Improved pinning regime by energetic ionsusing reduction of pinning potential

Roy Weinstein a,b,*, Alberto Gandini a,b, Ravi-Persad Sawh a,b,Drew Parks a,b, Bill Mayes a

a Beam Particle Dynamics Laboratory, Department of Physics, University of Houston, 632 Science and Research Bldg. I,

Houston, TX 77204-5005, USAb Texas Center for Superconductivity and Advanced Materials, 202 Houston Science Center, University of Houston,

Houston, TX 77204-5002, USA

Received 26 September 2002; received in revised form 25 November 2002; accepted 27 November 2002

Abstract

When ion damage is used to create pinning centers, full columnar pinning centers provide the largest pinning po-

tential, Upin, but not the greatest Jc or pinned field, Bpin. Some of the characteristics of columnar defects which limit Jcand Bpin are discussed, including reduction of percolation path, and the need for a larger number of columns of damage,for pinning, than are usually estimated. It is concluded that columnar pinning centers are limited to Bpin < 4 T, and alsoseverely reduce Jc. Evidence is reviewed that aligned damage, or broken-columnar pinning centers, described herein, canprovide orders of magnitude higher Jc, and higher pinned field, despite providing lower Upin. A pinning center mor-phology is discussed which utilizes multiple-in-line-damage (MILD). For, e.g., present day large grain HTS Jc, ob-tainable by MILD pinning, is estimated to be of the order of 106 A/cm2 at 77 K, even when crystal plane alignment and

weak links are not improved. Pinned field is increased by over an order of magnitude. An experiment is proposed to

confirm these observations, and to directly compare MILD to columnar pinning centers. It will also determine the

optimum MILD structure. Other measurements of interest, made possible by the same data set, are described.

� 2002 Elsevier Science B.V. All rights reserved.

PACS: 74.60.Ge; 74.60.Jg; 75.50.y; 81.40.Rs

Keywords: Critical current density; Pinning potential; Columnar pinning; Percolation current; Ionic irradiation

1. Background

The critical current density, Jc, of a supercon-ductor is a very important characteristic, second

only to the critical temperature, Tc. When both Jcand an applied field, BA, are present in Type IIsuperconductor a Lorentz force results, which

causes motion of the fluxoids, uo, of the field. Thisin turn creates a dissipative electric field, which

reduces Jc. The reduction of Jc can be prevented bypinning centers which hold the fluxoids in place.

Pinning centers are regions of low (or no) su-

perconductivity in which a fluxoid, uo, is in a lowerenergy state by an amount proportional to the

*Corresponding author. Address: Beam Particle Dynamics

Laboratory, Department of Physics, University of Houston,

632 Science and Research Bldg. I, Houston, TX 77204-5005,

USA.

0921-4534/02/$ - see front matter � 2002 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0921-4534(02)02361-4

Physica C 387 (2003) 391–405

www.elsevier.com/locate/physc

condensation energy. Generally, pinning centers

have been considered best if the pinning potential,

Upin, they provide is largest. Thus columnar pin-ning centers have been considered excellent since if

the fluxoid, uo, is parallel to the axis of the col-umn, the pinning potential, Upin, is maximized. It isgenerally assumed that maximizing the pinning

potential, Upin, maximizes Jc. We argue here thatthis is seriously misleading. The argument is given

in some detail because the assumption that maxi-

mum Upin results in maximum Jc is very broadlyheld. We argue that assumption has resulted in the

most promising pinning center morphology re-

maining largely unexplored.It is easily seen that the highest Upin need not

lead to the highest current. Upin increases with thelength of fluxoid pinned, L. It has also been shown[1] that the pinning potential of a columnar pin-

ning center increases with the diameter of the de-

fect, dd

Upin � ðH 2c =8pÞ2pn2L ln 1

�þ ½dd=2

ffiffiffi2

pn�2

�ð1Þ

where Hc is the critical field, and n is the coherencelength. Thus, the strongest pinning potential re-

sults from pinning centers with the largest diame-

ter, dd, due to the ln term. This has experimentallybeen confirmed [2].

However, it is easily seen that the strategy of

using columnar defects with large diameter in or-

der to achieve high Jc can result in zero currentcapability. For reducto ad absurdum consider

that, from Eq. (1), a single column with damage

diameter almost equal in size to the diameter of

the HTS, dd � dHTS, provides strongest pinning.However, such a pinning center, although it has

maximum Upin, consumes the entire area of theHTS available for current percolation, and results

in zero current. This strategy for pinning also failsfor large applied field, BA. If a pinning center ofvery large size pins only one fluxoid, uo, it is use-less at higher BA. In order to pin higher fields, onemust trade the strongest pinning potential for a

larger number of pinning centers. The conclusions

drawn in the remainder of this note are not quite

as simplistic as this, but the conclusions drawn are

similar, i.e., that the best strategy to obtain high Jc,and high pinned field, Bpin, requires trading re-

duced pinning potential for improved percolation

path.

Since, in order to obtain high Jc at high BA, wewill not take advantage of the logarithmic increase

of U for large dd, we consider pinning centers ofdiameter circa dd � 2

ffiffiffi2

pn. Then

Upin � ðH 2c =8pÞ2pn2L ð2Þ

The pinning potential is proportional to the

length L of the portion of the fluxoid pinned.Consider a pinning center which is a cylindrical

column of non-superconducting or poorly super-conducting material, with its axis parallel to a

fluxoid. The entire length of the fluxoid can

be bound when the fluxoid is parallel to the col-

umn. In this case the pinning potential is maxi-

mized.

Energetic ions of high nuclear charge, Z, havebeen shown to produce damage of columnar shape

and of approximately the diameter required forpinning centers [3]. If columnar pinning centers are

produced by energetic ions, it has been assumed [4]

that the number of ions striking the HTS should be

equal to the number of pinning centers created.

We argue below that this apparently obvious ob-

servation is not correct. However, assume initially

that it is correct. If one ion creates one column of

damage, and each column pins one fluxoid, uo �2 107 G cm2, the number of fluxoids pinned perunit area would be equal to the number of ions per

unit area, called the fluence of ions, Fi. The fieldpinned would then be [4]

Bu ¼ Fiuo ð3ÞIn the literature, Bu is referred to as the

‘‘equivalent field.’’ The equivalent field, Bu, is an

alternate way to express a fluence, Fi.Many studies of Jc vs. the number of columnar

defects per unit area, Fi, have been done (e.g. [5–7]). These have certain common features. Fig. 1

shows as an example the trapped magnetic field

enhancement, RM, in a sample of melt-texturedYBa2Cu3O7d superconductor (Y123) vs. the flu-ence of 7.86 GeV Xe ions used to create pinning

centers. Trapped field, and hence Jc, initially in-creases as the number of pinning centers increases,

because flux quanta are pinned. After this initial

increase, the value of Jc levels out as ion fluence, Fi,

392 R. Weinstein et al. / Physica C 387 (2003) 391–405

increases further, and then decreases. This behav-ior is common to all such experiments.

