Localization of Critical Temperatures by Means of the Chemical Potential Measurement

Matlak, M.; Pietruszka, Mariusz; Rówiński, E.

doi:10.1002/1521-396x(200104)184:2<335::aid-pssa335>3.0.co;2-s

Cited by 10 publications

(12 citation statements)

References 20 publications

(17 reference statements)

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“…From the formulae (50, (51) we can just obtain the information about the sign of ð@T ð1, 2Þ C =@pÞ N , ð@T ð1, 2Þ C =@N Þ p to see wether T ð1, 2Þ C increases (decreases) with the change of p and N. In the latter case, the situation is much more difficult because the measurement of the chemical potential of the electronic subsystem of solids is difficult. One can use, for this purpose, the work function method [62][63][64][65] or the method of the galvanic cell [66,67]. For continuous phase transitions, the formulae (50) and (51) cannot be applied.…”

Section: Discussionmentioning

confidence: 99%

“…This latter possibility has already succesfully been applied in the case of the high-T C superconductor YBa 2 Cu 3 O 7À to indicate for the hole-type superconductivity mechanism in this material (see [62,63] for details). This example, together with the results of the papers [64][65][66][67][68][69][70][71][72], evidently show how important is the measurement of the chemical potential of the electronic subsystem of solids. Note 1.…”

Section: Discussionmentioning

confidence: 99%

“…A special attention should, however, be paid to the method, which allows measurement of the temperature dependence of the chemical potential of the electronic subsystem of solids by using the work function method [62][63][64][65], or the method of the galvanic cell [66,67], which works well for metallic samples. Another interesting method is the contact electrode method, which uses the chemical potential induced phase transition in the electron gas of the metallic contact electrode attached to the investigated sample [68][69][70][71][72].…”

Section: Introductionmentioning

confidence: 99%

“…Another interesting method is the contact electrode method, which uses the chemical potential induced phase transition in the electron gas of the metallic contact electrode attached to the investigated sample [68][69][70][71][72]. The papers [62][63][64][65][66][67][68][69][70][71][72] experimentally demonstrate that the temperature behaviour of the chemical potential can successfully be applied to detect phase transitions in solids, and therefore, it is necessary to include it into the calculations presented in this article. It is important to stress that several of the derived relations can successfully be used to foresee whether the transition or characteristic temperature of a given material sample will increase or decrease under applied pressure or under doping (injection), without necessity to produce new samples.…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamical relations at characteristic points

Matlak

2008

Phase Transitions

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We define the characteristic temperature T C of a material by using the behaviour of the specific heat in the vicinity of this temperature: C p,N ðT Þ ¼ fð1 À ðT=T C Þ, p, N Þ for T 5 T C and C p,N ðT Þ ¼ gððT=T C Þ À 1, p, N Þ for T 4 T C where p is the external pressure and N is the number of particles. The characteristic temperature T C ¼ T C ( p, N ) can e.g. be identified with the transition temperature in the case of continuous phase transitions or with one of the two characteristic temperatures T ð1Þ C (on heating) and T ð2Þ C (on cooling) in the case of discontinuous phase transitions. Using the idea of the characteristic temperature, we present a new method on how to calculate the Gibbs potential G ¼ G (T, p, N ) in the vicinity of the characteristic temperature, without it being a necessity to know the explicite expressions for f and g. This general and uniform approach allows to derive many thermodynamical relations connecting measurable quantities at the characterisic point as e.g. Clausius-Clapeyron equation and its analogs, valid for discontinuous phase transitions and 15 relations valid for both continuous and discontinuous phase transitions, 6 of them are new. As a special case of these latter relations, we find six relations valid for continuous phase transitions (Ehrenfest equation and its analogs). The derived relations result exclusively from the definition of the characteristic point and are independent from the underlying microscopical mechanism leading to phase transitions (as e.g. solid-liquid, liquid-vapour, magnetic, ferroelectric, structural and superconducting transitions) and therefore, they are generally valid. These relations can be very important for material science. Using some of them it is possible to predict (without performing additional experiments) whether the transition or characteristic temperature T C of a given material sample will increase or decrease under doping (injection) or applied pressure. Similar 24 thermodynamical relations can also be found with ease for systems described by the Helmholtz potential F ¼ F(T,V, N ).

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Thermodynamical relations at characteristic points

Matlak

2008

Phase Transitions

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“…also Refs. [11][12][13][14][15][16][17][18][19][20][21][22][23]). For superconducting systems (see Ref.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamical Cross-Relations for Superconductors at the Critical Point

Grabiec

Matlak

2002

phys. stat. sol. (b)

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We investigate superconducting systems using the phenomenological Landau theory of second order phase transitions, including into the considerations the critical behaviour of the chemical potential. We derive in this way a variety of new thermodynamical relations at the critical point. Twelve basic relations connect critical jumps of different thermodynamical quantities (specific heat, chemical potential derivatives with respect to temperature, pressure (volume) and number of particles, volume (pressure) derivatives with respect to temperature and pressure (volume)) with the critical temperature or its derivatives with respect to the number of particles or pressure (volume). These relations allow to find plenty of cross-relations between different quantities at the critical point. The derived formulae can be practically used in many cases to find such thermodynamical quantities at the critical point, which are extremely difficult to measure, under the assumption that the other ones are already known. We additionally perform a test of two derived relations by using a two-band microscopic model describing superconducting systems. We calculate the specific heat, order parameter, and chemical potential as functions of temperature to show that the tested relations are very well fulfilled.

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Thermodynamical Cross‐Relations for Superconductors at the Critical Point

Grabiec¹,

Matlak²

2002

phys. stat. sol. (b)

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We investigate superconducting systems with the use of the phenomenological Landau's theory of second order phase transitions, including into the considerations the critical behaviour of the chemical potential. We derive in this way a variety of new thermodynamical relations at the critical point. Twelve basic relations connect critical jumps of different thermodynamical quantites (specific heat, chemical potential derivatives with respect to temperature, pressure (volume) and number of particles, volume (pressure) derivatives with respect to temperature and pressure (volume)) with the critical temperature or its derivatives with respect to the number of particles or pressure (volume). These relations allow to find plenty of cross-relations between different quantities at the critical point. The derived formulae can practically be used in many cases to find such thermodynamical quantities at the critical point which are extremely difficult to measure under the assumption that the other ones are already known. We additionally perform a test of the two derived relations by using two-band microscopic model, describing superconducting systems. We calculate the specific heat, order parameter and chemical potential as functions of temperature to show that the tested relations are very well fulfilled.

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Localization of Critical Temperatures by Means of the Chemical Potential Measurement

Cited by 10 publications

References 20 publications

Thermodynamical relations at characteristic points

Thermodynamical relations at characteristic points

Thermodynamical Cross-Relations for Superconductors at the Critical Point

Thermodynamical Cross‐Relations for Superconductors at the Critical Point

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