Gasars: a class of metallic materials with ordered porosity

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

OVERVIEW

Gasars a class of metallic materials withordered porosity

L Drenchev1 J Sobczak2 S Malinov3 and W Sha4

High porosity metallic materials are designed for special properties which can be used in many

industrial applications The development of new porous structures is a challenge for materials

scientists This paper discusses general characteristics structure properties and some

manufacturing practices of a class of relatively new metallic materials named gasars ordered

porosity materials or lotus type porous materials An overview of the metals and alloys used and

mechanical properties studied is presented Some relations between structure characteristics

and mechanical properties are discussed Basic relations between processing parameters and

structure characteristics are analysed Special attention is paid to the complex physical

phenomena in ordered porosity structure formation Conditions for production of high porosity

ingot are discussed

Keywords Porous materials Gasars Ordered porosity Lotus type porous materials

List of symbolsA A9 constants in Sievertrsquos law K

B B9 constants in Sievertrsquos law mol m23 Pa212

CE eutectic concentration mol m23

CL gas concentration in liquid mol m23

CS gas concentration in solid mol m23

C0 initial gas concentration in melt mol m23

C maximum gas concentration in melt at solidliquid interface mol m23

F1 empirical parameter dimensionless

g acceleration of gravity (981) m s22

k distribution coefficient (k5CSCL)dimensionless

KL KS coefficients mol m23 Pa212

p porosity dimensionless

peff effective pressure (peff5F21 PH) Pa

pM partial gas pressure Pa

Dpb driving force (Dpb5pM2peff) Pa

P pressure in gas bubble Pa

P1 P2 pressures Pa

PAr partial gas (Ar) pressure in surroundingatmosphere Pa

Phyd hydrostatic pressure in melt (Phyd5rgh) Pa

PH partial gas (H2) pressure in surroundingatmosphere Pa

Ptot total pressure in melt (Ptot5PHzPArzPhyd)Pa

DP pressure drop across curved meniscus inequilibrium (DP5P22P1) Pa

Q constant (PArPH) dimensionlessR radius of curvature m

Rb radius of bubble mRP radius of conical pit at the level of meniscus

mR0 critical radius mSl relative part of bubble surface contacting

with liquid dimensionlessSs relative part of bubble surface contacting

with solid dimensionlessT temperature K

Tm melting point of metal Knb velocity of bubble movement m s21

vcr solidification front velocity m s21

g melt viscosity Pa sr melt density kg m23

rg gas density kg m23

rs solid copper density kg m23

r gasar ingot density kg m23

s surface energy J m22

sgl surface tension for gasliquid interfacesJ m22

sgs surface tension for gassolid interfaces J m22

sy yield strength MPasUTS ultimate tensile strength MPa

hC half angle of conical pit uhW contact angle of melt on solid inclusion u

IntroductionThe development of metal matrix composites and porousmaterials is a very significant part of the progress inapplication of metals and alloys as structural materialsUsually this progress is based on the improved combina-tions such as between mechanical properties and density

1Institute of Metal Science 67 Shipchenski Prohod Street 1574 SofiaBulgaria2Foundry Research Institute 73 Zakopianska St 30 418 Krakow Poland3The Queenrsquos University of Belfast School of Mechanical and AerospaceEngineering Belfast BT7 1NN UK4The Queenrsquos University of Belfast School of Planning Architecture andCivil Engineering Metals Research Group Belfast BT7 1NN UK

Corresponding author email wshaqubacuk

2006 Institute of Materials Minerals and MiningPublished by Maney on behalf of the InstituteReceived 13 January 2006 accepted 13 March 2006DOI 101179174328406X118302 Materials Science and Technology 2006 VOL 22 NO 10 1135

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

and between properties and cost A great number ofparticle and fibre reinforced metal matrix compositeshave been investigated and some well known castingtechnologies have been adapted for production of suchcast parts for specific use Many technologies forproduction of porous metal materials have been devel-oped The efforts have been directed not only atdeveloping technologies for production of these materialsbut also at studying their characteristics and properties Aspecial class of metal porous media which appears as gasreinforced metal matrix composites is ordered porositymaterials Two of the main features of these materials arethat the porosity is predominantly ordered and that theirstructure is formed during directional solidification as aresult of the so called gas eutectic reaction A widediscussion on the manufacturing practice structureproperties and application of porous materials can befound1ndash3 The major advantages of ordered porositymaterials over other porous metals are

(i) improved strength and rigidity

(ii) possibility of making regular structures

(iii) a wide range of pore diameter (10 mm to10 mm)

(iv) feasibility for control of pore shape andorientation

(v) easy fabrication and relatively low cost

As all porous metals the ordered porosity metals have awide range of applications including filters catalysissilencers flame arresters heat exchangers fuel cellselectrolytic cells fluid substance separators ionic rocketengine parts self-lubricating bearings thermal screensand vibration dampers The development of solar andnuclear power generation technology has made porousmetal candidates for electromagnetic and neutronabsorbers It is highly probable that porous metals willbe used for the inner walls of nuclear fusion reactorsPermeable porous metals may be used as matrixes ofcomposite materials

Stainless steel of ordered porosity is a promisingmaterial for medical applications and especially forartificial bones or joints with good corrosion resistanceTo provide better biocompatibility of this materialIkeda and Nakajima applied laser deposition techniquefor surface coating of porous steel4 Titanium film ofseveral micrometres was coated on the flat surface andinside pores Tensile tests were carried out to evaluatethe adhesive strength between titanium layer andsubstrate of stainless steel It was found that theadhesive strength was strong enough for the use forbiomedical devices It is expected that if such material isused as artificial bone or joints the new bone can grow

into pores and thus the bond between natural bone andartificial bone becomes much stronger

The purpose of this article is to provide a compre-hensive view of characteristics properties and mainrelations between processing parameters and finalstructure of the ordered porosity materials Specialattention will be paid to the quantitative description ofphysical phenomena involved

General characteristics andrelationshipsUsually pores formed in metal castings and ingots aredetrimental to properties Higher amount of porosity ina casting results in greater deterioration in mechanicalproperties Depending on the nature of the metal poresform during solidification owing to shrinkage phenom-enon and higher gas solubility in the molten phasecompared with that in the solid phase Although a set ofrules can be followed in order to avoid such defects inthe cast product it is impossible to completely eliminatesuch defects One of the most effective ways to reducepore content is to remove as much gas from the melt aspossible Conversely gas supersaturation of the melt is aprecondition for the production of porous materialsespecially in the technology for production of orderedporosity materials

