COHERENT MAGNETO-CALORIC EFFECT HEAT ENGINE PROCESS CYCLE 

ABSTRACT
	This paper sets forth a thermodynamic argument that it is theoretically possible to cyclically process a particle of Type I superconductor in H‑T space so that all heat extracted from the high temperature heat reservoir is converted into work, no waste heat being rejected to the low temperature heat reservoir.  Importantly, a heat engine designed to operate according to this cycle would be able to convert the ambient heat of its surroundings into work.  The author's U.S. Patent 4,638,194 sets forth the structural and methodological considerations for carrying out the cycle in the form of a heat engine. 

BACKGROUND OF THE INVENTION
Type I Superconductors
	This paper addresses only "Type I" superconductors, as distinguished from Type II and high temperature superconductors.  Type I superconductors are of a class represented by pure metals, such as for example aluminum, indium, mercury and tin, which become superconductive below a critical temperature which is within a few degrees of absolute zero and below a critical magnetic field which is within a few hundred gauss.  
	Type I superconductors are known to be perfect diamagnets, wherein applied magnetic fields are screened from the specimen interior.  A unique aspect of Type I superconductors is their ability to expel applied magnetic fields simply by lowering the temperature below the critical value (even where the applied magnetic field remains constant).  This phenomenon is known as the Meissner Effect, and occurs when the "range of coherence", >(T), is larger than the magnetic field “penetration depth”, 8(T), which condition distinguishes Type I superconductors from Type II superconductors.  	The internal order of a superconductor is quite different between the normal and superconductive phases, as evidenced by a marked change in specific heat.  The phase transition process is first order, wherein evolution of a latent heat occurs during a phase transition at finite temperature (that is, 0<T<Tc).  According to the BCS Theory, a portion of the conduction electrons condense into a quantum mechanical state having an energy level below that of "normal" conduction electrons, the energy difference being referred to as an "energy gap".  Thus, the observed properties of superconductivity are a consequence of quantum mechanics.  
  	The issue addressed by the present invention is how this quantum mechanical condensation can be incorporated into a process cycle in which a heat input is directly converted into a work output.

Conventional Process Cycles
	The phase transition of a Type I superconductor (hereinafter, simply referred to as a "superconductor") is dependent upon crossing both a threshold maximum applied magnetic field,  referred to as the critical field Hc, and threshold maximum specimen temperature, referred to as the critical temperature, Tc.  In this regard, hereinafter "Tc" refers to the critical temperature in zero magnetic field, and "Hc" refers to the critical magnetic field at absolute zero.  The thermodynamic state of a superconductor is determined by its thermodynamic coordinate in field-temperature (H-T) space.  A phase transition curve (Tuyn curve) defines the boundary between the normal phase and the superconductive phase in H-T space.  The phase transition may be carried out isothermally. In this case, as the magnetic field is changed, the superconductor is in contact with a heat reservoir whereby the heat reservoir supplies or absorbs the latent heat evolved.  Alternatively, the phase transition may be carried out adiabatically.  In this case, as the magnetic field is changed, the superconductor is thermally isolated from its surroundings whereby the latent heat evolution cools or heats the specimen, a process known as the "magneto-caloric effect".   Accordingly, there are two possible process cycles: 1) a process cycle involving isothermal phase transitions, and 2) a process cycle involving adiabatic phase transitions.
		