The region of Jc increase is the expected effect ofpinning centers. However, studies tend to stop at

the point where the process becomes undesirable.

But attention must be paid to the region of Jcdecrease in order to learn the cause(s) of the de-

terioration in Jc (in the hope that these causes maybe avoided).

2. Columnar pinning centers

2.1. Columnar damage

Ionic bombardment of HTS acts to create pin-

ning centers by converting columns of HTS to anon-superconducting state. Incident ions lose en-

ergy to target electrons and nuclei via Coulomb

force, and to target nuclei only via nuclear force.

Energy losses to electrons dominate by a large

factor. Electronic loss per unit length of SeP 3:5keV/�AA creates continuous columnar damage [8].

The energy delivered to the HTS melts or vapor-

izes a column of crystalline HTS. The columnresolidifies as an amorphous column of dd � 68 �AA.

Shock damage and deoxygenation extends the

non-superconducting region beyond the amor-

phous core to a columnar diameter dd � 136 �AA[9,10].

The damaged HTS pins magnetic fluxoids, but

also markedly reduces the percolation path for Jc,lowers Tc, and broadens the transition region nearTc. A large number of studies of ionic damage haveinvestigated the Tc effects (e.g., [11–13]). Instead wewill focus first, in the following discussion, on the

number of pinning centers created.

2.2. How many pinning centers are created per

incident ion?

We approximate the diameter of the columnar

pinning center as the diameter of the ionic damage,

dd. Consider an area of HTS upon which ions areincident. The area lost to conduction, per incident

ion, is pd2d=4.If a number of ions, Nion, have struck an HTS

surface, an incremental increase in that number,dNion will increase the number of pinning centersby an incremental amount dNpin. However, theincrease in the number of pinning centers will not

equal the increase in the number of ions. Any ion

which strikes a region of HTS previously struck,

will not produce a new pinning center. If an ion

strikes within an area pd2d of an earlier ion, fourtimes the area of the damage, the resulting damagewill overlap, and form a single pinning center, as

shown schematically in Fig. 2d.

We designate the area remaining in which an

ion can strike, and form a new pinning center, as

Agood. The location at which an energetic ionstrikes is generally random, over the entire area of

the superconductor, Atot. Hence the probability ofstriking good area, and creating a new pinningcenter is Agood=Atot. As a result, the number of newpinning centers, dNpin, resulting from a number ofnewly incident ions, dNion, is

dNpin ¼ dNionðAgood=AtotalÞ ð4ÞEach new pinning center results in the removal

of an area pd2d from the ‘‘good’’ area, as shown

schematically in Fig. 2d. Thus

dAgood ¼ pd2d dNpin ð5Þ

Fig. 1. Improvement of trapped field, Bt, by 7.86 GeV Xe ions.Graph shows RM vs. fluence of Xe ions, at 77 K. Xe fluence isgiven both as FXe ¼ # Xe ions per cm2, and as ‘‘equivalentfield’’ � Bu � FXeuo, where uo is the flux quantum (uo � 2107 G cm2). The data is typical for introduction of pinning

centers: Jc (hence Bt) increases at first because of the addedpinning. It peaks, and then decreases because of the negative

effects of the pinning centers.

R. Weinstein et al. / Physica C 387 (2003) 391–405 393

The definition of ion fluence is

Fi � Nion=Atot ð6Þ

Eqs. (4)–(6) yield a linear differential equation,

the solution of which is

Agood ¼ Atotepd2dFi ð7Þ

i.e., as ions continue to strike the HTS, the area,Agood, available for new pinning centers decreasesexponentially.

Eqs. (4), (6) and (7) yield

Npin ¼Atotpd2d

1�

epd2dFi�

ð8Þ

Eq. (8) is a result of the finite size of the col-

umnar damage, the ion spacing required to form

separate pinning centers, and the random location

of ions within the ion beam. It indicates that thenumber of pinning centers created, Npin, is notequal to the number of incident ions, FiAtot.If we expand Eq. (8) in a power series,

[ex � 1 xþ x2=2 x3=6þ ] we findNpin � Nion N 2ionpd

2d=Atot þ ð9Þ

i.e., it is only in a first order approximation that

the number of pinning centers equals the number

of incident energetic ions. We will, below, evaluate

the magnitude of the error involved in the broadly

used but misleading assumption that Npin ¼ Nion.

We will find that even for a modest equivalent field

of, e.g., 6 T the error is 100%. However, first we

convert Eq. (8) to an estimate of the pinned field.

Assume that each pinning center pins one

fluxoid. This is the assumption usually made [4] topredict the field which can be pinned. i.e., we as-

sume Bpin ¼ uoNpin. Using Eq. (8), and the defini-tion of equivalent field, Bu given in Eq. (3) we find

Bpin ¼uopd2d

1�

eðpd2d=uoÞBu

�ð10Þ

2.3. Maximum pinnable field

In Eq. (10), the expression uo=pd2d plays the role

of a maximum pinnable field, Bmax

Bmax � uo=pd2d ð11Þ

In terms of Bmax, Eq. (10) becomes

Bpin ¼ Bmax 1�

eBu=Bmax�

ð12Þ

Fig. 3 shows Eq. (12) graphically.

If an HTS sample is irradiated to a known

fluence (or Bu), the only unknown in Eq. (10),needed to determine the pinned field, is dd. Datafrom nuclear physics experiments can be used to

evaluate dd. In the study of nuclear damage by ionsit is found that in order to form continuous col-

Fig. 2. Schematic of positions of columnar damage discussed in

text: (a) individual column of damage (seen end-on); (b) two

columns of damage, each of which is an independent pinning

center; (c) two columns of damage which overlap and act as a

single pinning center; (d) dot-dash line shows area within which

a second ion can strike and not form an independent pin; (e)

dotted line shows where a third ion can strike, and join two

previously independent pinning centers.

Fig. 3. Graph of Eq. (12), showing field actually pinned, Bpin,vs. the ‘‘equivalent field,’’ Bu ¼ Fiuo. Saturation value of pinnedfield is heavy line on right. In the text Bu is shown to be a first

order approximation to pinned field, which neglects overlap-

ping columns.

394 R. Weinstein et al. / Physica C 387 (2003) 391–405

umnar defects, the energy per unit length which

must be delivered to (e.g.) Y123, is SeP 3:5 keV/�AA,and that in this case dd � 136 �AA [8–10]. From thesedata Eq. (11) yields

Bmax ¼ 3:47 T ð13ÞWe conclude that full columnar defects cannot

pin over 4 T.

Using Eq. (8), and dd � 136 �AA, we find, as notedearlier, that even for a modest equivalent field,

e.g., Bu ¼ 6 T, the number of pinning centersgenerally estimated in the literature (Eq. (3)) is inerror by >100%. Thus a fluence of Bu ¼ 6 T pins afield of only Bpin < 3 T. For higher fields the va-lidity of assuming Bpin ¼ Bu grows rapidly worse.

