**7. Non-Uniform Evolution**

Two examples of world numbers are particularly interesting: Champernowne world number and Chaitin world number. A Champernowne world number in base two is given by the sequence


*2.7. Calculations and Statistical Analysis*

All experiments were performed three times per assay. The data for all experiments were given as the arithmetic mean percentage ± standard deviation in relation to control. Statistical analysis was performed using analysis of variance (ANOVA) followed by Dunnett's multiple comparison tests. Differences were considered significant in respect to the control group at *p* < 0.05 (\*), *p* < 0.01 (\*\*) and at *p* < 0.001 (\*\*\*).


**2. Test Overview**

#### *2.1. Overview of the Original Bridge Project*

The Tian'e Longtan Grand Bridge is an upper-bearing, steel tube-reinforced concrete rigid-frame arch bridge, with a main span of 600 m, a rise of 125 m, and a rise-to-span ratio of 1/4.8 [20], as shown in Figure 1. The main arch curve is in the form of a catenary, with an arch axis coefficient of m = 1.9. The arch ring adopts a concrete box section with constant width and variable height, with a box width of 6.5 m, a box height of 12 m at the arch foot, and a box height of 8 m at the arch crown. The transverse center distance of the arch rib is 16.5 m, and the thickness of the arch box web gradually changes from 0.45 m at the arch crown to 0.95 m at the arch foot. The top slab thickness is 0.65 m, and the bottom slab thickness gradually changes from 0.65 m at the arch crown to 1.3 m at the arch foot. The rigid steel skeleton primarily uses Q420 steel, while the internal concrete employs C80 self-compacting micro-expansion concrete, and the external concrete utilizes C60 concrete. Notably, the external concrete is cast using a segmented ring method, dividing the external concrete horizontally into three rings, including the bottom slab, the web, and the top slab, and adopting a symmetrical casting approach with eight working faces longitudinally.

**Figure 1.** Elevation view of Tian'e Longtan Grand Bridge (unit: m).

#### *2.2. 1:10 Scale Model Test of the Main Arch Ring*

A 1:10 scale model experiment was conducted on the main arch ring of the original bridge, with stress equivalence as the design principle [21,22]. To minimize the influence of the scale effect on the structural response [23], the overall geometric parameters of the model bridge, such as span and rise, were strictly converted according to the scale ratio. Local designs adhered to the principle of achieving rigidity similarity and construction requirements in order to replicate the actual project conditions to the greatest extent and to strive for consistency of stress conditions between the model bridge and the original bridge. Additionally, by conducting nearly one hundred sets of experiments on the concrete mix ratio, we ensured that the concrete material properties of the model bridge closely resembled those of the original bridge [24], thereby reducing the potential impact of the scale effect on the material side.

It is important to note that the scale effect primarily affects discontinuous regions where beam theories [25], such as the Euler–Bernoulli beam theory, are not applicable. However, in the context of the present experiment, the rigidity of the skeleton structure remains continuous throughout the investigation process. When integrated with the results from Section 4.3, it becomes evident that the scale effect has not significantly impacted the precision of our experimental outcomes.

#### 2.2.1. Scaled Model Test Scheme

The model test was carried out in the State Key Laboratory of Mountain Bridges and Tunnel Engineering at Chongqing Jiaotong University, with a main span of 60 m, as shown in Figure 2. This span exceeds the largest scaled test ever conducted for similar bridge types [14,26], making it the largest scaled model test for an arch bridge in the world to date.

**Figure 2.** Picture of model test. (**a**) Figure of the arch bridge model test under viewpoint 1; (**b**) Figure of the arch bridge model test under viewpoint 2.

This structure's arch axis adopts a catenary, with an arch axis coefficient (m) of 1.9, a calculated rise of 12.5 m, and a span-to-rise ratio of 1/4.8. The arch rib adopts a concrete box-type section with uniform width and variable height, as shown in Figure 3. The box is 0.65 m wide, the box height at the foot of the arch is 1.23 m, and the box height at the apex of the arch is 0.83 m. The thickness of the box web plate gradually varies from 55 mm at the apex to 95 mm at the foot of the arch. The top plate is 65 mm thick, while the bottom plate thickness gradually varies from 65 mm at the apex to 130 mm at the foot of the arch. To enhance the local stability of the main arch ring, transverse partitions with a thickness of 50 mm are arranged every 2 m along the length of the bridge.

The model test's main arch ring mainly includes three parts: a rigid steel framework, C80 internal concrete in the pipe, and C60 external concrete. The rigid steel framework was assembled using the large-section lifting method, with a total weight of approximately 5.0 tons. The internal concrete was pumped from both sides of the arch base section symmetrically toward the arch crown using the pumping and jacking method, with a total volume of approximately 1.5 m3.

