ON THE FERMI SURFACE OF BETA BRASS

1966 ◽  
Vol 44 (8) ◽  
pp. 1787-1793 ◽  
Author(s):  
J. -P. Jan
Keyword(s):  
Fermi Surface ◽  
Specific Heat ◽  
Brillouin Zone ◽  
Present Model ◽  
Energy Gap ◽  
Electronic Specific Heat ◽  
Cone Model ◽  
Best Fit ◽  
Structure Calculations ◽  
Good Agreement

Results of de Haas – van Alphen effect measurements on ordered β′-CuZn (50 at.% Zn) provide the area of contact of the Fermi surface with the faces of the second (dodecahedral) Brillouin zone. If the energy gaps at the faces of the first (cubic) Brillouin zone are ignored, a 12-cone model can be worked out. An energy gap of 3.49 eV at the second-zone faces and an effective mass m* = 1.045me, provide the best fit between the 12-cone model, the area of contact, and the measured electronic specific heat. The gap is in good agreement with present band-structure calculations. The first-zone gaps do give rise to de Haas – van Alphen oscillations, but their neglect in the present model should not affect the calculated electronic specific heat appreciably.

The specific heat of metals and alloys at low temperatures

1957 ◽  
Vol 240 (1222) ◽  
pp. 321-332 ◽  
Keyword(s):  
Fermi Surface ◽  
Specific Heat ◽  
Liquid Helium ◽  
Brillouin Zone ◽  
Low Temperatures ◽  
Metals And Alloys ◽  
Thermal Excitation ◽  
Electronic Specific Heat ◽  
Conduction Electrons ◽  
Elastic Shear

The effect of thermal excitation of the conduction electrons on the elastic shear constants is investigated in a metal in which the Fermi surface lies close to the Brillouin-zone boundaries. It is shown that in these circumstances electron-lattice interaction leads to an addi­tional term in the specific heat, linear in the temperature in the liquid-helium range, which, therefore, augments the pure electronic specific heat. The variation in magnitude of this linear term is considered in the α-brasses. It is suggested that this is the physical effect underlying the peculiarities of the ‘electronic’ specific heat of these alloys.

The Fermi surface of beryllium

1964 ◽  
Vol 282 (1391) ◽  
pp. 521-546 ◽  
Keyword(s):  
Band Structure ◽  
Fermi Surface ◽  
Cross Section ◽  
Brillouin Zone ◽  
Field Direction ◽  
Pulsed Magnetic Fields ◽  
Hexagonal Symmetry ◽  
Band Structure Calculations ◽  
Structure Calculations ◽  
Good Agreement

The Fermi surface of beryllium has been determined experimentally by studying the de Haas–van Alphen effect of single crystals in pulsed magnetic fields. The de Haas–van Alphen frequency (proportional to the extremal area of the Fermi surface normal to the field) was measured as a function of field direction. Consideration of the hexagonal symmetry of the Brillouin zone (discussed in the Appendix) shows that only six distinct classes of fre­quency variation with field direction are possible, and these considerations are used to deduce the locations and forms of the various sheets of the Fermi surface. The Fermi surface is found to consist of hole and electron surfaces of equal volume (each containing 0∙162 carrier per atom). The hole surface is somewhat like a coronet, i. e. a ring of six smoothed tetrahedra joined by small necks lying in the central (0001) plane of the first double Brillouin zone, and the electron surface is a set of six roughly ellipsoidal surfaces (cigars) lying on the vertical edges of the second double zone. Detailed shapes and sizes are deduced for the coronet and cigars such that the extremal areas of cross-section are consistent to within 1 % of those obtained from the observed de Haas–van Alphen frequencies. No oscillations of frequency corresponding to the outer (0001) orbit round the coronet were, however, observed; a study of the field dependence of amplitude of the oscillations from the coupled orbit round the cigar shows that this absence can be explained by magnetic breakdown of the {101̄0} band gap. The model described is in good agreement with the predictions of recent band structure calculations, and is consistent with other experimental evidence.