	1. The Isothermal Phase Transition (IPT) Process Cycle:
	The concept of utilizing a superconductor as the working medium in an IPT process cycle which converts an influx of heat into an electrical work output using a series of isothermal phase transitions was forwarded by Chester1.  Chester proposed a structural configuration in which a wire is tightly wound around a cylindrical armature made of superconductive material (Type I or Type II).  In operation, the armature is alternatively cycled isothermally through the normal and superconductive phases by variation in the applied magnetic field.  Variation in the magnetic susceptibility of the armature in response to changes in its phase induces electromotive force in the winding, resulting in an electrical energy output.  	
	A structure for carrying out an IPT process cycle for providing mechanical energy instead of electrical energy, was forwarded by Keefe2, which is schematically depicted by Figure 1.  In Process A, an armature in the normal phase and at a starting temperature T1 is moved toward a magnet; no work is expended to accomplish this movement since the armature is essentially non‑magnetic.  In Process B, the armature temperature is lowered to T2 (where T2 is arbitrarily set to equal T2 of the CAPT process cycle, discussed hereinbelow, for comparative purposes) so as to cause the phase of the armature to change from normal to superconductive; this phase change is accompanied by the Meissner Effect.  In Process C, the Meissner Effect expels the magnetic field from the interior of the armature, thereby creating magneto‑dynamic potential energy which is converted into mechanical work as the armature is moved away from the magnet.  In Process D, the armature temperature is raised to the starting temperature, T1, thereby causing the phase of the armature to change from superconductive to normal, which thereupon completes the IPT process cycle.
Thermodynamics of the Isothermal Phase Transition (IPT) Process Cycle
	The thermodynamics of the IPT process cycle can be understood with reference to Figure 2, which depicts in H‑T space the thermodynamic coordinates of the armature during the IPT process cycle.  For exemplary purposes, tin is the selected armature material, and the starting thermodynamic coordinates are chosen as T1 = .6Tc and H1 = .64Hc.  Calculations hereinafter in this section are based upon the usual thermodynamical relationships for Type I superconductors3 and the published temperature dependent specific heat for tin4. 
	The armature has a cross-section much larger than >(T).  The magnetic field is supplied by any constant source, such as a permanent magnet.  A high temperature heat reservoir is required having a temperature higher than T1.  A low temperature heat reservoir is required having a temperature at least as low as T2. 
	Step 1. An isothermal magnetization followed by an isomagnetic cooling:
	Path A to B:  Beginning at Point A of the IPT process cycle in which the armature is in the superconductive phase at thermodynamic coordinate (T1, H1) and in thermal contact with the high temperature heat reservoir, the applied field is raised slightly to H1+)H by movement of the armature toward the magnet.  As a result, the armature isothermally crosses the Tuyn curve and undergoes a first order phase transition into the normal phase with an accompanying latent heat absorption of LH1 being delivered from the high temperature heat reservoir, where, in the present example, LH1 = 3,433 ergs/cm3.  The magnetic field is further raised to H2 without work being performed on the armature since it is presently non‑magnetic, where H2 = .965Hc.  The armature is now at Point B of the IPT process cycle, in the normal phase at thermodynamic coordinate (T1, H2). 
	Path B to C:  The armature is caused to disengage thermal contact with the high temperature heat reservoir and to engage thermal contact with the low temperature heat reservoir in order to cool the armature to T2, where T2 = .186Tc.  The amount of heat extracted is given by:
Q_1=int FROM T_1 TO T_2  C_n dT CDOT V

where Cn is the normal phase specific heat, and where, in the present example, Q1 = 3,433 ergs/cm3.  The armature is now at Point C of the IPT process cycle, in the normal phase at thermodynamic coordinate (T2, H2).	
	Step 2. An isothermal demagnetization followed by an isomagnetic heating:
	Path C to D:  With the armature still in thermal contact with the low temperature heat reservoir, the applied magnetic field is decreased to H2‑)H by movement of the armature away from the magnet. As a result, the armature isothermally crosses the Tuyn curve and undergoes a first order phase transion into the superconductive phase with an accompanying latent heat evolution of LH2 being delivered to the low temperature heat reservoir, where, for the present example, LH2 = 499 ergs/cm3.  The magnetic field is further decreased to H1 with work being performed, given by: 
W=((H_2^2-H_1^2)/8 pi) CDOT V

where, in the present example, W = 1,945 ergs/cm3.  The armature is now at Point D of the IPT process cycle, in the superconductive phase at thermodynamic coordinate (T2, H1).
	Path D to A:  The armature is now caused to disengage thermal contact with the low temperature heat reservoir and to engage thermal contact with the high temperature heat reservoir in order to heat the armature to T1.  The amount of heat delivered is given by:  
Q_2 = INT FROM T_2 TO T_1 C_s dT CDOT V

