Fabian Kosse

Thomas Piketty

Amory Gethin

Julian Heid

Clara Martínez- Toledano

We Thank

Clara Bohle

Larissa Fuchs

Electoral Cleavages and Socioeconomic Inequality in Germany 1949-2017

This paper explores the changing relationships between party support, electoral cleavages and socioeconomic inequality in Germany since 1949. We analyze the link between voting behaviors and socioeconomic characteristics of voters. In the 1950s-1970s, the vote for left parties was strongly associated with lower education and lower income voters. Since the 1980s voting for left parties has become associated with higher education voters. In effect, intellectual and economic elites seem to have drifted apart, with high-education elites voting for the left and high-income elites voting for the right. We analyze how this process is related to the occurrence of new parties since 1980 and the recent rise of populism.

Introduction

This paper draws on political attitudes surveys to study the changing relationships between party support, electoral cleavages and socioeconomic inequality in Germany. The development of political cleavages in Germany is a particularly interesting case. On the one hand, the political system shows a high degree of stability and is strongly shaped by the interplay of two parties, which have led all federal governments since 1949. On the other hand, the relation between left voting and socio-economic characteristics has partly changed by leaps and bounds, driven by the occurrence and establishment of new parties since 1980.

Our main finding is that the general evolution observed in Germany shares many similarities with the rise of the "multiple-elite" cleavage structure (Brahmin Left vs Merchant Right) that was documented for the case of France, the United States and the United Kingdom (Piketty, 2018). We also stress a number of specificities related to the German trajectory and discuss future prospects for party realignments.

From the Weimar Republic to the Kanzlerdemokratie

We seek to analyze the electoral attitudes of voters in the Bundesrepublik Deutschland (Federal Republic of Germany) from 1949 to 2017. For the period from 1949 to 1989 we analyze data of "West Germany" and from 1990 onwards we analyze data of the unified Federal Republic of Germany. Regarding the political system, the united Germany is considered to be the enlarged continuation of West Germany and most former East German parties were absorbed by their West German counterparts (Winkel, 1997). Therefore, the West German political system experienced relatively little changes following reunification.

Resulting from the past experiences of a democracy's fragility, the political system of Germany is characterized by an institutional design aiming to avoid the systemic shortcomings the Weimar Republic suffered from. 1 Among other factors, this shaped an electoral system combining the systems of majority voting and proportional representation (mixed-member proportional representation). While allowing smaller parties to retain their political influence, it reduces the risk of a parliamentary fragmentation (Schmidt, 2016). The fear of instable majorities is mirrored in the implementation of a 5 percent electoral threshold to limit the number of small parties included in the Bundestag (federal parliament). Compared to the Weimar Republic, the role of the president within the political system has been significantly weakened. Instead, there is a strong focus on the Bundeskanzler (Federal Chancellor) and the Bundestag. The Bundeskanzler plays a central role in steering everyday politics, which has led some observers to describe Germany's political system as "Kanzlerdemokratie" [START_REF] Schmidt | Das politische System Deutschlands[END_REF][START_REF] Niclauß | Kanzlerdemokratie: Regierungsführung von Konrad Adenauer bis Angela Merkel[END_REF]. The Bundestag elects the Bundeskanzler and is the leading legislative organ. Together with a strongly federal political system, power in the parliamentary democracy of Germany is much more decentralized than in presidential democracies such as the US or France. 2 Given the decisive role of the Bundestag, we focus our empirical analysis on voting behavior in federal elections, which determine the composition of the Bundestag and are regularly held every four years. 1 The term Weimar Republic refers to the period between 1918 to 1933 in which Germany's first parliamentary democracy was in place. It started with the proclamation of the republic and ended with Hitler's Machtergreifung (seizure of power).

Classifying the Parties

In order to classify the parties within the German political system into a left-right schema we mostly rely on the expert survey conducted by Benoit and Laver (2007). Academics specializing in political parties and electoral politics rated all major parties' location on the left-right dimension on a scale ranging from 1 to 20, where 1 stands for the hypothetical case of an ideal left and 20 for the ideal right party. 3 Assuming the left-right dimension to be symmetric on both ends, parties with attributed values lower than 10 are categorized as left, while those with values higher than 10 are categorized as right. As the expert survey was conducted in 2003, a categorization based on these ratings assumes a relative stability of parties' positions in the party system. The literature indicates this assumption of stability across time to be plausible for the German context (Franzmann and Kaiser, 2006). This holds especially in the case of a comparatively coarse left-right distinction. While a shift of a party's position within its assigned category is plausible, shifts across the left-right distinction appear to be unlikely. Only the FDP appears to be potentially problematic due to the varying influence of social-and left-liberal groups over time. For convenience, we constantly categorize the FDP as right party, as suggested by the results shown in Benoit and Laver.

A categorization of (almost)4 all parties who have been in the Bundestag (1949-2017) is displayed in Table 1. Below the respective name of the party, we indicate in brackets how often and when the respective party has been elected into the Bundestag. A star behind the bracket indicates that the party is part of the Bundestag in the current period (2017-2021). Since the expert survey from 2003 did not cover parties which previously lost their relevance (KPD, DP, GB/BHE, BP, WAV, DRP) or have emerged since then (AfD), we updated the list according to their categorization in the literature. 5 Parties which never gained a mandate for the Bundestag are not considered for this classification and the following analyses. DP (German Party) [3, in 1949 & 1953 & 1957] GB/BHE (All-German Bloc/League of Expellees and Deprived of Rights) [1, 1953] BP

(Bavarian Party) [1, in 1949] WAV (Economic Reconstruction Union) [1, in 1949] DRP (German Right Party) [1, in 1949]

National Election Results

As already indicated by Table 1, the German political system shows a high level of stability regarding the parties that are represented in the Bundestag. While CDU/CSU, SPD and FDP In these elections, several exceptions allowed for a circumvention of the 5 percent electoral threshold, resulting in some mandates for several smaller parties. 7 As shown in Table 1, The first election after the reunification was held in December 1990 and resulted in the appearance of a fifth party in the Bundestag, the PDS (Party of Democratic Socialism), which was the legal successor of the SED (Socialist Unity Party of Germany), the governing party of the German Democratic Republic ("East Germany"). In the 1990s, the PDS gained most of their votes in the eastern parts of Germany and struggled to establish themselves at the federal level.

The PDS was part of the merger that formed Die Linke in 2007.

After the federal election in 1998, the SPD and, for the first time, B90/Grüne formed the governing coalition led by Bundeskanzler Gerhard Schröder. While the coalition was confirmed Initially, the AfD was predominantly seen as a Eurosceptic and national-liberal party, but it later moved to the far-right as a result of intra-party conflicts. In March 2020, Germany's domestic security agency classified parts of the AfD as "verifiable right-wing extremist" and therefore, placed them under intelligence surveillance.9

With the appearance of the AfD, for the first time since 1953, six parliamentary groups were represented in parliament. Figure A1 indicates that the (inverse) U-shaped pattern since 1990 is much more pronounced in the regions of former East Germany, while the different parts of Germany did not differ regarding the respective joint shares of left and right in 1990 and 2017.

Analysis of Political Cleavages

In order to explore individual-level determinants of voting behavior, we rely on a series of postelection surveys. 10 To do so, we built on the work of Arndt and Gattig (2007) who collected a list of post-election surveys for the years 1949 to 2005 and we extended this list using the German Longitudinal Election Study (GLES), which covers the years 2009-2017. An overview of these data sources is provided in Table A1. Given varying definitions and quality of available socio-demographic variables, we focus on a restricted set of individual characteristics which could be harmonized across surveys.

In the first step of our analysis, we look at the relation between left voting and education. To account for the structural change in the distribution of educational attainment, we estimated the evolution of the difference between the fraction of left vote within top 10 percent education voters and the fraction of left vote within bottom 90 percent education voters (education deciles are defined within a given year, and average decile-level vote shares are computed assuming a constant left score within each education-year cell, see Piketty (2018). Figure 3 plots the difference in voting left between the top 10% educated voters and the rest, and documents the same reversal of the education cleavage as found in France, Britain and the US (Piketty, 2018).

A special feature of the German political system seems to be that much of this development is driven by a jump in the 1980s. Figure A2 displays the same relation but controls for age, gender, religion, and income. 11 The inclusion of control variables moderately affects the levels of the 10 In all analyses we use inverse probability weighting to re-weight the post-election survey data to match the actual election outcomes.

11 For the definition of controls see Arndt and Gattig (2007). Controls are included as dummies for each category.

education-gradient indicator but does not affect the trend. Controlling for gender and age moves the education gradient downwards (young cohorts tend to be both more educated and more likely to vote left, see below), while including income moves it upwards (individuals with higher income tend to be both more educated and more likely to vote right, see below).