Techniques for productionAmong the methods for porous metals production thereis a specific and relatively new one offered byShapovalov5 to produce metals with ordered porosityoriginally named gasars (gaszar where lsquoarrsquo is abbrevia-tion of Russian lsquoarmirovatrsquo which means lsquoto reinforcersquo)The most important feature of the method is unidirec-tional solidification of gas supersaturated melt throughthe eutectic point (Fig 1) Owing to higher gas solubilityin the liquid phase solidification of the metal andnucleation of gas pores occur simultaneously whichresults in formation of an ordered gas eutectic composi-tion This phase transformation is very similar to theconventional eutectic reaction but one of the phases inthe resulting eutectic structure is a gaseous phase Rod-like eutectic of NiAlndashMo in Al matrix is shown in Fig 2and cross-sections of two copper ordered porosity ingotsare shown in Fig 3 Similarity between these structuresis evident

1 Schematic equilibrium phase diagram of metal (M)ndash

hydrogen (G) system (left) and eutectic growing

upward in directional solidification (right)

2 Image (SEM) showing transverse cross-section of

NiAlndashMo rod-like eutectic (after Ref 6)

Drenchev et al Gasars a class of metallic materials with ordered porosity

1136 Materials Science and Technology 2006 VOL 22 NO 10

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

Specific solidification conditions and obtained micro-structure provide lsquogas reinforcementrsquo of mechanicalproperties of ingot8 To describe such materials someinvestigators used phrases such as ordered porositymetal materials gas eutectic structure and lotusstructured porous metals In this paper the termslsquoordered porosity materialrsquo and lsquogasarrsquo will be consid-ered equivalent

Usually the gas used for melt saturation is hydrogenand a great number of metalndashhydrogen systems havebeen investigated1910 Oxygen and nitrogen can also beapplied1112 Metals and alloys that have been used inthis technology include113ndash18 Al Be Cr Cu Fe MgMn Mo Ni Ti AlndashCu (different compositions) alloysAlndashSi (different compositions) alloys steel8 andiron1920 The most common metals studied are coppernickel aluminium and cobalt Fabrication of orderedporosity silicon is also possible21

Real production process of the material consists oftwo stages

(i) gas saturation of melt

(ii) melt solidification in a conventional mould19 orapplying continuous zone melting technique82223

Some particular details of gas pore formation and poregrowth are given in a number of papers and compre-hensive studies of nucleation and evolution of hydrogenporosity in aluminiumndashcopper and aluminiumndashsiliconalloys are published13ndash1524 It is emphasised that nometal foaming occurs because the gas lsquoappearsrsquo as themelt solidifies Schematic representation of a gasar unitis shown in Fig 4 Variants of this design are applied inUkraine and Japan20 Such unit is suitable for Cu Aland its alloys of high thermal conductivity Howeverordered porosity materials fabricated by this techniquefrom metals and alloy of relative low thermal con-ductivity do not have uniform pore size and porosity25

because solidification rate becomes lower as the solidi-fication proceeds which results in an increase in the poresize In order to overcome this problem a newtechnique continuous zone melting technique schema-tically represented in Fig 5 has been developed26 Longrods of homogeneous ordered porosity metals and alloyscan be fabricated by this technology

The main process parameters that govern the amountof porosity and its geometrical characteristics including

the size shape and orientation of the pores are thehydrogen level in the melt gas pressure over the meltduring solidification initial melt and mould tempera-ture direction and rate of heat removal and alloycomposition Varying these parameters can control thepore structure and distribution over a wide range Forthis reason gasars are often called controlled porositymaterials Generalised diagrams of pore morphologyobtained under different conditions are depicted inFig 6 Typical structures of real copper gasars are givenin Fig 7

The gasar process has been used not only to produceporous metals but also some ceramics (glass aluminaaluminandashmagnesia) All these ordered structures provideattractive mechanical thermal tribological acousticand other properties

Porosity and pore characteristicsGenerally the porous structures may be characterisedby a set of parameters which provides quantitative andqualitative information for the material considered The

a porosity 326 b porosity 4473 Typical micrographic pictures of transverse (top) and

longitudinal (bottom) cross-sections of copper gasar

(after Ref 7)

1 ndash top and bottom covers 2 ndash heater 3 ndash melt to besaturated 4 ndash gas supply and evacuation system 5 ndashsolidifying metal 6 ndash heat supply system 7 ndash gasaringot with axial structure 8 ndash heat sink for directionalsolidification 9 ndash strong hermetic casing 10 ndash mouldcooling system 11 ndash heat shield

4 Schematic representation of gasar growth unit

a heating zone b fabricated porous metal5 Scheme of continuous zone melting technique (after

Ref 8)

Drenchev et al Gasars a class of metallic materials with ordered porosity

Materials Science and Technology 2006 VOL 22 NO 10 1137

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

most important parameters are porosity average poresize pore size distribution pore shape and orientationand degree of pore interconnection Regions of variationof pore size and porosity in the most popular porousmaterials are presented in Fig 8 Gasars differ structu-rally from other porous materials15 A great diversity ofporosity pore shapes and pore sizes is observed Thepore size varies between 10 mm and 10 mm and theporosity may reach 75 It allows producing metalmaterials of specific weight lower than 05 Physicalproperties of base materials and processing parametersdetermine these characteristics For instance the possi-ble porosity range in a material depends mainly on gassolubility within it and the range of pore sizes dependson the gas diffusion coefficient The specific porositypore length shape and direction for a particular gasaringot depend on processing parameters including cool-ing rate direction of heat removal and partial gaspressure above the melt Correlation between possibleporosity range and range of pore sizes obtained in somebase metals is shown in Fig 9

Because of the nature of liquidndashsolid transformationthe pore direction always coincides with the temperaturegradient ie pores are perpendicular to the movingsolidification front Thus pores shown on Fig 6b and eare related to radial heat removal and pores as given inFig 6c and f are related to axial heat removal

Physical phenomena in gasar structureformation processThe first stage of ordered porosity material production isgas saturation of the melt The solubility in the liquid aswell as in the solid state increases with the temperatureHydrogen dissolves in molten metals in atomic form andthe equilibrium concentration in the melt is given by thewell known temperature dependent Sievertrsquos law9

ln CL~A

TzBz05ln PH (1)

