parallel-plate collimator and a NaI scintillation counter, (b) thin film on a Kap-ton® substrate mounted in a tensile-testing machine (Kammrath & Weiss, Dortmund, Germany), (c) thin film on a wafer substrate mounted in an air-cooled DHS 900 heating chamber (Anton Paar, Graz, Austria) which can be operated at vacuum or at a specified gas atmosphere.

Figure 1.5: (a) Setup of the Rossendorf Beamline BM20 at ESRF in Grenoble, France, showing the radiation path and the DHS 900 heating chamber mounted in the Eulerian cradle, (b) part of the primary optics being located in the measurement hutch, (c) secondary optics with a linear detector (Mythen, Dectris Ltd., Switzerland).

Transmission electron microscopy (TEM) is a very powerful analysis method for direct observation of microstructures in a very confined specimen volume. By changing the mi-croscope setup also (local) diffraction information can be extracted, however, with less resolution compared to XRD. A detailed overview of operation of a transmission electron microscope and interpretation of TEM investigations was given by Edington [54]. High-resolution TEM (HRTEM) reveals information about the atomic structure of a specimen by using the phase contrast of the electron waves after penetrating the specimen. For both TEM and HRTEM investigation, the specimen thickness has to be decreased down to electron transparency (< 100 nm) which is very time-consuming and may change structural features. In-situ investigations by (HR)TEM are very promising to trace micro-structural changes but the results may be influenced by surface effects of the very thin specimens. Overall, TEM investigations help to understand microstructural features by direct imaging but are less suitable for in-situ investigations with statistical relevance.

Combining the advantages of (HR)TEM analyses with XRD analyses which give statis-tical information from a larger specimen volume, creates a powerful investigation tech-nique for ex-situ and in-situ observation of microstructural changes.

1.2.2 Stress analysis by X-ray diffraction

Thin films deposited onto substrates commonly exhibit residual stresses, i.e. mechani-cal stresses without presence of external loads, which may be generated by growth, lattice mismatch or different thermal-expansion coefficients of substrate and film. The know-ledge of the respective stress state of thin films is crucial due to the influence of residual stresses on properties as strength, fracture toughness and adhesion in a beneficial or nega-tive way. X-ray stress analysis is performed by measuring interplanar spacings in differ-ent directions (at differdiffer-ent

ψ

angles, see Figure 1.6b) and correlating the correspondingly determined strains with the components of the mechanical stress tensor by the use of

elas-tic constants [55,56]. The type of elaselas-tic constants to be used depends on the elaselas-tic na-ture of the specimen under investigation; three cases can be distinguished [57]: (i) elas-tically isotropic specimens, (ii) macroscopically elaselas-tically isotropic specimens exhibiting elastically anisotropic behaving crystals (‘quasi-isotropic’) and (iii) macroscopically elas-tically anisotropic specimens. Specimens are considered to be elaselas-tically anisotropic if a crystallographic texture and / or direction-dependent grain interaction is present. In this case, the factors correlating the measured strains with the mechanical stress tensor com-ponents are called X-ray stress factors which depend not only on the specific HKL reflec-tion but also on the angles

ψ

and

ϕ

at which the strain was measured.

The thin films investigated in the present study exhibit a special microstructure which has to be considered for stress analysis. The presence of crystallographic texture dictates the use of a stress-analysis method for macroscopically elastically anisotropic specimens. Further, the twin and stacking faults influence the Bragg reflections leading to the neces-sity of specific attention. Velterop et al. [58] developed a strategy to determine stresses and fault probabilities of textured and moderately faulted metallic films simultaneously: Stresses are evaluated from the positions of (fault-affected) reflection which are corrected by a geometrical construction. Then, the fault parameter γ, which is a function of the stacking- and twin-fault probabilities α and β, is evaluated by the use of the calculated reflection-position shifts due to faults and α and β are determined by diffraction-line analysis or by direct observation using electron microscopy. Although this method can be applied to various cases, it is not applicable in the present work due to the very high fault probabilities which lead to significant peak broadening impeding a precise determination of the reflection positions. Further, the proposed procedure by Velterop et al. is limited to specimens showing a linear dependence of the strain on sin²ψ (quasi-isotropy was as-sumed) which does not apply to the specimens used in this project. The newly developed stress-analysis method in the scope of the present work (Chapter 2) enables a precise stress determination for macroscopically elastically anisotropic specimens in spite of the presence of the high density of planar faults.

Figure 1.6: (a) Definition of the X-ray angles in the specimen frame of reference by the diffraction vector g; (b) basics of X-ray stress analysis: The introduction of the uniaxial stress state leads to a change of the lattice plane distances dhkl which depends on their orientation in the specimen frame of reference and can be measured by XRD. The measured dhkl(ψ) can be correlated to the stress (tensor components) by elastic constants.

1.2.3 Planar-fault analysis by X-ray diffraction

Planar faults often occur in real crystals and influence the kinematical diffraction ef-fects, leading to a change of the intensity in reciprocal space. These influences were stud-ied already for decades, beginning with the early work of Landau [59] and Lifschitz [60], which describes the diffracted intensity generated by arrangements of several types of layers. In the following years, different approaches were developed as the method based on correlation probability matrices [61-63], the difference equation method ([64-69], cf. review article [70]), the summed series method [71], a recursion method [72] and a kind of direct method [73]. Treacy et al. [74] developed a software to calculate ’diffracted in-tensities from faulted Xtals’ (DIFFaX) using the recursion method. Only recently, Leoni et al. [75] invented the software DIFFaXplus which is based on DIFFaX but includes a refinement algorithm (non-linear least-squares minimization) to quantitatively determine the probability of randomly distributed faults in powder samples.