The error made in assuming that pinned field

equals Bu is actually more severe than this. There

is at least one further physical effect, not included

in the above considerations. In a region of HTS

previously struck by, e.g., two ions, so as to suc-cessfully produce two independent pinning centers,

a third ion may cause damage which connects the

two previously independent centers, and thus de-

crease the number of pinning centers. (See Fig. 2e.)

In fact it is self-evident that at very high ion flu-

ence all pinning centers will be connected, and only

one large pinning center will exist. Fluxoids may

then wander freely. In terms of Fig. 3, a completetheoretical description would predict that as

Bu ! 1, Bpin ! 0.

Our intent here is not to pursue the exactly

correct form of Eqs. (8) and (12), but rather to

point out, and pursue, a method to greatly increase

the maximum pinnable field, Bmax. It is evidentfrom the preceding discussion that this will require

reduction of the diameter of ionic damage, dd,below the value associated with the formation of

full columns.

2.4. Loss of percolation area

We next consider the area of superconductor,

A0good, remaining for current percolation after ir-

radiation by a fluence of ions Fi. The area re-maining for current, A0

good, is larger than that

remaining for new pinning centers, Agood, and wedistinguish it by using a ‘‘prime’’ notation.

Whereas the area around a pinning center which is

unavailable for new pinning centers is pd2d (see Fig.2d), the area unusable for percolation is only the

area of actual damage, pd2d=4.Suppose a fluence of parallel ions, Fi, has hit

and damaged a superconductor, leaving an un-

damaged good area, A0good. The next increment in

the number of ions, dNi, will destroy more of thegood area, dA0

good. However, if some of these ad-

ditional ions strike previously destroyed area, no

additional harm can be done. For ions randomly

positioned, the probability of striking good area is

A0good=Atot, where Atot is the total initial area ofHTS. Thus the good area destroyed by an added

number of ions dNi is

dA0good ¼ dNiðpd2d=4ÞðA0

good=AtotÞ ð14Þ

Using dNi=Atot � dFi, we obtain a differentialequation whose solution is

A0good ¼ Atotepd2

dFi=4 ð15Þ

Eq. (15) may also be written in terms of

matching field, Bu, and maximum pinnable field

Bmax, by substituting Eqs. (3) and (11)

A0good=Atot ¼ eBu=4Bmax ð16Þ

We previously calculated Bmax � 3:47 T, basedupon dd � 136 �AA for full columns. Consider, forexample, Bu ¼ 14:6 T (equivalent to Fi ¼ 7:3 1011ions/cm2). Eq. (16) then indicates that

A0good=Atot ¼ 0:35 ð17Þ

i.e., under these conditions, 65% of the HTS has

been destroyed. One might guess that the critical

current is reduced by 65%. However, the situationis worse.

2.5. Percolation theory

Percolation theory treats the problem of a

conductor of size D, with many holes in it, each ofsize d � D. For the case in which the holes arecontinuous columns, theory and experiment agree[14] that for normal conductors if the fraction of

area remaining is A0good=Atot < 0:35, the conduc-

tance goes to zero. This is shown in Fig. 4. Thus we

expect that, at Bu ¼ 14:6 T, current may fall tozero. Rather than increasing Jc, the use of

R. Weinstein et al. / Physica C 387 (2003) 391–405 395

Bu ¼ 14:6 T would then reduce Jc to zero. To thebest of our knowledge, no percolation theory cal-

culation has been done specifically for supercon-

ductors for this geometry [15]. Theoretical work

which has been done [16] is in reasonably good

agreement with experiment [13], even in super-conductors [15]. Differences are, however, ex-

pected between the superconducting and resistive

cases. We return to this question in Section 4. At

present we conclude only that Jc should fall morerapidly than the area of the sample.

It is not the present aim of these considerations

to compute the accelerated loss of Jc due to per-colation theory. Instead, we conclude that colum-nar defects, in numbers sufficient to pin moderate

fields, have severely negative effects, one of which

can be to reduce Jc to zero. We will, in what fol-lows, seek modified forms of defects which may be

more useful, and less destructive.

Note that in addition to the reduction of Jcdescribed above, Jc is further reduced due to low-ering of Tc which accompanies irradiation [11–13].Note also that reduction of area, in a strict

sense reduces Ic, not Jc. However, pinning centersare well dispersed in the areas still conducting, and

the destroyed and conducting areas involved are so

intimately mixed, and so small, that the resulting

material practically is treated as homogeneous,

and the results are interpreted as Jc.

2.6. Summary of effects resulting from columnar

damage

(1) Columnar defects reduce the area available

for current percolation. This reduction in area,

given by Eqs. (15) or (16), is strongly dependent on

the diameter of the columns, dd. In the followingportions of this paper, we will consider the goal of

producing pinning centers having lower values of

dd. The solution we find does not produce com-plete columns. Thus the pinning potential, givenby Eq. (2), will also be reduced. The question to be

answered is which has greater effect, the reduction

of Upin, or the increase in percolation area.(2) The reduction of damage diameter, dd, will

also increase the value of fluence at which damage

reduces Jc to zero.(3) The large value of dd for full columnar de-

fects also limits the number of pinning centers tovalues of field which are quite low (below 4 T).

This occurs because the number of independent

pinning centers which can be produced is far below

the number of incident ions even for moderate

fields. Alternatively stated, the maximum pinnable

field given by Eq. (11) is markedly below the

‘‘equivalent’’ field, given by Eq. (3). If ions of

lower dd are used, and are effective, the fields whichcan be pinned will rapidly rise.

(4) The effects of columnar damage reviewed

above are in addition to the broadly recognized

effects on Tc, and on the width of the transitionregion.

3. MILD pinning centers

3.1. Obtaining higher Jc, at high BA, Albeit with

lower pinning potential

Can columnar pinning centers be modified so

that they increase Jc, even when applied in suffi-cient number pin at higher fields?

As we shall see below, high Jc at high BA can beattained by abandoning the generally adopted goal

of achieving the highest Upin (i.e., by giving up

Fig. 4. An example of data on reduction of conductivity by

columnar damage in a normal conductor. Graph shows nor-

malized conductance vs. the fraction of area of the conductor

remaining undamaged, p. Note conductance goes to zero atp � 0:35, not at p � 0. Sample is 0.13 mm steel, 15.5 cm on aside. Columnar holes are 0.318 cm diameter, drilled at random

positions. Data is from Lobb and Forrester [14].

396 R. Weinstein et al. / Physica C 387 (2003) 391–405

some pinning potential in exchange for reduced

damage). In this section we consider experimental

evidence that this strategy works. We then con-

sider a broad class of ionic damage, only sparsely

studied to date, which can be expected to dra-

matically increase Jc at higher BA. Finally we willdiscuss a method to experimentally test the ex-

pected results and also to experimentally deter-

mine the optimum structure of ionic damage for

maximizing Jc at high BA.