9 Porosity and pore sizes of gasar ingots formed in

some pure metals (after Ref 30)

a spherical b radial c cylindrical dndashf laminates6 Diagrams of pore morphologies potentially available

with gasar process (after Ref 27)

a and b rrS5061 c and d rrS50387 a and c longitudinal and b and d transverse cross-sections

of porous gasar copper28

1 ndash irradiation-induced pores 2 ndash sintered powders 3 ndashsintered fibres 4 ndash foamed metals 5 ndash gasars

8 Relationship between pore size and porosity in various

metals (after Ref 29)

Drenchev et al Gasars a class of metallic materials with ordered porosity

1138 Materials Science and Technology 2006 VOL 22 NO 10

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

The constants A and B are different for solid and liquidmetals and differ from metal to metal

The metal rich parts of the phase diagrams of somemetalndashhydrogen systems are shown in Fig 10

The second stage of ordered porosity materialproduction is unidirectional solidification It is consid-ered that the solidification runs in a vertical vessel withcooling system set at the bottom At the very beginninga thin nominally solid (non-porous) layer forms andsome quantity of gas is released at the solidliquidinterface This leads to gas supersaturation of the meltclose to the interface which increases probability for gasbubble nucleation

For a certain temperature for instance the solidustemperature and when equilibrium is valid equation (1)transforms into a simpler form

CL(T)~KLP1=2H (2)

for gas solubility in liquid and

CS(T)~KSP1=2H (3)

for gas solubility in solid

Usually liquid metals exhibit a propensity for gassupersaturation For instance under some specificconditions hydrogen concentration in aluminium canbe two or even three times higher than obtained byequation (2) To describe this fact equation (2) can bemodified as

CL(T)~F1KLP1=2H ~KL(F2

1 PH)1=2 (4)

here F1gt1 is considered to be a constant which gives thepropensity for gas supersaturation of the melt The lastrelation allows introducing an effective pressure peff

peff~F21 PH (5)

Equation (2) provides a relation between partial gaspressure above the liquid and the solubility of that gasunder equilibrium conditions When the conditions forequilibrium are not valid and gas concentration in liquidis CL the partial gas pressure in the melt can be definedlike this

pM~CL

KL

2

(6)

If pMpeff a quasi-boiling process starts in this region ofthe melt which means that bubbles of dissolved gasform homogeneously in the liquid and they moveupward resembling boiling The difference

Dpb~pMpeff (7)

is the driving force for homogeneous bubble nucleationin a supersaturated melt The parameter

DCL~KL (pM)1=2(peff )1=2

h i(8)

defines the gas quantity in unit volume which iscontained in the formed lsquoboilingrsquo bubbles The quasi-boiling process is undesirable for the gasar tech-nology because this process reduces the gas concentra-tion at solidliquid interface and in turn the ingotporosity

It is easy to show3435 that the probability forhomogeneous bubble nucleation in a melt is negligiblein comparison with the probability for heterogeneousnucleation at the same thermodynamic conditions Inother words homogenous bubble nucleation in the meltrequires extremely high values of Dpb and is thereforepractically impossible Heterogeneous nucleation startsat relatively low Dpb at preferred nucleation sites whichmay be of the following types

(i) microscopic pits and cracks on non-wettedinclusions in the melt

(ii) microscopic pits and cracks on the solidificationfront

A conical pit on an inclusion in the melt under vacuumwas considered (Fig 11) The pressure drop across the

10 Metalndashhydrogen phase diagrams for a Co (after

Ref 31) b Ni (after Ref 32) and c Cu (after Ref 33)

Drenchev et al Gasars a class of metallic materials with ordered porosity

Materials Science and Technology 2006 VOL 22 NO 10 1139

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

curved meniscus in equilibrium is defined by Laplacersquosequation

DP~P2P1~2s

R(9)

where P1 is the pressure on the convex side of themeniscus and P2 is the pressure on the concave side ofthe meniscus In the case of non-wetted inclusions asshown in Fig 11a P1 is zero and P2 is equal tohydrostatic pressure at the meniscus For this geometrythe pressure drop across the meniscus can be expressedby the equation9

DP~P2P1~P2~2scos(hWhC)

RP(10)

The last formula expresses correlation betweenhydrostatic pressure (P25Phyd) and the radius of theconical pit at the level of meniscus when a metal ismelting under vacuum The bottoms of pits and cracksof non-wetted inclusions will not be wet by the melt andwill exist as an empty volume (vacuum) in the liquidWhen a mixture of H2 and Ar is added over the meltwhich is typical for gasar technology hydrogen willsolute in atomic form in the liquid diffuse to theseempty volumes and come out of solution to exist as H2

again Thus the volumes are now bubble nuclei Thehydrogen pressure in these nuclei is given by Sievertrsquoslaw equation (1) and after certain period for satura-tion it becomes equal to the hydrogen partial pressureabove the melt PH Ar does not diffuse to thesevolumes because it is practically not soluble in theliquid As stated above the nucleation sites can be notonly inclusions but also microscopic pits and cracks onthe solidification front

In the case of wetted inclusions configuration asshown in Fig 11b is not feasible because P2 is zeroand formally according to equation (9) P1 must benegative which is nonsense If an inclusion is wetted the

melt will fill the cavity and there will be no emptyvolume for bubble nucleation

It should be noted that the prominent feature of thesebubble nuclei is their concave liquidgas interface withrespect to the liquid phase This allows the gaseousphase to exist at a pressure P15PH below that of theliquid

Ptot~PHzPArzPhyd (11)

as shown by equation (10) In order for the nucleus toform a bubble which means a convex interface to theliquid the pressure in the nucleus must increase to avalue greater than the pressure in the liquid Ptot