To shed light on the underlying dynamic and to explore the pronounced volatility in the 1980s, we plot the education gradient separately for all left parties in Figure 4. Focusing on the SPD indicates a continuous increase of the education gradient from the 1950s until today, although this trend is relatively flat and the education gradient was still slightly negative in the most recent elections. The figure indicates that the jump of the education gradient when considering the joint set of left parties in the 1980s is strongly driven by the emergence of the B90/Grüne, as their education gradient has always been strongly positive. In contrast, the emergence of Die Linke in the 1990s had only little impact on the joint left education gradient as their specific gradient was constantly around zero. Figure A3 shows the same analysis but separated for former West Germany and East Germany.12 While the gradients are, except for B90/Grüne, a bit bigger in East Germany, the patterns are similar in both regions. Note that in former East Germany in the 1990s the PDS (later Die Linke) shows a pronounced positive education gradient which decreases in later elections. The literature suggests that many former East German elites supported the PDS in the 1990s, after they lost their privileges and positions following the German reunification (Niedermayer, 2006). In Figures 6 and7, we analyze the gender and age cleavages in Germany. Figure 6 confirms the well-known results according to which female voters have become more left over time (see Piketty, 2018). Starting at a relatively low level in the 1950s, the female gradient strongly increased in the 1960s and 1970s and has constantly been close to zero since the 1980s. This development is not driven by the occurrence of B90/Grüne or Die Linke but is similar for all left parties.

Figure 7 shows that younger voters are more prone to left wing voting than older voters (median split). The age gradient was largest in the 1990s and has decreased since then. The general pattern is in line with findings regarding other countries but seems to be more stable in Germany (Piketty, 2018). Looking at the party-specific age gradients reveals a stable strongly positive age gradient for the B90/Grüne and a pronounced drop in the gradient of the SPD in the 1980s when the B90/Grüne emerged, followed by a steady decline since then.

Analyzing divisions between rich and poor in the German context is only possible to a limited extent, as surveys nearly never include information about wealth. In the 1980s, even net household income was not collected in the surveys. Nevertheless, we use the available information on income to explore the development of the income gradient in Germany. Figure 8 shows the evolution of the difference between the fraction of left vote within top 10 percent income voters and the fraction of left vote within bottom 90 percent income voters. As for most other countries, the income gradient has declined over time. This holds for the joint gradient of all left parties, as well as for the SPD specific gradient. However, as opposed to countries like

France or the US and more in line with the UK, the joint gradient has always remained negative at a sizable level (see Piketty, 2018). Only the B90/Grüne specific gradient is constantly positive. Figure A5 shows the declining but always positive gradient for the right parties. A notable exception is the AfD, which shows a negative income gradient of 7 percentage points in 2017.

Figure A5 shows the shares of left vote among different religious groups over time. Until 1990, almost all German voters were, with nearly equal shares, either Catholics or Protestants.

The fraction of voters being member of another church was only about 1% and the fraction of voters not being member of a church was about 5%. Since the 1990s, the fraction of voters not being member of a church strongly increased (36% in the 2010s). This rise was partly driven by reunification, as only a much lower share of voters from former East Germany were members of a church. However, irrespectively of the relative size of the certain religious groups, the voting patterns remained relatively constant over time. The share of left vote was always smaller among Catholics than among Protestants and was the largest for voters of "other" or "none" religion. Only since 2017, the data contain explicit information about Muslim voters. While being only a small minority among voters (1-2%), Muslims are the group with the highest share of left vote (72%) in the 2017 election.

Concluding remarks

The development of the education cleavages in Germany seems to have followed similar patterns as in most Western democracies. A phenomenon strongly influencing the German party system was the emergence and establishment of a green party in the form of Die Grünen, later B90/Grüne. This broadening of the left spectrum was associated with a slight increase in the joint share of left votes and was accompanied by a pronounced shift of the education cleavages in the 1980s. In line with France, the US and the UK, intellectual and economic elites seem to have drifted apart in Germany, with high-education elites voting for the left and highincome elites voting for the right. As described in Piketty (2018), this pattern is in line with the "multiple-elite" stabilization scenario and is mirrored by the rise of populism, as low education/low income voters might feel neglected. In the context of Germany, this phenomenon was accompanied by the emergence of the right-wing populist and partly extremist AfD which has been mostly supported by low-educated, low-income voters as indicated by its negative education and income gradients.

To understand the coexistence of two parties from the opposed ends of the left-right spectrum -the SPD and the AfD -both indicating negative education and income gradients, requires explicit models of multi-issue party positioning, which are far beyond the scope of this paper.

However, as a short outlook, in Table A2, we include political attitudes towards redistribution Figure A6: The category Protestant includes free churches. In the 1960s the categories "Others" and "None" were pooled in one category at the data collection. In all cases except for 2017, Muslims are included in the category "Others". The data from 2017 are also included for the 2010s period.

  have (almost) 6 always been represented in the Bundestag, B90/Grüne and Die Linke have continuously been represented since first gaining seats in 1983 and 1990. Only the results of the first two elections, 1949 and 1953, slightly differ from this pattern of persistence of parties.

  most of these parties were attributed to the conservative and right spectrum. Besides the SPD, the KPD was the only other left party to be elected in the Bundestag in the Bundesrepublik's early years. In 1949, the KPD gained 5.7 percent of votes but failed to reach the 5 percent electoral threshold in 1953 and was banned in 1956. Between 1949 and 1963 Konrad Adenauer (CDU/CSU), the first Bundeskanzler of the Bundesrepublik Deutschland, led conservative and right governing coalitions formed by the CDU/CSU, the FDP and/or smaller right-wing parties. Figure 1 indicates that during the 1950s the smaller mostly right-wing parties lost votes and the CDU/CSU established itself as the leading party of the right spectrum of the political party system in Germany. 8 In 1957, CDU/CSU won the first and, to date, only absolute majority for a single German parliamentary group in a free election. Adenauer's successor, Ludwig Erhard (CDU/CSU), led a right governing coalition with the FDP from 1963 until 1966. One year after the election in 1965, the FDP left the coalition due to conflicts about economic policies. In the following years, from 1966 to 1969, CDU/CSU and SPD formed the first "grand coalition" led by Kurt Georg Kiesinger (CDU/CSU).In the late 1950's the SPD developed towards a mainstream party and gave a commitment to reform capitalism rather than to fight it (Godesberg Program 1959). In the following, the SPD gained votes and in 1969, Willy Brandt became the first Bundeskanzler of the SPD. In the 1972 election the SPD gained its best-ever federal election result and, for the first time, won more seats than the CDU/CSU. Willy Brandt led a coalition with the FDP from 1969 until 1974, when he resigned after a member of his staff was exposed as an agent of the East German secret service. Brandt's successor was Helmut Schmidt (SPD) who also led a coalition with the FDP.In 1982, the FDP left the coalition due to conflicts about economic and social policies and joined a coalition with CDU/CSU. The new coalition was led by Bundeskanzler Helmut Kohl and persisted until 1998.The federal election in 1983 marks the emergence of Die Grünen (later B90/Grüne). It was the first time since 1957 that any other party than CDU/CSU, SPD or FDP secured representation in the parliament and only the second time ever that a left party other than the SPD was part of the Bundestag. In the following elections, B90/Grüne were repeatedly elected into the Bundestag and established themselves at the federal level. As indicated in Figure1, the early rise in votes received by the B90/Grüne was accompanied by a decline in votes received by the SPD.

  in the 2002 election, parts of the SPD and the trade unions were dissatisfied with the government's social policies, especially the labor market reforms. In 2004, several left-wing protest movements against the policies of SPD-B90/Grüne merged and formed the WASG (Labour and Social Justice -The Electoral Alternative), which collaborated with the PDS from early on and formally merged into Die Linke in 2007. As displayed in Figure1, the merged party nearly doubled the vote share of the PDS, which again was accompanied by a decline in votes received by the SPD.Since 2005, Bundeskanzlerin Angela Merkel (CDU/CSU) has led coalitions with the SPD(2005-2009, 2013-2017, 2017-2021) and theFDP (2009-2013). Figure1displays the phenomena that the SPD (in 2009 and 2017), as well as the FDP (2013) lost a significant share of votes in elections following governing coalitions led by Bundeskanzlerin Merkel.In 2013, the AfD narrowly missed the 5 percent electoral threshold but gained 12.6 percent of votes in 2017 and, thereby, for the first time since 1953, a new right party entered the Bundestag.

  Figure 1 indicates that CDU/CSU and SPD have lost significant vote shares since the times of a three-party parliament in the 1960s and 1970s. The first grand coalition of CDU/CSU and SPD in 1966 represented 86.9 percent of voters, while the current grand coalition of 2017 represents only 53.4 percent of voters.

Figure 2

 2 Figure2shows the respective joint shares of left and right parties over time. The patterns

Figure 5

 5 Figure 5 repeats the analysis of the development of the education gradient for the right parties

  and openness (pro-migration) into the analyses for 2013 and 2017. The results indicate that in these domains the voters of the SPD (which are pro-redistribution and pro-openness) and the AfD (which are anti-redistribution and anti-openness) fundamentally differ, which suggests the disruption of previous class-based redistributive coalitions and the rise of new cleavages. Finally, regarding the possibility of a unification of intellectual and economic elites within the same party in the future (similarly to what happened, to some extent, with the LRM vote in France and the Democratic vote in the US), the prospects look very uncertain at this stage. A possible government coalition between B90/Grüne and CDU/CSU could represent an evolution in this direction. But the possibility and sustainability of such a realignment remains to be demonstrated.

Table 1 :

 1 Right/left Scheme Party Classification.

	Left parties	Right parties
	SPD (Social Democratic Party)	CDU/CSU (Christian Democratic/Social
	[periods in parliament: 19, ever since 1949]*	Union) [19, ever since 1949]*
	B90/Grüne (Green Party)	FDP (Free Democratic Party)
	[10, ever since 1983]*	[18, ever since 1949 except for 2013]*
	Die Linke (The left)	AfD (Alternative for Germany)
	[8, ever since 1990]*	[1, in 2017]*
	KPD (Communist Party of Germany)
	[1, in 1949]

Table A1 : Overview "Wahlstudien" German Elections Year Short Name (GESIS Data Archive) Citation

 A1

To categorize parties on the left-right dimension, experts were asked to « locate each party on a general left-right dimension, taking all aspects of party policy into account ».