3.2. Experiments using fission fragments

The highest Jc (�300 kA/cm2 at 77 K) in bulkgrains of HTS has been obtained in Y123 by use of

fission fragments [17,18]. The highest Jc in bulkNd123 (�270 kA/cm2 at 77 K) has been obtainedin the same way [19].

Fission fragments are ions, of energy of �100MeV. This energy, and the average fragment

charge (Z ¼ 46), result in ionization energy lossper unit distance of typically Se6 1:7 keV/�AA [18].This rate of energy loss per unit distance does not

provide the rate of energy loss, Se ¼ 3:5 keV/�AA,needed to create full columnar defects [8]. An ex-

ample of Se for fission ions is given in Fig. 5.Specific energy loss of Se < 3:5 keV/�AA can,

however, create incomplete columns. Excitations or

ionizations can occur for one or several electrons

in the target atoms. Only the probability of these

various excitations is predictable, and hence Sevaries, statistically, along the ion track, around an

average value. As the ion traverses the target ma-

terial, upward statistical fluctuations in Se at somepoints along the ion track result in the formationof segments of columns. Thus, the tracks of fission

ions (Se6 1:7 keV/�AA) contain broken columns.The gaps between columnar segments have two

effects. One is to reduce damage. The other is to

reduce the pinning potential. Assume that along

the track of the ion, there are gaps of average gap

length hgi. Assume that there are columnar seg-ments of average column length hci. Relative tocontinuous columns, the total length of damaged

superconductor is reduced by a factor fL, where

fL ¼ hci=ðhgi þ hciÞ ð18Þ

The pinning potential of a fluxoid which is

parallel to the ion track is, in Eq. (2), reduced by

the factor fL.For Se P 3:5 keV/�AA, fL ¼ 1. As Se is reduced

below 3.5 keV/�AA, fL is reduced below 1. The valueof fL is not a well-measured parameter, althoughsome measurements exist [9,20]. For example, in

an experiment done with gold and silver ions, the

gold ions (Se � 3:48) were measured to have

fL � 1, as expected for full columns. The silverions (Se � 2:38) were measured to have fL � 0:5.Thus, fission ions will have fL < 0:5.The values of dd (Se) are experimentally fairly

well determined at the present time. At Se � 3:5keV/�AA, dd � 136 �AA. As Se drops below Se � 3:5keV/�AA, and columns become discontinuous, ddalso decreases. As Se decreases further, the damageresembles a string-of-beads, and dd is further re-duced. Both dd and fL decrease as Se decreases.Fig. 6 shows the microstructure of fission frag-

ment damage. The damage is made up of multiple

in-line defects (MILD). MILD pinning centershave proven successful in Y123 [17,18], Nd123 [19]

and BiSCCO [21–23]. In all three HTS systems

remarkable increases in Jc have been observedusing ions resulting from nuclear fission. In Y123

and Nd123, increases by one to two orders of

magnitude in Jc were observed in bulk HTS

grains. Without the need to improve crystal plane

alignment or improve weak links, Jc in Y123

Fig. 5. Examples of specific ionization, Se, vs. range, x. Forfission ion, the product fragment chosen is 116Pd (85 MeV). Also

shown are 580 MeV 116Sn, used by Civale et al. [4], and 3.5 keV/�AA, needed to produce continuous columns.

R. Weinstein et al. / Physica C 387 (2003) 391–405 397

increased from typical values of 20 kA/cm2 at 77 K

and low BA, to 270 kA/cm2 [18]. Experiments doneon Y123 at 50 K showed a factor of 15 improve-

ment in Jc, to �106 A/cm2, and the increase in Jcremained over a factor of 10 (at values of over 100

kA/cm2) at fields of 14 T [18]. This is to be con-

trasted to the �4 T limit posed by full columnardefects. In Nd123 under similar conditions, Jc in-creased from typical values of 30–274 kA/cm2 at

77 K, low field [19]. Pinning centers produced by

fission ions also resulted in increases of Ic in Ag–BiSCCO tape, by factors of up to 100, and in-

creased the irreversibility field, Hirr, by factors ex-ceeding two [20–22].

We attribute the large increases in Jc at fieldsexceeding 10 T to the reduced damage involved inMILD pinning centers. This improvement occurs

despite significant decreases in Upin.

3.3. Limiting value of low Se for the creation of

effective MILD pinning

In an effort to learn how low Se can be, and stillresult in large increases in Jc, an experiment wasperformed using a 6.88 GeV beam of Kr ions, in-

cident on 1 mm thick melt-textured grains of Y123

[24]. 6.88 GeV Kr ions barely penetrate 1.0 mm of

YBCO. Se vs. penetration distance, for such ions,is shown in Fig. 7.

Following bombardment of the Y123 by vari-

ous fluences of Kr ions, up to Bu ¼ 40 T, criticaltrapped fields, Bt, of the Y123 targets were mea-sured at the entrance and exit surfaces of the Kr

ions. Bt was found to be higher at the exit, where Seis high, showing that Jc is higher on the exit side ofthe sample, where Se is high.One of the Y123 targets, initially �1 mm thick,

was gradually thinned by polishing on the exit

side. As the target was thinned, trapped field was

repeatedly measured at the front and rear of theY123 target. Fig. 8 shows the results. The region of

the target containing the higher Jc was all con-tained in the last �0.1 mm of Kr ion track.

Analysis of these results indicates that high Jc isrestricted to the region of the sample where

SeP 0:8� 0:1 keV/�AA. The remaining 90% of the

Y123 target shows negligible increases in Jc com-pared to those seen for SeP 0:8� 0:1 keV/�AA.

Fig. 6. Example of quasi-columnar damage caused by fission

ions in melt-textured Y123. Scale bar is 200 nm. Large deposits

are (U0:6Pt0:4)YBa2O6. Thermal neutron irradiation has been

used to fission a small fraction of the 235U. Visible fission track

damage is estimated to be <26 �AA in diameter, and is the core of

the total damage to the HTS, which is estimated to be <52 �AA in

diameter. Columns, broken columns and string-of-bead dam-

age are observable.

Fig. 7. Graph of specific ionization, Se, vs. range of 6.88 GeVKr ions in melt-textured Y123, used by Weinstein et al. [24] to

measure Se;min.

398 R. Weinstein et al. / Physica C 387 (2003) 391–405

It is also found in the Kr experiment that Jccontinues to increase as the ion fluence is increased

to Fi � 1:9 1012 Kr/cm2 (i.e., to an ‘‘equivalentfield’’ of Bu � 38 T) [24].