where Cs is the superconductive phase specific heat, and where, in the present example, Q2 = 2,454 ergs/cm3.  
	The armature is now again at Point A of the IPT process cycle, in the superconductive phase at the original thermodynamic coordinate (T1, H1).
	Thermodynamic Analysis of the IPT Process Cycle:
	1)  The armature has been cooled by extraction of heat, Q1, which was delivered to the low temperature heat reservoir.
	2)  Waste heat, LH2, has been rejected to the low temperature heat reservoir.
	3)  Net heat input is given by  Qin = (LH1-LH2)+(Q2-Q1).
	4)  Total work output is given by W.
	5)  The efficiency is given by [1-(heat rejected)/(heat absorbed)]x100:

eta =[1-(Q_1+LH_1)/(Q_2+LH_2)]x100

which in the present example of a tin armature is thirty‑three percent.  Chester1 reports the efficiency may be as high as forty‑four percent for the IPT process cycle when the armature is made of Niobium.
	
	2. The Adiabatic Phase Transition (APT) Process Cycle:
	Adiabatic phase transitions at finite temperature result in the superconductor under study either self‑heating (during an adiabatic demagnetization when the phase transition is in the direction of normal to superconductive), or self‑cooling (during an adiabatic magnetization when the phase transition is in the direction of superconductive to normal).  These adiabatic phase transition processes, known as the magneto‑caloric effect, have been extensively investigated, typified by Yaqub5 and Dolecek6.    
	An Adiabatic Phase Transition (APT) process cycle involves an adiabatic magnetization process path followed by an adiabatic demagnetization process path.  The adiabatic magnetization process path involves a work input, Win, and the adiabatic demagnetization process path involves a work output, Wout.  Thermodynamics of the Adiabatic Phase Transition (APT) Process Cycle
	An APT process cycle is depicted in H-T space by Figure 3.  For exemplary purposes, tin is the selected armature material, and the starting thermodynamic coordinates are chosen as T1 = .6Tc and H1 = .64Hc.  Calculations hereinafter in this section are based upon the usual thermodynamical relationships for Type I superconductors3 and the published temperature specific heat for tin4. 
	The armature has a cross-section much larger than >(T).  The magnetic field is supplied by any constant source, such as a permanent magnet.  A high temperature heat reservoir is present having a temperature higher than T1, and a low temperature heat reservoir is present having a temperature at least as low as T2N (under ideal conditions, the heat reservoirs are obviated). 
	Step 1. An adiabatic magnetization:
	Path A to B:  Beginning at Point A of the APT process cycle in which the armature is in the superconductive phase at thermodynamic coordinate (T1, H1) and in thermal isolation, the applied magnetic field is raised in increments of )H by movement of the armature toward the magnet.  The increases in magnetic field strength cause the armature to enter an intermediate state of varying mixed phase along the Tuyn curve.
	Each )H increment involves an isentropic process characterized by:
LH cdot DELTA V =(int from T_a to T_b C_n dT)cdot V_n + (int from T_a to T_b C_s dT) cdot V_s

wherein the phase volumes are defined by:
V=(V_s - DELTA V)+(V_n + DELTA V)

and wherein magnetodynamic work is performed given by:
W=((H^2-(H- DELTA H)^2)/8pi)cdot V_s

	The armature is now at Point B in the normal phase at thermodynamic coordinate (T2N, H2N), wherein T2N= .339Tc and H2N= .885Hc.  The amount of magnetodynamic work performed was W = Win= 695 ergs/cc.
	Step 2. An adiabatic demagnetization:
	Path B to A:  The applied magnetic field is now lowered in increments of )H.  Again, an intermediate state of mixed phase ensues wherein the process is isentropic.  Path B to A retraces Path A to B, and the above equations apply where now W = Wout  and where now the phase volumes are given by: 
V=(V_s + DELTA V)+(V_n - DELTA V)

