Buschow K.H.J. (Ed.) Concise Encyclopedia of Magnetic and Superconducting Materials

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magnetic pigment is between 4 nm and 8 nm, depend-

ing on tape manufacturer and media type (this could

represent a signal loss of something less than 1 dB).

The coverage is sufﬁcient to protect the media sur-

faces against premature failure, although durability

increased with coverage.

Other forms of wear, if they occur, have negligible

effects on signal, although polymer interaction with

water vapor may have an effect on adhesion, abra-

sion, and fatigue. Our examinations of heads produce

some circumstantial evidence that Cl from degener-

ation of Cl-containing polymeric binders may under

some circumstances produce corrosion. In general,

high humidity reduces wear and increases durability

of particulate media, but adversely affects the head

and reduces signal through this route.

6. Metal Evaporated Media

ME media relies on a complete boundary lubricant

ﬁlm, about 2–3 nm thick, and operates under pseudo-

classical boundary lubrication conditions. The sur-

face of the evaporated metal ﬁlm is oxidized and

sometimes carbon coated to give additional protec-

tion in the case of a momentary breakdown of the

boundary lubricant. This provides a low surface en-

ergy contact which can survive occasional head/me-

dia asperity interaction, but the lubricant must be

capable of self-healing any breach if high wear is not

to ensue.

The lubricants used are usually perﬂuoropolyethers

with suitable functional end groups to anchor to

either a carbon overlayer or a metal oxide. Ideally

there should also be a semi-mobile component in the

lubricant layer to satisfy the self-healing requirement.

These lubricants are chosen for their good afﬁnity to

the surface, good viscosity range, low volatility, and

good chemical and thermal stability. More tradition-

al metal boundary or antiwear additives, such as

triaryl and trialkyl phosphites, may provide improved

tribological performance, but probably do not satisfy

anticorrosion requirements.

The asperity contacts on the tape will be mainly

elastic, with a small plastic component. This takes

into account the effect of the substrate-generated

texture included to prevent adhesion of the very

smooth surfaces. If lubricant breakdown does occur

then this can lead to transfer of material from media

to head. The roughening of the head can then lead to

abrasive grooving of the media and the possibility

of errors due to material removal. In the absence of

lubricant breakdown, the dominant wear mechanism,

however, is one due to fatigue.

Hempstock and Sullivan (1998) have studied the

wear of commercial ME Hi-8 video tape and corre-

lated this to signal performance. Single and double

magnetic layer structures were studied in this inves-

tigation and signal degradation and error growth

were monitored as functions of running time. Scan-

ning electron microscope (SEM) examination of the

surfaces clearly identiﬁed the wear mechanism. In

the initial stages of wear little change occurred at the

surface and few wear particles were produced. As

contact continued, delaminative removal of material

was observed in the media surface and consequent

micron-sized wear particles appeared. The increase in

delaminative craters on the surface correlated exactly

to an increase in measured signal errors. The thick-

ness of laminar particles removed from the tape

was less than the thickness on the ME layer, except

when the process proceeded until catastrophic fati-

gue, cracking, and delaminative failure of the ﬁlm

occurred at the ME substrate interface.

The single layered structures proved to be the most

durable. Here, the failure of the media corresponds to

the depletion of lubricant in the area of the scar. In

the case of the dual layer media both error growth

and ultimate failure occurred at an earlier stage (cor-

responding, for example, to 6–8 hours pause motion

in helical scan mode, compared to 10–12 hours for

the single layer tape). XPS analysis of dual layer me-

dia showed that substantial delamination and ulti-

mate failure of the media both occurred before the

lubricant ﬁlm showed significant signs of failure.

In both types of ME media the mechanism of wear

is classic Suh delamination (Jahanmir and Suh 1977),

where subsurface changes and fatigue lead to the

production of an immediate subsurface discontinuity

which acts to concentrate fatigue cracks. This then

leads to delaminative removal of material. In the case

of the single layer ﬁlm, gradual breakdown of the

lubricant ﬁlm allows more head–tape contact to oc-

cur and this will greatly accelerate fatigue-induced

crack formation and propagation, since under these

circumstances more energy will be dissipated in the

ME layer, and less in the lubricant ﬁlm. In the case of

the dual layered ﬁlms a discontinuity already exists at

the boundary between the two layers and this con-

centrates subsurface stresses and provides a location

for crack formation and propagation. Thus delami-

nation takes place at an earlier stage in this media

before substantial amounts of lubricant layer have

been removed from the surface. Thus although dual

layers may have magnetic advantages, such media are

inherently less durable than single layers.

Tape drive components and tape magnetic side/

back side contacts must also be taken into account.

In general, the wear mechanisms outlined above are

also evident in these situations with similar conse-

quences for signal loss.