We did not categorize the SSW (South Schleswig Voters' Association) which is a minority and regional party. The SSW gained one mandate in 1949. We also did not categorize the Zentrum (Centre Party) for which the left-right categorization is ambiguous. The Zentrum gained a few mandates in 1949 (3.1 percent) and 1953 (0.8 percent).

AfD[START_REF] Däubler | Links-Rechts und darüber hinaus -Eine Neuvermessung der Deutschen Parteienlandschaft mit einem auf die MARPOR/CMP-Daten angewandten IRT-Modell[END_REF]; GB/BHE (von Alemann, Erbentraut and Walther, 2018.); BP[START_REF] Massetti | From Class to Region: How Regionalist Parties Link (and Subsume) Left-Right into Centre-Periphery Politics[END_REF] DP (von Alemann, Erbentraut and Walther, 2018); DRP (ibid.); KPD (ibid.); WAV (ibid.)

The FDP was not represented in the Bundestag from 2013 to 2017, as they closely failed to reach the 5 percent threshold in the 2013 election.

In 1949 and in 1953, the 5 percent threshold was waived for parties, which won at least one district. Since 1957 parties have needed to win at least 3 districts to waive the 5 percent threshold. Moreover, in 1949, the 5 percent threshold did not hold on the national level but only on the state level. In 1990 it was sufficient to reach 5 percent either in the parts of former East Germany or former West Germany.

In Figure1and all other analyses, we consider the shares of votes, which determine the number of seats in the Bundestag. Since 1953 this is the 'Zweitstimme'. In 1949, there was only one vote.

https://www.verfassungsschutz.de/de/aktuelles/zur-sache/zs-2020-002-fachinformation-einstufungdes-fluegel-als-erwiesen-extremistische-bestrebung

For a detailed discussion about East-West-differences in voting behavior, see[START_REF] Arzheimer | Goodbye Lenin? Bundes-und Landtagswahlen seit 1990: Eine Ost-West-Perspektive[END_REF].

Table A2. Political attitudes towards redistribution are measured using the question "How is your position towards taxes and welfare benefits?" Answers were given on an 11-point scale (1 = lower taxes and duties, also if this means lower welfare benefits and 11 = higher welfare benefits, also if this means higher taxes and duties). Political attitudes towards openness are measures using the question (reversed) "How is your opinion towards migration opportunities of foreigners?" Answers were given on an 11point scale (1 = Immigration opportunities for foreigners should be facilitated, 11 = Immigration opportunities for foreigners should be restricted). Data are collected in 2013 and 2017. Source: Data sets ZA5701 and ZA6801 (see Table A1). * * * , * * , * indicate significance at the 1, 5 and 10 percent level, respectively.


Dongxin He

Xiaoran Wang

Hongshun Liu

Qingquan Li

Gilbert Teyssèdre

Space Charge Behavior in XLPE Cable Insulation Under ac Stress and Its Relation to Thermo-electrical Aging

Keywords: Space charge, XLPE insulation, ac, aging, cable

The space charge features of cable insulation peelings are investigated under ac stress as a function of electrical aging imposed previously on cable sections. The investigated samples are 230-μm-thick peelings of crosslinked polyethylene cable insulation. The space charge profiles are resolved into 32 symmetric phase angles under 50 Hz ac stress. The space charge density in the phase angle of maximum applied field is the largest, as expected, but does not change visibly as a function of aging time. A method that involves averaging space charge in all phases is proposed. The all-phase averaged space charge, which appears in essence as stationary charge, exhibits an obvious increasing trend with stressing time. The aging characteristics of space charge formed under ac stress are investigated considering the all-phase averaged profiles, and the mechanical properties and degree of crosslinking are characterized as complementary methods. The change in the accumulation of space charge under ac stress follows opposite trends unlike the degree of crosslinking, which means that space charge under ac stress has a close relationship with defect concentration in cable insulation. This research contributes to the understanding of space charge features under ac conditions and the understanding of the ac aging principle of cable insulation.

INTRODUCTION

Crosslinked polyethylene (XLPE) insulated cables are widely employed in power transmission and distribution systems because of their remarkable properties, such as high dielectric strength, low dielectric loss, good thermal and aging stress endurance, and convenient construction. The reliability of power cables is essential to the safety of power systems. However, the dielectric strength of cables declines under the effect of ac electrical and thermal stresses when in operation. The gradual degradation processes caused by composite stress on dielectrics, known as electrical aging, have a close relationship with the reliability of electrical equipment and are of special concern for electrical companies but are not completely recognized.

When dielectrics are subjected to electrical stress, space charges, which are electrical charges stored in a localized position, are generated in insulation bulk or at the surface and prominently influence the insulation properties [START_REF] Du | Temperature-dependent surface charge behavior of polypropylene film under DC and pulse voltages[END_REF][START_REF] Hao | Space charge behavior in thick oil-impregnated pressboard under HVDC stresses[END_REF]. Numerous research results postulate that space charge plays a significant part in the aging of cable insulation and might control the lifetime [START_REF] Jones | The contribution of field-induced morphological change to the electrical aging and breakdown of polyethylene[END_REF][START_REF] Dissado | The role of trapped space charges in the electrical aging of insulating materials[END_REF]. The energy released by space charge-mediated processes may indeed constitute the leading mechanism in material evolution [START_REF] Laurent | Charge dynamics and its energetic features in polymeric materials[END_REF]. In recent years, space charge has been shown to generate a high electric field and substantially distort the local electrical strength, with field intensification processes triggering partial discharges [START_REF] Bromley | Discharges, space charge, and the shape of electrical trees[END_REF]. At the interface level, charge injection and extraction are thought to destroy the microstructure of polymeric material and initiate electrical tree, which may propagate across the insulation and lead to dielectric breakdown [START_REF] Wu | Model for electrical tree initiation in epoxy resin[END_REF][START_REF] Mammeri | Influence of space charge buildup on the transition to electrical treeing in PE under ac voltage[END_REF].

Space charge characteristics under dc conditions have been studied for a long time, and their negative effect on dielectrics is caused by the continuous accumulation of charges of a given polarity producing local field strengthening [START_REF] Wei | Effect of space charge on breakdown characteristics of aged oil-paper insulation under DC voltage[END_REF][START_REF] Mazzanti | A protocol for space charge measurements in full-size HVDC extruded cables[END_REF]. Previous reports show that space charge quantity under dc stress has a positive correlation with aging time; thus, it can represent a characteristic index for the aging degree [START_REF] Montanari | Polarization and space charge behavior of unaged and electrically aged crosslinked polyethylene[END_REF][START_REF] Montanari | A molecular model to evaluate the impact of aging on space charges in polymer dielectrics [comment and reply[END_REF]. Space charges under ac stress have not been investigated extensively because of the difficulty of measuring space charge with a resolution along the ac phase [START_REF] Xu | An improved pulsed electroacoutic system for space charge measurement under AC conditions[END_REF] and the relatively smaller charge amount compared with dc stress. Intuitively and according to modeling, physical processes at interfaces should substantially affect space charge under ac [START_REF] Baudoin | Modeling electroluminescence in insulating polymers under AC stress: effect of excitation waveform[END_REF]. However, space charge theories under ac have not been corroborated by experience. Most electrical apparatuses are operated under ac stress. Hence, the space charge under ac conditions and its relationship with aging need to be studied in depth.

The net space charge quantity stored under ac stress is smaller than that under dc stress because of repeated injections and extraction of charges in negative and positive half-periods, and the quantity becomes low with the increase in frequency [START_REF] Montanari | AC charge injection investigated by means of space charge measurements: threshold and frequency dependence[END_REF]. Initial studies observed scarce space charge under ac stress with a frequency of 50 Hz, relatively low ac electrical field, and short stressing time [START_REF] Wang | Space charge characteristics in cross-linking polyethylene under electrical stress from dc to power frequency[END_REF]. Recent studies also reported the existence of space charge at power frequency. These studies have been conducted indirectly by using various approaches; for example, electroluminescence from dielectrics under ac stress, which is much more intense than that under dc stress, is considered to be related to space charge dynamic behavior under ac stress [START_REF] Laurent | Charge dynamics and its energetic features in polymeric materials[END_REF]. Reports on direct charge measurements can be distinguished between those carried in post-stressing under ac stress and those during ac stressing with or without phase resolution. The detection of residual space charge in the depolarization process does not require specific equipment unlike in the dc case, and several reports show evidence of such residual charge [START_REF] Fothergill | Advanced pulsed electro-acoustic system for space charge measurement[END_REF][START_REF] Dissado | Proposal of a space-charge life model for electrical polymeric insulation aged under AC voltage[END_REF][START_REF] Ho | Effect of semiconducting screen on the space charge dynamic in XLPE and polyolefin insulation under DC and 50 Hz AC electric stresses conditions[END_REF]. The production of charge profiles in specific phase angles under ac stressing as reported for polyethylene laminated samples requires the synchronization of acoustic or electric perturbation with the ac stress [START_REF] Zhao | Space charge behavior in polyethylene under AC electric fields[END_REF][START_REF] Ho | Measurement of space charge in XLPE insulation under 50 Hz ac electric stresses using the LIPP method[END_REF][START_REF] Notingher | Study of space charge accumulation in polyolefins submitted to ac stress[END_REF][START_REF] Thomas | A new method for signal averaging resorting to space charge measurements by the pulsed electro-acoustic method under AC stress[END_REF][START_REF] Thomas | A New Method for Space Charge Measurements Under Periodic Stress of Arbitrary Waveform by the Pulsed Electro-Acoustic Method[END_REF][START_REF] Bamji | Phase-resolved pulsed electro-acoustic technique to detect space charge in solid dielectrics subjected to AC voltage[END_REF]. Most results of the aforementioned studies were obtained on a flat specimen, and accumulation within cable insulation under ac stress was reported recently [START_REF] He | Space charge characteristics of power cables under AC stress and temperature gradients[END_REF]. Clearly, abundant experimental evidence shows that space charge behavior under ac voltage cannot be ignored.