When the melt solidifies it becomes supersaturatedwith hydrogen (see equation (4)) The partial gas(hydrogen) pressure in this supersaturated melt is peff

defined by equation (5) In the melt beside the nuclea-tion sites (pits and cracks on the solidification front orpits and cracks on the inclusions near to the solidliquidinterface) hydrogen comes out of solution to exist asmolecules in a nucleus because peff is greater than PH Ifpeff is also greater than Ptot at this point the pressure inthe nucleus will increase and will cause it to grow untilthe meniscus reaches the top of the conical pit If oneassumes that the opening of a conical pit has roundededges36 then further increase in the pressure in thenucleus will result in strengthening of the meniscus Itshould be noted that the contact angle is independent ofthe surface geometry and is the same on a curvedsurface as on a flat one37 The interface will becomeplanar when the pressure in the nucleus equals thepressure in the liquid If the pressure continues toincrease a small bubble will begin to formSubsequently the three phase interface will move overthe rounded part of the opening9 At the moment whenthis interface overcomes the roundness the radius ofcurvature is minimal This corresponds to the maximumpressure in the nuclei Any further increase in the bubblevolume owing to hydrogen diffusion from the super-saturated melt will result in an increase in the radius ofcurvature This also leads to a subsequent decrease inthe equilibrium pressure in the nucleus as given byLaplacersquos equation (equation (9)) Therefore bubblegrowth will occur rapidly and will either detach fromor engulf the inclusion

A gas nucleus on the solidification front or oninclusion close to this front was considered Suchnucleus may be engulfed by advancing solidificationfront or become a bubble flowing upward in the melt Athird possibility which is the basis of ordered porositystructure formation is this nucleus to be trapped by thefront and to grow as a pore of near cylindrical shapesimultaneously with the solid The hydrogen content inthe solid phase will be balanced through such pores andwill be defined again by Sievertrsquos law but with differentconstants

ln CS~A0

TzB0z05ln PH (12)

It is important to pay more attention to the gassolubility and diffusion at the solidification frontbecause this is where porosity develops The growingpore is bounded by gasliquid interface and gassolidone The pressure drop across this curved gasliquidinterface can be neglected because in most typical

11 Conical pit on a non-wetted and b wetted inclusion

Drenchev et al Gasars a class of metallic materials with ordered porosity

1140 Materials Science and Technology 2006 VOL 22 NO 10

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

structures the pore radius (hence the radius of curvature)is relatively large For instance equation (10) in the caseof cylindrical pore (hC50u) gives that for pore radiuslarger than 50 mm the pressure drop is 06 atm and forpore radius larger than 300 mm this pressure drop is01 atm in the case of Ni (s5181 J m22 hW5140uhC50u) There must be an equilibrium between thepressure in the pore and the pressure in the liquid iethe pressure in the pore must be equal to the pressurePtot The hydrogen solubility in the solid at thesolidification front is therefore given by

CS~ Ptoteth THORN1=2exp A0

Tm

zB0

(13)

Following the above discussion one can conclude thatthere is a large number of parameters controlling thestructure formation in production of ordered porositymaterials On the basis of thermodynamic conditionsthe gasar production regimes can be divided into threetypes

(i) pore depressing ndash this case is characterised byvery low percentages of H2 ie very highpercentages of Ar in the furnace atmosphereand a low superheat which conditions providePtotamppeff at the solidification front and CSCLTherefore as the solidification front advanceshydrogen goes from liquid solution to solidsolution and no porosity develops

(ii) pore forming ndash the partial pressure of H2 iscommensurate with partial pressure of Ar in thefurnace and the superheat is of a moderate valueThese conditions provide Ptotltpeff and thehydrogen content in the liquid exceeds thehydrogen solubility in the solid CSCLTherefore hydrogen is rejected by the advancingsolid thus supersaturating the liquid ahead ofthe solidification front Bubbles form in thesupersaturated liquid and are subsequentlycaught by the advancing solidification front tobecome pores The ordered porosity ingotsproduced under such type regimes possess thehighest amount of porosity

(iii) bubble forming ndash it is the same quasi-boilingprocess defined by equation (7) but here thebubbles are nucleated heterogeneously This caseis characterised by a large percentage of H2relatively low percentage of Ar in the furnaceatmosphere andor a large superheat whichconditions provide Ptotpeff at the solidifica-tion front and CSCL Because of this bubbleswill form in the liquid ahead of the solidificationfront These bubbles will float upward and willnot be trapped as porosity in the solid Thisprocess reduces porosity in the gasar ingotproduced

The experiments described in Refs 9 and 10 confirm theabove relations Generalised relations between porediameter and PAr PH and melt temperature are shownin Fig 12 The pore diameter is more sensitive tochanges in PAr than to changes in PH38 This is becauseaccording to equation (2) the partial hydrogen pressureinfluences the quantity of hydrogen dissolved into themelt but the partial argon pressure does not

As discussed above cracked or pitted non-wettedsolid surfaces are necessary and sufficient for hetero-geneous bubble nucleation The activation energies fornucleation in conical pits and wedge shaped cracks as afunction of apex angle for copper on alumina areestimated in other studies353940 These energies becomenegligible for apex angle less than 50u and nucleation isspontaneous in both cases More or less such surfacesexist always in a melt Kato22 has studied the mechanismof pore nucleation in hydrogen saturated copper meltThe author used high purity copper impurities of Al Siand Ag less than 002 003 and 026 ppm respectivelyDuring the hydrogen saturation of liquid copper themetal dissolved oxygen from melting atmosphere and Aland Si were oxidised even though their concentrationswere very low The solid copperndashhydrogen gas inter-facial energy is much larger than that of solid copperndashliquid copper and hence bubbles are not likely to format solidliquid interface In a hydrogen atmosphere thecontact angle between Al2O3 and liquid copper is 150uand that between SiO2 and liquid copper is 148u(Ref 41) Liquid copper does accordingly not wetthese oxides Furthermore there are many small pits onthe oxides that facilitate gas bubble nucleation andgrowth3435 Kato observed at the bottom of the poressuch oxide inclusions

While the nucleation is favoured by a low degree ofwetting of the melt on the solid the melt should havea low work of adhesion on the oxide sites Since thework of adhesion is dependent on the surface energeticproperties of the melt it can be changed by alloyingthe melt The model proposed by Coudurier andEstathopoulos42 and used in Ref 35 predicts that SnPb and Ag will lower the work of adhesion if theyare added to copper melts in small quantities Alincreases both work of adhesion and surface tensionwhereas Sn decreases both quantities Hence Snpromotes and Al inhibits the nucleation of bubblesGenerally small alloying additions may significantlychange the liquidus and solidus lines in metalndashhydrogensystems

The critical radius R0 for bubble nucleation on a solidsurface in the melt can be expressed by the well knownrelation3443

R0amps

P(14)

