scholarly journals Collective electron ferromagnetism III. Nickel and nickel-copper alloys

1949 ◽  
Vol 195 (1043) ◽  
pp. 434-463 ◽  
Keyword(s):  
Low Temperature ◽  
Temperature Variation ◽  
Curie Point ◽  
Copper Alloys ◽  
Experimental Results ◽  
General Character ◽  
Energy Bands ◽  
Nickel Copper ◽  
Wide Range ◽  
Electronic Heat

The collective electron treatment of ferromagnetism (Stoner 1938 a , 1939) is applied to the magnetic and thermal properties of nickel and nickel-copper alloys. In § 1 a brief description is given of the theoretical background, together with the necessary extensions of the basic treatment, in particular so as to cover the effects of the overlap of the electronic d and s energy bands. With simplifying assumptions regarding the effect of alloying on the electronic structure, and using a limited range of observational data, estimates are obtained of the variation of the specifying parameters, band width and interchange interaction, for nickel-copper alloys, over a wide range of composition (§ 2). A discussion is given in § 3 of the dependence of the electron distribution on temperature. Calculations are carried out of the variation of the number of holes in the d band, due to the temperature redistribution of electrons between the bands (transfer effect). Other temperature effects, such as the variation of the specifying parameters due to thermal expansion, are briefly discussed, though they are not included in the main treatment (§§ 1 and 4). The treatment is applied to the temperature variation of susceptibility above the Curie point (§4). For nickel-rich alloys satisfactory agreement is obtained with experimental results (figures 10, 11 and 12). For copper-rich alloys the observed high-temperature increase of susceptibility is well explained (figure 13), but no interpretation can be given of the observed low-temperature variation. It is suggested that this may be due to inhomogeneities in composition. A discussion is given in § 5 of the bearing of the treatment on the electronic heat at high temperatures. Comparison is made with the relevant experimental results for nickel above the Curie point. Application is also made to the low-temperature electronic heat of nickel-copper alloys (§5). The general character of the variation of the electronic heat with composition is covered satisfactorily in the nickel-rich regions, but in the copper-rich regions discrepancies occur, similar to those for the low-temperature susceptibility (§4). In §6 a brief account is given of the results of a preliminary analysis of the magnetic properties of nickel alloys other than those with copper.

Overlapping energy bands and the theory of collective electron ferromagnetism

1953 ◽  
Vol 49 (1) ◽  
pp. 115-129 ◽  
Author(s):  
A. B. Lidiard
Keyword(s):  
Curie Point ◽  
Energy Band ◽  
Spontaneous Magnetization ◽  
Copper Alloys ◽  
Implicit Assumption ◽  
Energy Bands ◽  
Unknown Parameters ◽  
Nickel Copper ◽  
Predicted Values ◽  
A Minor

ABSTRACTThe theory of collective electron ferromagnetism given by Stoner applies to a system of electrons in a single energy band; for iron, cobalt and nickel this is identified with the band of states derived from atomic 3d functions. To bring in the generally assumed overlapping of the 3d band by the wide 4s band in these metals, the theory has been extended to take account of the transfer of electrons from 3d to 4s states with change of temperature. A previous calculation of this transfer effect must be regarded as inadequate, for the part played by the exchange energy in determining the distribution of electrons between the two sets of states was omitted. The general equations are derived in § 2 and used as a basis for discussion of the properties of nickel-copper alloys at absolute zero in § 3. In §§4 and 5 numerical results are presented which show the effect of the overlapping 4s band on the magnetic properties of a system such as nickel both above and below its Curie point. Comparison with the measured paramagnetic susceptibility of pure nickel above the Curie point strongly suggests that for this metal the overlapping 4s band has only a minor influence, although in principle the effect could be very large (cf. Fig. 4). This result is not unambiguous, however, because values thus inferred for the two unknown parameters lead to inaccurate predictions below the Curie point. First, the predicted values for the spontaneous magnetization are too small. Secondly, the theory demands that the nickel-copper alloys should only be ferromagnetic below a copper content of about 20 %, whereas experimentally the limit is known to be about 60 %. In conclusion, it is suggested that the implicit assumption of Stoner's theory that the exchange integrals between all pairs of 3d states are equal to one another is a more serious restriction on the theory than the consideration of only a single energy band.