Different methods are used to determine planar-fault probabilities in various materials as clay minerals, intermetallics and close-packed metals. Obviously, the most works are concerned with polycrystals and some also with single crystals. The investigation of tex-tured polycrystals is only established in the clay community, e.g. [76,77]: An intended crystallographic texture enhances the intensity of the so-called basal reflections (i.e. with diffraction vector perpendicular to the fault plane, e.g. the (00L)hex reflections in Figure

1.7c); the so-called non-basal reflections (e.g. the (01L)hex reflections in Figure 1.7c) are

not considered. Only very few works are concerned with textured metals (e.g. [58], see Section 1.2.2) due to several complications; such textured metals are addressed in the present thesis (cf. Chapter 5).

The presence of twin and stacking faults gives rise to asymmetry, broadening and even displacement of Bragg reflections. It was demonstrated for cubic materials being faulted on (111)fcc planes only that the reflections fulfilling the equation [67,69]

3 0, ±1, ±2, ... H K L N N + + = = (1.1)

where H, K, L are the Laue indices, are not affected by twin and stacking faults and are denoted as fault-unaffected reflections. It follows that the reciprocal space of a {111}fcc

fibre-textured film exhibiting planar faults parallel to the surface only, as illustrated in Figure 1.7, exhibits rings (fault-unaffected reflections) and cylinders (fault-affected re-flections). The latter occurs due to the fault-induced smearing of the intensity distribution in reciprocal space along the [111]fcc direction, leading to so-called streaks.

This special arrangement in reciprocal space is discussed and utilized in the present work to evaluate planar-fault probabilities using the intensity distribution along these streaks and to evaluate stresses using fault-unaffected reflections (cf. Section 1.2.2). The stacking sequences of textured polycrystals are determined on the basis of measured in-tensity distributions along the (01L)hex streak, applying a statistical model implemented in

the software DIFFaXplus (including some modifications in the DIFFaXplus procedure since it was initially developed for powder samples). Therewith, the here-presented method differs from earlier works dealing with evaluation of (fault-affected)

reflection-position shifts by a geometrical construction to deduce the fault parameter γ of moderate-ly faulted metals ([58]; see Section 1.2.2) and with the investigation of basal reflections only for planar-fault analysis of textured clay minerals (e.g. [77]).

Figure 1.7: (a) Scheme of the specimens investigated in the present study, demonstrating the nanot-wins oriented parallel to the film surface; (b) illustration of the intensity distributions in reciprocal space for the Ni-based thin films showing fault-affected and fault-unaffected reflections; the rotation-al symmetry occurs due to the {111}fcc fibre texture; (c) cross section parallel to the page plane

1.3

Outline of the thesis

This thesis is dedicated to the investigation of nanocrystalline, nanotwinned Ni-based thin films as demonstrated in the next four chapters. Based on first investigations of the Ni(W) thin films [78,16], advanced methods are developed in the course of the present project leading to a detailed description of microstructure, stability and properties of the investi-gated thin films.

Chapter 2 presents a stress-analysis method paying attention to the elastically aniso-tropic nature of the Ni-based thin films and the presence of planar faults. Thereby, only fault-unaffected reflections are evaluated and the (anisotropic) stress-analysis method is selected on the basis of the relationship between crystallographic texture and stress state. The method is applied to Ni and Ni(W) films, determining their stress-strain behaviour in-situ during tensile loading.

Chapter 3 demonstrates a comparison of two Ni-based alloy systems showing both pla-nar faulting after deposition. The microstructure and stability of Ni(W) and Ni(Mo) films with different compositions is investigated, namely the planar-fault structure, the segrega-tion tendency and the thermal stability.

Chapter 4 deals with the description of and reasons for the planar-faulted microstruc-ture of Ni(W) thin films with different W contents. In fact, a strong influence of the W content on the planar-fault density is demonstrated and an unexpected hcp-like stacking is identified for Ni(W) films having a specific composition. To understand these observa-tions, first-principles calculations are performed by cooperation partners from TU Ham-burg-Harburg. The findings are compared with experimental investigations of as-deposited and heat-treated Ni(W) films, emphasizing on the developed microstructure and thermal stability of these films.

Chapter 5 is concerned with the quantitative analysis of planar faults by a new, sophis-ticated method using intensity distributions along streaks in reciprocal space measured by XRD and the software DIFFaXplus for evaluation of the data, assuming a statistical mod-el. The validity of this XRD analysis is demonstrated by comparison with direct examina-tion of the stacking sequences by (HR)TEM images. Fault probabilities are quantitatively determined for as-deposited and heat-treated Ni(W) films exhibiting different W contents. Further, the thermal stability is investigated by in-situ annealing experiments.