7. Read Write Heads: Wear

7.1 General Wear

There are many types of recording heads for tape

systems, including ferrite, metal in gap and sandwich

640

Magnetic Reco rding: Flexible Media, Tribology

heads for helical scan, and inductive write/MR read

based heads for linear recording formats. All are

similar in that they are multicomponent and are con-

structed from materials which are hard. With current

thin ﬁlm head constructions the allowable wear is

very small, being perhaps less than a micron over the

life of the component. The tribology of these hard

materials is still at a very immature stage. The ma-

terials generally have high elastic modulus, high

fracture strength, high chemical stability, and high

thermal stability, but because of the ionic and/or

covalent nature of their bonds, they are also brittle.

The high chemical stability means that interfacial

adhesion and the shear strength of the junction are

low compared with bulk cohesive forces, hence ad-

hesive transfer from head to tape does not occur.

The surface roughnesses and particle sizes associ-

ated with current tape formats ensure that conven-

tional two-body abrasive wear cannot take place. The

materials are not ideally brittle, however, and plastic

ﬂow and hence abrasion can occur with large third-

body particles. Polishing (a form of adhesive at the

nanoscale), however, can take place. Here, the hard-

ness of the tape particles need to fulﬁl the Richardson

(1967) criteria, but can be relatively low. Conven-

tional polishing normally occurs when small hard

particles imbedded into an elastic backing medium

are passed at high speed and low load over the sur-

face to be treated. This is exactly the situation which

occurs in head/ particulate media contact. Polishing

has been described by Suh (1986) in terms of micro-

delamination of the wearing surface. The soft mag-

netic materials, for example NiFe, CoZrTa alloys,

used in MIG and sandwich heads, and the MR

elements and shields in linear recording heads, are of

similar hardness to the ceramics and exhibit similar

wear mechanisms.

Reaves and Sullivan (1992) showed that this form

of wear was the dominant mechanism in ferrite video

heads, Harrison et al. (1999) and Bijker et al. (2000)

have shown that it is also the dominant mechanism in

terms of volume of material removed in sandwich

heads and linear recording heads, respectively. In

none of the cases, however, was it the most important

mechanism in terms of signal degradation. In the

case of the ferrite head, signal degradation was

caused by gap damage due to third bodies becoming

entrapped between head and tape, and in the case of

the sandwich and linear heads was caused by pole

tip recession. This mechanism is operative in glass,

ceramics, and ferrites. With ferrite single crystals,

however, there is the additional effect of crystal

orientation. It is far more pronounced in some iron

oxide or metal particle media than it is in chromium

dioxide media and this may be explained in terms of

plastic deformation in the ferrite crystal. This effect

must be taken into consideration when, for magnetic

reasons, the two halves of a head are aligned in dif-

ferent directions. In this case the different wear rates

lead to pole piece height differences which result in

spacing loss.

Although abrasive wear should not be possible in

these systems, relatively deep scratches are observed

on heads and these are obviously caused by three-

body abrasion, possibly as a result of agglomerate

debris from the tape becoming entrapped between

head and media. Such scratches not only change the

surface topography, which may effect spacing, but

may also destroy MR elements. If the loading in

particulate tape becomes too high and the complex

modulus falls, more such third bodies will be formed.

Third-body abrasion will be even more important in

GMR heads, when the damage could have cata-

strophic consequences for head performance.

7.2 Differential Wear and Pole Tip Recession

In terms of signal loss, differential wear is of greater

importance than absolute wear, since this introduces

spacing between media and the active areas of the

head. When using a combination of different mate-

rials in the recording head, it is very difﬁcult to ex-

actly match wear rates. Since there is poor correlation

between static measurements of elastic/plastic prop-

erties and wear over a range of different materials,

model experiments must be devised, but even then it

is not certain that the modes of wear measured in

these experiments are appropriate in practice. The

choice of materials is a compromise and the best in-

dividual material may not be suitable for use in a

given head application because of mismatch in wear

properties. This is the reason that a number of two-

phase ceramics are used in head applications. Even

with careful choice of materials, differential wear still

occurs and is a major cause of spacing loss.

Harrison et al. (1999) have studied pole tip reces-

sion in sandwich video heads, where the recession is

caused by differential wear. The soft magnetic metal

sandwich is worn at a greater rate than the sur-

rounding ceramic. In many circumstances this results

in hollowing out the metal to a depth where contact

with the media cannot occur. In these heads the soft

magnetic materials and ceramic body have compara-

ble wear rates, measured by simulation tests. Harri-

son et al. (1999) found that the major material

removal mechanism for soft magnetic materials

and ceramics was nanoadhesion (polishing), but this

could not account for the recession. This was the re-

sult of two separate effects: fatigue wear of the ce-

ramics, which resulted in the plucking out of laminar

crystallite-sized particles from the surface, and the

entrapment of these particles in the soft magnetic

sandwich region, which produced erosive wear. The

ensuing pole tip recession was then a function of

the relative fracture toughness rather than hardness.