Nodal gap behavior of Bi2Sr2−xLnxCuO6+δ (Ln = La, Eu) investigated by specific heat measurements

2015 ◽  
Vol 29 (25n26) ◽  
pp. 1542014 ◽  
Author(s):  
M. Shimizu ◽  
Y. Moriya ◽  
S. Baar ◽  
N. Momono ◽  
Y. Amakai ◽  
...  
Keyword(s):  
Low Temperature ◽  
Magnetic Fields ◽  
Fermi Surface ◽  
Specific Heat ◽  
Excitation Spectrum ◽  
Cuprate Superconductors ◽  
Electronic Excitation ◽  
Linear Term ◽  
Electronic Specific Heat ◽  
Low Temperature Specific Heat

We performed low-temperature specific heat measurements on slightly underdoped samples of monolayer cuprate superconductors [Formula: see text] (Ln = La, Eu, Ln-Bi2201) under magnetic fields [Formula: see text]. In La-Bi2201, the coefficient [Formula: see text] of [Formula: see text]-linear term in the electronic specific heat [Formula: see text] at [Formula: see text] shows [Formula: see text] dependence, as expected in [Formula: see text] -wave superconductors. In Eu-Bi2201, [Formula: see text] shows almost the same [Formula: see text] dependence as that of La-Bi2201 below [Formula: see text] T, while [Formula: see text] is suppressed above [Formula: see text] T and deviates downward from the [Formula: see text] curve of La-Bi2201. This result suggests the the gap and the electronic excitation spectrum near nodes are modified in Eu-Bi2201 except the region of the Fermi surface in the immediate vicinity of nodes.

Band Structure of Monovalent Metals and Their Alloys

1960 ◽  
Vol 13 (2) ◽  
pp. 238 ◽  
Author(s):  
PG Klemens
Keyword(s):  
Band Structure ◽  
Fermi Surface ◽  
Physical Properties ◽  
Specific Heat ◽  
Thermoelectric Power ◽  
Quantitative Comparison ◽  
Electronic Specific Heat ◽  
Phonon Drag ◽  
Conduction Properties

The consequences of the Bloch theory of the conduction properties of metals can be evaluated only for a band of spherical Fermi surface, isotropic in all respects. Quantitative comparison with observations is thus possible only for the monovalent metals. It appears that even the monovalent metals do not satisfy this requirement, but that their Fermi surface departs significantly from sphericity. The information derived from the various conduction properties and the electronic specific heat is discussed, paying attention to Umklapp processes and phonon drag effects. The thermoelectric power is difficult to interpret. Systematic measurements of the changes of various physical properties on alloying may provide useful information.

scholarly journals An experiment on the mechanism of superconductivity

1946 ◽  
Vol 185 (1001) ◽  
pp. 225-239 ◽  
Keyword(s):  
Specific Heat ◽  
Energy Gap ◽  
Absolute Zero ◽  
Magnetic Data ◽  
Electronic Specific Heat ◽  
Small Energy ◽  
Electronic Term ◽  
Apparent Specific Heat ◽  
Direct Experiment ◽  
Thomson Coefficient

The Thomson coefficient of superconductive lead has been determined by a direct experiment and found to be zero (<4x 10 -9 V/deg.). It has been concluded from this result that the electrons engaged in a superconductive current remain energetically at absolute zero. The apparent electronic specific heat of a superconductor is assumed to be due to an excitation of electrons from the lowest state. The magnetic data suggest that this apparent specific heat is proportional to T 3 . A purely empirical model of the electronic term system for a superconductor has been suggested in which a small energy gap ( ~10 -4 eV) separates the upper limit of the Fermi distribution at absolute zero from a continuum of higher states. The frictionless transport of electrons is supposed to be due to metastable states within the gap in which energy cannot be dissipated. In such a model the number of superconductive electrons at absolute zero has been calculated to be of the order of 10 -3 of the number of atoms. Attention has been drawn to a peculiar similarity between the frictionless transport in superconductors and that in liquid helium II. It has been concluded that the cause for both phenomena may be essentially the same—an aggregation of freely mobile particles of zero thermal energy which follows similar rules irrespective of the nature of the particles involved.

