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Article
Publication date: 8 February 2011

Z. Moser, P. Fima, K. Bukat, J. Sitek, J. Pstruś, W. Gąsior, M. Kościelski and T. Gancarz

The purpose of this paper is to investigate the influence of In additions on the wetting properties of the Sn2.86Ag0.40Cu (in wt%) eutectic‐based alloys, on a copper…

Abstract

Purpose

The purpose of this paper is to investigate the influence of In additions on the wetting properties of the Sn2.86Ag0.40Cu (in wt%) eutectic‐based alloys, on a copper substrate, in the presence of a flux. The main goal was to find correlations between the results of the wetting balance (WB) and the sessile drop (SD) method, in relation to the contact angles.

Design/methodology/approach

The WB method was applied for the wetting measurements, at 250°C, in an air atmosphere and in the presence of a flux. The SD measurements were conducted at the same temperature, in the presence of the same flux, but in an Ar atmosphere, while the maximum bubble pressure (MBP) and dilatometric measurements were conducted in an Ar+H2 atmosphere. The density data from the dilatometric method were used for the determination of the surface tension by means of MBP, and the WB method was used to determine the surface and interfacial tension. Next, the surface tension data from these two methods were compared. The WB data were used to calculate the contact angles and the obtained indirect data were compared with the results of the direct SD measurements of the contact angle.

Findings

A higher In content in the alloy resulted in a lower contact angle on the copper, and the WB results agreed well with the results of the SD experiments. It was confirmed that, in liquid In‐Sn and the alloys containing In and Sn (Ag‐In‐Sn, Sn‐Ag‐Cu‐In, Sn‐Zn‐In), the improvement of the wettability was indicated only by the increase of the contact angle with the increasing In content.

Research limitations/implications

Further studies are necessary for the confirmation of practical application, but they should be directed to the soldering of high indium alloys on printed circuit boards, with different finishes and qualities of the solder joint performance.

Practical implications

Taking into account the contact angle data from the WB and SD methods, the best results of the SAC‐In alloy on copper were obtained for the alloy of the highest In content. It was found that the contact angles from SD after 4 s were higher (non‐equilibrium conditions) than the values calculated from WB after 3 s. In contrast, the contact angles from SD after 10 min (equilibrium conditions) were lower than those from WB after 3 s. The comparison suggests that the contact angles from WB are situated within the data from SD, showing the same lowering tendency with the increasing content of In, and they may be well accepted for practical purposes. On the other hand, the sample of the solder in the SD method, after a prolonged time – in order to get the equilibrium contact angle – may be used to study the interfacial phenomena with the Cu substrate. The differential thermal analysis results indicate that the melting temperature decreases with increasing tin concentration. Taking into account the results of this study and the available literature data, alloys containing 8‐10 wt% of In can be recommended for practical application.

Originality/value

The WB and SD methods were used for the contact angle determination of a wide range of solder compositions, in the same temperature and flux conditions. Also, the surface tensions for these alloys were determined with the use of two independent methods: the MBP and the WB methods. The results obtained made it possible to draw conclusions regarding the correlation between the output of different methods and the conditions in which a comparison of the results can be made. It is supposed that these observations apply to many other alloy systems.

Details

Soldering & Surface Mount Technology, vol. 23 no. 1
Type: Research Article
ISSN: 0954-0911

Keywords

Book part
Publication date: 15 December 1998

Andrew Battye, Mike Smith and Yanling Xiang

This paper outlines a steady state multi-modal equilibrium transportation model which contains elastic demands and deterministic route-choices. The model may readily be…

Abstract

This paper outlines a steady state multi-modal equilibrium transportation model which contains elastic demands and deterministic route-choices. The model may readily be extended to include some stochastic route-choice or mode choice. Capacity constraints and queueing delays are permitted; and signal green-times and prices are explicitly included. The paper shows that, under natural linearity and monotonicity conditions, for fixed control parameters the set of equilibria is the intersection of convex sets. Using this result the paper outlines a method of designing appropriate values for these control parameters; taking account of travellers' choices by supposing that the network is in equilibrium. The method may be applied to non-linear monotone problems by linearising about a current point. An outline justification of the method is given; a rigorous proof of convergence is as yet missing. Thus the method must now be regarded as a heuristic.