Diffraction-stress analysis of planar-faulted, elastically anisotropic films

2

Diffraction-stress analysis of highly

planar-faulted, macroscopically elastically anisotropic thin

films and application to tensilely loaded nanocrystalline

Ni and Ni(W)

S.J.B. Kurza, U. Welzela, E. Bischoffa, E.J. Mittemeijera,b

a

Max Planck Institute for Intelligent Systems (formerly Max Planck Institute for Met-als Research), Heisenbergstraße 3, D-70569 Stuttgart, Germany

b

Institute for Materials Science, University of Stuttgart, Heisenbergstraße 3, D-70569 Stuttgart, Germany

SYNOPSIS

A convenient, efficacious stress analysis for highly planar-faulted, fibre-textured films is presented, separating the fault-induced and the stress-induced diffraction-peak shifts. This method is applied to a Ni(W) film during tensile testing, highlighting the enormously enhanced stiffness and strength compared to a pure Ni film.

ABSTRACT

The presence of planar faults complicates the diffraction-stress analysis enormously owing to fault-induced displacement, broadening and asymmetry of the Bragg reflec-tions. A dedicated stress-analysis method has been developed for highly planar-faulted, fibre-textured thin films of cubic crystal symmetry, using only specific reflec-tions for diffraction-stress analysis. The effect of unjustified use of other reflecreflec-tions has been demonstrated in the course of application of the method to Ni and Ni(W) thin films exhibiting excessive faulting and subjected to (1) a planar, rotationally symmetric stress state and (2) a planar, biaxial stress state. In case 1 the crystallite-group method has been used, whereas in case 2 the stress-analysis method based on X-ray stress factors had to be applied. The successful separation of stress- and fault-induced reflection displacements has enabled the investigation of the mechanical be-haviour of Ni and Ni(W) thin films by in-situ stress measurements during tensile load-ing, thereby exposing pronounced stiffness and strength increase by alloying with W. Keywords: diffraction-stress analysis, planar faults, tensile loading, Ni(W) thin films

2.1

Introduction

The most often used stress-analysis method by (X-ray) diffraction is the conventional sin²ψ analysis which can be applied in many cases [57]. However, severe complica-tions can occur which impede its straightforward use: (i) Due to the presence of tex-ture and / or direction-dependent grain interaction, existing frequently in thin films, specimens behave macroscopically elastically anisotropic. Then, the so-called X-ray stress factors are required for stress analysis; in special cases the so-called crystallite-group method can be applied [56,79]. (ii) The position of Bragg reflections is not only sensitive to stresses but also to microstructural features as the presence of planar faults which cause displacement, broadening and asymmetry of the Bragg reflections [67].

Hence, for a reliable stress-analysis method, the effects of stress and microstructure on Bragg reflections have to be separated. The (sole) influence of planar faults on diffraction lines was studied more than 40 years ago by e.g. Paterson [80], Wagner [81], Warren [67]. The latter proposed an analysis which is often used to interpret peak shifts according to stacking-fault densities. This analysis was corrected and ex-tended by Velterop et al. [69] to higher fault probabilities, the presence of texture and non-uniform fault probabilities. Moreover, a simultaneous analysis of stresses and fault probabilities was proposed by Velterop et al. [58] assuming macroscopically elastic isotropy.

The method presented here utilizes the unique microstructure occurring frequently in thin films to simplify the stress analysis for the simultaneous presence of planar faults and (macro)stress, in particular for macroscopically elastically anisotropic spec-imens.

The method is applied to nanocrystalline, thin Ni and Ni-W films which were re-cently studied extensively due to the outstanding properties of Ni-W alloys, as e.g. wear and corrosion resistance [27,29], hardness [43,32] and thermal stability [37,16]. The sputtered Ni-W films possess an interesting microstructure: they are constituted of highly planar-faulted columnar grains [16]. The effect of planar faults on mechani-cal properties and their stability was also studied for other material systems as pure Cu films [21,82,83], Cu / 330 stainless steel multilayers [84] and pure Ag films [85], demonstrating improved mechanical stability (hardness, strength and fatigue re-sistance) compared to their non-faulted counterparts.

Two different specimen types were investigated: Ni and Ni-W films on wafer sub-strates and Ni and Ni-W films on Kapton® substrates. The experimental procedures for thin film deposition, microstructural investigation and stress measurement will be presented in Section 2.3. The results regarding characterization of the microstructure of the deposited films are gathered in Section 2.4. The stress evaluation of the as-deposited films is presented in Section 2.5, accounting for the simultaneous presence of a high planar-fault density, the texture and the state of (macro)stress. The devel-oped method is applied to tensile testing experiments of the Kapton® specimens in Section 2.6. It will be shown that the presence of W enhances significantly the stiff-ness and mechanical strength of films upon tensile loading.

2.2

Theoretical background

2.2.1 Stress analysis by (X-ray) diffraction

Three different cases are distinguished for diffraction-stress analysis: (i) elastically isotropic specimens, (ii) specimens which are only macroscopically elastically iso-tropic (i.e. quasi-isoiso-tropic) and (iii) macroscopically elastically anisoiso-tropic specimens [57]. A polycrystal pertains to group (i) if the individual crystals are elastically iso-tropic, as tungsten, i.e. the specimen is intrinsically elastically isotropic. Hence, Young’s modulus and Poisson’s ratio can be employed to correlate lattice strains with mechanical stresses in the polycrystal. Group (ii) comprises polycrystals exhibiting intrinsically elastically anisotropic crystals, but the aggregate behaves macroscopical-ly elasticalmacroscopical-ly isotropic. In this case, so-called X-ray elastic constants (XEC), which are dependent on the HKL reflection, are required for relating lattice strain to mechanical stress. If a crystallographic and / or morphologic texture is present and / or direction-dependent grain interaction occurs, the specimen has to be considered as macroscopi-cally elastimacroscopi-cally anisotropic and belongs to group (iii). In this latter, most general case, the so-called X-ray stress factors relate the lattice strain to mechanical stress as de-rived rigorously for the first time by Welzel and Mittemeijer [79].