The casting of the external concrete is consistent with the original bridge, dividing the external concrete into three rings in the transverse direction: the bottom plate, the web, and the top plate. In the longitudinal direction, each ring is divided into eight working faces, with each working face being divided into six segments for casting. The model test's segmented positions and the casting length of each segment are consistent with the original bridge, which has been scaled proportionally, and the age difference between the concrete segments is basically the same as the original bridge.

The main test content of this experiment included the strain, displacement, environmental temperature fields, and structural temperature field throughout the construction process [27]. The strain testing primarily involved the establishment of test cross-sections at 16 longitudinal points of the bridge (a total of 17 test sections are shown in Figure 4a), with fiber-optic strain sensors being arranged at each cross-section on the main steel tube, bottom plate, web, and top plate, as shown in Figure 4a. The displacement testing was mainly conducted at 8 longitudinal points of the bridge (a total of 7 test sections are shown in Figure 4b), with four measurement points set near the upper and lower chord steel tubes at each cross-section. The related testing was completed using wire-drawing displacement sensors, as shown in Figure 4b. The environmental temperature field and structural temperature field were monitored using PT100 sensors. Given that the temperature distribution of the lab environment and the structure was relatively uniform, an environmental temperature sensor and a structural temperature sensor were placed along the bridge longitudinally at intervals of 10 m.

**Figure 3.** Cross-section of the main arch ring of the model bridge (unit: mm). (**a**) Dimensional drawing of mid-span section; (**b**) Dimensional drawing of arch foot section; (**c**) Dimensional drawing of the cross-section of the mid-span diaphragm.

2.2.2. Model Test Construction Stages

By referring to the original bridge's construction process, the construction of the main arch ring is divided into 20 stages, with the specific content of each stage shown in Table 1.

**Table 1.** Division of the construction stages of the main arch ring.

**Figure 4.** Schematic diagrams of test cross-sections and test methods. (**a**) Cross-section of strain test and sensor display diagram; (**b**) Displacement testing cross-section and display diagram of testing equipment.


**1. Introduction**

Twenty-five years post-apartheid the profession of psychology in South Africa has been beset by identity tensions regarding its relevance and value to a continuously transforming South African society [1–3]. The identity dilemmas of the psychology profession seem evident in the disagreement among its practitioners about changing the Regulations Defining the Scope of the Profession of Psychology. The original regulations defined a scope of practice for psychologists registered with the Health Professions Council of South Africa (HPCSA) to distinguish the different categories of counselling: industrial and organisational (IO), clinical, educational and research. The original regulations were however amended in 2011 without an adequate consultation process. Unlike the original widely accepted demarcated scope of practice, the amendments narrowed down practice opportunities for some of the psychology categories and seemed more favourable to others. The process was criticized for being forced upon the profession, for creating power disparities between the different categories of psychology and for marginalising certain practitioners, preventing them from contributing to sectors in society in dire need of mental health and well-being [1,4]. A large section of the profession was therefore dissatisfied and angry, resulting in a court order on 14 November 2016 by the High Court of South Africa (Western Cape Division, Case No: 12420/13) declaring the amended regulations invalid [5]. A notice by the Department of Health not to proceed with any amendments that were recently published [6] declared the original Regulations Defining the Scope of the Profession of Psychology of 2008 to remain in force.

Disputes about the amended scope of practice reflected underlying identity tensions within the psychology fraternity. On the positive side, the discussion also aligned with evolving frames of thought about the profession and its impact on society at large and about opportunities for continued professional development and multidisciplinary collaboration. One such opportunity was created in a doctoral programme specialising in consulting psychology. The programme is offered in collaboration by the Departments of Psychology and IO Psychology at UNISA. Students admitted to the programme include registered and practising psychologists across the five different HPCSA registration categories. These educational, clinical, IO, counselling or research psychologists entering the field of consulting psychology invariably experience a role identity transition [7] or an altering of their professional identity [8].

When transitioning to a new role, people naturally experience identity tensions between previously known meanings of the self and new role expectations [9]. They attempt to resolve these tensions by engaging in identity work [10]. Identity work entails the restructuring, reframing and development of identity meanings that constitute the self in specific social contexts [11–13]. It refers to the intrapersonal process in which individuals engage to form, repair, maintain, strengthen or revise their identities [14]. Identity work is therefore relevant to intrapersonal coping, because it enables individuals to cope with difficult work-life demands [10,15] and adjust to important work-life transitions [16,17]. Breakwell introduced the idea that identity work is based on intrapsychic and interpersonal coping strategies [9]. Observation of identity work is therefore expected to reveal the intrapersonal coping strategies that individuals apply to resolve the identity tensions they experience consequent to role transitions.