	The armature is now again at point A in the superconductive phase at the thermodynamic coordinate (T1, H1).  The amount of magnetodynamic work performed was W = Wout = 695 ergs/cc.
	Thermodynamic Analysis of the APT Process Cycle:
	1)  The armature has been cooled from T1 to T2N and heated from T2N to T1 by latent heat evolutions.
	2) Ideally, no waste heat has been rejected to the low temperature heat reservoir.
	3)  There is no heat input or output.
	4)  The work input is equal to the work output.
	5)  The cycle is reversible.  
	Ideally, there is no heat exchange with the environment during the APT process cycle, and Win = Wout.  Observed reversibility of the process paths arises because an intermediate state, which transpires during each magneto‑caloric process, yields the presence of continually varying amounts of superconductive phase all during each APT process cycle path, which, as Dolecek reports6 is a linear function only of H.  
	Clearly, therefore, if a net work output derived from a net heat input is to be achieved in a closed process cycle involving a series of adiabatic phase transitions, then somehow precaution must be taken to ensure that the intermediate state will not appear during the magneto‑caloric processes.  How to achieve this is the subject of the present invention, hereinafter recounted.

THE PRESENT INVENTION
	It is very well established that superconductivity is a non‑local phenomenon.  According to the Ginzburg‑Landau (G-L) Theory7 there is a spatial uniformity of the order parameter of the superelectrons over a (temperature dependent) "range of coherence", >(T), which typically has a length of 10‑4 centimeters.  A. B. Pippard8 forwarded an hypothesis that if there is a finite spatial distance over which the superconducting order parameter is uniform, then it is quite conceivable that a small enough superconductive particle, one having a cross‑section on the order of the length of the range of coherence, cannot experience an intermediate state during its phase transition, but must be at all times either wholly superconductive or wholly normal in phase.  Support for this view is found in the experiments by Lutes and Maxwell9 which demonstrate the impossibility of appearance of the intermediate state during the phase transition of very thin whiskers of tin, the sizable demagnetization factor of which, combined with a transverse orientation of the applied magnetic field, should otherwise have resulted in an observable intermediate state (larger diameter whiskers did exhibit an intermediate state, as expected).  Accordingly, when a superconductive armature, having a cross‑section on the order of the length of the range of coherence, undergoes an adiabatic phase transition, the resulting magneto‑caloric effect process must proceed without the appearance of an intermediate state.  A process cycle based upon a series of such phase transitions will be hereinafter referred to as a Coherent Adiabatic Phase Transition process cycle.
Thermodynamics of the Coherent Adiabatic Phase Transition (CAPT) Process Cycle
	The thermodynamics of the CAPT process cycle will be described with reference to Figure 4, which depicts in H‑T space the thermodynamic coordinates of an armature during the CAPT process cycle.  Tin is the selected armature material, and the armature has a cross‑section, d, where d=>(T), wherein >(T) is considered essentially constant between T1 and T2.  Further, as in the conventional IPT and APT process cycles recounted hereinabove, the starting thermodynamic coordinates are T1 = .6Tc and H1 = .64Hc.  Calculations hereinafter in this section are based upon the usual thermodynamical relationships for Type I superconductors3 and the published temperature dependent specific heat for tin4. 
	The armature has a cross-section equal to >(T).  The magnetic field is supplied by any constant source, such as a permanent magnet.  A high temperature heat reservoir is required having a temperature higher than T1.  A low temperature heat reservoir is not required. 
	Step 1. An adiabatic magnetization accompanied by a magneto‑caloric cooling:
	Path A to B:  Beginning at Point A of the CAPT process cycle in which the armature is in the superconductive phase at thermodynamic coordinate (T1, H1), the magnetic field is increased to H1+)H by moving the armature slightly closer to the magnet.  This results in the phase of the superconductor changing from superconductive to normal, first evidenced by a change in magnetization from diamagnetic to non‑magnetic.  The armature is now at Point B of the CAPT process cycle at thermodynamic coordinate (T1, H1+)H).
	Path B to C:  The latent heat of the phase transition at T1, LH1, evolves, causing the temperature of the armature to drop during the ensuing magneto‑caloric process.  Attendantly, the armature is moved closer to the magnet so that always the armature remains on the normal side of the Tuyn Curve.  The final temperature and magnetic field arrived at is T2 = .186Tc and H2 = .965Hc, where T2 is defined by:
LH_1 = INT FROM T_1 TO T_2 C_n dT CDOT V