12 Pore diameter as functions of a argon partial pressure b hydrogen pressure and c initial melt temperature

Drenchev et al Gasars a class of metallic materials with ordered porosity

Materials Science and Technology 2006 VOL 22 NO 10 1141

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

where s has two components related to gasliquid andgassolid interfaces

s~SssgszSlsgl

SszSl~1(15)

Relation (14) means that if the pressure increases thenR0 will decrease ie higher pressure will stimulatebubble nucleation in smaller pits and cracks onsolidification front and impurities Thus the numberof the pores per unit area transverse to the growth axiscan be controlled by external gas pressure This resulthas been proven in practice

If a bubble has already formed it may grow as a poresimultaneously with the solid may float up be engulfedby advancing solidification front or be included in someexisting pore When a bubble of radius Rb moves in theStokes regime (Reynolds number 02) its terminalvelocity vb may be calculated by

vb~2R2

b(rrg)g

9g(16)

When vb is greater than solidification front velocity vcrthe bubble will rise to the hotter area of the melt and candissolve in it On the other hand if

vcrcentvb (17)

the bubble can be caught by moving solidliquidinterface and remain as a small closed pore in solid orbe included in concurrently growing gas phase

Pore shape depends on the microstructure of theprimary solid phase Elongated pores are associated withcellular or cellularndashdendritic growth Paradies et al10

studied this matter on four types of aluminium alloysand pure nickel A region of elongated pores was foundin the region of casting where the primary dendritesexhibited columnarndashdendritic growth Only one of thealloys studied (AA2195 ndash Weldalite) exhibited both alarge columnarndashdendritic region and a comparativelyhigh total porosity To maximise the total porosity apressure sufficient to keep the pores from growing fasterthan the dendrites is required Otherwise a bubble willeither grow to block the columnar dendrites surround itincreasing its radius or a portion of the gas will getdetached and float to the melt surface If the pores growat a slower rate than the advancing dendrites thedendrites would interact causing closing of the pores

As stated earlier the prominent characteristic of theordered porosity materials is rod-like gas eutecticstructure However a variety of pore shapes and sizescan be observed in a gasar ingot Three types of pores ina porous copper gasar were found (see Fig 13)44

(i) large pores y300 mm in diameter and up to somecentimetres in length

(ii) intermediate pores y25 mm in diameter and afew hundred micrometres in length which aregreatly predominant in number

(iii) small pores usually 1 mm in diameter and ofapproximately spherical shape

These types of pores can be explained by distinction ofnucleation and growth of gas phase It is emphasisedthat the copper grains in this case are markedlycolumnar y400 mm in diameter and 1 cm in length

Nucleation sites of large pores are impurities forexample Al2O3 particles at the bottom of the ingotdetached from the mould coating or introduced bythe melt The hydrogen supersaturation of the meltahead of the solidliquid interface is usually at itsmaximum value just before the start of bubble nuclea-tion If a bubble is formed at some of these particlesclose to the interface it is able to grow extremely rapidto relatively large size The reason for this is the highlevel of dissolved gas in this zone Underneath thebubble gas diffusion in the melt is hindered and the gasremoval is only for the bubble filling In contrast the gasremoval at the zone level with the bubble is due tobubble filling and diffusion upward in the melt(Fig 14a) Because of this gas concentration is higherbeneath the bubble The melt of lower concentrationsolidifies earlier (see Fig 1) so the surface of thesolidification front becomes concave and ultimatelyforms a channel (see Fig 14b) Finally the channelgrows enough depresses bubble filling closes and formsa large pore (Fig 14c)

The nucleation of bubble that is the basis ofintermediate pores happens at the interface whensolidification runs either on line 1 (gas eutectic reaction)or line 2 (Fig 1) In the first case whole quantity of gasdissolved in the melt remains in solid as pores and thereis not long distance gas diffusion in the melt In thesecond case the bubble forms in the two phase zone Inboth cases the pore grows simultaneously with the solidHere the gasliquid interface the area through whichthe pore is filled with gas is smaller compared with the

13 Optical micrographs of a transverse section through copper gasar ingot showing large and intermediate pores and

b longitudinal section showing intermediate and small pores (after Ref 44)

Drenchev et al Gasars a class of metallic materials with ordered porosity

1142 Materials Science and Technology 2006 VOL 22 NO 10

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

case in Fig 14 Because of this such pores are manytimes smaller

According to other authors44 the small approxi-mately spherical pores are the result of precipitationfrom copperndashhydrogen solid solution They are formedbehind the solidliquid interface presumably again onalumina or other impurity particles

When total pressure in the system is equal to thehydrogen partial pressure the hydrogen concentrationin the melt is equal to the eutectic one and thesolidification runs through the eutectic point (line 1 inFig 1) The line in phase diagrams between lsquoLrsquo andlsquoLzGrsquo regions in metalndashhydrogen phase diagrams isalmost vertical This leads to some essential difficultiesin achieving gas eutectic reaction without quasi-boilingbecause very small deviations in gas concentration at theinterface can cause formation of floating up bubbles Tohinder this process Ar is added to hydrogen above themelt Ar increases the total pressure in the system butholds the partial hydrogen pressure constant In thiscase the phase boundaries shift right and down and thehydrogen concentration CE

1 is not yet the eutecticconcentration (Fig 15) Here the solidification runs notthrough the eutectic point but close to line 1 AdditionalAr pressure moves solidification line to the left relativeto the eutectic point Generally the ratio

Q~PAr

PH(18)

expresses a quantitative measure of deviation fromeutectic solidification If Q50 (PAr50) a gas eutecticreaction takes place and a large value of Q deviates thesolidification from the eutectic significantly Instead ofAr other inert gas such as He can be used8

If solidification starts in eutectic composition and thegas quantity in liquid is equal to the gas quantity insolid the final ingot will be of the highest porosity Thisis the result of the gas eutectic reaction Whensolidification starts in under eutectic composition apart of the gas ejected at the solidliquid interfacecontributes to nucleation and growth of bubbles in twophase zone which consequently form porosity Theother part of the gas diffuses in the melt to regions of

lower concentration ie to the upper melt surface Thisis one of the reasons that the solidification of undereutectic composition results in smaller porosity ingotAnother reason is that high total gas pressure in thesystem leads to smaller volume of gas bubbles and gaspore