The production of fatigue ‘‘pull outs’’ from the cera-

mic is probably increased for multiphase ceramics.

641

Magnetic Reco rding: Flexible Media, Tribology

The pole tip recession observed in these heads was

greatest for ME media because the material removed

by nanoadhesion was far less than that removed in

the case of the aggressive MP media. Thus smoother,

more compliant ME tape allowed more fatigue-

induced particles to form than in the case of MP

tape, where the surface was being removed at a

greater rate, thus removing fatigue cracks.

This form of wear has also been shown to be re-

sponsible for pole tip recession in other systems.

Hempstock et al. (2000) have shown similar mecha-

nisms in different linear recording systems. In these

systems it is found that pole tip recession is most

pronounced under conditions of high humidity. The

effect of humidity on ceramics is a very complex

problem. In many ceramics there is a tribo-chemical

reaction at the wearing surface which generally pro-

duces hydroxides. This effect can either reduce wear

by providing an easily sheared, low surface energy

ﬁlm at the surface, or, if the ﬁlm is removed too rap-

idly due to the wearing conditions, can increase wear.

If chemical interaction does not occur, mechanical

process due to water molecule ingress may be re-

sponsible for wear. This effect is well known in the

pitting of metals. Sintered ceramic materials are

always porous. Water under hydrostatic pressure

can enhance crack formation and propagation within

individual ceramic grains within the surface.

The crack depth relates to the region of maximum

stress and may be calculated from Hertzian analysis

of the subsurface stresses within the ceramic surface.

This can lead to two possible effects: (i) increased

rates of removal of the surface due to microfatigue

which enhances polishing wear, and (ii) fatigue-in-

duced granular delamination which can lead to the

formation of ‘‘third body’’ abrasive particles. Those

particles are then fragmented and result in pole tip

recession. In the case of the most popular ceramic

used in linear heads, that is Al

/TiC, delaminative

wear occurs preferentially at the TiC phase. In the

cases cited above simple wear ranking experiments

would not be expected to predict the differential wear

observed in the ﬁnal product.

8. Coatings

Most differential wear problems could be reduced

either by using more abrasive tapes and suffering

higher overall wear or by using coatings on the head.

The ﬁrst of these solutions is not acceptable in mod-

ern media. The second is the only viable solution and

much effort needs to be expended in the development

of an ultrathin surface coating. This is particularly

true if GMR sensors are to be used in future gener-

ation heads, where coatings will be necessary, not

only for wear protection, but also as an essential

corrosion barrier. The most likely candidates for such

a ﬁlm are diamond-like carbon (DLC) or chromium

oxide based ﬁlms such as those developed by Philips/

Onstream, but the challenges here are enormous. The

coatings must be no more than about 7 nm thick and

be capable of lasting the life of the head in continuous

contact with tape.

There are two modes of wear with such thin coat-

ings, one due to the microadhesions/microabrasions

detailed in previous sections and one due to delam-

ination. In order to survive the ﬁrst of these modes

with conventional advanced MP tape containing

head-cleaning agents (HCA), the coatings should

have a hardness (determined by the Richardson

criteria) of about twice that of the HCA particles,

that is about 50 GPa. Filtered cathodic arc deposition

of DLC ﬁlms is probably the favored process for the

production of such a ﬁlm. An alternative solution

may be to substantially reduce the hardness of the

HCA in the tape, but results of this change on trans-

fer ﬁlm formation (head stain) are difﬁcult to predict.

Similarly, the effects on tape durability cannot be

predicted, since a major function of HCA is to act

as a bearing surface and give the tape mechanical

stability.

If other forms of wear can be eliminated, fatigue-

induced delamination at the ﬁlm/substrate interface

will still present a major problem which may only

be solved by the formation of very high strength

adhesive junctions. Such junctions have not been

developed at this time.

9. Altered Layers

A further consequence of wear, particularly at ferrite

heads, is the production of a work-hardened amor-

phous magnetic dead layer, or Beilby layer, at the

surface of the crystalline ferrite. Such a layer might

also be present in metal elements of linear heads.

These layers have been identiﬁed and measurements

of thickness attempted using magneto-optic Kerr

effect measurements, but the evidence so far only

conﬁrms the possible presence of Beilby layers at

thicknesses of less than 100 nm. Some reliable method

needs to be developed for these measurements before

the effect on signal spacing loss can be properly

assessed.

