Surface Engineering of Metals - Principles, Equipment and Technologies Part 12 pot

The microhardness of superficial layer zones may changeduring service, especially during wear, as the result of microstructuralchanges caused by surface tempering, secondary hardening gr

Fig 5.18 Orientation values of thickness and hardness of some superficial diffusion layers.

In addition to surface hardness (the measurement of which was duced to industry as late as the 20th century) it is important to know thehardness of structural elements of the particular zones of the superficiallayer, e.g., grains and structural components, especially on cross-sections

intro-This last parameter, known as microhardness, came into use only after

World War II [28]

Fig 5.19 Hardness profile: a) Nitralloy 135M, hardened and tempered to 30±2 HRC;

1 - glow discharge nitrided at 520°C for 9 h; 2 - implanted by nitrogen ions with energy

of 100 keV and ion dose of 2·10 17 ions of N2+ per cm 2; 3 - electron beam hardened with

power density of 2230 kW/cm 2 and exposure time 0.74·10 -4 s; 4 – laser hardned with

power density of 1.4 kW/cm 2 and exposure time of 0.13 s; b) 18HGT grade steel, gas nitrided at 530°C for 36 h

Hardness (microhardness) is one of the most basic, universally acceptedproperties of materials, especially of metals and their alloys, easily measured

by various methods, and connected with many other properties of the ficial layer, e.g., wear resistance, strength, residual stresses, plasticity Usu-ally, the higher the stress loading to which the part is subjected, the highershould be the hardness of the surface Unfortunately, a rise in hardness isoften connected with a rise in brittleness

super-Hardness depends on the type of material and its structure which, inturn, depends on treatment, especially strain-hardening, heat and thermo-chemical treatment (Fig 5.19) The hardness of crystalline bodies depends

on the limit of elasticity under compressive loading and on the modulus

of elasticity The microhardness of superficial layer zones may changeduring service, especially during wear, as the result of microstructuralchanges caused by surface tempering, secondary hardening (grindingburns), the breakdown of residual austenite and other factors [21,32]

5.7.3.4 Brittleness

Brittleness is a material property, consisting of permanent partition ofmaterial under the influence of internal or external forces The partitionbegins at the tip of the propagating crack and is formed without the pres-ence of any significant plastic deformation Brittleness depends on thetype of material, its phase composition, structure, etc and on externalfactors such as stress distribution, method of loading, temperature, chemi-cal composition of the environment and others Usually, brittleness oc-curs in solids within certain temperature ranges [26] The majority ofmaterials exhibit brittleness at ambient temperature (so-called cold short-ness); others, as e.g., unalloyed open-poured steel, exhibit greater brittle-ness at elevated temperatures (so-called hot shortness) Metals may ex-hibit different types of brittleness, e.g., the already mentioned cold short-ness and hot shortness, hydrogen embrittlement (caused by excessive dif-fusion of hydrogen into the metal), pickling embrittlement or embrittlementcaused by electroplating of metal objects, temper embrittlement, blue brittle-ness, etc

In the case of superficial layers and coatings, brittleness is an undesirableeffect, e.g., brittleness of superficial layers after diffusion, caused by excessiveconcentration of saturating element, like nitrogen Often, although not al-ways, brittleness is connected with hardness: the higher the hardness, thegreater the brittleness of the layer

A property opposite to brittleness is ductility - the susceptibility of

metals to permanent plastic deformation without the formation of cracks.Ductility is one of the basic characteristics of the metallic state Often theterm “ductility” is used as a synonym of plasticity but it means a qualita-tive, non-measurable characteristic, strongly dependent on structure, pro-cesses occurring at the atomic level and on the type of slip

Usually it is desired that hard but not brittle layers be formed over aductile core [26, 27]

5.7.3.5 Residual stresses

Types of residual stresses In all materials subjected to extraneous effects - be

they mechanical, thermal, chemical or a combination of any or all of them there occur non-uniform volume changes, both reversible and irreversible,causing the formation of stresses Stresses describe the state of internal forcesand moments of forces, brought about by the interaction, in a given locality,