Studies also focused on the aging characteristics of space charge under ac stress. This has been done for example with by recording the volt-off charge profiles of aged samples and analyzing the evolution of the charge density after electrical aging [START_REF] Chong | Space charge and charge trapping characteristics of cross-linked polyethylene subjected to ac electric stresses[END_REF][START_REF] Chen | ac aging and space-charge characteristics in low-density polyethylene polymeric insulation[END_REF]. A significant influence of ac charge transport on the breakdown process was reported [START_REF] Zhou | Space charge and AC electrical breakdown strength in polyethylene[END_REF]. In the same way, space charge decay after dc poling of samples aged under ac stress and thermal endurance was measured by Tzimas et al. [START_REF] Tzimas | Effect of electrical and thermal stressing on charge traps in XLPE cable insulation[END_REF]; the origin of space charge was interpreted in relation to impurities and additives in the cable. Mechanistic approaches of aging and failure under ac stress with the mediation of space charge processes were also discussed [START_REF] Montanari | Bringing an insulation to failure: the role of space charge[END_REF][START_REF] Mazzanti | A space-charge life model for ac electrical aging of polymers[END_REF][START_REF] Laurent | Charge dynamics and its energetic features in polymeric materials[END_REF]. However, reports on space charge on samples aging usually adopted space charge measurement under dc voltage or the volt-off profile and did not use space charge profile under ac stress, which requires further research.

In this work, phase-resolved space charge measurements obtained on cable peelings were presented. A method that involves averaging all the charge profiles in all phase angles was presented to clearly recognize features of space charges formed under ac stress. The all-phase averaged space charge in cable peelings under different aging degrees were compared to obtain aging characteristics in relation to space charge. The mechanical properties and degree of crosslinking of cable insulation were conducted to provide an auxiliary explanation of its aging characteristics. The purpose of this study is to make contributions for the explicit comprehension of the essence of space charge under ac conditions and the relation between ac stress aging and space charge accumulation.

SAMPLES AND METHODS

CABLE PEELINGS

Samples were taken from an XLPE insulated HVAC cable manufactured by Qingdao Hanlan Group Co., Ltd. The insulation thickness was 4.5 mm, and the rated voltage was 10 kV. The insulation of the cable was cut into 230-μm-thick and 45 × 45 mm² wide peelings for space charge measurement. The cutting method is schematized in Figure 1. A section of the cable was installed in a rotary machine and cut by a lathe whose knife was moving forward in a tangential direction. The width and flatness of the peelings were determined by revolving the rotation speed of the cable and the moving speed of the lathe knife. The choice of working with flat specimen was motivated by the goal to obtain the charge profile with a high spatial resolution and under a relatively high field, which would not be easily possible with medium-voltage cables. The cutting method was also employed in the European ARTEMIS Program [START_REF] Tzimas | Space charge characterization of XLPE peelings with a cable prehistory: Before and after ac endurance tests[END_REF][START_REF] Tzimas | Effect of long-time electrical and thermal stresses upon the endurance capability of cable insulation material[END_REF], and the equivalence of peelings with a full-size cable for electrical and material property investigation and space charge measurement was confirmed [START_REF] Fothergill | Electrical, microstructural, physical and chemical characterization of HV XLPE cable peelings for an electrical aging diagnostic data base[END_REF]. XLPE peelings taken from the middle layer of the cable insulation were selected for space charge measurements.

SPACE CHARGE MEASUREMENT METHOD

UNDER AC STRESS Space charge profiles were measured through the space charge measurement system for laminated samples under ac stress, whose structural diagram is shown in Figure 2. The design principle is similar to the space charge measurement system for cables introduced in a recent work [START_REF] He | Space charge characteristics of power cables under AC stress and temperature gradients[END_REF]. The principle of the measurement system is based on pulsed electro-acoustic method, that is, the sample is submitted to pulsed electric field generated by high-voltage pulse power supply, which generates electrostatic forces on existing charges. Thus, ultrasonic waves are induced and transformed into electric signals by a piezoelectric sensor, which reflects the distribution of space charge in the sample [START_REF] Cooke | Pulsed electro-acoustic measurement of volume charge accumulation and decay in polyethylene[END_REF].

For charge measurement under ac stress, the difficulty is the match of measurement time with ac phases compared with charge measurement under dc stress. In addition, acoustic signals need to be recorded over several periods to be averaged afterwards. In previous works, either trains of pulses were produced at desired positions of the phase of the ac stress [START_REF] Wu | Space charge measurements in polyethylene under dc and ac operating conditions using the PEA technique[END_REF][START_REF] See | Measurement of space-charge distributions in solid insulators under rapidly varying voltage using the high-voltage, high speed pulsed electro-acoustic (PEA) apparatus[END_REF] or the phase of a given acoustic response was determined a posteriori using a phase recognition algorithm [START_REF] Thomas | A New Method for Space Charge Measurements Under Periodic Stress of Arbitrary Waveform by the Pulsed Electro-Acoustic Method[END_REF]. In this paper, the ac phase-matching circuit is designed to solve the matching problem, as shown in Figure 2.

The ac sinusoidal signal obtained from the capacitive voltage divider is transformed into a square waveform signal synchronous with high ac voltage. The square waveform signal triggers the signal generator to output 32 short square waveform signals, which control the switch of high-voltage pulse power supply. Electroacoustic signals in 32 phase angles can be measured in one sinusoidal period due to the control of phase-matching circuit on high-voltage pulse power supply. Space charge waveforms were produced by averaging more than 500 sinusoidal periods in one time, and the averaged space charge profiles in 32 phase angles were achieved with an interval of 11.25°.

In the space charge measurement process, 35 kV/mm (r.m.s. value) and 50 Hz ac electrical field were applied on the XLPE cable peeling samples for 6 h. Space charge profiles in 32 phase angles were tested intermittently when ac voltage was applied. After stressing for 6 h under ac electrical field, XLPE samples were placed in short circuit, and the space charge profiles were recorded as a function of time with stress off.

THERMO-ELECTRIC AGING CONDITIONS

Some cable sections aged prior to their preparation into peelings. The structure of aged cable samples is shown in Figure 3. The total length of cable section was 340 mm, and after treating the cable terminations, the length of the remaining outer semiconducting layer in the middle part was 90 mm. Two stress cones were installed on both sides of the cable to avoid corona or flashover under ac stress. The cable samples for aging were placed in an oven with suited high-voltage bushing to transmit the ac high voltage to the cable sample.

Stress cone

Spherical

Increasing the temperature caused the XLPE to soften and the mechanical performance of the XLPE to reduce considerably. XLPE material was still stiff at 103 °C. At temperatures above 105 °C, deformation of XLPE readily occurred, and at 114 °C, the crystalline regions completely melted. The aging heat treatment temperature prescribed by IEC 60502-2-2005 is 135 °C. Therefore, we chose three temperatures, 103, 114, and 135 °C, as thermal stresses for aging. The real cable insulation in the power system was aged in the way of electrochemical aging. If the electric field applied during aging tests is too high, then the aging mechanisms may change. Hence, we chose an ac stress that is three times the rated voltage (the rated phase voltage is 8.7 kV for 10 kV XLPE cable), i.e., 26.1 kV for aging. The aged cable samples were taken out in five stages and cut into laminated peelings for space charge measurements. Table 1 shows the total aging time and sampling intervals at the three different aging conditions. The cable samples for aging were placed in three ovens set at three different aging temperatures. A picture of the integral thermo-electric aging system is shown in Figure 4.

RESULTS

3.1 SPACE CHARGE VS. PHASE ANGLE UNDER AC VOLTAGE One cable section was aged for 300 days under aging conditions of 103 °C temperature and 26.1 kV ac voltage. Examples for space charge characteristics obtained on samples peeled from this cable are given in Figure 5. Space charge profiles in 32 different phase angles under ac voltage application for 6 h are depicted in different colors. Inner space charge within the bulk of the sample was found, whose polarity was the same as that of the upper electrode (located at the right side of the figures). The polarity of the interface charge and the inner space charge varied with the ac phase angle. It must be stressed here that there is apparently, a substantial attenuation in space charge signal, as the charge peak amplitude at the upper electrode is much lower than that at the bottom electrode. However, the space charge profile in cable peeling under dc stress did not have such attenuation, the influence charge peak at the top electrode being of the same magnitude as that at the bottom [START_REF] He | Space charge characteristics of power cables under AC stress and temperature gradients[END_REF]. This finding means that it is not due to the attenuation of acoustic waves, all the more that test samples are relatively thin. The reasons for such apparent strong attenuation of the response under ac stress are still not known at present. Possibly the upper semiconducting electrode does not behave as a pure conducting electrode under AC stress, i.e., the influence charge may be distributed into the semiconductor electrode, thereby producing an attenuated response in the electroacoustic signal.