10. Conclusion

This is a brief review of the tribology of ﬂexible

magnetic recording media, and the effect on signal

performance. Where possible, original tribological

source material has been quoted. The review shows

that much of the pioneering work in tribology may be

used to elucidate mechanisms of wear in these sys-

tems, with the proviso that scale effects must be taken

into account. The contact between media and heads

is complex, but is largely elastic in nature. Fatigue-

induced delamination is the major wear mechanism

642

Magnetic Reco rding: Flexible Media, Tribology

in media. Microabrasion is the major wear mecha-

nism in head materials, although other mechanisms

such as delamination, three-body wear, and erosion

may be more important in terms of signal degrada-

tion. Hence the major mechanisms of material re-

moval do not necessarily have the greatest effect on

signal output performance.

See also: Magnetic Recording Materials: Tape Par-

ticles, Magnetic Properties; Metal Evaporated Tape;

Magnetic Recording: VHS Tapes; Magnetic Record-

ing Technologies: Overview

Bibliography

Bhushan B 1984 Analysis of the real area of contact between a

polymeric magnetic medium and a rigid surface. J. Trib.

Trans. ASME 106, 26–34

Bhushan B J 1987 Magnetic head-media interface temperatures.

1: Analysis. Trib.-Trans. ASME 109, 243–56

Bijker M D, Draausna E A, Eisenberg M, Jansen J, Peersat N,

Sourty E 2000 Future directions in advanced digital record-

ing technology. Tribol. Int. 33, 383–90

Greenwood J A, Williamson J B P 1966 Contact of normally

ﬂat surfaces. Proc. Roy. Soc. A292, 300

Gulino R, Blair S, Winer W O, Bushan B J 1987 Temperature-

measurement of microscopic areas within a simulated head

tape using infrared radiometric technique. J. Trib. Trans.

ASME 108, 29–34

Halliday J S 1955 Surface examinations by reﬂection electron

microscopy. Proc. Inst. Mech. Eng. 169, 221–35

Harrison M, Sullivan J L, Theunissen G A S 1999 Pole tip

recession in sandwich heads incorporating a FeTaN magnetic

track. Tribol. Int. 31 (9), 491–500

Hempstock M S, Sullivan J L 1997 The durability and signal

performance of metal evaporated and metal particle tape.

IEEE Trans. Magnetics 322, 3723–32

Hempstock M S, Sullivan J L 1998 Characterisation of surface

changes to metal evaporated and metal particle media fol-

lowing durability tests helical scan Hi-8 recorders at ambient

and high humidity conditions. Tribol. Int. 31 (8), 419–24

Hempstock M S, Wild M, Sullivan J L 2000 Interactions of

head-tape interface of a linear tape system. Tribol. Int. 33,

391–9

Hempstock M S, Wild M A, Sullivan J L, May P I 1998 A study

of the durability of ﬂexible magnetic media in linear tape

systems. Tribol. Int. 31 (8), 435–41

Jahanmir S, Suh N P 1977 Surface topography and integrity

effects on sliding wear. Wear 44, 87–99

Reaves L M, Sullivan J L 1992 The effect of head cleaning

agents on the wear mechanism of video heads. J. Phys.

D. (Appl. Phys.) 25, 328–34

Richardson R D C 1967 Abrassive wear and relative hardness.

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Suh N P 1986 Tribophysics. Prentice-Hall, NJ, Chap. 7

Sullivan J L, Sharma P J 1992 Factors affecting the durability

of repeatedly stressed ﬂexible magnetic recording media.

J. Phys. D. (Appl. Phys.) 25, 321–8

J. L. Sullivan

Aston University, Birmingham, UK

Magnetic Recording: Particulate Media,

Micromagnetic Simulations

Colloidal magnetic dispersions of submicron acicular

magnetic particles have been used for many years as

precursors of particulate storage media. Advances in

the production of the advanced metal particle (MP),

Okamoto et al. (1996), and its use in the production

of advanced ultra-thin media, Richter and Veitch

(1996), mean that particulate media remain techno-

logically competitive for a number of applications,

including tapes for digital video and back-up appli-

cations. In order to understand and optimize partic-

ulate recording media for these high-density storage

applications, it is necessary to understand the micro-

structure of the media that ultimately has its origins

in the behavior of the dispersion itself.

A magnetic colloidal dispersion is a careful blend

of ﬁne magnetic particles, surface-active agents to

provide stability against aggregation via short-range

forces, secondary pigments, resins, and other addi-

tions such as lubricants. These are generally dispersed

in a mixture of one or more solvents. Generally

speaking, the resin system is the critical element in the

dispersion since it is used to separate the particles in

the ﬁnal coating as well as for binding them together.