which, in the present example, is 3,433 ergs/cm3, and where the magneto‑dynamic work to move the armature is zero (since the armature is non-magnetic).  The armature is now at Point C in the CAPT process cycle, in the normal phase at thermodynamic coordinate (T2, H2).
	Step 2. An adiabatic demagnetization accompanied by a magneto‑caloric heating:
	Path C to D:  The magnetic field is decreased to H2‑)H by moving the armature slightly away from the magnet.  This results in the phase of the superconductor changing from normal to superconductive, first evidenced by a change in magnetization from non‑magnetic to diamagnetic by operation of the Meissner Effect.  The armature is now at Point D in the CAPT process cycle at thermodynamic coordinate (T2, H2‑)H).  
	Path D to E:  The latent heat of the phase transition at T2, LH2, evolves, causing the temperature of the armature to increase during the ensuing magneto‑caloric process.  Attendantly, the armature is moved away from the magnet so that always the armature remains on the superconductive side of the Tuyn Curve.  The final temperature and magnetic field arrived at is T3 = .407Tc and H3 = .834Hc, where T3 is defined by:
LH_2 = INT FROM T_2 TO T_3 C_s dT CDOT V

which, in the present example, is 499 ergs/cm3 and where the magneto‑dynamic work output from moving the armature is given by:
W_1=((H_2^2-H_3^2)/8) pi CDOT V

which, in the present example, is 878.5 ergs/cm3.     
	The armature is now at Point E in the CAPT process cycle, in the superconductive phase at thermodynamic coordinate (T3, H3).
	Step 3. A demagnetization followed by a heating:
	Path E to F:  The armature is moved away from the magnet so that the magnetic field decreases from H3 to H1.  The magneto‑dynamic work output derived from moving the armature is given by:
W_2=((H_3^2-H_1^2)/8 pi) CDOT V 

which, in the present example, is 1,066.5 ergs/cm3.
	Path F to A:  The temperature of the armature is allowed to increase from T3 to T1 by causing the armature to thermally contact an external high temperature heat reservoir.  The amount of heat required to achieve T1 is defined by:
Q = INT FROM T_3 TO T_1 C_s dT CDOT V

which, in the present example, is 1,945 ergs/cm3.  
	The armature is now again at point A in the superconductive phase, at thermodynamic coordinate (T1, H1).  The amount of magnetodynamic work performed was (W' + W'') = 1,945 ergs/cm3, and the net heat input was Q = 1,945 ergs/cm3.
	Thermodynamic Analysis of the CAPT Cycle:
	1) The armature has been cooled to the low temperature coordinate of the cycle, T2, by a magneto‑caloric process exhibiting during an adiabatic magnetization of the armature.  Note that T2 of the CAPT process cycle is considerably below T2N of the APT process cycle.
	2) No heat has been rejected at the low temperature coordinate of the CAPT process cycle because this heat, LH2, has been used in a magneto‑caloric process exhibiting during an adiabatic magneto‑caloric demagnetization of the armature.  A low temperature heat reservoir is obviated; however, a high temperature heat reservoir (at or above T1) is requisite.
	3) The total heat input, Q, is, in the present example, 1,945 ergs/cm3 and occurs only during Step 3.
	4) The total work output, W1 + W2, is, in the present example, 1,945 ergs/cm3 and occurs during Steps 2 and 3. 
	5) The efficiency of the CAPT process cycle is given by [1 ‑ (heat rejected)/(heat absorbed)] x 100, which, in the present example (and for any CAPT process cycle), is one‑hundred percent.  This result can be achieved only under the following CAPT process cycle conditions:  a) the armature material selected is a Type I superconductor, preferably having >(T)>58(T); b) the cross‑section of the armature does not exceed the length of the range of coherence; and c) each phase transition is performed adiabatically.  Because only a Type I superconductor is used, there is present a positive interphase boundary surface energy; accordingly, the Meissner Effect is operable at the phase transition from the normal to the superconductive phase at (T2, H2).  Because the cross‑section of the armature does not exceed the length of the range of coherence, each phase transition must affect the entire armature at once; accordingly, no intermediate state is possible during the magneto‑caloric processes.  Because each phase transition is performed adiabatically, there is no thermal coupling between the armature and a heat reservoir; accordingly, a magneto‑caloric process can be expected at each adiabatic phase transition.  