3.4. Conclusions from experiments involving MILD

pinning

In the literature, early work on columnar pin-

ning assumed that it was a priorie evident the best

pinning centers would be those with maximum

Upin (e.g., Ref. [25], 1993). As time went on thisassumption grew to the status of dogma. Morerecently it is stated that (e.g., Ref. [26], 2000) ‘‘the

columnar morphology of such defects make them

the most effective pinning centers in high tempera-

ture superconductors,’’ and ‘‘For effective local-

ization of a vortex the defect must extend along its

entire length.’’ (Italics are ours.) MILD pinning

centers violate these strong statements that Upinshould be maximized [25,26], because for MILDcenters fL is considerably below 1.0 [9,20]. Nev-ertheless MILD pinning provides superior results.

Although complete columns are not produced, and

pinning potential is reduced by the factor fL < 0:5[9,20], the MILD pinning resulting from low val-

ues of Se, have proven to be the most effectivepinning centers utilized to date.

It is known that, for full columnar defects, Jc isincreased by a factor of �3 in melt-textured grains.Additionally, from fission fragment data, involv-

ing MILD pinning, it is known that Jc is muchmore strongly improved for 0:86 Se6 1:7 keV/�AAin textured grains. Furthermore, it is known that Jcis negligibly improved for Se < 0:8� 0:1 keV/�AA.Consequently, there must exist a value of Se in therange 0:86 Se6 3:5 keV/�AA which results in an op-

timum increase of Jc.A review of the literature indicates that MILD

pinning centers have not been systematically

studied as a way to improve Jc in HTS. Appar-ently, the focus on maximizing Upin has discour-aged such work.

We conclude that there is an optimum value of

Se for ionic damage which results in Jc and Bpin farsuperior to that achieved by full columnar defects,and is at least as good as that produced by fission

ions. We seek an experiment to confirm this con-

clusion, and determine the optimum value of Se.

3.5. Se as a controlled variable

In general, Se is a function of ion energy, Eion[27]. There are usually two choices of ion energy

which will provide a chosen value of Se; one a verylow energy, and one a much higher energy. For

very low values of Se there is a third possible choiceof Eion [28]. These regions are shown schematicallyin Fig. 9.

The rate at which an ion of charge Z 0 loses en-

ergy to target electrons is proportional to Z 02=v2

[27]. Here, v is the ion velocity, and Z 0 is the charge

of an ion at a given point in its trajectory (the

nuclear charge, þZe, minus any electron charges).The highest value of Se obtainable is achieved forthe slowest moving, completely ionized, uraniumatom. This value is Se � 4:2 keV/�AA for Y123, andoccurs for EU � 4:4 GeV [29]. Values of Se belowthis highest value can generally be produced by

either lower or higher ion energy.

On the higher energy side of the peak value of

Se, ions are stripped of their electrons when they

Fig. 8. Data from experiment of Weinstein et al. [24] (6.88 GeV

Kr ions incident on Y123). Open points are trapped field, Bt,measured at surface at which incident ions enter. Filled points

are Bt at rear of sample. Data shown is at 77 K, and measuredas Y123 sample is thinned from the rear. Solid lines are calcu-

lated for Jc unchanged before and after irradiation (20 kA/cm2)except in final 0.1 mm of Kr track in which Jc increases stepwiseto 90 A/cm2. Dotted line is expected result if Jc is unchanged infinal 0.1 mm. Interpretation is that Jc is much higher at the rearof the sample, where Se > 0:8� 0:1.

R. Weinstein et al. / Physica C 387 (2003) 391–405 399

penetrate matter. Thus, U of Ei P 4:4 GeV be-

comes fully ionized in Y123. The ionic charge is

constant and, until energies are so high that rela-

tivistic effects occur (i.e., until Ei � Mionc2), Se be-haves as Se / Zion=v2, where Z is the nuclearcharge.

The behavior on the lower energy side of the

peak of Se is not so simple. In that region, in ad-dition to statistical fluctuations in the ionization

and excitation of the target atoms, there is pick up

and loss of electrons by the incident ion. When the

ion finally stops, it is neutral. It has picked up Znegatively charged electrons which neutralize itsnuclear charge of þZe. Generally as the ion slowsto a velocity v comparable to the orbital velocity ofsome electron in the target atoms, it has the

highest probability of picking up that electron to

neutralize a portion of the positive ionic charge.

As a result, ionic charge is a function of velocity.

As an ion slows down, the decrease in ionic charge

due to electron pick up dominates over the de-crease in velocity, and Se / Z 02=v2 decreases to-ward zero.

Another drawback to using low ionic energy is

that there is more Coulomb scattering at low Eion,and consequently less certainty about the direction

of the ion in the sample. At higher energies,

Coulomb scattering is, on average, negligible [28].

For these reasons we prefer to consider tests of the

ideas proposed herein at higher energies (region B

in Fig. 9).

3.6. Damage diameter, dd , vs. Se for MILD pinning

centers

The column of damage produced by an ion has

a core which is the result of melting (or vaporiza-

tion) of the crystalline material and resolidifying in

an amorphous form [8]. Around this core is an

area damaged by shock wave and reduced oxy-

genation [9,10]. Extensive literature exists on the

core portion of dd (e.g., [3,8–10,30–37]). The corediameter depends primarily on Se, but may alsodepend on Eion, and on the direction of the ionrelative to the HTS axes [10]. For given values of

Eion, Se, and direction relative to the HTS crystalaxes, the diameter of the core is relatively well

determined in the literature. The increase in radius

due to shock and deoxygenation is less well de-

termined. The relatively well determined values ofthe radius of the core, and the more speculative

shock/deoxygenation radii are both shown in Fig.

10, which summarizes dd vs. Se, at high energy, forions in Y123. Features of Fig. 10 have been used

earlier in this discussion. For example, dd � 136 �AA,for full columnar defects produced by ions with

SeP 3:5 keV/�AA, was used to estimate Bmax.

Fig. 9. Schematic of energy loss, Se, vs. ion energy, Eion for atypical ion. In region A, incident atom is only partially ionized.

In region B atom is fully ionized and non-relativistic. In region

D, relativistic effects cause increase of electric field transverse to

v*. Region C is referred to as the region of minimum Se. Inregions A and B, Se / Z2ion=v

2ion.

Fig. 10. Radius of damage to Y123 by incident ion having

specific energy loss, Se. Solid line shows radius of amorphouscore of damage. Dashed line shows approximate damage radius

including region of shock wave and deoxygenation.

400 R. Weinstein et al. / Physica C 387 (2003) 391–405

Note that dd decreases as Se decreases. For ex-ample, at the highest values of Se involved in theuse of fission fragment ions (Se < 1:7 keV/�AA),dd6 52 �AA. Thus, the damage area resulting fromfission ions is, at its largest, only ð52=136Þ2 ¼14:6% of the damage area resulting from completecolumns. This upper limit for the value of dd forfission ions may be used in Eq. (11) to find Bmax.The result is that, using fission ions, pinning cen-

ters sufficiently numerous to trap at least 23.7 T

can be produced. This has been experimentally

tested and confirmed up to 14 T [38]. For these

values of Se, fL � 0:5. Therefore, damage de-creases due to fL also. Fission fragments utilize0:86 Se6 1:7 keV/�AA, and hence 06 dd6 52 �AA, in-dicating that Bmax may be much higher.Note in Fig. 10 that dd ! 0 at �0.7� 1 keV/�AA.