Thus, dispersions are a very complex physical system

in which the magnetic particles are merely one com-

ponent, albeit an important one. A prerequisite to

understanding storage media is an understanding of

the magnetostatic interaction between particles and

its inﬂuence on the magnetic and physical properties

of the dispersion. The overall properties of disper-

sions have been reviewed by O’Grady et al. (1991)

and show a rich variety of phenomena of physical

interest and technical importance.

The complexity of the interaction problem requires

that realistic theoretical approaches must be based on

computational solutions. The microstructure of the

dispersion and the magnetic media is sensitive to phys-

ical and magnetic history, therefore particular attention

must be given to the generation of realistic microstruc-

ture in micromagnetic studies of particulate media.

A computer model of particulate media was pro-

posed by Voss et al. (1993), treating the particles as

single spins exhibiting coherent rotation, but taking

into account interparticle interactions. More recently,

Bertram and Seberino (1999) produced simulations

taking into account incoherent reversals by repre-

senting individual particles as chains of spheres. Both

these approaches suffer from the disadvantage that

the microstructure of the system studied is nonreal-

istic, though gross features such as particle alignment

can be simulated. The model and simulation de-

scribed below is a ﬁrst attempt to simulate the phys-

ical and magnetic properties of Advanced MP media

from ﬁrst principles.

643

Magnetic Reco rding: Particulat e Media, Micromagnetic Simulations

The starting point for the simulation of magnetic

media is a dispersion model. A model is usually based

around a specific dispersion where, in an effort to

maximize the available computer facilities, only the

relevant physical properties of the particulate and

continuum phase are taken into account. From these

considerations, a choice of the most appropriate sim-

ulation method must then be made. A useful and

practical introduction to simulation methods can be

found in Allen and Tildesley (1990). One of the ﬁrst

simulations undertaken with elongated magnetic pig-

ment in viscous medium was that of Deymier et al.

(1994) using a Stokesian dynamic method.

The calculation of the long-range magnetostatic

interaction is always problematic due to its compu-

tation demand, particularly for large systems. An

approach to the development of an efﬁcient compu-

tational algorithm can be found in the Brownian dy-

namic simulation of colloid aggregation made by

Gunal and Visscher (1996). It is pertinent to note here

that the choice of the micromagnetic model employed

for the interaction calculation, and its relation to

particle geometry, has been shown by Visscher and

Gunal (1997, 1998) to be an important inﬂuence on

the simulation predictions.

The basis of the multistage model described below

is an Advanced Metal Particle Molecular Dynamic

model developed by Coverdale et al. (1997, 1998). It

has been designed to simulate dynamic particle

behavior in a Newtonian ﬂuid arising from particle

interactions, surface interactions, simple shear, and a

uniform magnetic ﬁeld.

The model is ﬁrst used to investigate the inﬂuence

of shear and magnetic ﬁeld on the microstructure of a

magnetic pigment dispersion. It is then used in a

multistage simulation of the production of magnetic

media. Each stage of media production has been

simulated by modeling the process assumed to be the

dominant inﬂuence on the determination of the

microstructure. The stages employed in the model

are summarized as follows. A rectangular slab of

dispersion in magnetostatic equilibrium is generated.

The computation cell is 0.8m 0.8m 0.4m with a

particle volume packing fraction (VPF) of 20%. The

microstructure of the initial coating is modeled

by shearing for 5 10

4

ms at a shear rate of

5 10

1

, being analogous to a model line speed

of 120 m min

1

. The dispersion is allowed to relax

towards equilibrium for 1 ms after shearing. The dis-

persion is then ﬁeld-oriented at 2000 Oe for 4 ms and

dried to yield a 0.2 m coating at a VPF of 40%.

1. Molecular Dynamic Model of a Particulate

Dispersion

Several of the more common algorithms used for

molecular dynamics are unsuitable for a viscous sys-

tem because they have a tendency to overestimate the

particle velocity during a given time-step, and as a

result cause problems with the estimation of the ve-

locity-dependent viscous forces and torques. Rather

than accept an unreasonably small time-step as a

possible solution in order to stabilize an algorithm, it

is better to choose a less sophisticated algorithm with

the advantage of being more rugged and simpler to

implement for a strongly interacting system.

The modeling of the motion of a particle ensemble

in a viscous medium would require a full hydrody-

namic description to take account of regions of ﬂow

induced by a disturbance, for example a rotation, in

the neighborhood of a particle. As of 2001, it is only

reasonable to address a simple case where the con-

straint on particle motion due to the viscous medium is

approximated via the forces and torques resulting from

the motion of an isolated particle in a Newtonian ﬂuid.