Details

Mathematics in Transport Planning and Control
Type: Book
ISBN: 978-0-08-043430-8

Book part
Publication date: 16 December 2017

Gabriel Brondino and Andres Lazzarini

The present essay re-examines the scope of Sraffa’s critique of Marshall’s supply curves that the former developed in his 1925 and 1926 articles showing that neoclassical…

Abstract

The present essay re-examines the scope of Sraffa’s critique of Marshall’s supply curves that the former developed in his 1925 and 1926 articles showing that neoclassical supply curves derived from non-proportional returns are not robust both in the short and in the long run. After examining what a short-run and a long-run equilibrium means both for the original Sraffa’s articles and for Marshall’s pioneer contribution, the chapter discusses the common procedure in conventional economics to introduce the limitations to the growth of the firm. The argument of the chapter will be based on the 1920s articles as well as on the ‘Lectures on Advanced Theory of Value’ delivered in 1928–1931 by Sraffa at Cambridge University, now publicly available online by the Wren library, Trinity College, Cambridge. For short-run analysis, it must be assumed that the number of firms is fixed. This assumption entails serious problems with regards to the notions of competition and competitive behaviour. For long-run analysis, the sources of increasing costs are problems of management and control. However, this idea is untenable both on logical and empirical grounds. We argue that contemporary mainstream microeconomic treatment of costs and supply in the context of perfect competition still presents several problems. These problems, rather than being superficial, lie at the root of the supply and demand approach of value and distribution.

Details

Including a Symposium on New Directions in Sraffa Scholarship
Type: Book
ISBN: 978-1-78714-539-9

Keywords

Book part
Publication date: 7 November 2011

Gary Mongiovi

In the 2010 volume of Research in Political Economy, Alan Freeman put forth the intriguing and original hypothesis that “capitalism's inner laws express themselves in …

Abstract

In the 2010 volume of Research in Political Economy, Alan Freeman put forth the intriguing and original hypothesis that “capitalism's inner laws express themselves in … different ways during booms and during crises” (Freeman, 2010, p. 217). When the business cycle is in an upswing, Freeman argues, the tensions and contradictions that will eventually interrupt the process of capital accumulation are camouflaged by the commodity form, and so appear as natural laws of motion. With the onset of a crisis, however, these tensions erupt into overt class conflict and so become transparent. The open political struggle represents an opportunity for transformative progressive action. While Freeman's development of this hypothesis is in many respects illuminating, his analysis is marred by a gratuitous methodological argument that has little bearing on what he wants to say about crises. His remarks on method would be merely distracting if they were accurate. But they are in fact misleading and therefore stand in the way of productive discussion of the essay's many useful observations.

Details

Revitalizing Marxist Theory for Today's Capitalism
Type: Book
ISBN: 978-1-78052-255-5

Article
Publication date: 1 October 1952

F.E. Osborne

AT temperatures commonly attained in the reaction of liquid propellents at operative pressures in rocket combustion chambers, the significant gaseous end products can be…

Abstract

AT temperatures commonly attained in the reaction of liquid propellents at operative pressures in rocket combustion chambers, the significant gaseous end products can be shown to consist at chemical equilibrium of some or all of the following types: H2O, CO2, N2, CO, H2, O2, OH, NO, H, O, N and (rarely) C‐gaseous. The concentrations of these constituents are dependent, for a given propellent combination, upon the temperature (and to a less extent the pressure) conditions under which the reaction proceeds to equilibrium. Thus at temperatures below 2,500°K., the products H2O, CO2, N2 alone are of significance for the case of oxygen balance, whilst to these are added O2 for the oxygen excess case, and CO and H2 for oxygen deficit. The other products are formed by dissociation of these, and their concentrations increase sharply as the temperature rises above some 2,700°K.