The aim of this study was to develop an understanding of the coping dynamics that consulting psychology doctoral students manifest when transitioning their professional role identity. Understanding how the students cope with the identity tensions they experience will enable them to develop a self-efficacious service offering to their clients and broaden the reach of psychology in the South African context. Identity work is a natural and involuntary [7] or subconscious [18] process, which in the context of this study happens in both the individual student and in the bigger systemic context of the psychology fraternity. It was therefore deemed useful to explore coping with transitioning a professional identity by applying a systems psychodynamic perspective.

#### **2. Literature Review**

#### *2.1. System Psychodynamics*

Systems psychodynamics is rooted in psychoanalysis, object relations, systems theory and the Tavistock Human Institute of Human Relations [19,20]. Although Freud was the father of psychoanalysis, it was Klein's object relations theory, group relations and open systems theory that contributed significantly to the systems psychodynamic paradigm [21,22]. The systems psychodynamic approach developed as a suitable stance to explore beneath-the-surface behaviour in organisations [23] and to the study of organisational change dynamics [24,25]. The central tenets of system psychodynamics lie in the semantic co-occurrence of the words systems and psychodynamic. Open systems principles are firstly applied in understanding behaviour, and individual behaviour is regarded as a function of systemic dynamics as much as it is a representation of (mirroring) systemic behaviour. Secondly, psychodynamic theory represents a fundamental focus on unconscious behavioural dynamics and includes the spectrum of psychoanalytic perspectives on individual and social experiences and mental processes. This includes un understanding of anxiety as the basis of group and unconscious systemic behaviour [26,27] and the involuntary use of defence mechanisms to cope with anxiety [28].

Central to psychodynamic thinking is the assumption that part of the mental life of individuals is hidden and affects them in ways of which they are not always aware—the unconscious life [29]. Furthermore, in system psychodynamics, anxiety is regarded as the driving force of all relational dynamics in a system, as any change is seen to arouse anxiety naturally [25]. Anxiety manifests itself as personal anxiety, task-related anxiety or role anxiety but always in a systems context and representative of larger anxieties in the system [26]. Typically, transitions in the work environment arouse performance and survival anxiety [30]. In response to this anxiety, defence mechanisms are used unconsciously [20,31] to remain in control and to experience a sense of safety, security and acceptance [27,32].

Defences are fundamental to coping in psychodynamic theory [33–35]. In systems psychodynamics, defences manifest themselves as basic assumption behaviour, which includes dependence, fight-flight, pairing [21], one-ness, we-ness and me-ness [20]; in primary defences such as splitting, introjection, suppression, denial, projection and projective identification [22,28,36] and in more sophisticated defences such as rationalisation and intellectualisation [37]. Defences operate on a continuum, ranging from primitive, debilitating impairments to more sophisticated competence-enhancing adaptations [25,38]. These defence mechanisms have a protective function and are neither good nor bad [39]. Individuals develop defences as coping strategies from an early age to deal with reality and to maintain a functional sense of self [28].

There is a longstanding link between coping theory and psychodynamics [40], yet contemporary perspectives on coping strategies typically focus on cognitive-behavioural perspectives such as emotion-focussed, problem-focussed, social-support coping and religious coping [41]. Such coping strategies have been distinguished as involving conscious, purposeful effort [33]. This paper takes the stance that coping is a process of psychological adjustment [42,43] that includes conscious and unconscious coping as means of adaptation [33,34,44]. Applying a system psychodynamic stance to understand coping is of value, since it provides a more holistic and systemic understanding of coping behaviour [45] and uncovers the unconscious as a creative source of knowledge [23,46]. When experiences are explored from a systems psychodynamic stance, one can enhance awareness, understanding and learning of both conscious and unconscious dynamics [47,48]. Such knowledge is deemed essential in managing and facilitating real behavioural change [25] and prevents anxiety and defences from becoming destructive in the workplace [49].

#### *2.2. Systems Psychodynamics and Identity Work*

Systems psychodynamics approaches identity firstly from a group relations stance, relating the individual's role identity to a systemic role identity [22]. From this perspective, taking up a new role entails a psychosocial dynamic that emerges from the interface between the person and the formal role as defined by a particular context [50]. As such, viewed from a psychodynamic perspective, identity work involves cognitive, emotional and social processes that are social or systemic in nature (i.e., cannot be done in isolation) [12,13], and such identity work is often stimulated by anxiety [51].