The assumption is also made that the motion of a

particle over a computation time-step is predomi-

nately determined by a ‘‘terminal velocity’’ and a

‘‘terminal angular velocity’’ which is a consequence

of the forces acting on the body being balanced by the

forces of resistance to the motion. This gives rise to a

motion of constant velocity and a constant angular

velocity over each computation time-step.

2. Translational Motion

The equations of translational motion of a particle of

mass M subject to a resultant force F due to the

magnetostatic and surface interactions is given

by, M

’

¼ F

N

’

v, where the viscous ‘‘drag’’ Nv

on the particle is proportional to the velocity.

Motion parallel, //, to the particle axis can be ex-

pected to give rise to less drag than motion perpen-

dicular, þ, to the axis and so the velocity must be

resolved into the appropriate components. The term

N is therefore written,

¼ R

ðe

 v

Þe

þR

ðv

 e

Þ e

where e

is a unit vector in the direction of the particle

axis. The terms R

and R

provide the essential hy-

drodynamic terms and have been employed following

Newman and Yarbrough (1969). These terms depend

on the individual particle dimensions and the viscos-

ity of the medium.

In order to derive a computation algorithm, this

equation is put in a form with dependence directly on

the velocity components,

¼ R

þ R

The term N

will now be derived. Employing an

intermediary matrix,

B ¼ e

 v

644

Magnetic Reco rding: Particulate Media, Micromagnetic Simulations

the components of the corresponding vector are

extracted as,

¼ðe

 e

¼ðe

 e

¼ðe

 e

The expression may now be derived,

¼ B  e

ðe

 e

Þðe

 e

Þðe

 e

Expansion and manipulation yields,

¼ R

ðe

þ e

Þe

e

ðe

þ e

Þe

e

ðe

þ e

Now considering the right-hand vector term and

following a similar method:

¼ R

ðe

 v

Þ e

¼ðv

þ v

Therefore:



¼ R

For the translational motion, with the equilibrium

condition M

’

¼ 0,

F ¼ R

þ R

The velocity of a particle during each time-step may

now be derived from the resultant force acting on a

single particle.

3. Rotational Motion

The angular velocity o

is not used in the formulation

of the rotational motion but the unit vector in the

direction of the particle axis e

and the velocity u

the axis vector, after Fincham (1993), where

’

¼ u

and

’

¼ G

Nu

ðu

 u

Þ e

First, the torque T

mag

due to the magnetostatic forc-

es is considered,

mag

 f

¼ e



¼ e

 g

It is convenient to resolve only the perpendicular

component:

¼ g

 e

ðe

 g

Thus:

mag

¼ e

 g

The torque due to rotational viscosity is propor-

tional to the angular velocity,

¼ R

The term Rf is the hydrodynamic term and has been

employed following Newman and Yarbrough (1969).

The rate of change of angular velocity may now be

written,

’o ¼ I

1

ðT

mag

 T

Employing,

’

¼ o

 e

and differentiating with respect to time,

’

’o  e

þo

’

Therefore,

’

¼ I

1

ðT

mag

 T

Þe

þo

ðo

 e

to yield the second equation of motion,

’

¼ I

1

 I

1

ðu

 u

Þ e

Note that the term ðu

 u

Þ e

is the centripetal force

that is necessary to maintain the constant length of

the axis vector by balancing the force generated by

the rotation.

The rotational motion is dealt with in a similar way

to the translational motion but ﬁrst the centripe-

tal term is removed. The effect of this term is then

645

Magnetic Reco rding: Particulat e Media, Micromagnetic Simulations

replaced by a normalization of the unit vector e

after

each time-step, together with the condition that the

time-step, thus the displacement, is kept small.

For the translational motion, with the condition

’

¼0,

1

¼ I

1

The velocity of the axis vector during each time-step

may now be derived from the torque.

4. The Microstructure of a Magnetic Dispersion

Study of the dispersion is made to clarify the inﬂu-

ences that determine the behavior of the microstruc-

ture.

The dispersion simulation is based on an advanced

metal particle dispersion with a volume packing frac-

tion of 3.8%. Simulations of the zero-ﬁeld equilibri-

um state show that the microstructure consisted of a

‘‘honeycomb’’ structure brought about under the in-

ﬂuence of the magnetostatic interactions (Fig. 1).

This equilibrium state was used as the starting point

for all the dispersion simulations that follow. Any

change in microstructure must be brought about by

overcoming the magnetostatic interaction energy that

gives rise to this low-energy state.

A well-deﬁned structure is also found in a strong

magnetic ﬁeld, which has the characteristic structure

of long ﬁlaments of particles aligned in the ﬁeld di-

rection. The formation of ﬁlaments, viewed trans-

verse to the ﬁeld direction in Fig. 2(a), gives rise to a

network of open channels, viewed along the ﬁeld di-

rection in Fig. 2(b).