In this work, two different stress-analysis methods belonging to group (iii) are con-sidered: the general X-ray stress factor method (see Section 2.2.1.1), and the crystal-lite-group method. The crystalcrystal-lite-group method represents a simplification for mac-roscopically elastically anisotropic specimens which exhibit a strong and sharp crys-tallographic texture (see Section 2.2.1.2).

2.2.1.1Macroscopically elastically anisotropic specimens; use of the X-ray stress factors

For macroscopically elastically anisotropic specimens, the most general case of stress analysis is based on the X-ray stress factors, XSF, Fij (dependent on the

direc-tion of the diffracdirec-tion vector and the type of diffracting (hkl) planes) which correlate the lattice strain ε (i.e. the strain in the direction of the diffraction vector) with the

components of the mechanical stress tensor, S

ij σ :

(

, , ,

)

( , ,

)

ε σ ϕ ψ

S

=

ϕ ψ

σ

S ij ij

HKL

F

HKL

(2.1)

where φ denotes the rotation of the specimen around the specimen-surface normal and

ψ the angle of inclination of the specimen-surface normal with respect to the

diffrac-tion vector. The superscript S indicates the stress tensor component concerned as de-fined in the specimen frame of reference (see Welzel et al. [57] for more details). The stress components can be evaluated by fitting the calculated strains

ε

_icalc (employing Equation (2.1)) to the measured strains

ε

_imeas by the use of the weighted minimization function 2 2 calc meas 2 [ ( , , , ) ( , , )]

χ

=

∑

ω ε

σ ϕ ψ

S −

ε

ϕ ψ

i i i i HKL HKL (2.2)

where the weighting factors

ω

_i represent the statistical relevance of the measured lat-tice-strain values and can be taken as the inverse of the standard deviation of the measured lattice strains. The XSFs can be calculated from single-crystal elastic con-stants adopting a grain-interaction model [57,79]. The grain-interaction model used in this study is the Eshelby-Kröner model [86,87] which assumes that the grains sur-rounding an individual grain (inclusion) in a polycrystal are conceived as an elastical-ly homogenous matrix with the elastic properties of the entire poelastical-lycrystal recognizing the crystallographic texture, i.e. the orientation distribution function (for details, see Welzel et al. [57]). Grain-shape (morphological) texture can be taken into account as well by adopting ellipsoidal shapes of the inclusion (for details, see Koch et al. [88]). Since the effect of grain-shape (morphological) texture on the XSFs is much less pro-nounced as compared to the effect of crystallographic texture (see Koch et al. [88]), a spherical grain shape was adopted in this work for all specimens.

2.2.1.2Macroscopically elastically anisotropic, strongly and sharply textured specimens; use of the crystallite-group method

In the special case of a sharp and strong crystallographic texture, the orientations of the individual crystals might be designated by one or several ideal orientations (so-called crystallite groups). Then, the crystallite-group method (CGM) can be employed for diffraction-stress analysis: All individual grains of one group are considered as one single crystal, i.e. possible grain interactions due to different surroundings are neglected [89]. For each crystallite group, the lattice strains measured at specific ori-entations of the diffraction vector (related to specific (hkl) planes) can be correlated with the macroscopic, mechanical stress components by the direct use of single-crystal elastic compliances sij and transformation to the specimen frame of reference

(dependent on the orientation of the particular crystallite group). For cubic, {111} fibre-textured specimens and a planar, rotationally symmetric stress state (i.e. <σ11> = <σ22> ≡ <σ||>, all other components <σij> are zero) it holds

12 0 44 2 1 2 sin ² 3 2 εΨ ψ σ   = + +   s s s  (2.3) with 0 11 12 44 1 2 s =s −s − s . (2.4)

The strain-free direction ψ* follows as

12 0 44 2 ( 2 ) 3 sin ² * 1 2

ψ

= − s − s s . (2.5)

According to the conventional sin²ψ method, the lattice parameter aψ (or the strain εψ)

is plotted against sin²ψ and the strain-free lattice parameter a0 and the stress <σ||> can

be obtained by interpolation at the strain-free direction sin²ψ* and from the resulting slope, respectively.

One limiting case of the CGM will be discussed in the following, recognizing that a strong and sharp texture alone does not guarantee applicability of the CGM, since putting up all crystals into one or several crystallite groups is only possible if the tex-ture symmetry coincides with the stress-state symmetry. As an example, consider a cubic, {111} fibre-textured film which is uniaxially loaded perpendicular to the fibre axis in an arbitrary in-plane direction. The induced strains perpendicular to different {hkl} planes have been calculated by the general XSF method using an adequate ori-entation distribution function and the Eshelby-Kröner grain-interaction model (cf. Section 2.2.1.1). Evidently, the calculated lattice strain εψ does not linearly depend on

sin²ψ, as would be expected from Equation (2.3) (see Figure 2.1). This is a straight-forward consequence of (isotropic) grain interaction. As an example, the reflections 311 and 331 pertain to lattice strains in very similar directions in the specimen frame of reference, i.e. at ψ ≈ 82° (what corresponds to sin²ψ ≈ 0.98, see green circle and magenta diamond in Figure 2.1). Obviously, the lattice strain at constant φ deviates for these two types of grains, having a crystal orientation with the same (hkl) plane parallel to the surface but a different angle of rotation around the fibre axis. The (un-justified) use of the CGM for stress analysis of a uniaxially loaded, {111} fibre-textured specimen thus can lead to high errors in the stress value and the strain-free lattice parameter. Therefore, the stress-evaluation method of choice for non-equibiaxial loaded fibre-textured specimens is the general XSF method.