System psychodynamics further focus on understanding unconscious experience. In doing identity work, a person therefore consciously, but also unconsciously, negotiates personal beliefs, needs and aspirations in adjusting to latent role demands. Projective processes that relate to psychodynamic defence dynamics, in the form of projective identification, transference and counter-transference, are benign parts to be worked with by individuals in the process of identity work [52]. Psychodynamically, identity work is therefore essential in everyday coping with tensions in the self and maintaining well-being [44].

A psychodynamic lens to identity enriches our understanding of identity work beyond current identity theory [44]. System psychodynamic literature emphasises that creating reflective spaces is essential to facilitate constructive role transition [49,53]. In this regard and relevant to the consulting psychology programme context of this study, the concept of identity workspaces refers to institutions that provide a holding environment for individuals to do their identity work [54]. This holding environment serves as a social context that not only reduces distressing emotions but also actively facilitates sense-making, either aimed at identity stabilisation or identity transition [55].

A significant portion of identity work is emotional, dynamic and complex and lies beneath the surface of conscious behaviour [18,44]. Taking a systems psychodynamic stance stresses that this intrapsychic dimension of identity work must also be worked with. Thus, by "focusing on the ongoing dynamic interaction of individual and social, cognitive and emotional, conscious and unconscious factors, the system psychodynamic perspective is particularly well suited to enriching our understanding of identity and identification" [54].

### **3. Materials and Methods**

This paper is part of a larger project studying the experiences of master's and doctoral students to improve academic curricula and the throughput of postgraduate students. The next sections give an outline of the research methodology that directed the study, an explication of the research setting, the data protocols and participants, as well as the analytic strategy applied.

#### *3.1. Research Methodology*

A qualitative inquiry was deemed most appropriate for the exploratory and descriptive nature of the study. The study followed a hermeneutic phenomenological approach in its overall design. In hermeneutic phenomenology knowledge generation equates to the co-construction of meaning between the researcher and the researched [56]. It allows for ascribing meaning to participants' experiences through critical interpretation, inevitably influenced by researcher experience and theoretical preconceptions [57–59]. Fundamentally, from a hermeneutic phenomenological perspective, researchers' critical interpretation of participants' phenomenological experiences is imperative for rigorous scientific research [60]. To achieve the stated objective, researchers' interpretations were influenced in particular by applying a systems psychodynamic lens or meta-theoretical orientation during data analysis. System psychodynamics refers to an extensive body of scholarship [46] that provides a sound meta-theory to develop truthful, useful and credible insights and hypotheses [48]. Both researchers (a black man and a white woman) hold PhDs in psychology and are part of faculty in an open-distance, e-learning tertiary institution. They are registered psychologists with the HPCSA with a keen research interest in socio-analytic research methodologies, hermeneutically informed by system psychodynamics. They are also both involved in the teaching of the course work component of the Consulting Psychology doctoral programme.

#### *3.2. Research Setting*

The doctoral programme in Consulting Psychology offered at a tertiary open distance and e-learning (ODeL) institution in South Africa constituted the setting for this research. The institution's two main campuses are located in the Gauteng region, with satellite campuses across South Africa. Gauteng is the smallest province yet the most densely populated (742.6 per square metre) in South Africa, accommodating 1.349 million of the 55.9 million South Africans (https://www.southafricanmi.com/ sa-by-numbers.html). National and international student enrolments at this ODeL institution varied between 354,743 and 381,483 in the 2015 to 2018 registration periods. The Consulting Psychology doctoral programme has enrolled eight to 12 students per annum since its inception in 2005. The first year of the programme entails course work involving 11 focus areas, of which one focusses on consulting as process. The learning outcome of this focus area is intended to develop students' capability to explore their consulting profile and develop a personal frame of reference for consulting. During the course work component of the Consulting Psychology doctoral programme, students attend five block weeks of face-to-face training and complete several individual and group-based projects as part of their formative assessment. Another primary focus of the first year is the successful defence of a research proposal, which forms the basis for continued research-based study from the second year until completion of the degree.