Details

Aircraft Engineering and Aerospace Technology, vol. 24 no. 10
Type: Research Article
ISSN: 0002-2667

Book part
Publication date: 7 November 2011

Alan Freeman

Gary Mongiovi accurately cites my thesis, presented in Freeman (2010a) (henceforth referred to as Positivist Marxism and abbreviated to PM), that “capitalism's inner laws…

Abstract

Gary Mongiovi accurately cites my thesis, presented in Freeman (2010a) (henceforth referred to as Positivist Marxism and abbreviated to PM), that “capitalism's inner laws express themselves in … different ways during booms and during crises” and that “When the business cycle is in an upswing … the tensions and contradictions that will eventually interrupt the process of capital accumulation are camouflaged by the commodity form, and so appear as natural laws of motion.” He also expresses general agreement with this thesis, but complains that the way I present it is “marred by a gratuitous methodological argument” which is “misleading and therefore stand[s] in the way of productive discussion.” The methodological argument in question is that no theory based on the method of static equilibrium can provide an explanation of endogenous capitalist crisis; this is the main issue I address in this response. PM applies this argument in order to examine a theoretical current that dominates Western, academic, Marxism. This current interprets Marx's theory as a variant of general equilibrium. In this response I refer to it as simultaneist Marxism (SM).

Details

Revitalizing Marxist Theory for Today's Capitalism
Type: Book
ISBN: 978-1-78052-255-5

Book part
Publication date: 13 December 2013

Federico Echenique and Ivana Komunjer

In this article we design an econometric test for monotone comparative statics (MCS) often found in models with multiple equilibria. Our test exploits the observable…

Abstract

In this article we design an econometric test for monotone comparative statics (MCS) often found in models with multiple equilibria. Our test exploits the observable implications of the MCS prediction: that the extreme (high and low) conditiona l quantiles of the dependent variable increase monotonically with the explanatory variable. The main contribution of the article is to derive a likelihood-ratio test, which to the best of our knowledge is the first econometric test of MCS proposed in the literature. The test is an asymptotic “chi-bar squared” test for order restrictions on intermediate conditional quantiles. The key features of our approach are: (1) we do not need to estimate the underlying nonparametric model relating the dependent and explanatory variables to the latent disturbances; (2) we make few assumptions on the cardinality, location, or probabilities over equilibria. In particular, one can implement our test without assuming an equilibrium selection rule.

Details

Structural Econometric Models
Type: Book
ISBN: 978-1-78350-052-9

Keywords

Article
Publication date: 1 May 1986

Brian J. Loasby

Style and Purpose “It's all in Marshall”. There is more truth in that once‐familiar claim than there would be in a similar claim about any other economist; yet as…

Abstract

Style and Purpose “It's all in Marshall”. There is more truth in that once‐familiar claim than there would be in a similar claim about any other economist; yet as Samuelson (1967, p. 25) rightly observed, what is in Marshall cannot be revealed by the reading of Marshall alone. What one sees is very largely a reflection of one's own viewpoint; often it is only after thinking about a specific issue that one realises that Marshall had thought about it too, and had set down his ideas in his usual unemphatic way, as if they were already common property. His manner is very different from that of Hicks, who always explains what he is doing and why; neither in the Principles (1961) nor in Industry and Trade (1919) does Marshall attempt to distinguish his own contributions, though frequently acknowledging those of others; and his clear views on how economists should proceed, though not suppressed, are not allowed to mark out a distinctively Marshallian programme. As a consequence, though he gained a great reputation, his ideas have had very little influence.

Details

Journal of Economic Studies, vol. 13 no. 5
Type: Research Article
ISSN: 0144-3585

Article
Publication date: 1 August 2001

Jaroslav Mackerle

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography…

1639

Abstract

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

Details

Engineering Computations, vol. 18 no. 5/6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 January 1991

Stephen Shmanske

An examination of imperfect price discrimination, modelled as a linear combination of perfect price discrimination and uniform pricing, is used to analyze the impact of…

1236

Abstract

An examination of imperfect price discrimination, modelled as a linear combination of perfect price discrimination and uniform pricing, is used to analyze the impact of imperfect discrimination on firm size and product diversity. Additionally, claims that perfect price discrimination leads to the welfare optimum are shown to be generally false.

Details

Studies in Economics and Finance, vol. 14 no. 1
Type: Research Article
ISSN: 1086-7376

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