Further Considerations on the Coherent Adiabatic Phase Transition Cycle
	1. Armature Dimension and Its Affect on the Latent Heat Evolution:
	While the order parameter of the superelectrons may tend to be spatially uniform on the scale of the range of coherence, >(T), it can be uniformly smaller in the presence of a magnetic field.  Indeed, when the cross‑section of a superconductor is less than %58(T), the order parameter goes to zero at the thermodynamic critical field, and a second order phase transition is observed.10  D. H. Douglass11,12  has considered the consequence of diminishing thickness of a superconductive thin film on the energy gap.  In a first paper11 Douglass reports that, according to the G‑L Theory, as long as the thin film thickness is larger than about ten times the magnetic field penetration depth, 8(T), no significant diminution in energy gap will be observed at the phase transition.  However, in a second paper12 Douglass reports that this prediction is modified by an experiment involving thin films of aluminum, where no significant diminution in the energy gap at the phase transition was observed for thin films having a thickness larger than 58(T).  Thus, for an armature having a cross‑section on the order of 58(T) or more, the phase transition is first order with the latent heat evolution being expected to equal that of a bulk dimensioned armature (that is, an armature where d»>(T)).  Therefore, a superconductor utilized as the armature in the CAPT process cycle should have >(T)$d>58(T).  Superconductive materials exceeding this requirement are aluminum, where  >/8=32, and indium, where >/8=6.875.  Tin marginally meets this requirement, where >/8=4.5.  In this paper, the simplifying assumption has been made that tin meets this requirement.
	In order that the intermediate state be absent from the magneto‑caloric processes, the cross‑section of the particle must not exceed >(T).  For armature cross‑sections exceeding >(T), an intermediate state will appear until the last nucleus of cross‑section >(T) remains, whereupon the phase transition will be sudden.  For armatures having a cross‑section larger than about 5>(T), the CAPT process cycle reduces, for all practical purposes, to the APT process cycle.  
	The size dependency effects discussed above may be understood by reference to Figure 5, which shows the effect on the low temperature coordinate, T2, attained by the CAPT process cycle adiabatic magnetization at T1 due to both increasing and decreasing cross‑section of the tin armature.  It will be seen that very small variations from d=>(T) have a pronounced effect on the observed low temperature coordinate T2.  
	2. Armature Dimension and Its Affect on the Specific Heat:
	Tsuboi and Suzuki13,14 as well as Rao, Garland and Tanner15 have considered the effect of decreasing specimen size on the heat capacity of the superconductive phase.  These papers report that for tin particles having a cross‑section on the order of length of the range of coherence, the heat capacity remains very nearly identical with that of bulk dimensioned specimens.
	3. Armature Dimension and Its Affect on Hysteresis of the Phase Transition:
	The origin of hysteresis of the superconductive phase transition caused by supercooling in bulk‑sized specimens has been considered by Faber.16  The effect and origin of hysteresis of the phase transition of superconducting thin films has been theoretically and experimentally investigated by Caswell.10  Pippard8 has considered the origin of supercooling phenomena in superconductive particles having a cross‑section on the order of the length of the range of coherence.  Feder and McLachlan17 have experimentally investigated superheating and supercooling of the phase transition of single spheres of tin and indium.  There is nothing to suggest in these papers that the predicted maxima for supercooling and superheating would be any different if the phase transition process were to be carried out either isothermally or adiabatically.  
	Figure 6 shows the effect of critical magnetic field hysteresis on T2 of the CAPT process cycle caused by increasingly higher superheating magnetic fields at T1.  It will be seen that the value of T2 is quite hysteresis sensitive; nonetheless, this sensitivity should not be interpreted as suggesting that practical implementation of the CAPT process cycle is unlikely.  In practice, G‑L Theory based calculations of the maximum values for superheating and supercooling critical fields are not ordinarily observed owing to the fact that any nucleation center anywhere on the surface of the particle could cause it to slip out of the metastable state which characterizes supercooling and superheating phenomena.18  
	4. Practical Considerations:
	Other CAPT process cycles are possible, a discussion of which is unnecessary for the purpose of this paper, which is merely to lay a theoretical foundation.  The other CAPT process cycles are elaborated in Patent 4,628,194.
	The net work output can be in any form: mechanical (ie., a motor), electrical (ie., a generator), or as a heat mover.  In the latter two cases, work is producible without moving parts.
	Although the work produced per each cycle is small, the number of cycles possible per second is quite high.  Accordingly, the power production per cubic foot is estimated to be about 50 horsepower.
	From an engineering point of view, owing to the very small size of the armature necessary to ensure absence of the intermediate state during the magneto‑caloric processes transpiring at each of the adiabatic phase transitions, commercialization of the CAPT process cycle would necessitate utilization of a composite armature, composed of an ensemble of particles, each mechanically linked, but each thermally isolated.19