#### *3.3. Data Protocols*

One of the individual tasks students are required to do in their first year of study is to keep a personal diary in which they journal about becoming a consulting psychologist. The students then write self-reflective essays that entail a summative and critical reflection based on periods of five and eight months' journaling. To explore the coping dynamics of students transitioning into a consulting psychology role, self-reflective essays constituted the data protocols for this study. Critical reflexivity refers to the process in which one questions one's positionality and basic assumptions about life, people and oneself, while seeking alternative ways of being and looking at things [61–63]. In this regard, self-reflective practice is akin to identity work as defined by Sveningson and Alvesson [14]. In Nagata's definition of self-reflexivity [64], coping as an adaptational endeavour underlying identity work is furthermore evident. He defined self-reflexivity as having a conversation with the self about one's experiences while one is experiencing them, leading to the ability to regulate internal psychological and unconsciously driven responses. Self-reflective essays were moreover deemed appropriate to the purpose and system psychodynamic orientation of this study, as reflective practice elicits a meta-level of thinking and feeling about the self [64] and makes the "unthought known" observable and conscious [65].

Instructions for the self-reflective essays were based on circular existential and relational questions relevant to experiential learning activities aimed at developing critical reflexivity [61]. The questions were formulated as a guide to facilitate critical self-reflection in line with the objective to engage with and develop a personal frame of reference as a consulting psychologist. The intention with these questions was not to be prescriptive but to offer some direction to the task of self-reflecting. The first question aligns with Cunliffe's existential (who am I?) and relational (who am I in relation to something/someone?) approach [61] and asks the student to reflect on the question: Where am I at this moment regarding my personal frame of reference? The second and third questions refer to the circular influence approach [61], examining how existential and relational learnings influence one's responses and ways of acting, behaving and responding. The second question asks: How does your evolving personal frame of reference affect your understanding of the landscape of consulting psychology? The third is: What is the impact of your evolving personal frame of reference on your personal consulting profile?

Self-reflective essays are shared with lecturers after five months' journaling and again after another three months' journaling. Through purposive, convenience sampling, the transcripts that constituted the data sets for this study included all the self-reflective essays of the current course work students after eight months. By that time, the students had already completed most of their course work-related projects and workshops.

#### *3.4. Participants*

To ensure the confidentiality and anonymity of participants, they are not identified as individuals but described as a group. The participants included three women and five men. In terms of population group, three were white, one was Indian and four were black, with an age range of 29–58, and average age of 40. Participants were approached face to face during their first block period on campus, and the nature and purpose of the research were explained to them. This was followed up by individual e-mails requesting their participation. Inclusion criteria entailed that participants had to have a master's degree in a specific psychology domain; be registered psychologists with the HPCSA, practising for at least three years; be registered doctoral students in Consulting Psychology; be willing to share their self-reflective experiences and be willing to participate in the research. Four participants were registered in the category of IO psychology, and one each was registered as clinical, educational, counselling and research psychologist. All the participants had gained a minimum of three years' experience since obtaining their professional HPCSA registration. Pseudonyms are used in the findings to indicate the number of the participant, for example, P4 refers to participant number four.

#### *3.5. Ethical Considerations*

Ethics approval was obtained from the relevant Institutional Senate Ethics Committee (REF#:2017\_RPCS\_018). Participants consented in writing that data generated from their self-reflective work on being a consulting psychologist could be used for research purposes relevant to the bigger project. The researchers abide by the ethical codes of conduct as prescribed by the UNISA ethics policy, as well as the ethical code of psychologists registered under the HPCSA. The researchers also declare that the research was conducted in compliance with the ethical principles enunciated in the Declaration of Helsinki. As such, ethical principles of anonymity, confidentiality and informed consent were upheld by reporting on the data in a collective, interpretive sense and by using pseudonyms.

#### *3.6. Data Analysis*

Eight self-reflective essays were loaded as primary data documents in Atlas.ti to ease the management of the data analysis process. Data were analysed through hermeneutic phenomenological analysis according to the analytic stages of naïve reading, structural thematic analysis and comprehensive understanding [66]. The fundamental premise of the hermeneutic circle was applied throughout these stages of analysis. Initially, we considered each individual's experience in relation to the meaning we constructed from the participants' collective experience and vice versa [26]. We also compared findings from each stage with findings in the previous stage in a consistent, circular manner [67]. At this point the themes provided a richness in terms of saturation and no more themes emerged to add to the clear description of coping dynamics from a system psychodynamic perspective.