Recall that the point at which the enhancement of

Jc was lost in the Kr data [24] was 0:8� 0:1 keV/�AA.This indicates that it is the string-of-beads and

broken-column morphology of multiple-in-line-

damage which is associated with large increases inJc, and that large Jc enhancement does not resultfrom nuclear collisions. This view is reinforced by

the observation that the diameter of the ionic

damage is a good match to the diameter expected

theoretically for pinning centers when the log

factor of Eq. (1) is not utilized.

The variation of dd with Se is, within experi-mental errors, linear. Therefore we can represent

dd vs. Se, approximately, by the expression

dd ¼ 136 �AA½ðSe 0:7 keV=�AAÞ=2:8 keV=�AA� ð19Þ

in the interval 0:7 < Se < 3:5 keV/�AA. Eq. (19) plusEq. (11), yields the value of Bmax expected for anygiven value of Se.Fig. 11 shows data on Se vs. dd for BiSCCO.

4. Design of an experiment to determine the

optimum MILD pinning centers

We have reviewed the negative aspects of ionicfull columnar damage acting as pinning centers.

We noted that MILD ionic damage is experimen-

tally proven to result in higher Jc at higher appliedfields, BA, despite the fact that the pinning poten-tial, Upin, is reduced by more than a factor of 2. Weattribute the improvement in Jc and pinned field,Bpin, to smaller diameter of damage, dd, and lowerdamage length, fLL, for MILD pinning. Except forexperiments such as those involving fission ions,

the MILD region of Se remains largely unexplored.We next consider whether there exists the possi-

bility of a practical experimental confirmation of

these conclusions, including a method to deter-

mine the optimum MILD pinning morphology.

4.1. General approach

Following the arguments given above, we seek

an ion beam (or beams) which can explore the full

range of Se known to be effective in increasing Jc

0:7 < Se < 3:5 keV=�AA

Since Se varies continuously as an ion loses energy,we will let very energetic (low Se) ions impinge onan HTS target. As they lose energy, Se will in-crease. We will use a sandwich of thin targets todefine intervals of Se, so that we may explore alarge range of Se in one experiment. (See Fig. 12.)We will expose these targets to a variety of flu-

ences, Fion. After irradiation, we will measure Jc vs.BA and T , for each separate layer of the sandwich,and thus obtain JcðB; T Þ as a function of Se and Fi.

Fig. 11. Radius of damage to BiSCCO by incident ion having

specific energy loss, Se. Solid line shows radius of amorphouscore of damage. Dashed line shows approximate damage radius

including region of shock wave and deoxygenation.

R. Weinstein et al. / Physica C 387 (2003) 391–405 401

We will also measure other characteristics of the

superconductors which vary with Se and Fi (e.g.,Hirr, Tc, creep, etc.). Other questions of interest, asoutlined in the next section, can also be explored in

the same data sample.

4.2. Other questions of interest

In the proposed work, we can additionally

measure parameters of ion damage which are not

presently well known. We will determine the

fraction, fL, of the track length which pins, andhence the fraction of Upin which is utilized. We willalso determine average column length hci and gaphgi as Se varies.We expect the optimum value of Se for ‘‘stiff’’

fluxoids (e.g., in Y123) to differ from that of flex-

ible fluxoids (e.g., in BiSCCO) because the pinning

gap hgi varies with Se; i.e., we expect that largergaps in the pinning center will be better tolerated

in HTS with stiff fluxoids, such as Y123.

To the best of our knowledge there have been

no tests of percolation theory involving the effects

of broken-columnar damage on percolation inHTS. (In percolation theory this is related to the

‘‘Swiss cheese model’’ [39].) The sample set will

provide a test of percolation effects for broken

columns in HTS, in which comparison to full

columns is particularly straight forward, since full

columnar samples are generated in the same data

set as broken columns.The data set generated by the proposed exper-

iments will also permit measurement of the effect

of pinning center diameter. Consider, as an ex-

ample, Y123 for which dd vs. Se is shown in Fig.10. Note that 0 < dd < 136 �AA. At 77 K, the valueof the coherence lengths n in Y123 are [40]: nc � 7�AA and nab � na ¼ nb ¼ 20 �AA. Thus, for MILD de-fects in which a fluxoid parallel to the c-axis ispinned, dd will vary from 0 to �7nab, at 77 K. i.e.,

the proposed experiment will permit a meaningful

study of Jc vs. the variable dd=n. Such data allowsinterpretation in terms of pinning force vs. dd=nab

[46]. Eq. (2) indicates a quasi-saturation of pinning

potential at a value of dd � 2ffiffiffi2

pnab � 57 �AA, at 77

K. The data set will permit study of Jc at values ofdd as high as 2.4 times this expected saturationvalue, and as low as zero, at 77 K.

4.3. Details of a proposed experiment

The design of the experiment is discussed for

the HTS Y123, although any HTS may be used

(e.g., Nd123, Sm123, BiSCCO, or MgB2).

We desire to use targets thick enough to be self-

supporting. For example, for textured Y123, made

in our laboratories, this requires a thickness

DX P 0:2 mm.In each slice of sample (Fig. 12), we aim to re-

strict Se to an interval of about �10% or less, inorder to meaningfully determine, e.g., Jc ¼ JcðSeÞ.We find that the region 0:76 Se6 3:5 keV/�AA can

be spanned by two ion beams, and meet the above

constraints, if 56 GeV 238U92, and 110 GeV 197Au79

are used, for example. These beams are scheduled

at the GSI Accelerator, Darmstadt. Figs. 13 and

14 show Se vs. penetration distance for these twoion beams, each incident on Y123 [29].

The study of Se vs. range for 56 GeV 238U shows

that the interval of Se available is about 1:22 <Se < 4:2 keV/�AA. We do not use the very end ofrange of the Uion, where the ion velocity is very low,for reasons discussed earlier. Se ¼ 3:7 keV/�AA is

Fig. 12. Schematic of HTS targets. Energetic ions are incident

from left. It is planned to irradiate entire sandwich at one time,

thereby spanning the range of Se noted in Figs. 13 and 14.Sandwich layers then will be separated for analysis.

402 R. Weinstein et al. / Physica C 387 (2003) 391–405

the highest value used in the proposed 238U ex-

periment. Thus the 238U measurement covers the

range 1:226 Se6 3:7 keV/�AA.For the 110 GeV 197Au ions, we plan to utilize a

range of 0:646 Se6 2:6 keV/�AA. As a result, there isa significant interval of Se (1:226 Se6 2:6 keV/�AA)which is tested by both beams, and provides an

overlap region in which to test consistency of in-

terpretation.

Figs. 13 and 14 also indicate target thicknesses

of Y123 which can be used to define Se to 6�10%.