-of two parts -of the material, situated on either side -of an apparent section, the forces in question acting on a unit area of the cross-section.After the removal of external effects, reversible changes (elastic defor-mations) undergo atrophy, along with stresses caused by them However,some irreversible changes (plastic deformation) remain in the material,along with stresses caused by them which are referred to as residual stresses[33]

cross-Residual stresses, in earlier times referred to as rest or final stresses,are those which are in mutual equilibrium within a certain zone of thematerial and which remain after the removal of external loading Depend-ing on the zone where this equilibration occurs, the following types aredistinguished:

1) according to the classification by E Orowan [34], two types of residualstresses include:

– macrostresses - formed as the result of any external loading, and

balanced out in the entire volume of the body They are regarded as theresult of the joint, average interaction of microstresses A definition of thistype assumes the material to be homogenous, i.e., having isotropic proper-ties;

– microstresses - formed as the result of heterogeneity of the material

(blocks of grains, single grains), which usually generate a genous stress field, often connected with texture and therefore exhibitingpreferred orientation (so-called stress-texture) [29];

non-homo-2) according to the classification by N.N Davidenkov [34, 35] three types

of residual stresses are distinguished (Fig 5.20):

– stresses of the I st kind, termed macrostresses (body stresses), caused

by the mutual interaction of macroscopic-size zones of the material, ancing out within volumes of the same order of magnitude as the object,within the limits of the entire superficial layer, in zones of dimensionsapproximating those of the superficial layer or in major zones of the su-perficial layer (e.g., in a zone with a very big number of grains) They areformed when external effects in the form of, e.g., mechanical loading causesnon-uniform plastic deformation or as the result of thermal effects, caus-ing non-uniform expansion of neighboring macrozones For this reason,they were once referred to as thermal stresses The conservation of bodycontinuity requires the formation, between such macrozones, of mutualinteraction, tensile or compressive, which we call macrostresses [33].Macrostresses are caused directly by non-uniform plastic deformation,temperature changes, changes in the material structure or a combination

bal-times referred to as structural stresses Microstresses often constitute theresult of the formation of a superficial layer Their chief source is differentcrystal orientation and the associated anisotropy of elastic and plasticproperties of the various crystals Since after treatment (mainly deforma-tion) the microstructure usually exhibits a definite texture, stresses also

exhibit a preferred orientation, called stress texture Its final result is the

anisotropy of the material’s properties Microstresses may be regarded asthe result of total, average interaction of submicrostresses;

– microstresses of the III rd kind, termed submicrostresses, balancing out

within the space of one crystal, thus within zones corresponding to the crystallattice parameters They are treated as stresses of the material’s crystal lattice,especially in zones with defects In such zones the proper structure is dis-rupted by the occurrence of own or foreign atoms in improper interstitial andnodal sites or the existence of voids Foreign atoms introduce into the latticetheir stress fields, nodal voids cause the absence of stress fields to balance thefields from neighboring atoms Stress fields from foreign atoms in nodal sitesalso do not balance out stress fields from neighboring atoms The energy of thelattice in the vicinity of a defect is in all cases higher than its minimum valuecorresponding to the state of equilibrium The result of that is the stress fieldaround the defect The range of stress fields is small due to the small range ofaction of atomic forces and may reach several lattice spacings Stress fieldsaround defects interact with atoms but only with the neighboring ones, upset-ting them from their state of equilibrium [33, 35-37]

If an atom of gas, e.g., hydrogen, is introduced by diffusion into thecrystal lattice of steel, it generates around it compressive residual stresses

of the IIIrd kind Next, as the result of desorption of gas molecules in theinternal discontinuities of microstructure, very high pressures are gener-ated in such sites, giving rise to compressive residual stresses of the IInd

kind After the saturation of the superficial layer with this element it isusual that a gradient of its concentration will occur (and along with it agradient of properties) The final result will be that residual stresses of the