#### **4. Findings**

The naïve reading revealed how some students struggled to engage with the task of self-reflection in that they recited textbook definitions of the skills and competencies of a consulting psychologist. Without reflecting on their emotional responses to the personal development journey they were on, they merely noted that they were busy developing the mentioned list of skills and competencies. Others provided less detached accounts of their experience of becoming a consulting psychologist, but their performance anxiety in relation to the task topic of becoming a consulting psychologist was evident in how they engaged in anti-task behaviour. Performance anxiety was coped with in various ways, mostly to avoid the required identity work or to resist the professional identity role transformation they were experiencing. Especially, students who did not engage in self-reflection consistently throughout the year seemed to struggle with performance anxieties and integrating identity tensions. Three themes were constructed in the thematic analysis to describe the students' coping with the identity tensions and demands from a systems psychodynamic perspective. The first theme described how they resisted the primary task of self-reflection and, consequently, resisted identity work through basic assumption (anti-task) behaviour. The second theme described their coping dynamics by applying primary defences against the perceived incongruence of conscious (normative) and unconscious (phenomenological and existential) roles. The third theme described their coping along the more sophisticated defences the students applied to resolve the identity tensions and performance anxiety they experienced. The three themes are conceptualized below in terms of their different sub-themes and related categories. Verbatim data from the participants' narratives are used to illustrate the meaning-making during analysis.

#### *4.1. Resisting the Primary Task through Basic Assumption Behaviour*

The first sub-theme entails resisting the task of deep self-reflection and identity work through basic assumption (anti-task) behaviour, which manifested in dependency, fight behaviour, pairing and me-ness.

#### 4.1.1. Dependency

Students idealised several external objects such as lecturers, the programme and consulting knowledge. In doing so, they expressed their dependency on external structures and authority figures to feel successful in their career or profession. The Consulting Psychology doctoral programme was related to the mother figure and several instances of how the programme or lecturers or the consulting psychology knowledge domain was made the hero or saviour were evident in the data. Such "heroing" usually followed students' expressed feelings of insecurity, low self-confidence and uncertainty or the need to succeed or fantasise about career opportunities and personal change. In this way, some students seemed to cope by relying on the doctoral programme to help them deal with the identity transition they were seeking and working with, while doing the task of self-reflection in the role of becoming a consulting psychologist. Table 1 below summarises pertinent verbatim extracts supporting how students acted out or expressed their dependency in an effort to cope with the identity tensions and insecurities they were experiencing.

**Table 1.** Dependency behaviour as seen in the data cited.

#### 4.1.2. Fight

Fight reactions were a way of coping with the need to preserve the self and resist the identity tensions felt during self-reflection. One student attacked the task of self-reflection by denigrating its value in light of preserving what she feels more comfortable with, namely to be a practitioner: "When confronted by theory and philosophy, my question is always what does this look like in practice? If I can't figure that out, or it is not clear to me, it is not useful, no matter how beautiful or elegant it is" (P1). Another student demonstrated fight behaviour by attacking team work as irreconcilable with her leadership style. Again, the student is trying to preserve her known leadership identity. She reveals the identity tension she experiences and demonstrates how she copes with it through fight behaviour: "I naturally take a leadership role (my current role at work requires this) and develop innovative ideas in a team setting; this had to be suppressed at times" (P2).

#### 4.1.3. Pairing

Students attempted to pair with an authoritative form or powerful other, by aligning themselves with the programme, with a lecturer or with the class as a team. In expressing her need to be part of the group, P2 copes with the anxiety she experiences in transitioning into the consulting psychologist role: "after the week, I realised that I needed the group. In May, I became more involved with the team, working in groups. Even though it was a bit uncomfortable for me working as a member of a team, I did not just play my role but enjoyed it. Furthermore, the course seemed easier as we shared similar experience and could relate." Several students strongly aligned themselves to the doctoral programme and the consulting psychology knowledge domain, proclaiming a new-found sense of confidence and security in their own abilities. P4, for example, states: "this programme has broadened my horizons. It has help[ed] me to appreciate that there are three different levels of intervention that any qualified and properly trained psychologist must be able to operate in, namely, individual, group and organisational level. The above, is an illustration of the significant impact that this programme is having on me as a professional". Similarly, P8 notes that she feels more confident as a psychologist because "there is no better programme I would recommend to my peers and colleagues than that of the Consulting PhD programme". She continues to align herself to the group in order to cope with the potential loneliness that she experiences in the identity transition process that she embarked on: "My classmates and I have an exceptional relationship where we assist each other not only academically but also personally and professionally." Through pairing, it seems that the students constructively cope with the performance anxieties that emanate from the identity demands they experience in the context of the consulting psychology doctoral programme.