In fact during an under eutectic composition solidi-fication gas concentration in melt close to the interfaceincreases The highest ingot porosity will be reachedwhen the concentration ahead of solidification front isequal to the eutectic one ie C5CE The maximumvalue of this concentration corresponds to the casevcr5const and is given by45

C~C0

k(19)

It is mentioned that CE is a function of Ptot but C0 is afunction of PH CE5CE(Ptot) and C05C0(PH) Usingrelation (19) the initial hydrogen concentration in themelt can be obtained like this

C0(PH)~kCE(Ptot) (20)

Such initial concentration corresponds to the partialhydrogen pressure defined by Sievertrsquos law in

a initial growth b engulfment by advancing solidification front c end of bubble growth14 Schematic representation of bubble evolution nucleated ahead of solidliquid interface

15 Effect of pressure on metalndashhydrogen phase diagram

solid lines correspond to pressure P9 and broken

lines correspond to pressure P 0 P9P 0

Drenchev et al Gasars a class of metallic materials with ordered porosity

Materials Science and Technology 2006 VOL 22 NO 10 1143

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

equation (2) Thus the partial hydrogen pressure forinitial melt saturation which provides maximum gasaringot porosity can be written in the form

PmaxH ~

frac12kCE(Ptot)2

KL(21)

This maximal porosity will be achieved after certain timefrom the start of solidification This time is needed forthe value of gas concentration in the melt to reach CAll pressures of PHPmax

H will result in porosity smallerthan the maximum Formula (21) is an importantrelation which can be very useful in practice

Some general qualitative relations between gasarstructures and processing parameters are given in otherpapers291029

Gasar propertiesProperties such as electrical and thermal conductivityliquid and gas permeability acoustic damping for allporous materials in general can be qualitatively pre-dicted using the relative property of basic material andamount of porosity Most attractive differences betweenordered porosity materials and the other porousmaterials are in their mechanical properties Usuallystrength decreases faster than the solid volume fractionin a certain material The mechanical properties stronglydepend on pore shape It is well known46ndash49 that poreedges concentrate stress and thus reduce plasticity andstrength Atypically in a specific range of porositygasars are stronger not only than the other porousmaterials but also than the solid base metal150 Forinstance at 20 porosity the strength of sinteredporous copper is approximately 05 of the strength ofcopper gasar and 025 at 45 porosity Moreoverstrengthening was observed in gasars at porosity 20and pore diameter 50 mm Ordered porosity materialsposses better impact resistance and plasticity than otherporous materials as well

The gasndashmetal systems initially used were non-reactiveat temperatures near the melting point Later somereactive systems were also studied The mechanism ofmechanical properties improvement at certain porosityfor some ordered porosity materials is not wellestablished Hyun et al19 compared some mechanicalproperties of porous iron fabricated in nitrogen andhydrogen The nitrogen concentration in solid ironfabricated under nitrogen atmosphere increases linearlywith partial pressure of nitrogen leading to theimprovement of mechanical properties The ultimatetensile strength and the yield strength of the porous ironwith the pore orientation parallel and perpendicularto the tensile direction are about two times higherthan those of porous iron obtained under hydrogenatmosphere In the case of porous iron fabricatedunder nitrogen it is observed that the increase inVickers microhardness of as cast iron is due to solidsolution hardening with interstitial nitrogen close topore surface20

The pore growth is coupled to the growth of thedendrites in the solid Spheroidal or irregular pores canbe observed at grain or subgrain boundaries of equiaxeddendrites Elongated pores usually grow betweencolumnar dendrites in columnar zone of ingotTherefore pore size shape and pore direction are very

sensitive to primary solid structure and pore morphol-ogy can be controlled by thermal condition duringsolidification1051

The specific morphology (unidirectional longitudinalpores) of the gasars defines anisotropic structure whichin turn determines anisotropic properties of the porousmaterials For instance compressive strength stronglydepends not only on the porosity but also on theorientation of the pore axis relative to the applied forceThe compressive yield strength of porous copper withpores parallel to compression direction decreaseslinearly with increasing porosity17 The compressivestressndashstrain curves depend on the angle between thecompressive direction and the pore direction Theabsorption energy of a specimen with pores parallel tothe compressive direction is higher than that of thespecimen with pores perpendicular to the compressivedirection Temperature dependence of elastic propertiesof ordered porosity copper was measured modelled andanalysed in Ref 52 The same investigation for orderedporosity magnesium was presented in Ref 53

Internal friction of ordered porosity copper wasmeasured by Ota et al18 The material investigated had16 25 and 33 porosity and was compared with thefriction of nominally nonporous copper The porediameter ranges from 90 to 140 mm and length rangesfrom 05 to 20 mm Volume fraction of open pores inspecimens was 5 The internal friction was evaluatedfrom the phase angle d between applied stress and strainby the relation q215tan d Frequency of 1 Hz was usedduring the measurements The results are shown inFig 16 For samples of all porosity the internal frictionup to 500 K was equal and coincided with that of non-porous copper The internal friction of the porouscopper increased with increasing temperature andreached a maximum at between 720 and 750 K Theinternal friction of non-porous copper increases mono-tonically with temperature The authors observed thatrepeated heating in subsequent measurements caused thepeak value to decrease (Fig 17) In the case of annealedspecimen no peak was observed up to 1100 K and thevalues of internal friction were approximately threetimes that of non-porous copper for all temperatures700 K It must be mentioned that the internal frictionof porous copper in which all pores are open is almost

16 Internal friction of ordered porosity copper as func-

tion of temperature (after Ref 18)

Drenchev et al Gasars a class of metallic materials with ordered porosity

1144 Materials Science and Technology 2006 VOL 22 NO 10

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

the same as that of the non-porous copper There is noclear explanation of above discussed phenomena

Simone and Gibson27 have studied the microstructureand uniaxial tensile behaviour of ordered porositycopper Stressndashstrain curves for the porous and nomin-ally solid copper are compared in Fig 18 Linear elasticbehaviour at small strains is followed by yield and strainhardening up to the peek stress The ductility of thetested specimens decreased with increasing porosity Theauthors measured the yield and ultimate tensile strengthsfor nominally solid copper and gasars of porosity from015 to 050 and pore diameters from 20 mm (nominallysolid specimen) to 200 mm They applied linear regres-sion analyses to the experimental data (excluding thenominally solid material) and obtained the followingequations

sy~769 961p (22)

sUTS~172 263p (23)