The molecular dynamic (MD) method will allow

the introduction of a velocity gradient and thus sim-

ulate the dynamic behavior of the particles, i.e., the

microstructure, in a shear ﬂow. In the absence of

an applied ﬁeld, the simulations predict that for a

Figure 2

(a) Field equilibrium, view transverse to ﬁeld direction.

(b) Field equilibrium, view along ﬁeld direction.

Figure 1

Zero-ﬁeld equilibrium.

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Magnetic Reco rding: Particulate Media, Micromagnetic Simulations

relatively low shear rate, 1000 s

1

, the magnetostatic

interactions give rise to localized structure within the

ﬂow (Fig. 3). The structures are continuously break-

ing up and reforming under the inﬂuence of the

velocity gradient but structure is observed at each

time-step.

The microstructure may be investigated both in the

shear ﬂow alone and in a shear ﬂow subjected to a

magnetic ﬁeld, thus the simulation may be used to

model shear magnetometry experiments (Veitch

1996). There are two directions in which a ﬁeld may

be applied so that it is transverse to the direction of

particle ﬂow. The simulated effect of shearing the

dispersion is modeled between two parallel plates

aligned in the x–y plane moving with equal and

opposite velocity in the y direction. In this conﬁgu-

ration, a transverse ﬁeld may be applied along the

x-axis or the z-axis. The more common conﬁguration

used in a shear magnetometer employing a rotating

cylinder is the transverse x direction.

The model has been employed to predict the

microstructure for shear ﬂow in the two transverse

directions for a relatively strong applied ﬁeld of

2000 Oe. When the applied ﬁeld is in the transverse x

direction, the particles orient into the ﬁeld direction

and thus lie transverse to the ﬂow ﬁeld. A typical

particle conﬁguration to be found at each time-step is

shown in the two views of Fig. 4(a) and Fig. 4(b).

Although the particles are strongly orientated in the

ﬁeld direction, they do not exhibit a tendency to form

ﬁlament structures that are characteristic of zero-

shear simulations.

A very different response for the same ﬁeld mag-

nitude and shear rate is predicted when the ﬁeld is

applied in the transverse z direction, shown in the two

views of Fig. 5(a) and Fig. 5(b). It can be seen that a

very well-deﬁned microstructure has been developed,

which may be described as curtains of particles ar-

ranged parallel to the ﬂow direction and magnetically

orientated in the ﬁeld direction.

Figure 3

Zero-ﬁeld shear ﬂow, low shear breaking up equilibrium

structure.

Figure 4

(a) Transverse ﬁeld x-direction, high shear, transverse to

ﬁeld view. (b) Transverse ﬁeld x-direction, high shear,

ﬂow direction view.

647

Magnetic Reco rding: Particulat e Media, Micromagnetic Simulations

Thus, enhanced magnetization in shear magneto-

metry experiments, at least in systems of highly elong-

ated particles, can be partially interpreted in terms of

a combination of mechanical orientation due to

the shear ﬂow as well as the aligning torque of the

magnetic ﬁeld. The structures appear to retain their

form in conditions of medium shear rate of around

10000 s

1

, but become less well deﬁned at the very

high shear rates.

5. The Drying Process

The drying algorithm, used to model the transition

from the dispersion to the media, is an important stage

in the simulation of media with realistic microstruc-

ture. This is because the microstructure of the disper-

sion is retained as a ‘‘memory’’ and acts as a significant

inﬂuence on the microstructure of the media.

The drying process is difﬁcult to model because the

dispersion undergoes rapid solvent loss, which may

give rise to local chaotic behavior, while at the same

time the resins are cross-linking to form long-chain

polymer molecules that tend to inhibit particle mo-

bility. As a result of these processes, there is expected

to be a large variation in media viscosity on the local

scale during drying.

For these reasons, a phenomenological approach

to the drying model is taken whilst attempting to re-

tain some of the important physical properties. The

drying simulation is based on the MD-dispersion

simulation with the additional feature of a forced-

settling algorithm that acts as the volume-reducing

scheme.

The model employed here assumes that the particle

environment remains at a constant viscosity of 1 P

throughout the simulated drying, although in reality

the viscosity increases dramatically as the solvent es-

capes and the resins tend to cross-link. At each MD

time-step, the height z of each particle above the base

of the media is reduced by an amount dz ¼zD(t)

proportional to z. The parameter D is a function of

the drying time t and is calculated so that the reduc-

tion in coating thickness occurs at a rate proportional

to log(t). This is in keeping with observations made

on solvent loss in particulate media by Gilson (1993),

Fig. 6.