Experimental evidence for the Fermi surface overlap effect in ε-phase Ag—Zn alloys, obtained from low temperature specific heats

1975 ◽  
Vol 343 (1634) ◽  
pp. 375-387 ◽  
Keyword(s):  
Theoretical Model ◽  
Low Temperature ◽  
Specific Heat ◽  
Brillouin Zone ◽  
Band Gaps ◽  
Electronic Specific Heat ◽  
Specific Heats ◽  
Ε Phase ◽  
Specific Heat Coefficient ◽  
Zn Alloys

Measurements of the electronic specific heat coefficient and of the limiting Debye temperature are reported for ten Ag-Zn alloys in the range of the h.e.p. ε-phase. After a correction for the electron-phonon enhancement, the trend of the electronic specific heat coefficient is consistent with a nearly rigid band behaviour, showing a general decrease of the density of states at the Fermi level when the corners of the Brillouin zone are filled. A slight deviation from this trend occurs at electron concentration values exceeding approximately 1.85 5 , in agreement with other measured properties and confirming a theoretical model involving overlaps of electrons across the {00.2} planes of the Brillouin zone. The estimated band gaps are of the order of 2 eV. I t appears that whereas in the dilute rj-phase alloys of zinc with silver the rigid band condition is not valid the opposite is true in the concentrated ε-phase alloys.

scholarly journals The Energy Dependence Of The Effective Interaction In Superconductivity

1966 ◽  
Vol 19 (4) ◽  
pp. 509
Keyword(s):  
Experimental Data ◽  
Integral Equation ◽  
Critical Temperature ◽  
Specific Heat ◽  
Critical Field ◽  
Energy Gap ◽  
Effective Interaction ◽  
Electronic Specific Heat ◽  
First Order ◽  
Energy Dependent

The effective interaction in the BCS model of superconductivity is usually approximated by a constant. We expand the interaction in a power series in <k/llw and treat the energy-dependent terms to first order. This introduces one more parameter in the theory. The gap, which now becomes energy dependent, is obtained by solving an integral equation by iteration. The critical field and specific heat are calculated. The value of 2~(0,0)/kBTe and the jump in the electronic specific heat at the critical temperature Te are now dependent on the parameters of the superconductor. Calculated values for the energy gap and the critical field He agree rather well with the experimental data.

Change of the de Haas – van Alphen frequency of potassium with pressure

1980 ◽  
Vol 58 (3) ◽  
pp. 370-375 ◽  
Author(s):  
Z. Altounian ◽  
W. R. Datars
Keyword(s):  
Band Structure ◽  
Fermi Surface ◽  
Pressure Dependence ◽  
Charge Density Wave ◽  
Energy Gap ◽  
Density Wave ◽  
Surface Anisotropy ◽  
Band Structure Calculations ◽  
Structure Calculations ◽  
Fermi Surface Anisotropy

The pressure dependence of the de Haas – van Alphen frequency in oriented potassium samples has been investigated with pressures up to 4.6 kbar. The change of frequency with pressure is less than that expected from free-electron scaling and the Fermi surface anisotropy increases from 0.13% at zero pressure to 0.47% at 4 kbar. These results are discussed in terms of band structure calculations and the charge density wave (CDW) model of potassium. The CDW energy gap changes with pressure for the CDW model to be applicable.

The band structure of aluminium I. Determination from experimental data

1957 ◽  
Vol 240 (1222) ◽  
pp. 340-353 ◽  
Keyword(s):  
Experimental Data ◽  
Low Temperature ◽  
Band Structure ◽  
Fermi Surface ◽  
Specific Heat ◽  
Electron Energy ◽  
Brillouin Zone ◽  
Free Electron ◽  
The Third ◽  
Low Temperature Specific Heat

The band structure and particularly the shape of the Fermi surface are deduced mainly from the available experimental data on the de Haas-van Alphen and anomalous skin effects, and from the low-temperature specific heat. Since these data are rather incomplete, it is found necessary to use in conjunction with them a theoretical band-structure calcula­tion, which, however, unavoidably contains rough approximations. Except near the surface of.the Brillouin zone, E (k) is found to be very close to the free-electron energy. The first zone is found to contain 3.6 × 10 -3 holes per atom around the zone comers. There is overflow of electrons into the second zone across all the zone faces, and these regions of the Fermi distribution are joined together near the centres of the zone edges; the third zone contains a very small number of electrons.

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