5. Discussion and conclusions

all, which implies that the effect of terrace is confined to within a couple of layers. Moreover, a substantial hybridization is seen between the Ti *d* and Si (C) *p* levels below *E* F, which indicates the formation of covalent bonding. The covalency is also reflected in the charge-density plot (Fig. 22(a)) showing lobes for the C in SiC and charge accumulation along the bonds in Ti3SiC2. These, along with the charge distribution on C at expense of Ti and Si (Fig. 22(b)), indicate that +\* %\*#z\*!.z0!..!z%/z#%\*z,.%).%(5z%+\*%\_z5!0z)%\*0%\*/zz!.0%\*z !#.!!z+"z+2(!\*5^z%¥ nally, both the electron density and density difference for some atoms near terrace (indicated 5z..+3/dz !2%0!z/!2!.!(5z".+)z0\$+/!z"+.z0\$!%.z1('z+1\*0!.,.0/\_z%),(5%\*#z\*z!//!\*0%(z!(!¥

Figure 23. Isosurface plots for (a) small, (b) intermediate, and (c) large terrace along the (11-20) plane in an energy

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the fact that the Ti3SiC2 is intrinsically metallic, whereas the SiC is semiconducting.

tronic role of the Ti3SiC2 in the semiconductor.

172 Physics and Technology of Silicon Carbide Devices

window (*E*F–0.5 eV, *E* F). The charges on Ti3SiC2 are omitted for clarity [20].

4.3. Electron distribution near Fermi energy

The current understanding of formation origin of Ohmic contact, which is based mainly on !4,!.%)!\*0(z/01 %!/z+"z,.+,!.05z)!/1.!)!\*0z\* z/0.101.!z\$.0!.%60%+\*\_z\*z!z/1)¥ marized in three main points [27-30]: (1) the deposited Al (80 at%) might diffuse in part into the SiC and dope heavily the semiconductor because Al is well-known to act as a *p*-type +,\*0z"+.z%\_zcEdz0\$!z\$%#\$z !\*/%05z+"z,%0/\_z/,%'!/\_z+.z %/(+0%+\*/z)5z!z#!\*!.0! z1\* !.¥ \*!0\$z0\$!z+\*00/z"0!.z\*\*!(%\*#z/+z0\$0z1..!\*0z\*z0.\*/,+.0z,.%).%(5z0\$.+1#\$z0\$!/!z !¥ fects due to the possible enhancement of electric field at these features and semiconductor +,%\*#z0z0\$!/!z(+0%+\*/\_zcFdz"+.)0%+\*z+"z%\*0!.)! %0!z/!)%+\* 10+.z(5!.z!03!!\*z0\$!z !¥ posited metals and semiconductor, which consists of silicides or carbides, could divide the high barrier height into lower ones, thus reducing the effective barrier height.

\$!z"%\* %\*#/z,.!/!\*0! z"%./0z !)+\*/0.0!z0\$0z\*+z(z%/z(!.(5z/!#.!#0! z.+1\* z0\$!z%\*0!."¥ %(z.!#%+\*\_z%\*z,.0%1(.z0z0\$!z0+,z"!3z(5!./z+"z%\_z3\$%\$z.1(!/z+10z0\$!z,+//%%(%05z+"z %¥ tional Al doping. Though a small amount of residual Al is found to be present, mostly in a form of Al4C3 compound, it may locate on the surface of annealed contacts rather than in the (5!.z %.!0(5z +\*00! z 0+z 0\$!z %\_z 0\$1/z,(5%\*#z z \*!#(%#%(!z .+(!z%\*z\$)%z +\*00z "+.)¥ tion. The majority of deposited Al is evaporated during annealing because of its low melting ,+%\*0z\* z\$%#\$z!-1%(%.%1)z2,+.z,.!//1.!^z\$!z +)%\*\*0z.+(!z,(5! z5z(z%\*z0\$!z%(z/5/¥ 0!)z%/z 0+z //%/0z 0\$!z "+.)0%+\*z +"z(%-1% z ((+5z /+z /z 0+z "%(%00!z \$!)%(z .!0%+\*^z 1.0\$!.¥ more, careful characterization of the interfacial region reveals that the substrate and the generated compound are epitaxially oriented and well matched at interface with no clear evidence of high density of defects. This suggests that the morphology might not be the key to understanding the contact formation. In support of this speculation, it has been observed previously that Ti Ohmic contacts can be possibly generated without any pitting and that pit-free Ohmic contacts can be fabricated.