CITATIONS

1.  Thermodynamics of a Superconducting Energy Converter, M. Chester, J. App. Phy. 33, 643  (1962).

2. A Thermodynamic Comparison between the Magneto-Mechanically and Magneto-Calorically Induced Superconductive Phase Transitions in a Type I Superconductor Culminating in a Proposal for a New Type of Superconductive Motor, a Thesis, P. Keefe, University of Detroit, Detroit, MI (1974).

3.  Superfluids, Vol. I, F. London, Dover Publications, Inc., New York (1961).

4.  Low-Temperature Specific Heat of Indium and Tin, C. Bryant, P. Keesom, Phy. Rev. 123, 491 (1961).

5.  Cooling by Adiabatic Magnetization of Superconductors, M. Yaqub, Cryogenics, December 1960, 101.

6.  Adiabatic Magnetization of a Superconducting Sphere, R. Dolecek, Phy. Rev. 96, 25 (1954).

7.  On the Macroscopic Theory of Superconductivity, V.L. Ginzburg, JETP 2, 589 (1956).  

8.  Magnetic Hysteresis in Superconducting Colloids, A.B. Pippard, Phil. Mag. 43, 273 (1952).

9.  Superconducting Transitions in Tin Whiskers, O. Lutes, E. Maxwell, Phy. Rev. 97, 1718 (1955).

10. Magnetic Hysteresis in Superconducting Thin Films, H. Caswell, J. App. Phy. 36, 80 (1965).

11. Magnetic Field Dependence of the Superconducting Energy Gap, D. Douglass, Phy. Rev. Lett. 6, 346 (1961).

12. Direct Experimental Measurement of the Magnetic Field Dependence of the Superconducting Energy Gap of Aluminum, D. Douglass, Phy. Rev. Lett. 7, 14 (1961).

13. Specific Heat of Superconducting Fine Particles of Tin I. Fluctuations in Zero Magnetic Field,  T.  Tsuboi, T. Suzuki, J. Phy. Soc. Japan 42, 437 (1977).

14. Specific Heat of Superconducting Fine Particles of Tin II. Fluctuations under Magnetic Field, T. Tsuboi, T. Suzuki, J. Phy. Soc. Japan 43, 444 (1977).

15. Thermodynamic Transition of Small Superconducting Particles, N. Rao, J. Garland, D. Tanner, Phy. Rev. B, 29, 1214 (1984).

16. The Phase Transition in Superconductors, T. Faber, Proc. Roy. Soc. A214, 405 (1952).

17. Superheating and Supercooling in Single Spheres of Tin, Indium, and Gold-Plated Indium, J. Feder, S. McLachlan, Phy. Rev. 177, 763 (1969).
18. Ibid. 

19. U.S. Patent 4,638,194, P. Keefe, (1987).