The amplitude and polarity of space charge in XLPE peelings change simultaneously with the phase angle under ac voltages. The charge density is largest in the phases of 90° and 270° (corresponding to voltage maxima) and lowest in the phases of 0° and 180°. The amplitude of space charge is nearly proportional to real-time voltage amplitude. We considered first how space charge profiles at maximum voltage evolve with stressing time under ac. Figure 6 shows the evolution of charge profiles at 90° and 270° during the 6 h stressing time under 35 kV/mm. Meticulous inspection revealed that the space charge next to the bottom electrode in the phase of 270° became slightly larger during voltage application, whereas the space charge next to the bottom electrode in the phase of 90° became slightly lower. However, the variation is so faint that it is difficult to recognize in the phases of 90° and 270. A previous study [START_REF] Thomas | Space-charge dynamic in polyethylene: from dc to ac stress[END_REF] also indicated a slight variation of space charge in the phase angles from 0° to 120° under 2 h application of 10 Hz ac voltage. To reveal the variation of space charge formed under ac conditions, we developed a method called all-phase averaged method to identify space charge features. The method includes averaging all the space charge profiles in the 32 phase angles measured in one run; therefore, the space charge whose polarity changed between the positive and negative period was counteracted through the average.

The all-phase averaged waveforms of XLPE peelings in the 6 h voltage application process are shown in Figure 7. All the charge peaks of the averaged waveform increased with stressing time. Before the application of the ac stress, there was little space charge inside the sample bulk. Two space charge peaks close to the left-hand electrode appeared and grew gradually due to the action of the ac stress. The interface charge at the bottom electrode increased to a large extent, whereas the interface charge to the top electrode grew only slightly. The space charge amount increased quickly in the first 1 h of voltage application time, especially in the initial 3 min, at which point it grew very fast. With the increase in voltage application time, the ac charge accumulation speed gradually slowed down. The experimental results show that the all-phase averaged charge waveform presents a distinct variation under the action of the ac stress and represents space charge that are more exploitable than the charge profile in the phase of 90° or 270°. It must be realized that only a few space charge measurements under ac stress were reported in the previous studies, and often, the data were exploited at zero field crossing [START_REF] Chong | Space charge and charge trapping characteristics of cross-linked polyethylene subjected to ac electric stresses[END_REF][START_REF] Montanari | Investigating ac space charge accumulation in polymers by PEA measurements[END_REF]. Since in general, the residual charge is weak, it is best resolved when the capacitive charges are not present on the electrodes and overwhelm the response.

Therefore, we used all-phase averaged charge profiles to identify space charge characteristics under ac thermo-electrical aging.

AC SPACE CHARGE VS. AGING CONDITIONS

The all-phase averaged charge density increased with the application time of ac stress and reached maximum after 6 h application. Thus, we used the all-phase averaged space charge waveform at 6 h ac stress application to compare the space charge characteristics in different stages. The all-phase averaged space charge profiles at 6 h ac stress application of insulation peelings in different aging times at temperatures of 103, 114, and 135 °C are shown in Figure 8.

As shown in the figure, the all-phase averaged charge density generally increased with the aging time for the cable sections. For 103 °C and 114 aging, the interface charge density in the bottom electrode and the upper electrode reached the maximum in the last aging stage. For the 135 °C aging, the interface charge density in the bottom electrode the fifth stage was slightly smaller than that in the fourth stage, whereas the interface density in the upper electrode was the largest in the fifth stage. The net charge quantity was obtained through the integration of all-phase averaged charge density, taken in absolute value, over the thickness. Figure 9 shows the charge quantity at 6 h ac stress application of cable peelings in different aging stages.

As shown in the figure, the trend of the charge quantity decreased at the beginning and then increased in the latter stages for the aging at all three temperatures. In the first stage, the charge quantity decreased slightly and then gradually augmented from the second stage until the fifth aging stage. The charge quantity in the last stage was 50% to 100% larger than that before aging. The kinetic of charge increase was the same at temperatures of 135 and 114 °C. The increase is clearly slower at a temperature of 103 °C.

MECHANICAL AND STRUCTURAL CHANGES

To explain space charge characteristics, we conducted relevant mechanical and chemical analyses on aged cable samples to provide auxiliary information. The tensile strength and elongation at break were tested to represent mechanical properties. The degree of crosslinking is a significant index of XLPE material integrity, which is generally characterized by the gel content [START_REF] Mao | Investigation of the radial in homogeneity of the crosslinking degree in XLPE cable insulation[END_REF].

A test on tensile strength and elongation at break was conducted according to IEC 60811-1-1:2001. Cable insulation was cut into dumbbell-shaped pieces and measured by a CWT6502 computer-controlled testing machine with a stretching velocity of 250±50 mm/min. The gel content was obtained through xylene immersion [START_REF] Li | Comparison between the test methods for the measurement of the gel content in XLPE insulation compounds[END_REF], in which the non-crosslinked portion was dissolved by xylene. Thus, the remaining fraction of polymer was considered the gel content.

The variations of tensile strength and elongation at break of cable insulation versus aging time at 103, 114, and 135 °C are shown in Figure 10. As shown in the figure, the tensile strength and the elongation at break increase at the first stage and decrease from the second stage. The elongation at break decrease from 490% before aging to 376%, 325%, and 281% in the fifth stage under 103, 114, and 135 °C. The tensile strength decreased from 20.0 N/m 2 before aging to 17.7, 15.5, and 14.6 N/m 2 in the fifth stage under 103, 114, and 135 °C, which represent substantial reduction of mechanical strength.

A comparison of different aging temperatures shows that the tensile strength and the elongation at break have a faster decrease speed when aged under high temperature. The evolution in the degree of crosslinking, i.e., the gel content, in cable insulation versus aging time under aging temperatures of 103, 114, and 135 °C is shown in Figure 11. With the aging process under the three temperatures, the degree of crosslinking increased initially and then decreased from the second or third stages with a decreasing rate as the aging temperature increased. The degree of crosslinking in the fifth aging stage under all three temperatures was lower than that before aging.

A comparison of Figures 10 and11 shows that the tensile strength, elongation at break, and degree of crosslinking of cable insulation follow the same variation with aging time; all increased at the beginning of aging and decreased afterwards. This finding means that mechanical properties have a strong correlation with the degree of crosslinking. When the degree of crosslinking increases or decreases, the mechanical properties correspondingly become strong or weak.

DISCUSSION

ESSENCE OF SPACE CHARGE IN ALL-PHASE AVERAGED METHOD

As described in a previous report [START_REF] He | Space charge characteristics of power cables under AC stress and temperature gradients[END_REF], in cable insulation operated in a power system for 15 years, space charge under ac electric field can be divided into two categories: periodic charge, whose magnitude and polarity change within a phase of the ac stress, and stationary charge, which remains almost stationary in a period and slowly evolves as a function of the stressing time. The periodic charge does not obviously evolve with aging and is close to symmetrical for positive and negative half-periods of the stress. By contrast, stationary charge gradually increases as aging progresses.

On the basis of previous research results, we can evaluate the significance and the input of all-phase averaged method. The 32 phases are symmetrical in two consecutive half-periods. Hence, the influence charge (capacitive and image charges) and the periodic charge are counteracted due to the opposite polarity between negative and positive periods. The stationary charge remains and is revealed in the all-phase averaged charge profile. Clear support to the statement is given in the following.

After 6 h of ac stress application, the XLPE peeling sample was placed in short circuit, and the volt-off space charge was measured in the depolarization process. This followed the tests on the cable aged under 103 °C and 26.1 kV for 300 days with phase-averaged space charge profile shown in Figure 7. The volt-off space charge profiles in the first 180 s of the depolarization time are shown in Figure 12. The interface charge peak on the bottom electrode and the two inner space charge peaks close to the bottom electrode decreased considerably in this time interval. Within approximately 100 s, the inner space charge decayed nearly to zero, and the image charge to the bottom electrode was substantially reduced. A comparison of Figures 7 and12 shows that the all-phase averaged charge waveform and the volt-off space charge profile have similar shapes; both have two inner space charge peaks close to the bottom electrode, and the charge peaks have the same position and relative amplitude. Notably, the volt-off space charge profile at approximately 5 s after switch-off of the ac stress was just slightly smaller in amplitude than the all-phase averaged charge at 6 h of ac stress application. This finding indicates that the volt-off space charge comes from the all-phase averaged charge, which is virtually a stationary charge. The periodic charge vanished immediately after the switch-off of ac stress, whereas the stationary charge had a certain residence time and decreased gradually in the depolarization process.

As shown in the analysis above, the stationary charge presented a more remarkable variation than the periodic charge. The stationary charge has a close relationship with the application of ac aging stresses and requires particular attention. The essence of the all-phase averaged method is to clearly reveal the stationary charge, which is of great use for resolving space charge features under ac stress.