Collective electron ferromagnetism: a generalization of the treatment and an analysis of experimental results

1953 ◽  
Vol 216 (1124) ◽  
pp. 103-117 ◽  
Keyword(s):  
Temperature Variation ◽  
Temperature Change ◽  
Spontaneous Magnetization ◽  
Copper Alloys ◽  
Experimental Results ◽  
Fourth Power ◽  
Large Temperature ◽  
Electron Theory ◽  
Nickel Cobalt ◽  
Nickel Copper

The collective electron theory of ferromagnetism is extended to include in the expression for the energy associated with the magnetization a term in the fourth power of the magnetization. A second adjustable parameter, similar to the kθ'/ϵ 0 of the Stoner treatment, is thus introduced. Detailed comparison with experiment of a number of properties of nickel, nickel-cobalt and nickel-copper alloys, is carried out. A high degree of co-ordination of the properties of nickel is obtained by a suitable choice of the two parameters, which are thereby determined within fairly close limits. The temperature variation of electronic specific heat and spontaneous magnetization of nickel is quantitatively covered, as is the magnetocaloric temperature change accompanying changes in external field. The spontaneous magnetization, temperature curves of cubic cobalt and four nickel-copper alloys are similarly covered, and a simple interpretation can be given of the adherence to the law of corresponding states of nickel-cobalt alloys and the deviation therefrom of the nickel-copper alloys. The model accounts qualitatively for the field-magnetization isothermals and for the variation of the magnetocaloric temperature change with magnetization. A detailed examination shows that the differences between theory and observation, where they exist, are due to effects not covered by the collective electron theory. The main discrepancies can be accounted for on the assumption that a small fraction of the volume of the material is made up of groups of atoms of varying size with a Langevin distribution of their magnetic axes. These groups may be called small domains. The problem is complicated by the fact that the field values computed theoretically are critically dependent on the parameters, of which a sufficiently close estimate cannot be made. However, for particular values of both kθ'/ϵ 0 and A a good fit with experiment over a wide temperature range is obtained when it is assumed that the domains are of sizes varying from 10 3 atoms upwards, the largest proportion of domains being of 10 4 to 10 5 atoms, and the volume occupied by such domains probably being much less than 10% of the total volume of material. It is shown that the hitherto unexplained large temperature variation, derived from the experimental results, in the value of —1/ σ (∂ E /∂ σ ) T corresponding to the Weiss molecular field coefficient, is an almost direct consequence of the basic physical premises of the collective electron treatment.

The low-temperature specific heats of some nickel-based iron and copper alloys

1968 ◽  
Vol 303 (1474) ◽  
pp. 339-354 ◽  
Keyword(s):  
Low Temperature ◽  
Spin Wave ◽  
Copper Alloys ◽  
General Character ◽  
Specific Heats ◽  
Computer Methods ◽  
The Third ◽  
Cu Alloys ◽  
Nickel Copper ◽  
Order Of Magnitude

Measurements have been made of the specific heats over the range 1.2 to 4.2°K of a series of face-centred cubic alloys of nickel with iron (nine alloys) and nickel with copper (seven alloys). The low-temperature specific heat of the ferromagnetic alloys may be represented by the equation C = γT + βT 3 + αT 3/2 , the successive terms corresponding to the electronic, lattice and spin-wave contributions. If the third term is appreciable the standard plot of C/T against T 2 will show a concavity towards the T 2 axis. Such plots are given for all the alloys. The best values of γ, β , and α , and the standard errors, are obtained by the analytical and computer methods previously described. The results are presented in two tables, and particular features of them and comparisons with other results are shown graphically. (For the paramagnetic nickel—copper alloys the third term does not apply, and a fairly satis­factory fit is obtained by replacing it by a constant, ϵ .) Although the results for the variation of γ with composition are believed to be more reliable than those previously given, the general character of the curves is similar. The values of β for Ni and the Ni-rich alloys agree closely with those deduced from the elastic constants, but over the whole range of composi­tion, especially for the Ni-Cu alloys, there is more scatter than was expected. This is tenta­tively attributed to residual inhomogeneities or clustering effects. For the Ni-Fe alloys a spin-wave contribution is definitely indicated of the same order of magnitude as that deduced by other methods. For the Ni-Cu alloys the presence of a spin-wave contribution is less certain, partly owing to the greater scatter in the values for β .