\*!z .!)%\*%\*#z 0\$!+.5z %/z 0\$!z ((+5w//%/0! z \$)%z +\*00z "+.)0%+\*^z \$%/z ((+5z %/z !0!.¥ mined to be ternary Ti3SiC2, which has also been corroborated by other expriments. Since the bulk Ti3SiC2 has already been found to be of metallic nature both in experiment and theory, the contact between Ti3SiC2 and its covered metals should show Ohmic character and thus the SiC/Ti3SiC2 interface should play a significant role in Ohmic contact formation. This idea is supported by the fact that the determined interface has a lowered SBH due to the large dipole shift at interface induced by the partial ionicity and the considerable charge transfer. In addition, the interfacial states, as indicated by the electron distribution at *E F*, are (/+z2%!3! z/zz+\*0.%10%\*#z"0+.z%\*z.! 1%\*#z0\$!z-^z\$!/!z/00!/z)%#\$0z!z"1.0\$!.z!\*¥ \$\*! z5z 0\$!z,+//%(!z,.!/!\*!z+"z,+%\*0z !"!0/z0z%\*0!."!\_z(0\$+1#\$z 0\$!/!z/0.101.(z !¥ fects have not been detected by the TEM study.

Interestingly, our calculations predict that an atomic layer of carbon emerges as the first monolayer of Ohmic contacts, which eventually affects interface electronic structure. Such trapped carbon was previously studied in both other interfacial systems theoretically by z\* z0\$!z%%z\$)%z+\*00/z+\*zGw%z!4,!.%)!\*0((5z5z1#!.z!(!0.+\*z/,!0.+/+¥ ,5^z 0z3/z,.+,+/! z0\$0z0\$!z.+\*z+1( z!z/!#.!#0! z0+z0\$!z%\*0!."%(z.!\_z/0.!\*#0\$!\*¥ ing interface substantially and reducing the Schottky barrier dramatically. Further, it was reported that the Ohmic contact can be realized by depositing carbon films only onto the SiC substrate, indicative of the determinative role of carbon in the Ohmic contact formation. The important role played by carbon in our study can be traced to the two interfacial Si layers, which provide possible sites for carbon segregation due to the strong Si-C interaction. However, direct imaging of the trapped carbon is still difficult in present study and further characterization requires the high-voltage EM and/or other advanced microscopic techniques.

We then demontrate that atomic-scale TigSiC2-like bilayer can be embeded in the SiC interior, forming an atomically ordered multilayer that exhibits an unexpected electronic state with the point Fermi surface, in stark absence in repestive bulk constituents. The valence charge is tound to be confined largely within the bilayer in a spatially connected way, which serves as a possible conducting channel to enhance the current flow over the semiconductor. Such a heterostructure with unusual properties is mechanically robust, rendering its patterning for technological applications likely. Finally, the atomic structures of terraces at the contacts in SiC devices are investigated and bridged to their electronic properties at an atomic scale. Experimentally, newly formed carbide TigSiC2 is demonstrated to bond directly to silicon carbide in the terrace region in an epitaxial and atomically ordered fashion, regardless of dimension of terraces. Further first-principles calculations reveal gap states in the semiconductor layers and a substantial charge accumulation around terraces in a connected and broadly distributed manner. The presence of gap states at Fermi energy and the likelihood to serve as electron conduction channels to allow current flow over the semiconductor identify the terraces as one of the origins underlying the ohmic contact in silicon carbide electronics. Such a combined experimental and theoretical investigation provides insight into the complex atomic and electronic structures of buried terraces, which should be applicable to addressing contact issues of interest in other electronic devices.

To summarize, we have determined in this chapter atomic-scale structures of Ohmic contacts on SiC and related them to their electronic structures and electric properties, aimed at understanding the formation mechanism of Ohmic contact in TiAl-based system. The combined HAADF-DFT study [31] represents an important advance in relating structures to device properties at an atomic scale and is not limited to the contacts in SiC electronics. Our results show that the main product generated by chemical reaction can be epitaxial and have atomic bonds to the substrate. The contact interface, which could trap an atomic layer of carbon, enables lowered Schottky barrier due to the large interfacial dipole shift associated with the considerable charge transfer. The atomic-scale Ti,SiC-like bilayer is embedded well in SiC bulk interior in an epitaxial, coherent and atomically abrupt manner, which exhibits an unexpected state with a point fermi surface. Moreover, the formed TisSiC2 can even be epitaxial and atomically ordered on SiC substrate near terrace, which inudces pronounced gap states at Ep in the semiconductor layers. Charges are accumulated heavily surrounding terrace in a spatially connected fashion, irrespective of dimension of the terraces, which suggests the possiblity of terraces as likely electron conduction channels to allow current transport across the semiconductor. The inducing of gap states and the capability to enable current flow over the semiconductor identify the terraces as one of the origins underlying the Ohmic nature in the metal/SiC contact system as well. These findings are relevant for technological improvement of contacts in SiC devices, and this chapter presents an important step towards addressing the current contact issues in wide-band-gap electronics.