RELATIONSHIP BETWEEN SPACE CHARGE AND THE DEGREE OF CROSSLINKING

The tensile strength and degree of crosslinking increase at the first aging step and decrease afterwards. The increase in these quantities in the first step is revealed whatever the aging temperature. The variation in the degree of crosslinking with aging steps can be related to the competition between chain scission and crosslinking reactions, i.e., destruction and reforming of chemical bonds [START_REF] Oshima | Chemical structure and physical properties of radiation-induced crosslinking of polytetrafluoroethylene[END_REF][START_REF] Chiniwalla | Crosslinking and decomposition reactions of epoxide functionalized polynorbornene. Part I. FTIR and thermogravimetric analysis[END_REF][START_REF] Vondráček | Slow decomposition of silicone rubber[END_REF][START_REF] Li | Physicochemical origin of space charge dynamics for aged XLPE cable insulation[END_REF]. Under the combined effect of high electric field and thermal stress in the aging process, the microstructure of XLPE material in cable insulation is damaged due to the reduction of degree of crosslinking. At the same time, the free radicals generated from fractured chemical bonds tend to combine under the action of the temperature, which results in the reforming of molecular bonds and the enlargement of the degree of crosslinking.

In the early stage of aging, the microstructure of the material is presumably damaged to a small degree, whereas a certain amount of dissociative end groups in molecular chains combine with each other under thermal stress. Therefore, the probability of chain crosslinking is stronger than that of chain decomposition in early aging, which accounts for the increase in the degree of crosslinking. In the middle and late aging stages, XLPE material suffers from the long-time action of electric field and thermal stress, which leads to severe damage of the microstructure. The probability of chain decomposition is stronger than that of chain crosslinking in the middle and late stages; hence, the degree of crosslinking decreases. Similar phenomena were reported recently, as revealed by infrared spectroscopy and thermo-kinetic analysis [START_REF] Chen | Thermo-oxidative aging analysis of HTV silicone rubber used for outdoor insulation[END_REF][START_REF] Liu | Effect of thermal stress on the space charge distribution of 160 kV HVDC cable insulation material[END_REF].

A comparison of shows that the space charge quantity formed under ac stress has an opposite change tendency compared with the mechanical properties and the degree of crosslinking. Therefore, the variation of space charge with aging could be explained by change in material microstructure. In the early aging stage, chain crosslinking in XLPE material has a larger probability of occurrence than chain scission; thus, the defect is less concentrated in the cable insulation, and the space charge density captured by traps is correspondingly reduced [START_REF] Liu | Effect of thermal stress on the space charge distribution of 160 kV HVDC cable insulation material[END_REF]. In the middle and late aging stages, the structure of molecular chains is significantly damaged, and a large amount of chemical bonds are fractured. Therefore, the defect density increases, thereby increasing the space charge density.

CONCLUSIONS

The space charge features of cable insulation peelings under ac stress are studied using a space charge measurement system. Space charge under ac stress can be divided into two types: stationary charge and periodic charge. The space charge seems to change synchronously with ac phase angles, that is, space charge has the largest amplitude in angles of 90° and 270° in phase with voltage maxima. However, the space charge density in specific phase positions (90° or 270° for example) does not increase visibly. Thus, the all-phase averaged method is proposed to clearly present space charge build-up under ac stress, which can eliminate the periodic charge and reveal the stationary charge. Experimental results show that the stationary charge density increases as the thermo-electric aging time progresses.

The space charge characteristics of insulation peeling taken from cables aged in different ac conditions are compared by the all-phase averaged waveform. The trends for the stationary charge density exhibit a small reduction at the beginning of aging and an increase in the latter stages of aging, which has the opposite change tendency from the degree of crosslinking and the mechanical properties. The change of space charge with ac aging has a close relationship with defect concentration in cable insulation.

In the early aging stage, chain crosslinking in XLPE material has a larger probability of occurrence than chain decomposition. Thus, the defect concentration is reduced in the cable insulation, and the space charge density captured by traps is correspondingly reduced. In the middle and late aging stages, the structure of the molecular chains is damaged. Thus, the defect density increases, thereby increasing the space charge density.

Figure 1 .

 1 Figure 1. Cutting method scheme of cable insulation.

Figure 2 .

 2 Figure 2. Space charge measurement system for laminated sample under ac conditions.

Figure 3 .

 3 Figure 3. Structure of aged cable samples.

Figure 4 .

 4 Figure 4. Picture of thermo-electric aging system.

Figure 5 .

 5 Figure 5. Space charge profiles at 32 phase angle values in cable peelings previously aged under 103 °C and 26.1 kV for 300 days. The angles of 90 and 270 °C respectively correspond to a maximum positive and negative voltage applied to the top electrode, as shown in the right side in the figure.

Figure 6 .

 6 Space charge profiles in XLPE cable peelings at phase angles of maximum voltage and its evolution with 6 h stressing time under a r.m.s. ac field of 35 kV/mm. The cable was aged for 300 days at 103 °C under 26 kV stress prior to peeling.

Figure 7 .

 7 Figure 7. All-phase averaged charge profiles of XLPE peeling in 6 h ac stress application process. The cable was previously aged under 103 °C and 26.1 kV for 300 days.

Figure 8 .

 8 Figure 8. All-phase average space charge waveform at 6 h of ac stress application of cable peelings taken from cables aged in different aging stages under temperatures of (a) 103 °C, (b) 114 °C, and (c) 135 °C.

Figure 9 .

 9 Figure 9. Charge quantity at 6 h ac stress application of cable peelings in different aging stages under 103, 114, and 135 °C.

Figure 10 .

 10 Figure 10. Change in mechanical properties of the insulation as function of cable aging time.

Figure 11 .

 11 Figure 11. Change in degree of crosslinking in cable insulation versus aging time.

Figure 12 .

 12 Figure 12. Volt-off space charge profiles in the depolarization process after 6 h ac stress application. The cable was previously aged under 103 °C and 26.1 kV for 300 days.

Table 1 .

 1 Total aging time and sampling interval

	Aging voltage			26.1 kV
	Aging temperature Total aging time (days)	114℃ 135℃	103 °C 375	114 °C 135 °C 200 150
	Sampling interval (days)		75	40	30

ACKNOWLEDGMENT

This work is supported by the National Natural Science Foundation of China (Grant No. 51777117).


H Yibole

W Hanggai

Z Q Ou

R Hamane

V Hardy

F Guillou

Magnetic properties, anisotropy parameters and magnetocaloric effect of flux grown MnFe 4 Si 3 single crystal

Keywords:

The transition-metal based alloy MnFe 4 Si 3 not only is a potential candidate for room temperature magnetocaloric applications, but also shows a large magnetic anisotropy forming an interesting case study in the search for rare-earth free permanent magnets. However, former polycrystalline and single crystal studies led to major disagreements about the order of the magnetic transition and the magnetocrystalline anisotropy scheme, which are two essential points for the understanding of this alloy. Here, magnetic, magnetocaloric properties and the magnetic anisotropy of MnFe 4 Si 3 (Mn ~0.86 Fe ~4.24 Si ~2.90 ) are investigated on a high quality single crystal grown by flux method, and compared to polycrystalline materials. Using the recently proposed criterion of field dependence of the magnetocaloric effect, we show that the ferromagnetic transition is more likely to be of second order, which is fully compatible with the absence of thermal hysteresis at the ferromagnetic transition in the present MnFe 4 Si 3 crystal. The c axis is confirmed to be the hard magnetic axis, both in single crystal and polycrystalline MnFe 4 Si 3 , and a large, dominant, K 1 anisotropy constant (~-2.5 MJ m -3 ) is found at low temperatures.

Introduction

Initially investigated in the 60s and 70s [1][2][3][4], transition metal-based compounds deriving from Mn 5-x Fe x Si 3 are currently receiving a renewed interest for their rich magnetic properties and for their potential use in magnetocaloric applications [5][6][7][8][9][10][11]. Mn 5-x Fe x Si 3 compounds were originally believed to crystallize in the hexagonal structure with Mn and Fe distributed on 4d and 6g sites, and Si metalloid atoms on 6g sites with different coordinates. Magnetic properties were found to be highly dependent on the Fe content [5,6]. Of particular interest is the x ≈ 4 composition, MnFe 4 Si 3 , which is ferromagnetic with a saturation magnetization of 1.5-1.7 µ B /T.M. and presents a Curie temperature around 300 K making it a potential candidate for magnetocaloric applications near room temperature [5]. Some recent studies have deepened the understanding of this materials family using single crystals grown by Czochralski method [8]. Combined neutron and X-ray diffraction data have led to the emergence of a new structural model [8] and detailed inelastic neutron scattering experiments and Mössbauer spectroscopy have clarified the spin and lattice dynamics of MnFe 4 Si 3 [9,10].

Despite these extensive investigations on MnFe 4 Si 3 , some controversies persist. First, the order of the magnetic transition MnFe 4 Si 3 is unclear. The ferromagnetic transition was originally classified as a contin uous second order transition, due to the absence of field-induced transition on the magnetization curves of bulk polycrystalline materials [5]. However, the recent observation of a large thermal hysteresis of ~10 K in single crystal is characteristic of a first order transition [8]. Further physical properties pointed out a complex behavior potentially closer to a second order behavior [9]. Usually, observing a large thermal hysteresis at a magnetic transition is typical of a first order transition with a significant latent heat and large discontinuities in the lattice parameters or a change in crystal symmetry. All these features should in turn lead to appreciable magnetocaloric entropy change [12]. On the contrary, MnFe 4 Si 3 seems to combine a relatively large thermal hysteresis with only a modest entropy change of 2-2.5 J kg -1 K -1 for 2 T, making it an unusual magnetocaloric compound [5,8,9]. The second debated issue in MnFe 4 Si 3 concerns the magnetic anisotropy, originally believed to correspond to a c easy axis from neutron diffraction measurements and X-ray diffraction on in-field oriented powders [3], but later proposed to be a c hard axis with an easy (a,b) plane based on single crystal data [8].

