THREE TEMPERATURES FROM THERMODYNAMIC DATA («4)

coo

700

500

40 60

AT o/o C r -

80

FI

tue_{is «U}:

19 (b) REVISED LOW - TEMPERATURE PHASE DIAGRAM OF _{IRON - CHROMIUM SYSTEM. DATA ^ -s- c<‘ Ci S3.116,117)}

,w THERMODYNAMICS PLUS HIGH TEMPERATURE

DATA. ^il5- ll4'

S i

particles in these alloys and was confirmed by TEM. Some further improvement in magnetic properties were demonstrated by Mo (103) and Si (lO^f) additions. Part of the chromium may also be replaced by vanadium without loss of magnetic properties (107)* The introduction of small amounts of Kb and Al to the ternary alloys allow the cobalt

content to be reduced to 1 3 wt% maintaining similar magnetic

properties (1 0 6).

An f.c.c. phase may also be present in these alloys as shown in the vertical sections in Fig 20, however the presence of the Nb and Al also allows cooling in a magnetic field analogous to the heat treatment for Alnico 3«

All the Fe-Cr-Co appear to be ductile in the quenched state in contrast to the Alnicos which are brittle unless transformed partially to the f.c.c. structure which is however difficult to remove afterwards.

1.4* Mechanism forthe formation of shape anisotropic fine particle

structures in permanent magnet a l l o y s ______________

Prior to the work establishing fine particle shape anisotropy theory it was supposed (61) that when heat treated to the optimum permanent magnet state, the Alnico alloys consisted of a structure in a state of "pre-precipitation” with a lattice parameter intermediate

between that of the solid solution and those of the O C + phases

at equilibrium, thus creating a highly heterogeneous structure with a large internal strain. It was further supposed that the internal strain was sufficient to account for the coercivity. The work of Nesbitt (118) showed however that the magnetostriction of some of the Alloys is zero when the coercivity is 32 kA/m or more.

(400 CC

p iooo

FIG.20(g)

VERTICAL

SECTION

OF. -‘Fe-Cr-Co

SYSTEM AT i5v/fc. °/o Co.

1400 oc 1200 1000 oo 600

FIG.20 (b)

VERTICAL

SECTION OF

Fe-C r-C o

N b-A l

SYSTEM

AT I S v / t . ^ C g lv;t.% M b AND

lv;t°/o Al.

are sufficient requirement for coercivities of these levels,

discussion of the kinetics of formation of such particles was made

on the basis of nucleation and growth (

119

51

requirement for good permanent magnets is that the particles should be distributed homogeneously implying the possibility of homogeneous nucleation.

l.^fel# Spinodal Decomposition

Daniel & Lipson (122) interpreted observations, by Bradley (123) in Cu-Ni-Fe alloys, and by Bergers and Snoek (7&) in Fe-Ni-Al alloys of "side-bands" on X-ray diffraction lines, as due to modulat­ ions or a wave-like periodicity of composition within the alloys on

a scale of the order of 5 - 1 5 nm.

The deduction was made by interpretation of the side bands by analogy with radio frequency theory (hence the term "side-band"^) where the superposition (modulation) of a larger wavelength signal on the carrier wave produces side-bands round the normal frequency), and the numerous observations of such structures by electron

microscopy in Fe-Ni-Al and Alnico have already been reviewed, and similar X-ray diffraction observations have also been made in the Cu-Ni-Fe (12^,125,126) and Cu-Ni-Co (12?) systems, and the persistence of the side-bands to the earliest ageing times indicates that this modulated structure exists at the earliest stages of decomposition even in the quenched state.

Hillert (128) first pointed out that there could be a

thermodynamic reason for the formation of modulated structures inside the miscibility gap. He derived an equation which was capable of explaining the main characteristics of the formation and morphology of modulated structures which answered the two criticisms made by

Guinier (129) of the modulation interpretation of side bands; the diffuseness of the side-bands being due to a spectrum of wavelengths and provision of a mechanism of wavelength growth by the theory* Hillert's model was based on compositional variations in one dimension only, and a more flexible three dimensional continuum

model was subsequently developed by Cahn and his associates (130-136)* In Cahn‘s theory, which is a theory of spinodal decomposition inside the miscibility gap,in addition to the free energy of the homogenous phase Cahn introduces other terms, an interfacial energy term, a

term for the effect of coherency strains and included the effects of external fields such as stress and magnetic fields*

If initially only the interfacial energy term is considered then the total free energy '■

= Ac / [ 6 + K f e ) 2]d X ... - (1*33)

Where A is the cross sectional area of the solid, G the free

energy of the homogeneous phase and K I dx J is the interfacial energy

term representing the surface energy differences between planes of atoms of different composition; K is a constant - the gradient energy coefficient.

Free energy is related to the interdiffusion coefficient by

D = M_ d2 G ... (1.34)

Nv dxiJ

where M is the mobility, Hv the number of atoms per unit volume and

x represents displacement. Using equation (1*3^-) and the minimum value of the integral, equation (1*33)» Fick’s second law of diffusion is obtained but with an extra term (other non-linear terms of higher order are ignored)

"be

= D

~ x .... (1.35)

■^t dx Nv dx

If the strain due to composition differences are taken into account then the equation is further modified.