Figure 2.1: Calculated strains perpendicular to different {hkl} planes of a {111} fibre-textured specimen which is uniaxially loaded by 1 GPa in a random in-plane direction, using the Eshelby-Kröner model and an adequate orientation distribution function with FWHM = 10° for the pole at ψ = 0°. The sin²ψ plot is evidently not linear.

2.2.2 Influence of planar faults on Bragg reflections

Twin and stacking faults are known to influence Bragg reflections by asymmetry, broadening and displacement [67]. The fault-induced peak displacement can occur in the positive as well as in the negative direction on the 2θ scale and is a function of the fault probability. The systematics of these deviations were described by Velterop et al. [58,69] and an analytical formulation of the peak displacement was derived for fcc materials exhibiting uniform faulting on only special lattice planes, relating the fault-induced peak displacement to a faulting parameter [58]. The value of this faulting parameter can be realized by various combinations of stacking and twin fault proba-bilities. Whereas twin faults cause mainly peak broadening, stacking faults induce more pronounced peak shifts. The excessive faulting in the thin films investigated in this work (cf. also Kurz et al. [90]) leads to pronounced peak asymmetry and broaden-ing, impeding the accurate determination of peak positions and, therefore, the analysis method proposed by Velterop et al. [58] cannot be used. To overcome this problem, a more convenient analysis method has been developed in this work for cubic, {111} fibre-textured materials exhibiting planar faults on the (111) planes parallel to the surface only. The method is based on the statement that reflections of cubic systems, which exhibit planar faults on the (111) planes only, satisfying the equation [69]

3 0, ±1, ±2, ... H K L N N + + = = (2.6)

are not affected by the presence of twin and stacking faults and will be denoted as

unaffected reflections in the following (here H, K, L are the Laue indices). In contrast

to the general consideration for the case of overlapping component reflections as dis-cussed by Velterop et al. [58,69], this work demonstrates that the {111} fibre texture observed for the investigated films (see Section 2.4) enables the isolated recording of unaffected and affected reflections (for visualization see Figure 2.4). Then, the unaf-fected reflections can be used for stress analysis without considering complications caused by planar faults.

2.3

Experimental

2.3.1 Film deposition and chemical analysis

Ni and Ni-W films with a thickness of 500 nm were produced by magnetron (co-)sputtering at ambient temperature and an argon pressure of 5.6 · 10−3 mbar. Sput-ter powers of 200 W and 78 W were used for the pure Ni and W targets, respectively. Two different substrates were used: (1) silicon wafers (<100> oriented, 4 inch, thick-ness of 525 µm, coated with two amorphous, 50 nm-thick layers: SiO2 and Si3N4) and

(2) polyimide foils (Kapton®, DuPont, dog-bone shape, 125 µm thick). All substrates were rotated around the specimen-surface normal during deposition. For more de-tailed deposition information see Welzel et al. [16]. The wafers were cut into pieces of 14 × 14 mm²; the deposited film size on the Kapton® substrates was 24 × 6 mm². The

specimens will be referred to as Ni-wafer, wafer, Ni-Kapton and Ni(W)-Kapton in the following.

The chemical analysis was performed by inductively coupled plasma optical emis-sion spectroscopy (ICP-OES) after dissolving the film in an acid solution. The short-hand symbols for the different films, as well as their chemical composition, have been listed in Table 2.1.

Table 2.1: Short-hand symbols and chemical compositions of the deposited films, analysed by ICP-OES.

short-hand

symbol cNi (at.%) cW (at.%)

short-hand

symbol cNi (at.%) cW (at.%)

Ni-wafer 100 0 Ni-Kapton 100 0

Ni(W)-wafer 83.5 16.5 Ni(W)-Kapton 80.5 19.5

2.3.2 Transmission electron microscopy

Transmission electron microscopy (TEM) was performed at a Philips CM 200 mi-croscope operating at 200 kV. The cross-sectional specimens were prepared by the sandwich method in the case of the wafer substrates: gluing two cross-sectional pieces with the film surface at each other and grinding, dimpling and ion thinning this spec-imen down to electron transparency (for further details see Strecker et al. [91]). In the case of the Kapton® substrates, a FIB instrument Nova Nanolab (FEI, Hillsboro, OR, USA) was used to cut out, by Ga+ ions, 100 nm-thick lamellae, which were trans-ferred to a TEM specimen holder utilizing a micro-manipulator.

2.3.3 X-ray diffraction measurements

X-ray diffraction patterns and pole figures were measured with Cu Kα radiation employing an X’Pert MRD Pro diffractometer (Panalytical, Almelo, The Netherlands) equipped with a Cu X-ray tube operating at 45 kV and 40 mA. The X-ray lens in the primary optics provides a collimated beam; the secondary optics consists of a parallel-plate collimator, a monochromator and a proportional counter.