The purpose of this work is to clarify the two aforementioned points, by a detailed study of the order of the transition from magnetization and magnetocaloric measurements, and by investigating the magnetic anisotropy of MnFe 4 Si 3 both in single crystal and polycrystalline forms. A single crystal growth technique different from Ref. [8] was selected for this study in order to investigate whether sample preparation can explain part of the disagreements in the literature. In addition, a quantitative estimate of the magnetic anisotropy parameters over a large temperature range turns out to be needed for MnFe 4 Si 3 , since other 5:3 transition-metal:metalloid alloys such as Fe 5 (Si,B) 3 or Fe 5 (P,B) 3 are currently explored for their potential use as rare-earth free permanent magnets [13][START_REF] Lamichhane | Canfield[END_REF][15].

Experimental details

MnFe 4 Si 3 single crystals were grown by tin flux method. High-purity Mn (99.9%), Fe (99.99%) and Si (99.999%) starting materials were arc-melted with Sn (99.999%) in Ar atmosphere in a water-cooled copper crucible. Due to the smaller solubility of Si in molten Sn relative to Mn and Fe, we used extra amount of Si starting materials compared to the metal:metalloid stoichiometric ratio of 5:3. The resulting ingot was then sealed in quartz ampoule in 200 mbar Ar. The charge to flux ratio was 1:20 wt%. The sealed ampoule was then placed in a vertical furnace and heated up to 1423 K. The sample was maintained at this temperature for 100 h, and then slowly cooled at a rate of 2 K/h down to 700 K, at which temperature the excess of Sn was removed. The remaining flux was finally removed by etching with diluted hydrochloric acid. The as-grown crystals present the well-formed prismatic shape of an elongated needle. Microanalyses were performed using Hitachi SU-8010 scanning electron microscope (SEM) equipped with an energy dispersive spectrometer (EDS). The chemical compositions of the single crystals were determined with EDS by probing several locations on each crystal at an accelerating voltage of 15 keV. Reference materials were used to correct EDS data and make the chemical analysis more quantitative.

A polycrystalline MnFe 4 Si 3 ingot was prepared by arc-melting elemental starting materials in purified Ar atmosphere. The button was flipped 6 times to ensure homogenization. The grain size distribution of this as-prepared button is quite large, with a few crystallites at the button surface having an elongated shape and reaching the mm in length, while the inner part of the button present a columnar microstructure with an average grain size of approximately 120 μm × 40 μm. The resulting sample is then cut, ground using an agate mortar and sieved. Particles smaller than 36 µm are used for powder x-ray diffraction, and part of the powder is oriented in a magnetic field of 11 kOe using epoxy glue as binder. Powder x-ray diffraction XRD experiments were carried out at room temperature using a Panalytical Empyrean diffractometer employing Cu K α radiation.

Magnetic measurements were performed in a VersaLab Quantum Design system employing a Vibrating Sample Magnetometer option. To limit possible thermalization artefacts, magnetization measurements as a function of the temperature were carried out while settling the temperature at each point and/or using slow temperature sweep (<1 K min -1 ). The limited size of the sample (m ~0.019 mg, estimated from SEM pictures and the theoretical density of MnFe 4 Si 3 ) makes such measurements challenging. First, to avoid contamination, the needle is mounted under optical microscope on a fresh half-straw quartz holder using nonmagnetic tools and only a tiny amount of superglue as fixer. A background signal with only the glue was measured to ensure it results only in a minor diamagnetic contribution. Then, large oscillations (4 mm) and long integration times (up to 10 s/point) were used to optimize the signal/noise ratio. Even in the most unfavorable situation, such as M-T curve recorded along the hard axis with an external field of 100 Oe, the signal in the paramagnetic phase (9.10 -6 emu) remains significantly larger than the noise taken as the scattering between different points in the same conditions (noise level ~2.10 -7 emu). Neglecting potential error on the density, most of the uncertainty on the massic or volumic magnetization actually originates from the determination of the radius of the needle on SEM pictures, Δr/r ≈ 4%, which leads to sizable uncertainty on the sample volume ΔV/V ≈ 8% and thus on the normalized magnetization, estimated as ΔM/M ≈ Δm raw /m raw + ΔV/V ≈ 10%. The magnetization versus temperature curves are presented in terms of external magnetic field. For M vs H measurements with H//(a,b) plane, i.e. for a magnetic field applied perpendicular to the long axis of the needle, a demagnetization factor of N = ½ was accounted for in order to present M-H data in terms of internal magnetic field H in , according to the usual approximation , where H represents the applied magnetic field.

Results and discussion

Fig. 1(a) shows an SEM image of the as-grown crystal used in this study. The surfaces of the crystal are regular and homogeneous without noticeable flux contamination, and the needle shape presents a length: diameter ratio more than 30:1. The composition calculated from EDS spectrometry is approximately Mn ~0.86 Fe ~4.24 Si ~2.90 , i.e. close to the targeted composition but with possibly a slight excess of Fe. For simplicity only the MnFe 4 Si 3 nominal composition is mentioned hereafter. Fig. 1(b) and (c) show magnetization curves for the single crystal measured along different directions. In the direction perpendicular to the c axis, i.e. perpendicular to the long axis of the needle, the only distinguishable feature is the magnetization step corresponding to the ferromagnetic transition at 323 K taken from the dM/dT maximum in an external field of 1 kOe. This transition temperature is slightly higher than the range 300-310 K reported in former studies on MnFe 4 Si 3 , a feature which can be ascribed to the small deviation in stoichiometry inherent to our flux crystal growth method. As a matter of fact, observing T C slightly higher than 300-310 K is fully compatible with a minor Fe excess (x ≥ 4) in the Mn 5-x Fe x Si 3 phase diagram [6]. While no significant magnetic anisotropy could be distinguished when measuring magnetization along 3 random directions with H⊥c (not shown), the shape of the M(T) curve is strongly modified and the magnetization strongly reduced when performing measurements in H//c direction. This indicates a combination of an easy (a,b) plane with an hard c axis uniaxial magnetic anisotropy, in line with recent single crystal investigation [8]. However in contrast to a former study reporting a 10 K thermal hysteresis [8], our data shows that the shift between heating and cooling M(T) curves is smaller than 0.1 K (both for measurements parallel or perpendicular to the c axis), pointing to the absence of significant thermal hysteresis at the ferromagnetic transition in the present crystal. On the one hand, the presence of thermal hysteresis at a magnetic transition can be regarded as a signature of its first-order nature. On the other hand, absence of hysteresis does not demonstrate one is dealing with a second-order transition, since there are first-order magnetic transitions with very small thermal hysteresis [16].

To get further insight into the ferromagnetic transition order in MnFe 4 Si 3 , we used the method recently proposed by V. Franco et al. which consists in analyzing the temperature and field dependence of the magnetocaloric effect [17,18]. It requires to first determine the magnetocaloric ΔS, as presented in Fig. 2 in the easy plane direction, which is the most relevant for caloric purposes. Given that no significant thermal hysteresis could be detected, the entropy change was calculated based on magnetization versus field curves measured at different temperatures and using the magnetocaloric Maxwell equation [19]. Finite entropy change values are found over a broad temperature range around the Curie temperature. The maximal ΔS are -1.8, -2.9 and -3.7 J kg -1 K -1 for field changes ΔB = 1, 2 and 3 T, respectively. These entropy change values are -as expected-larger than the ~2 Jkg -1 K -1 for ΔB = 2 T reported in polycrystalline materials [5], and in line with 2-2.9 Jkg -1 K -1 reported for single crystals [8,9] or calculated by Monte Carlo simulations [11]. While sizable, these entropy values are nevertheless relatively limited, as the magnetocaloric effect spreads over a large temperature range, mimicking the broadening of M(T) curves at high field. Such a behavior is most often typical of magnetocaloric materials with second order continuous transitions. Then, assuming that the field-dependence of the isothermal entropy change obeys a power law ( ), one calculates the exponent n from the expression: [18]. Several studies have shown that the field dependence of the magnetocaloric effect is intrinsically different depending on the order of the magnetic transition [17,18,[START_REF] Pecharsky | Thermodynamics of the magnetocaloric effect[END_REF]. In particular, it has recently been proposed that n > 2 in the transition region is characteristic of first order magnetic transition [18]. Bottom panel of Fig. 2 ues (not shown). Not only the n values, but also their temperature evolution, ~1 → minimum → ~2, are typical of materials with second order transition [18]. When T ≫ T C , n tends toward 2, the values expected for a conventional paramagnet. The analysis of the field dependence of the ΔS thus demonstrates the second order character of the ferromagnetic transition, in line with the relative broadness of transition at intermediate magnetic fields and the absence of thermal hysteresis on the M(T) curves on this crystal.