4.4. Direction of beam relative to HTS axes, and

splay

The proposed experiment utilizes ions moving

parallel to the c crystal axis of Y123. As notedpreviously, the damage diameter, dd, depends inpart on the angle of v

*ion with respect to the crystal

axes [10]. Also, variation of angle in a single target

(splay) leads to fluxoid entanglement [41] which

merits study. Initially, parallel MILD pinning

centers can be studied, leading to a predominance

of individually pinned fluxoids. In later studies

angle of ion incidence can be changed to investi-gate, e.g., dependence on crystal axis orientation,

or can be varied in a given target, in order to test

the effects of splay, and consequent fluxoid en-

tanglement.

4.5. Estimate of radioactivity of the resulting

material

Radiation methods for introducing pinning

centers generally result in the highest Jc. Thehighest values of Jc in textured materials are thoseproduced by fission products. These are created by

the inclusion of 235U within the HTS, followed by

thermal neutron irradiation (called the U/n pro-

cess) [17–21]. This process also produces very low

residual radioactivity. Comparable Jc can also beproduced by high energy proton bombardment of

a fissile nucleus such as 209Bi [23], albeit with in-

creased radioactivity. Nevertheless, the application

of materials produced by the U/n process is limited

because they are radioactive. It is therefore of in-

terest to estimate the radioactivity of HTS material

containing MILD pinning centers.

We first note that the energetic ions used toproduce the MILD pinning traverse the HTS ma-

terial; they do not stop in it. In particular, the

energetic 238U exits the HTS, which then contains

no residual uranium.

We next consider induced radioactivity, caused

by the energetic ions. Using the liquid drop model

of the nucleus [42], and normalizing to earlier data

on proton irradiation [43], we calculated the ap-proximate gamma ray radioactivity for Y123 with

MILD pinning suitable for pinning BA ¼ 10 T,and compared it to other irradiated HTS. We find

Fig. 13. Se vs. penetration distance for 56 GeV 238U ions inci-

dent on melt-textured YBCO superconductor. Thickness of

regions a–e are designed to define Se to about �10%. Thicknessof regions a, b are thinnest practical, self-supporting targets of

textured YBCO made in our laboratory.

Fig. 14. As in Fig. 13, but using beam of 110 GeV 197Au ions.

Combination of U and Au beams cover region 0:6 < Se < 3:7keV/�AA. Overlap occurs for 1:26 Se6 2:6 keV/�AA.

R. Weinstein et al. / Physica C 387 (2003) 391–405 403

A 2 cm diameter, 1 cm thick, trapped fieldmagnet (TFM) with MILD pinning, capable of

trapping over 2 T at 77 K, will have a radioactivity

of �94 nCi. At a distance of 3 cm, this source givesa dose about equal to the ever-present cosmic ray

background. The radioactivity of this sample does

not require registration and is so low it can be

shipped through the mail. Comparison of the level

of radioactivity of a TFM with MILD pinningcenters to radioactivity of objects encountered in

everyday life may be more intuitively meaningful.

As an example of this, consider that the gamma

radioactivity ingested with milk averages 1.4 nCi

per quart [44]. Thus, a child drinking 1 quart of

milk per day ingests over 500 nCi of gamma ra-

dioactivity per year. This exceeds the amount of

radioactivity in five TFMs, each 2 cm diameter 1cm thick, containing MILD pinning centers.

4.6. Expected Jc

Fig. 1 shows the results of an experiment in

which melt-textured Y123 was irradiated with ions

for which 1:2 < Se < 2:5 keV/�AA, with a fluence ofFi � 2:5 1011 (Bu ¼ 5 T). This resulted in an in-crease in Jc by a factor of 3.5. Also, fission frag-ments, using 0 < Se < 1:7 keV/�AA (which is

effectively 0:76 Se < 1:7 keV/�AA) result in an in-crease in Jc by a factor of P 10 [17–19,38,45].Additionally, Gandini et al., in an analysis of Jc inU/n-BiSCCO, [21,22] concluded that Jc could beincreased by an additional factor of 2–3 if ion

damage, still remaining in the U/n process, could

be reduced by a factor of 2. Similar conclusions

may be drawn concerning removal of the de-

structive effects of ion bombardment from U/n

processing of Y123.Such experiments and calculations are summa-

rized schematically in Fig. 15. There, RJ vs. Se ispresented, where RJ represents the factor by which

Jc increases (or the factor by which we expect Jc toincrease when MILD pinning centers are used).

We therefore speculate that RJ may be about 40

for MILD pinning centers in textured large grain

HTS. This would, for example, increase Jc in Y123at 10 T and 50 K, to Jc � 106 A/cm2. We note thatthis value of Jc is what we expect to be produced inbulk grains of HTS without resorting to im-

provement of crystal axis alignment, or reduction

of weak links.

Acknowledgements

We wish to thank Dr. Jianxiong Liu for many

discussion of Se vs. E for various ions. We grate-fully acknowledge the support of this work by the

US Army Research Office, the Texas Center for

Superconductivity and Advanced Materials, and

The Welch Foundation.

References

[1] D. Nelson, V. Vinokur, Phys. Rev. B 48 (1993) 13,060.

[2] S. H�eebert, V. Hardy, M. Hervieu, G. Villard, Ch. Simon, J.

Provost, Nucl. Instrum. Meth. B 146 (1998) 545.

[3] G. Fuchs, F. Studer, B. Balanzat, D. Groult, M. Toule-

monde, J. Jousset, Europhys. Lett. 3 (1987) 321.

[4] L. Civale, A. Marwick, T. Worthington, M. Kirk, J.

Thompson, L. Krusin Elbaum, Y. Sun, J. Clem, F.

Holzberg, Phys. Rev. Lett. 67 (1991) 648.

[5] D. Bourgalt, M. Herview, S. Bouffard, G. Groult, B.

Raveau, Nucl. Instrum. Meth. B 42 (1989) 70.

[6] Y. Ren, R. Weinstein, R. Sawh, J. Liu, Physica C 282

(1997) 2301.

Fig. 15. Estimate of expected RJ vs. Se for pinning centersproduced by energetic ions of fluence Bu � 15 T. Labeling ofpoints, in order of decreasing Se, refer to calculations in Section2.5; Civale et al. [4]; Section 1, Fig. 1; experiments on fission

fragments, Refs. [17–19]; and Gandini et al. [7].

P+ irradiated Y123: 200,000 nCi/gm,

U/n processedY123: 200 nCi/gm,

MILD (10 T) Y123: 5 nCi/gm.

404 R. Weinstein et al. / Physica C 387 (2003) 391–405

[7] A. Gandini, R. Weinstein, D. Parks, R. Sawh, S.X. Dou,

Presented at Applied Superconductivity Conf., August

2002, IEEE Trans. Appl. Supercond., in press.

[8] M. Toulemonde, S. Bouffard, F. Studer, Nucl. Instrum.

Meth. B 91 (1994) 108.