It was noticed that the nominally solid specimenscontrary to the expectation had a significantly loweryield strength compared with specimens with porositiesbetween 015 and 025 Their ultimate tensile strengthwas approximately the same as that of porous specimenswith p5015 This is because the nominally solid copperhas a larger grain size relative to that of ordered porositycopper leading to a reduction in yield strength bothfrom the HallndashPetch effect and from the reduction in theconstraint from neighbouring grains This resultexplains why certain porous gasar materials may havebetter mechanical properties than the solid

The uniaxial compressive behaviour of gasar copperwith cylindrical pores oriented in the direction ofloading was also studied It was reported28 that theYoungrsquos modulus and compressive yield strength of theporous materials increased linearly with increasingrelative density Initial plastic deformation was foundto be due to plastic yielding of the solid rather thanbuckling of the cell walls The characteristic densifica-tion strain decreased linearly with increasing relativedensity

It has been proved experimentally50 that enhance-ment of the yield strength of gasar copper relativeto nonporous copper is possible with a uniform

distribution of porosity Additionally specimens withuniform porosity (large cylindrical pores) were found tohave higher yield strengths than specimens with similarvolume fraction but non-uniform porosity On the otherhand the tensile strength was less sensitive to micro-structure If the net cross-section is considered thetensile strength of samples with uniform porosity isretained or enhanced up to 30 porosity

A number of authors have applied mathematicalmodels to study some aspects of the unusual mechanicalbehaviour of gasars Kee and coworkers54 have reportedan investigation of gasar copper 215 pore volumefraction under tension deformation based on finiteelement modelling The purpose was to evaluategeometric features affecting bulk yield strain andstrength of the material Pore dimensions of 18 mm indiameter 108 mm in length and 60 mm transversespacing between centres were used for the model Theresults provide insight into the role of pore interactionsand local geometric constraint in the comparatively highbulk strength observed in these materials Full trans-verse constraint is also responsible for the deformationlocalisation consistent with the appearance of thefracture surface

Bonenberger and coworkers55 have studied experi-mentally and theoretically samples of a gasar aluminiumiron alloy of porosity levels from 9 to 17 to quantifytrends in mechanical properties in relation to porosityThe applied mesoscale finite element models haveverified that pore configuration has an effect on bulkstiffness The best pore configurations lead to a decreasein modulus slightly below the volume porosity Thecapability to incorporate the geometrical parameters ofthe porous material facilitates the investigation of manydifferent pore configurations to determine an optimalarrangement

Pore deformation and pore interactions as a functionof pore size and morphology were examined byappropriate electron optical and image analysis techni-ques56 The results of the microstructural analysis werethen incorporated into a finite element model for thesimulation studies on pore deformation and interactionThe results obtained indicated that the smaller near tospherical pores played a minor role during deformation

17 Effect of thermal cycle and heat treatment on internal

frictionndashtemperature curves porosity 33 (after

Ref 18)18 Stressndashstrain curves for a nominally solid copper b

gasar copper p50154 c gasar copper p50215 d

gasar copper p5046 (after Ref 27)

Drenchev et al Gasars a class of metallic materials with ordered porosity

Materials Science and Technology 2006 VOL 22 NO 10 1145

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

It appeared that the intermediate elongated poresdominantly determined the deformation and fractureprocess It is remembered that such pores are typical forthe ordered porosity materials and they are the productof the specific casting technology applied

Acoustic energy dissipation in a porous media dependson type of pores (opened or closed) and complex shape ofpores Xie et al235758 investigated sound absorptioncharacteristics of ordered porosity magnesium andcopper It was found that the porous magnesium exhibitsexcellent sound absorption characteristics It was estab-lished that the absorption coefficient increased withincreasing frequency decreasing pore diameter increas-ing porosity and the thickness of material

Electrical conductivity of the porous material wasinversely proportional to the amount of porosity

Heat transfer in ordered porosity materials has threecomponents conduction in solid convection and radia-tion Gas convection in the closed pores in orderedporosity materials has important contribution to theheat conduction because hydrogen has high thermalconductivity and low viscosity Measurement andanalysis of effective thermal conductivities of orderedporosity copper was discussed59 It was found thatthermal conductivity parallel to the pores was (12p) andperpendicular to the pores was 1p

1zpof conductivity of

nominally nonporous material

Closing remarksThe ordered porosity materials (gasars) are a specificclass among the porous materials They possess attrac-tive mechanical heat conductive damping and soundabsorption properties Owing to unidirectional long-itudinal predominantly closed pores their properties areanisotropic The porosity of these materials can reach75 and the pore size varies between 10 mm and 10 mmIt allows producing metal materials of specific weightlower than 05 Morphology of the porous media can bemanaged in relatively simple ways This allows produc-tion of materials with graded structure The recentlyelaborated continuous zone melting technique forproduction of ordered porosity materials expands therange of metals and alloys and also enables fabricatingnon-metallic materials of such porosity The orderedporosity materials can be applied in different branchesof industry chemistry and medicine The results of mostrecent investigations have indicated that these materialscan be successfully used as biocompatible elements inmedicine and effectively applied in space industries

The formation of ordered porosity materials involvessimultaneous evolution of heat and mass transfersolidification gas diffusion in liquid and solid bubblenucleation and pore growth These physical phenomenadetermine the gasar structure and its properties in acomplicated way To control the process the relation-ship between these parameters and final structure mustbe established as accurate as possible In this respect acomprehensive mathematical model and numericalsimulation of integral structure formation process canbe extremely helpful