Stress measurements of the as-deposited films were performed with a D8 Discover diffractometer (Bruker AXS, Karlsruhe, Germany) equipped with a Cu X-ray tube (40 kV, 30 mA), an X-ray lens, a parallel-plate collimator and an energy-dispersive detector (Bruker Sol-X) set to select Cu Kα radiation.

Due to a pronounced {111} fibre texture in the case of the Ni-wafer, Ni(W)-wafer and Ni(W)-Kapton films (see Section 2.4 for details), the accessible HKL reflections have to be measured at specific tilt angles ψ (see Table 2.2) selected recognizing the crystallographic texture of the films. Variation of the rotation angle φ was used to calculate the in-plane stress in different directions of the film, i.e. at 0°, 45° and 90°.

In the case of the weakly textured Ni-Kapton film (cf. Section 2.4), an experimen-tally determined crystallographic orientation distribution function (called ‘eODF’ in the following) was necessary. Three diffraction lines were measured, namely the 111, 200 and 220 reflections, at φ = 0°, 45° and 90° using a step size of 3° in ψ. The

inte-grated intensity was determined by fitting Pearson-VII functions (see end of this sec-tion) and used to generate pole figures. The obtained integrated intensity of the reflec-tions had to be corrected for the change of the illuminated and detected diffracting area of the films, for variable ψ, to relate the intensity with volume fraction, as re-quired for ODF calculations, using the correction procedure outlined by Welzel and Leoni [92] and Leoni et al. [93]. To this end, six reflections of a standard specimen (non-textured tungsten powder), having the same lateral size as the Ni-Kapton film, were measured at different tilt angles ψ (in steps of 3°) to deduce the correction fac-tors. The integrated intensity was found to be independent of φ, revealing a fibre tex-ture, and, therefore, only data from φ = 90° were used for the eODF calculation. By the use of the software package X’Pert Texture (version 1.0a, Philips Electronics NV, The Netherlands) the eODF was calculated from the (corrected) pole figures 111 and 200. Further details on the ODF calculation can be found in Welzel et al. [94]. The validity of the eODF was proven by calculation of pole figures from this eODF and comparison with the measured data (also for the 220 reflection which was not used for the eODF determination). For the stress analysis of the as-deposited Ni-Kapton film, the measured 111, 200 and 220 reflections were used.

Table 2.2: HKL reflections (Laue indices) and corresponding tilt angles, ψ, applied for the stress measurements of the as-deposited, {111} fibre-textured Ni-wafer, wafer and Ni(W)-Kapton films, measured at rotation angles of 0°, 45° and 90°.

unaffected reflections affected reflections

HKL ψ (°) HKL ψ (°) HKL ψ (°) 111 0 331 22 22-2 70.53 222 0 113 29.5 0-24 75.04 402 39.23 220 35.26 -1-13 79.98 3-11 58.52 002 54.74 13-3 82.39 2-20 88 11-1 70.53

In-situ X-ray stress measurements were performed at different tensile loads at am-bient temperature. The application of tensile loads was realized using a motor-driven tensile testing machine (Kammrath & Weiss, Germany, 50 N load cell). The distance of the crossheads of the tensile testing machine is used as measure for the imposed strain, even if the true elongation of the film might differ from that value, because this difference is irrelevant in the present methodologically focused study. The Kapton® specimens were used for these experiments because Kapton® can bear high elastic strain and is stable against radiation. The experiments were performed as a series of loading steps (see Figure 2.2). At each step the strain was kept constant, i.e. constant distance of crossheads (see above). The transition from one loading step to the next occurred under control of a strain rate of 1 µm / s. The exemplary tensile testing pro-gramme shown in Figure 2.2 demonstrates a load change, directly after reaching the new loading level of a step, which is caused by the Kapton® substrate. To minimize any effects related to this load evolution, a waiting time of 5 min was chosen before

each diffraction measurement was started. A short measuring time is important to have a reasonable resolution in time and load. To obtain good measurement statistics for thin films exhibiting a nanocrystalline microstructure, synchrotron measurements are essential for these experiments. Therefore, the measurements were carried out at the Surface Diffraction Beamline of the Ångstrømquelle Karlsruhe (ANKA), Germa-ny. The beamline is provided with radiation by a dipole bending magnet and is equipped with a Rh-coated Si mirror and a Si(111) double crystal monochromator [95]. The latter was set to a wavelength of 1.5303 Å. The tensile testing machine was mounted on an Eulerian cradle and a parallel-plate collimator was inserted before the scintillation counter (NaI) in the secondary beam path.

Figure 2.2: Exemplary tensile testing programme, showing the constant distance of the cross-heads at each loading step and the load evolution after reaching a new loading level.

For diffraction-stress analysis of the weakly textured, lightly faulted pure Ni-Kapton film, the 311 reflections at φ = 0° and φ = 90° at different accessible tilt angles

ψ were measured at each loading step (see Table 2.3). Certain ψ angles could not be

accessed due to beam blocking by the tensile testing machine.