Another point of controversy that emerged from past studies concerns the magnetic configuration and magnetic anisotropy. The first powder neutron diffractions studies reported for MnFe 4 Si 3 spin arrangement with moments tilted by ~40°of the c axis [6] or oriented along the c axis [7], in a way similar to the parent Fe 5 Si 3 [2]. On the other hand, more recent studies based on single crystals revealed a spin arrangement with moment in the (a,b) plane from magnetization measurements and at 136°to [1 0 0]-direction from neutron diffraction [8]. Magnetization versus field curves were systematically recorded on our single crystal in the (a,b) plane and along the c axis, a selection of the most representative temperatures are presented in Fig. 3. Only the first quadrant is shown, but the measurements were performed along 5 quadrants and pointed toward a negligibly small magnetic hysteresis. For instance, at 50 K, the coercive field H C is less than 5 Oe and remnant magnetization M rem less than 0.05 Am 2 kg -1 . In agreement with temperature dependence of the magnetization in Fig. 1, M(H) data indicate an (a,b) easy plane with a c hard axis anisotropy. At 50 K, the magnetic anisotropy appears particularly large, as the anisotropy field (H an ) is significantly higher than our applied field of 3 T. A graphical linear extrapolation suggests that H an is of the order of ~6 T. This anisotropy slowly decreases while increasing the temperature until approaching the Curie temperature T C ≈ 323 K where it decreases more rapidly. Around 300 K, the magnetization parallel and perpendicular to the c axis does not coincide, which points toward a certain anisotropy of the magnetization and the presence of non-zero orbital moments in MnFe 4 Si 3 . These observations, in particular the c axis being the hard magnetic axis, are in line with formerly reported magnetization curves on single crystals [8] and at odd with polycrystalline studies [3,6,7]. As the cooling rate during single crystal synthesis is much slower than polycrystalline materials prepared by induction melting [7] or arc-melting with annealing followed by quenching [6], preferential site occupation maybe different in materials with different crystalline forms. To investigate this possibility we prepared a polycrystalline batch of MnFe 4 Si 3 by arc-melting. Then, the sample is hand crushed into particles and part of this powder is mixed with an epoxy binder, shaped into a plate, and oriented in magnetic field with the orientation field perpendicular to the plate. XRD measurements were made on the plate surface. XRD measurements for random and oriented powders show a stark contrast. As a result of magnetic orientation, one observes an almost complete disappearance of the reflections having a c axis component like for instance the [0 0 2] direction; while Bragg peaks having an a or b axis component are strongly enhanced, for instance [2 0 0], [2 1 0] and [3 0 0] directions. These results appear opposite to that obtained for Fe 5 Si 3 and MnFe 4 Si 3 by a similar method, which were indicating an easy axis along the c axis for both alloys [3]. Our powder oriented polycrystalline sample indicates that in polycrystalline materials the (a,b) plane is an easy plane and c is the hard axis, in agreement with single crystal magnetization data. Different crystalline forms can thus not explain the discrepancy in magnetic anisotropy reported for MnFe 4 Si 3 .

The large magnetic anisotropy of MnFe 4 Si 3 turns out to deserve a more quantitative determination, in particular as transition metal-based alloys could be considered as potential candidates as rare-earth free permanent magnets. Usually for an hexagonal system, the first (K 1 ) and second-order (K 2 ) anisotropy constants are considered for the magnetocrystalline anisotropy energy . To determine K 1 and K 2 from magnetization measurements along the hard c axis direction, the Sucksmith and Thompson method has been used [21]. This method is more customarily employed to derive the two magneto-crystalline anisotropy constants of materials with c being the easy magnetic axis. It can nevertheless be applied to the case of an easy magnetization direction perpendicular to the hexagonal axis. In such a case, the slope and intercept of an H/M vs M 2 plot will correspond to , respectively [21]. The applicability of the Sucksmith and Thompson method to various magneto-crystalline anisotropy scheme has been confirmed from modelling studies [22] and used in different materials with a combination of easy plane and hard c axis [23,24]. Beside systematic error, due to the significant relative error on magnetization, the differences between maxima and minima for the intercepts and slopes of H in /M vs (μ 0 M) 2 linear fits are large too, resulting in sizable uncertainties on K 1 and K 2 . Fig. 4 presents the temperature evolution of K 1 and K 2 . K 2 appears negligible compared to the large K 1. While K 1 exhibits negative values, K 2 might experience a change of sign around 150 K. The predominance of K 1 and its negative sign is in line with an easy plane magnetic direction perpendicular to the c axis [START_REF] Buschow | Physics of Magnetism and Magnetic Materials[END_REF]. Neglecting K 2 , our estimate of the anisotropy field (H an ~6 T at T = 50 K) provides us a mean for an alternative estimation of K 1 considering M = M S at H an , it results in K 1 ≈ -½ (H an M S ) ≈ -3.0 MJm -3 . This estimate of K 1 is fully compatible with that obtained by H/M vs M 2 fittings (K 1 ≈ -2.8 MJ m -3 ). The binary parent Fe 5 Si 3 is ferromagnetic with a T C ~380 K, but its magnetic anisotropy could unfortunately not be compared to MnFe 4 Si 3 , as being a metastable phase at room temperature stabilized by rapid solidification or nanostructuration, little single crystal information could be found. On the other hand, ternaries with metalloid substitutions on Si have recently received a great interest as they offer a possibility to reach Curie temperatures higher than those of the binary parents, making them potential candidates for rare-earth free permanent magnet. In tetragonal Fe 5 SiB 2 , between T C ~784 K and 140 K (spin re-orientation transition) the easy magnetic axis is along the c axis with an anisotropy K 1 = 0.25 MJ m -3 , and an easy plane anisotropy below 140 K with only a modest anisotropy (MAE = -0.28 MJ m -3 ) [13,15]. In this latter tetragonal compounds, P for Si substitution favors an easy axis magnetization with magnetic anisotropy K 1 ~0.38 MJ m -3 at room temperature [13,[START_REF] Lamichhane | Canfield[END_REF]. In hexagonal ternary alloys deriving from Fe 5 Si 3 such as MnFe 4 Si 3 , a different configuration is observed with a relatively strong hard c axis anisotropy and an easy plane. Beside the difference in crystal structure, the incorporation of Mn in Fe 5 Si 3 may also play a role in the strengthening of the magnetic anisotropy. Mn atoms carry a significantly larger overall magnetic moment than Fe [6,7], and may also favor a stronger spin-orbit coupling. In addition, spin-polarized calculations pointed out the important role played by Mn d states in the filling of the electronic structure near the Fermi level [7]. Therefore it appears that minor Fe:Mn compositional changes in Mn 5-x Fe x Si 3 alloys can yield major changes in magnetic configuration, which might in turn explain (at least partly) the observed scatter in the literature about the magnetic anisotropy scheme for MnFe 4 Si 3 .

Conclusions

Both the magnetocaloric properties and magnetic anisotropy of MnFe 4 Si 3 single crystal grown by flux method were investigated. By analyzing the field dependence of the magnetocaloric effect, the ferromagnetic transition at T C ~323 K is found to be of second-order, which is fully compatible with the absence of thermal or magnetic hysteresis related to the transition. A relatively strong magnetic anisotropy for a transition-metals alloy is observed in MnFe 4 Si 3 single crystal with the c axis being a hard magnetic direction and an easy plane perpendicular to c. The anisotropy constants are determined over a broad temperature range, leading to a relatively large negative K 1 . In contrast to former reports, X-ray diffraction experiments on field oriented polycrystalline materials confirm the present magnetic anisotropy scheme, indicating that the crystalline form or the single crystal preparation method is not the primary origin for the differences existing in the literature on MnFe 4 Si 3 .

CRediT authorship contribution

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .

 1 Fig. 1. SEM picture of MnFe 4 Si 3 crystal used in this study (a) and magnetization measurements as a function of the temperature in an external field of 1 kOe upon cooling (open symbol) and upon heating (line) and 10 kOe perpendicular to the long axis (b) and parallel (c).

  presents the local field dependence of ΔS in MnFe 4 Si 3 single crystal. Clearly, n remains lower than 2 near T C for ΔB = 2 T, and similar results were obtained for other field change val

Fig. 2 .

 2 Fig. 2. Entropy change as a function of the temperature for MnFe 4 Si 3 crystal in the easy plane direction. Bottom panel, local field dependence of the entropy change at 2 T.

Fig. 3 .

 3 Fig. 3. Magnetization curves for MnFe 4 Si 3 at selected temperatures along and perpendicular to the c axis (Panels a to c) with in inset the determination of the anisotropy constants by the Sucksmith and Thompson method. Panel d, comparison between random (top curve) and oriented (bottom curve) powder XRD with peak experiencing large changes being indexed.

Fig. 4 .

 4 Fig. 4. Temperature dependence of the magneto-crystalline anisotropy parameters for MnFe 4 Si 3 .

  statement H. Yibole: Conceptualization, Investigation. W. Hanggai: Investigation. Z.Q. Ou: Investigation. R. Hamane: Investigation. V. Hardy: Investigation. F. Guillou: Investigation.

Acknowledgments

The work is supported by Inner Mongolia Normal University (grant Nos. 2018YJRC002 and 2018YJRC003) and the Natural Science Foundation of China (grant Nos. 51850410514 for F.G.; 51961033, 11904188 for H.Y.; 11864031 for Z.Q.O.).

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi. org/10.1016/j.jmmm.2020.166597.