References1 V I Shapovalov Proc TMS Fall Meet St Louis MD USA

October 2000 TMS 291ndash302

2 V I Shapovalov MRS Symp 1998 521 281ndash290

3 J Sobczak Proc Int Conf on lsquoMechanical engineering technol-

ogiesrsquo Varna Bulgaria September 2004 NTS Transactions 67ndash

81

4 T Ikeda and H Nakajima Mater Lett 2004 58 3807ndash3811

5 V I Shapovalov US patent 5181549 1993

6 H Bei and E P George Acta Mater 2005 53 69ndash77

7 H Nakajima S K Hyun K Ohashi K Ota and K Murakami

Colloid Surf A 2001 179A 209ndash214

8 T Ikeda T Oaoki and H Nakajima Metall Mater Trans A

2005 36A 77ndash86

9 J Apprill D Poirier M Maguire and T Gutsch MRS Symp

1998 521 291ndash296

10 C Paradies A Tobin and J Wolla MRS Symp 1998 521 297ndash

302

11 S Hyun Y Shiota K Murakami and H Nakajima Proc Int

Conf on lsquoSolid-solid phase transformationrsquo Kyoto Japan May

1999 Japan Institute of Metals 341ndash348

12 H Nakajima Gas Rev 1998 168 10ndash17

13 P D Lee and J D Hunt Acta Mater 1997 45 4155ndash4169

14 R Atwood S Shridhar W Zhang and P D Lee Acta Mater

2000 48 405ndash417

15 P D Lee and J D Hunt Acta Mater 2001 49 1383ndash1398

16 S K Hyun and H Nakajima Adv Eng Mater 2002 4 741ndash

744

17 S K Hyun and H Nakajima Mater Sci Eng A 2003 A340 258ndash

264

18 K Ota K Ohashi and H Nakajima Mater Sci Eng A 2003

A341 139ndash143

19 S K Hyun T Ikeda and H Nakajima Sci Tech Adv Mater

2004 5 201ndash205

20 S K Hyun and H Nakajima Adv Eng Mater 2002 4 741ndash744

21 T Nakahata and H Nakajima Mater Sci Eng A 2004 A384

373ndash376

22 E Kato Metall Mater Trans A 1999 30A 2449ndash2453

23 Z K Xie T Ikeda Y Okuda and H Nakajima Mater Sci Eng

A 2004 A386 390ndash395

24 P D Lee and J D Hunt Scripta Mater 1997 36 399ndash404

25 T Ikeda M Tsukamoto and H Nakajima Mater Trans 2002

43 2678ndash2682

26 H Nakajima T Ikeda and S K Hyun in lsquoCellular metals

manufacture properties and applicationsrsquo (ed J Banhart and

N A Fleck) 191ndash195 2003 Berlin MIT Verlag

27 A Simone and L J Gibson Acta Mater 1996 44 1437ndash1447

28 A Simone and L J Gibson J Mater Sci 1997 32 451ndash457

29 V I Shapovalov MRS Bull 1994 4 24ndash28

30 D M Valukas lsquoGASAR materials a novel approach in the

fabrication of porous materialsrsquo Internal Report USP Holdings

Ann Arbor MI USA 1992

31 V I Shapovalov Russ J Phys Chem 1980 54 1659ndash1663

32 V I Shapovatov and N P Serdyuk Russ J Phys Chem 1979

53 1250ndash1252

33 O M Barabash and Y N Koval lsquoCrystal structure of metals and

alloysrsquo 296ndash297 1986 Kiev Naukova Dumka

34 D A Porter and K A Easterling lsquoPhase transformations in

metals and alloysrsquo 2nd edn 1992 London Chapman amp Hall

35 S Sridhar and K C Russell J Mater Synthesis Proc 1995 3

215ndash223

36 P Pugachev lsquoSurface phenomena in metallurgical processesrsquo 152ndash

165 1965 New York Consultants Bureau Enterprises Inc

37 J Israelachvili lsquoIntermoleqular and surface forcesrsquo 2nd edn 319ndash

321 1992 New York Academic Press

38 L Drenchev J Sobczak W Sha and S Malinov J Mater Sci

2005 40 2525ndash2529

39 Y Zheng S Sridhar and K C Russell MRS Symp 1995 371

365ndash370

40 S Sridhar Y Zheng and K C Russell Proc TMS Symp on lsquoHigh

temperature coatingsrsquo Chicago IL USA October 1994 TMS

259ndash269

41 S Nakano and M Ohtani J Jpn Inst Met 1970 34 562ndash567

42 J G Li L Coudurier and N Estathopoulos J Mater Sci 1988

23 238ndash242

43 M C Flemings lsquoSolidification processingrsquo 34 148 207 234 1974

New York McGraw-Hill

44 A Pattnaik S Sanday C Vold and H Aaronson MRS Symp

1994 371 371ndash376

45 W Kurz and D Fisher lsquoFundamentals of solidificationsrsquo 3rd edn

188 1992 Aedermannsdorf Switzerland Trans Tech

46 G J Davies and S Zhen J Mater Sci 1983 18 1899ndash1903

47 S V Belov lsquoPoristye metally v mashinostroeniirsquo 247 1981

Moscow Metalurgia Publishing House

Drenchev et al Gasars a class of metallic materials with ordered porosity

1146 Materials Science and Technology 2006 VOL 22 NO 10

Pub

lishe

d by

Man

ey P

ublis

hing

(c)

IOM

Com

mun

icat

ions

Ltd

48 B F Shibryaev lsquoPoristye pronitsaemye spechennye materialyrsquo

168 1981 Moscow Metalurgia Publishing House

49 S V Belov lsquoPoristye pronitsaemye materialy spravochnoe

izdaniersquo 335 1982 Moscow Metalurgia Publishing House

50 J M Wolla and V Provenzano MRS Symp 1994 371 377ndash

382

51 L Drenchev J Sobczak R Ashtana and S Malinov J Comp

Aid Mater Des 2003 10 35ndash54

52 M Tane T Ichitsubo M Hirao R Takeda T Ikeda and

H Nakajima Mater Lett 2004 58 1819ndash1824

53 M Tane T Ichitsubo M Hirao R Takeda T Ikeda and

H Nakajima J Appl Phys 2004 96 3696ndash3711

54 A Kee P Matic and J M Wolla Mater Sci Eng A 1997 230A

14ndash24

55 R J Bonenberger A J Kee R K Everett and P Matic MRS

Symp 1998 521 303ndash314

56 V Provenzano J M Wolla P Matic A Geltmacher and A Kee

MRS Symp 1994 371 383ndash388

57 Z K Xie T Ikeda Y Okuda and H Nakajima Jpn J Appl

Phys Part 1 2004 43 7315ndash7319

58 Z K Xie T Ikeda Y Okuda and H Nakajima J Jpn Inst Met

2003 67 708ndash713

59 T Ogushi H Chiba H Nakajima and T Ikeda J Appl Phys

2004 95 5843ndash5847

Drenchev et al Gasars a class of metallic materials with ordered porosity

Materials Science and Technology 2006 VOL 22 NO 10 1147