In the case of the strongly textured, highly faulted Ni(W)-Kapton film, the 111, 222, 3-11 and 402 reflections (unaffected reflections, see Section 2.2.2) were meas-ured at φ = 0°, 45° and 90° at each loading step as indicated in Table 2.4. Some reflec-tions could not be obtained at all rotation angles due to beam blocking effects. At

φ = 0°, the 111 reflection was measured at the beginning and at the end of the

meas-urement series to control condition changes during the measmeas-urement series. It was found that the 2θ position of this reflection changed in the order of magnitude of (10−4)° 2θ, which is within the experimental accuracy.

Table 2.3: HKL reflections and corresponding tilt angles, ψ, applied for the stress measurement of the pure Ni-Kapton film during loading by the tensile testing machine.

HKL φ (°) ψ (°)

311 0 0, 20, 40, 60

311 90 0, 30, 60

Table 2.4: Unaffected HKL reflections (Laue indices) and corresponding tilt angles, ψ, applied for the stress measurement of the Ni(W)-Kapton film during loading by the tensile testing machine.

HKL φ (°) ψ (°)

111 0 and 45 0

222 0 and 90 0

402 0 and 90 39.23

3-11 0, 45 and 90 58.52

An instrumental offset of the diffraction angle 2θ was determined by measuring a

LaB6 powder specimen (Standard Reference Material SRM 660a provided by the

Na-tional Institute of Standards & Technology). For the case of the synchrotron meas-urements, this reference specimen was used to determine simultaneously the instru-mental offset of the 2θ angle and the wavelength. Diffraction-profile fitting was per-formed employing a custom Fortran program, using a Pearson-VII function, a linear background, a free asymmetry parameter and a constant Kα2 / Kα1-ratio of 0.5 in the

case of Cu Kα radiation. The peak position was defined to be the maximum of the diffraction line, which is less susceptible to a possible background subtraction error than the centroid of the diffraction line.

2.4

Microstructural investigation

The films on wafer substrates consist of a single fcc-like phase and are {111} fibre-textured, as revealed by X-ray diffraction patterns and {111} pole figures (see Figure 2.3). The Ni-wafer film exhibits a columnar grain structure with (mainly) twin faults0F

1

on (111) planes parallel to the surface and, additionally, on (111) planes inclined to the surface as shown by both TEM (not shown here) and weak additional intensity maxima in the {111} pole figure (see Figure 2.3a) at tilt angles of about ψ = 22°, ψ = 39° and ψ = 56° (the intensity maximum at ψ = 39° originates from multiple twinning on (111) planes inclined to the surface [96]). The Ni(W)-wafer film consists of a sub-stitutional solid solution of W in Ni, as indicated by the measured strain-free lattice parameter and the absence of any further reflections in the X-ray survey scan (cf. dis-cussion in Welzel et al. [16]; the presence of a solid solution will be denoted by the notation Ni(W) in the following). TEM investigations showed a well-defined

1 _{High-resolution TEM revealed the presence of stacking faults but the predominating fraction of planar} faults is provided by twins.

nar grain structure with excessive twin faulting on (111) planes parallel to the surface (see Figure 2.4). The selected area electron diffraction pattern (SADP) of a cross-section parallel to the fibre axis of the film consists of rows of discrete spots and of rows of spots connected by intensity streaks. These intensity streaks in reciprocal space are due to the presence of planar faults (cf. Section 2.2.2). Indeed, by indexing the spots in the SADP, it follows that the discrete ones (blue dots on dashed line in Figure 2.4c) correspond to unaffected reflections satisfying Equation (2.6). For con-venience, hexagonal indices have been introduced, labelling the rows of spots with a running index Lhex. The observed intensity streak through the affected reflections,

visualised by the vertical solid line in Figure 2.4c, will be denoted as the (01L)hex

streak in the following. Due to these intensity streaks, additional intensity maxima are visible in the X-ray diffraction patterns taken at different inclination angles of the dif-fraction vector with respect to the surface, which occur between the expected Bragg reflections for the {111} fibre-textured film: e.g. between the 11-1 and the 002 reflec-tion (see Figure 2.3d).

Figure 2.3: (a) Ni-wafer: {111} pole figure indicating a {111} fibre texture; (b) Ni-wafer: X-ray diffraction patterns at different inclination angles of the diffraction vector (tilt angle ψ); (c) Ni(W)-wafer: {111} pole figure showing a {111} fibre texture stronger and sharper than in (a); (d) Ni(W)-wafer: X-ray diffraction patterns at different inclination angles of the diffraction vector, demonstrating additional intensity humps between the Bragg reflections compatible with the {111} fibre texture.

Figure 2.4: (a) Bright field TEM image of a Ni(W)-wafer film (with a W content of 13 at.%). A small part of the substrate is shown at the bottom. The columnar grains exhibit excessive twin-ning parallel to the film surface. (b) SADP of the Ni(W)-wafer film, showing rows of discrete spots and rows of spots connected by intensity streaks; the direction of the surface normal has been indicated. (c) Indexing of the SADP, distinguishing affected (red dots on solid line) and un-affected (blue dots on dashed line) reflections, labelling by adopting hexagonal notation and graphical explanation of the geometric relation between tilt angle ψ and the location of cutting of the (01L)hex streak and thus the 2θ position of the intensity hump in the XRD pattern (cf. Figure

2.3d).