The reaction of 2-butyne with hydrogen catalyzed by nickel, copper, cobalt, iron, and nickel–copper alloys

1970 ◽  
Vol 48 (13) ◽  
pp. 2075-2089 ◽  
Author(s):  
R. S. Mann ◽  
C. P. Khulbe
Keyword(s):  
Copper Alloy ◽  
Hydrogen Pressure ◽  
Copper Alloys ◽  
Kcal Mole ◽  
Temperature Dependent ◽  
Nickel Cobalt ◽  
Nickel Copper ◽  
Wide Range ◽  
Cobalt Iron ◽  
Initial Hydrogen Pressure

The reaction between hydrogen and 2-butyne over unsupported nickel, copper, cobalt, iron, and nickel–copper alloys has been investigated in a static constant volume system between 30 and 250 °C for a wide range of reactant ratios. The reaction over metals and their alloys is simple hydrogenation, the early stages being principally a selective production of cis-2-butene with small yields of polymers. The order of reaction with respect to hydrogen was one and independent of temperature. While the order of reaction over cobalt and copper with respect to 2-butyne was zero, it was slightly negative and temperature dependent for nickel and nickel–copper alloys. The selectivity was independent of initial hydrogen pressure for nickel, cobalt, copper and most of the nickel–copper alloys. The overall activation energy for nickel, cobalt, and copper were 9.1, 6.6, 33.5 kcal/mole, respectively. Selectivity and extent of polymerization increased with increasing amounts of copper in the nickel–copper alloy.

The spontaneous magnetization of nickel + copper alloys

1958 ◽  
Vol 248 (1253) ◽  
pp. 145-152 ◽  
Keyword(s):  
Curie Temperature ◽  
Marked Decrease ◽  
Spontaneous Magnetization ◽  
Magnetic Moments ◽  
Copper Alloys ◽  
Nickel Copper ◽  
Wide Range ◽  
Magnetic Techniques ◽  
Good Agreement

The spontaneous magnetization (σ 0 , T ) of a ferromagnetic may be deduced exclusively from the determination of magnetic isothermals, or in conjunction with magnetocaloric measurements. Values of σ 0, T of a nickel + copper alloy containing 30·75 at. % of copper have been obtained near its Curie temperature using both of these techniques and are shown to be in good agreement. Measurements of spontaneous magnetization and Curie temperature ( θ f ) of nickel + copper alloys containing up to 54·11 at. % of copper using the purely magnetic techniques are described. These measurements were performed over a temperature range from θ f down to 80 °K in all cases, and to 23 °K in the cases of alloys containing over 30 at. % of copper. The magnetic moments per atom ( p B ) of the alloys, which are deduced from the measurements, vary linearly over a wide range of composition, extrapolating to p B = 0 at 53 at. % of copper. This value is in good agreement with that obtained by Meyer & Wolff (1958), and contrary to that based on the familiar measurements of Alder (1916). The reduced magnetization-temperature curves of some of the alloys are given and these show a continuous marked decrease in fullness with increasing copper content.

scholarly journals The Angular Distribution of Atoms Sputtered from Monocrystalline Gold

1967 ◽  
Vol 20 (3) ◽  
pp. 283 ◽  
Author(s):  
GE Chapman ◽  
JC Kelly
Keyword(s):  
Angular Distribution ◽  
Single Crystals ◽  
Temperature Variation ◽  
Experimental Results ◽  
Wide Range ◽  
Argon Ions ◽  
Metal Single Crystals ◽  
Theory And Experiment

The angular distribution of atoms sputtered from metal single crystals has been used to study atom ejection processes. By analysing this distribution into the sum of a Gaussian and a cosine contribution it is shown that the isotropic background can be removed and considerably improved agreement obtained between theory and experiment. This is applied to the temperature variation of the width of Wehner spots. New experimental results are presented for gold sputtered by 10 keY argon ions over a wide range of temperatures.

On the nominal transverse shear strain to characterize the severity of creasing

TAPPI Journal ◽  
2018 ◽  
Vol 17 (04) ◽  
pp. 231-240
Author(s):  
Douglas Coffin ◽  
Joel Panek
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Elastic Limit ◽  
Experimental Results ◽  
Transverse Shear Strain ◽  
Maximum Strain ◽  
Machine Direction ◽  
Engineering Approach ◽  
Wide Range ◽  
Analytic Expression

A transverse shear strain was utilized to characterize the severity of creasing for a wide range of tooling configurations. An analytic expression of transverse shear strain, which accounts for tooling geometry, correlated well with relative crease strength and springback as determined from 90° fold tests. The experimental results show a minimum strain (elastic limit) that needs to be exceeded for the relative crease strength to be reduced. The theory predicts a maximum achievable transverse shear strain, which is further limited if the tooling clearance is negative. The elastic limit and maximum strain thus describe the range of interest for effective creasing. In this range, cross direction (CD)-creased samples were more sensitive to creasing than machine direction (MD)-creased samples, but the differences were reduced as the shear strain approached the maximum. The presented development provides the foundation for a quantitative engineering approach to creasing and folding operations.

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