[9] Y. Zhu, Z.X. Cai, R. Budhavi, M. Suenaga, D.O. Welch,

Phys. Rev. B 48 (1993) 6436.

[10] Y. Zhu, R. Budhavi, Z. Cai, D. Welch, M. Suenaga, R.

Yoshizaki, H. Ikeda, Philos. Mag. Lett. 67 (1993) 125.

[11] V. Hardy, D. Groult, J. Provost, M. Hervieu, B. Raveau,

S. Bouffard, Physica C 198 (1991) 225.

[12] R. Hensel, B. Roas, S. Henke, R. Hopfengartner, M.

Lippert, J. Strobel, M. Vildic, G.S. Ischenko, Phys. Rev. B

42 (1990) 4135.

[13] D. Bourgault, D. Groult, S. Bouffard, M. Hervieu, J.

Provost, F. Studer, B. Reveau, Radiat. Eff. Def. Solids 110

(1989) 211.

[14] C.J. Lobb, M.G. Forrester, Phys. Rev. B 35 (1987) 1899.

[15] M. Costantini, F. Brisard, A.M. Meftah, F. Studer, M.

Toulemonde, Radiat. Eff. Def. Solids 126 (1993) 233;

See also B. Roas, B. Hensel, S. Henke, S. Klaum€uunzer, B.

Kabius, W. Watanabe, G.S. Ischenko, L. Schultz, K.

Urban, Europhys. Lett. 11 (1990) 669.

[16] E.S. Gorbac, M.F. Thorpe, M.S. DeVries, A.R. Day, Phys.

Rev. A 43 (1991) 6473.

[17] R. Weinstein, Y. Ren, J. Liu, I. Chen, R. Sawh, V. Obot,

C. Foster, in: Advances in Superconductivity VI, Springer-

Verlag, Tokyo, 1994, p. 855.

[18] R. Weinstein, R. Sawh, Y. Ren, D. Parks, J. Mater. Sci.

Eng. B 53 (1998) 38.

[19] R. Weinstein, R. Sawh, D. Parks, M. Murakami, T.

Mochida, N. Chikumoto, G. Krabbes, W. Bieger, Physica

C 383 (2002) 214.

[20] E. Dartyge, P. Sigmund, Phys. Rev. B 32 (1985) 5429.

[21] A. Gandini, R. Weinstein, Y.R. Ren, R.P. Sawh, D. Parks,

Y.C. Guo, B. Zeimetz, S.X. Dou, S. T€oonies, C. Klein,H.W. Weber, Physica C 341 (2000) 1453.

[22] A. Gandini, Improvement of critical current, irreversibility

field, and anisotropy in BiSCCO tape by the U/n method.

Thesis submitted in partial fulfillment of the requirements

for the Ph.D., University of Houston, August 2001.

[23] H. Safar, J. Cho, S. Flashler, M. Maley, J.O. Willis, Y.

Coulter, J. Ullmann, P. Lisowski, G. Riley, M. Rupich,

J.R. Thompson, L. Krusin-Elbaum, Appl. Phys. Lett. 67

(1995) 130.

[24] R. Weinstein, R.-P. Sawh, J. Liu, D. Parks, Y. Ren, V.

Obot, C. Foster, Physica C 357 (2001) 743.

[25] R. Wheeler, M. Kirk, A.D. Marwick, L. Civale, F.

Holtzberg, Appl. Phys. Lett. 63 (1993) 1573.

[26] Chapter on columnar defects, by R.C. Budhani, in: A.

Narlikar (Ed.), Studies of High Temperature Supercon-

ductors, Nova Science Publishers, Huntington, NY, 2000,

p. 116.

[27] R. Weinstein, Interactions of Radiation and Matter,

McGraw-Hill, NY, 1964, p. 30.

[28] Particle Physics Booklet, Subset of Review of Particle

Physics, Eur. Phys. J. C 3 (1998) 181.

[29] J.F. Ziegler, J.P. Biersack, V. Littmork, in: The Stopping

and Range of Ions in Solids, vol. 1, Pergamon Press,

Oxford, 1985;

See also J.F. Ziegler, www.SRIM.org.

[30] D. Bourgault, M. Hervieu, S. Bouffard, D. Groult, B.

Raveau, Nucl. Instrum. Meth. B 42 (1989) 61.

[31] M. Toulemonde, N. Enault, J. Yun Fan, F. Studer, J.

Appl. Phys. 68 (1990) 1545.

[32] M. Konczykowski, F. Rullier-Albenque, E.R. Yacoby, A.

Shaulov, Y. Yeshurun, P. Lejay, ORB 44 (1991) 7167.

[33] V. Hardy, J. Provost, D. Groult, M. Hervieu, B. Raveau,

S. Durcok, E. Pollert, J.C. Frison, J.P. Chaminade, M.

Pouchard, Physica C 191 (1992) 85–96.

[34] L. Civale, L. Krusin-Elbaum, J.R. Thompson, R. Wheeler,

A.D. Marwick, M.A. Kirk, Y.R. Sun, F. Holtzberg, C.

Feidl, Phys. Rev. B 50 (1994) 4102.

[35] S. H�eebert, V. Hardy, G. Villard, M. Hervieu, Ch. Simon, J.Provost, Physica C 259 (1998).

[36] D.X. Huang, Y. Sasaki, Y. Ikuhara, Phys. Rev. B 59 (1999)

3862.

[37] N. Kuroda, N. Ishikawa, Y. Chimi, A. Iwase, H. Ikeda, R.

Yoshizaki, T. Kambara, Phys. Rev. B 63 (2001) 2245.

[38] R. Weinstein, R. Sawh, Y. Ren, M. Eisterer, H. Weber,

Supercond. Sci. Technol. 11 (1998) 959.

[39] R. Zallen, The Physics of Amorphous Solids, John Wiley

and Sons, NY, 1983.

[40] P. Poole, Handbook of Superconductivity, Academic

Press, 2000.

[41] T. Hua, P. Le Doussal, D. Nelson, V. Vinokur, Phys. Rev.

Lett. 71 (1993) 3545.

[42] R. Weinstein, Nuclear Physics, McGraw-Hill Book Co,

NY, 1964, p. 82.

[43] R. Weinstein, I. Chen, J. Liu, J. Xu, V. Obot, C. Foster, J.

Appl. Phys. 73 (1993) 10.

[44] Human Health Fact Sheet, Argonne National Lab, Octo-

ber 2001.

[45] R. Weinstein, Y. Ren, R. Sawh, A. Gandini, W. Hennig,

M. Murakami, T. Mochida, N. Chikumoto, N. Sakai, G.

Krabbes, W. Bieger, D. Milliken, S.X. Dou, S. T€oonies, M.

Eisterer, H.W. Weber, Physica C 341 (2000) 1415.

[46] D. Dew-Hughes, Philos. Mag. 30 (1997) 293.

R. Weinstein et al. / Physica C 387 (2003) 391–405 405