Analogous to the films on the wafer substrates, the films on the Kapton® substrates consist of a single fcc-like phase. The Ni-Kapton film possesses a very weak {111} fibre texture as follows from the eODF (cf. Section 2.3.3): see the α section of Euler space shown in Figure 2.5. The grain morphology is globular at the substrate-film interface and becomes almost columnar towards the surface (see Figure 2.6a). A few twin faults are present, which are randomly oriented in the specimen frame of refer-ence. The Ni(W)-Kapton film shows very similar features as the Ni(W)-wafer film: It exhibits well-defined columnar grains with a high density of twin faults aligned paral-lel to the film surface (see Figure 2.6b). The {111} fibre texture is somewhat broader, having a FWHM of the peak maximum at the centre of the {111} pole figure of 10° compared to 5° for the Ni(W)-wafer film. Still, the {111} fibre texture is quite sharp and strong and can, therefore, be approximated by an ideal fibre texture with FWHM = 10° instead of determining its ODF experimentally, i.e. a calculated ODF, called cODF, was used. The X-ray and TEM diffraction patterns show the same dif-fuse intensity between Bragg reflections, e.g. along the (01L)hex streak, as discussed

for the Ni(W)-wafer film. Due to the broader fibre texture, the SADP shows a radial intensity spread with reference to the origin of reciprocal space (see Figure 2.6c).

Figure 2.5: α section in Euler space of the eODF of the Ni-Kapton film (notation after Roe and Krigbaum [97]), showing a weak {111} (fibre) texture.

Figure 2.6: (a) TEM dark-field image of the Ni-Kapton film, extracted from the 111 ring of the SADP, showing globular grains at the substrate-film interface and almost columnar grains at the film surface; (b) TEM bright-field image of the Ni(W)-Kapton film demonstrating columnar grains which are excessively twinned along the (111) planes parallel to the surface; (c) TEM dif-fraction pattern of the Ni(W)-Kapton film showing affected and unaffected reflections but with a radial intensity spread (with reference to the origin of reciprocal space) due to the pole width of the fibre texture.

2.5

Residual stress analysis: The as-deposited state

2.5.1 Films on wafer substrates

It was verified experimentally that a rotationally symmetric, planar state of stress is present in both films on wafer substrates. Due to the combination of this state of stress and the strong {111} fibre texture, with fibre axis perpendicular to the surface, all crystallites can be assigned to one single crystallite group. Therefore, the CGM was employed for stress analysis (cf. Section 2.2.1.2). For the Ni(W)-wafer film, the

re-quired constants were calculated from pure Ni and W single-crystal elastic constants [98] weighted by their molar fraction. In view of the rotational symmetry of the stress state, only measurements at the specimen rotation angle φ = 0° will be shown in the following.

The ε-sin²ψ plot pertaining to the Ni(W)-wafer film is shown in Figure 2.7. Where-as, in accordance with Equation (2.3), a straight line would be expected for a {111} fibre-textured film subjected to the above described rotationally symmetric, planar state of stress, a pronounced scatter of the individual data points corresponding to the different reflections is apparent in the sin²ψ plot. However, a linear dependence of ε on sin²ψ occurs if the stress analysis is restricted to lattice strains pertaining to reflec-tions which are not affected by planar faulting (see the black squares and the dashed line in Figure 2.7). The apparent lattice strains calculated from affected reflections (red triangles in Figure 2.7) do not fall on a straight line at all. Ignorance of this effect could result in a totally wrong stress value, possibly even of the wrong algebraic sign. The diffraction-line shapes of affected and unaffected reflections can be observed in Figure 2.8. Whereas the unaffected reflections (black, solid lines) are very sharp, the affected reflections (red, dashed lines) are partly highly broadened and pronouncedly asymmetrical. The peak maxima of these reflections cannot be determined reliably (see large error bars in Figure 2.7) and show, moreover, shifts of the reflection posi-tions which are not caused by residual stress but by planar faults (cf. discussion above).

As a consequence, the stress and strain-free lattice parameter of the Ni(W)-wafer film has to be obtained by using the unaffected reflections only (see Table 2.5). To analyse the effect of including affected reflections in the stress analysis, several tests were performed. As an example, the 111 reflection at ψ = 0° (unaffected reflection) and the 11-1 reflection at ψ = 70.53° (affected reflection) were used for stress evalua-tion on the basis of the CGM (see red triangles and red, dashed line in Figure 2.9 and Table 2.5). The thus derived strain-free lattice parameter exhibits only a small error which can be explained as a consequence of the range of strain in the sin²ψ plot being small and thus a change in the slope shifts the strain-free lattice parameter (deter-mined by interpolation at sin²ψ*, cf. Equation (2.5)) only by less than 0.2 %. Howev-er, the stress value, derived from the analysis incorporating the affected 11-1 reflec-tion, differs strongly from the one calculated by using only unaffected reflections. The stress value is very sensitive to a change of the slope in the sin²ψ plot, which might lead to errors higher than 100 % as found in the course of this project. Considering all affected reflections, it should be noted, that the strain calculated from the affected 11-1 reflection at ψ = 70.53° still fits best to the straight line obtained for the unaf-fected reflections (see Figure 2.7). This observation can be understood considering Figure 2.4c: The largest influence of planar faults on diffraction peaks is present at low tilt angles ψ. Measuring the 11-1 reflection at ψ = 70.53° corresponds to an al-most perpendicular cut through the (01L)hex streak in reciprocal space, leading to a