6. Magnetization Modeling

The magnetic behavior of the dispersion in the coat-

ing and drying stages has been modeled via a pole–

pole interaction model. This scheme is assumed to be

a good approximation for the high-coercivity parti-

cles while they exhibit reasonable mobility. Magnet-

ization modeling of the media has been carried out

using a chain-of-spheres model in order that nonuni-

form magnetic states of a particle may be taken into

account. The behavior of a particle moment is deter-

mined by a Landau-Lifshitz equation with the addi-

tion of a stochastic ﬁeld term after Chantrell et al.

1998. This method employs estimations of the usual

anisotropy, exchange, dipole and interaction ﬁeld

terms together with the behavior associated with

thermal effects.

Figure 5

(a) Transverse ﬁeld z-direction, high shear, transverse to

ﬁeld view. (b) Transverse ﬁeld z-direction, high shear,

ﬂow direction view.

648

Magnetic Reco rding: Particulate Media, Micromagnetic Simulations

The Landau-Lifshitz equation, describing the mo-

tion of a unit vector m

in the magnetization direction

¼ m

, of volume element V

may be written,

d m

1 þ a

 H



ð1 þ a

ðm

 H

where g is the gyromagnetic constant, a is a damping

constant.

The total local ﬁeld H experienced by a moment i is

the sum of contributions from the dipole ﬁeld,

ðm

Þr



where V

is the volume of volume element J, and r

the unit vector from element to j to i. The exchange

ﬁeld derived from moments in the same particle,

where A is the exchange constant between elements

in the same particle, and d

is the distance between

elements of the same particle.

The anisotropy ﬁeld is representative of the crys-

talline and shape anisotropy,

ðe

m

Þ e

where K is the anisotropy constant, and e

is the unit

vector in the direction of the anisotropy axis.

The thermal ﬂuctuation ﬁeld is implemented in the

computation algorithm so that after a large number

of statistical samplings it will exhibit a Gaussian dis-

tribution with variance according to Brown (1979) as

ð1 þ a

ÞDt

where k

is the Boltzman constant, T is the temper-

ature, and Dt is the integration time-step. Finally,

there is the applied ﬁeld term.

7. The Microstructure of Magnetic Media

This study of the effect of the coating process on the

bulk magnetization properties of coated media rep-

resents ﬁrst-principle micromagnetic calculations

since the microstructure has been realistically derived

at the microscopic level.

Starting from a ‘‘wet’’ precursor with a VPF of

around 20%, the model has been employed to study

two extreme cases of drying, which yield the two ex-

treme values of hysteresis properties for media, 40%

vpf. The two cases being (i) drying without an ori-

enting ﬁeld (Fig. 7(a)), and (ii) drying in a strong

orienting ﬁeld (Fig. 7(b)). Both the sections shown

are 0.8 m 0.8 m 0.2 m in cross section.

Three ﬁne 3D sections of the simulated micro-

structure are shown in Fig. 7(c). The top view of

Fig. 7(c) is a 0.8 m 0.2 m 0.1 m cross section, taken

along the web direction of media dried in zero ﬁeld

which clearly shows the poor orientation of the par-

ticles. The middle view is the corresponding section of

ﬁeld-dried media (Fig. 7(b)), which shows very strong

alignment in the web/ﬁeld direction. The lower view

is a ﬁner section of the middle view showing more

clearly the lack of homogeneity in the distribution of

particles. The microstructure of the ﬁeld-dried media

contains small voids predominantly aligned in the

ﬁeld direction. These voids can be traced back to

open regions in the dispersion microstructure. They

are predicted to act as ‘‘drying channels’’ through

which the solvent can evaporate. It has been pro-

posed by Gilson (1993) that channels are necessary to

allow the coating to dry rapidly enough and so it

would appear that voids in the ﬁnal coated medium

are an unavoidable consequence of the drying process

itself.

Particle orientation is an important property of

media and may be characterized for study by a suit-

able correlation function. The function employed

here correlates particle alignment with respect to the

plane of the medium web, the x–y plane, with the

plane perpendicular to the media web aligned along

the web, the y–z plane. (Certain correlations are seen

to be physically forbidden, such as, for example, a

particle lying perpendicular to both planes.) The cor-

relation function of the zero-ﬁeld media made from

nonsheared coating is shown in Fig. 8. The dispersion

does not exhibit any preferential alignment but the

drying process tends to alignment in the plane of the

media; the x–y plane.

Strong shearing of the dispersion tends to align

the particles in the shear direction but the drying

process disrupts and weakens this strong orientation.

The strong particle alignment seen in the dispersion

Figure 6

A typical drying curve from production of a modern

data tape product, indicating the presence of three

regimes.

649

Magnetic Reco rding: Particulat e Media, Micromagnetic Simulations