Ist kind will be generated between layers or between the superficial layerand the core [38]

In the superficial layer there exist three kinds of residual stresses; theyare manifest predominantly as macrostresses Micro and submicrostressesaffect the limit of elasticity of the material but have only a small influence

on its strength They are added to stresses caused by external effects andfor that reason they determine the moment of exceeding of the material’sstrength, manifest by the formation of microcracks Submicrostresses may

be the cause of high hardness and strength of metal alloys [33] dently of the kind of stresses, the result of their action is the same - theyalways induce defects and elastic deformations of the crystal lattice Fur-ther on in this book the term “residual stresses” should be understood asresidual stresses of the Ist kind

Indepen-Each surface treatment in which the limit of elasticity is exceeded by anyelement of the superficial layer or core structure leaves behind a trail in the

form of residual stresses, especially those of the Ist kind In the majority offinished machine parts and structures there exist residual stresses left be-hind by treatment or assembly operations.

Residual stresses are characterized by their sign (“-” compressive and

“+” tensile), their value, distribution, gradient and depth of penetration

Factors causing the formation of residual stresses Such factors can

usually be classified as being of three kinds:

– mechanical, stemming from non-uniform plastic deformation of

su-perficial layers during mechanical cold work They are accompanied bynon-uniformly distributed and interconnected processes of force action,reorientation, refinement, expansion or contraction of structural compo-nents Macrodeformations give rise to reorientation of structural compo-nents in layers situated closer to the real surface relative to deeper situ-ated zones Microdeformations, on the other hand, reveal themselves withinthe volumes of separate components, due to their refinement into frag-ments and blocks and to mutual elastic-plastic interaction of neighboringgrains Resulting from that is local increase or decrease in material den-sity, enhanced by the movement of dislocations, their distribution andkind [37] Plastic deformation due to cold work causes changes in mate-rial density (a rise in volume of approximately 0.3 to 0.8 [21]), conducive tothe rise of compressive stresses Plastic stretching of the superficial layer byforces of friction and by machining chips also causes the formation of com-pressive stresses Residual stresses caused by mechanical factors are some-

times termed mechanical residual stresses;

– thermal, caused by thermal expansion of the material and

stem-ming from non-uniform heating or cooling of various layers of the terial (macrodeformations) or of its particular fragments (microdefor-mations) During heating, especially if it is non-uniform, there occursnon-uniform thermal expansion causing plastic deformation which pre-vails all the way up to melting point In the liquid state, the volume ofall metals (with the exception of bismuth and antimony) is smallerthan in the solid state Fig 5.21 shows a diagram of the formation ofresidual stresses using water quenching of 100 mm dia heated steelbar as an example [39, 40] Upon heating, surface temperature is usu-ally slightly lower than that of the core With progress of cooling time,

ma-the difference between surface temperature (curve S) and core ture (curve C), in other words - the temperature gradient - rises The

tempera-material of the superficial layer and of layers situated deeper ishes in volume with the progress of the cooling process, shrinking(linear changes of approximately 0.5%), causing the formation of ten-

dimin-sile stresses (curve 1) At the same time compression of the still hot core, gives rise to compressive stresses there (curve 3) The temperature gradient between surface and core rises until it reaches point M The

maximum temperature difference (approximately 600 K) corresponds

to maximum tensile stresses at the surface and maximum compressive

panied by a simultaneous process of stress formation The stresses are pressive if the specific volume is increased and tensile if decreased In turn,all volumetric changes within the volume of a given component are accom-panied by changes in neighboring zones [37] Greatest residual stresses areformed during hardening, caused by the transformation of austenite to mar-tensite which proceeds at a very high linear rate (in ferrous alloys the rate ofgrowth of martensite nuclei is approximately 33% that of the speed of sound

com-in a crystal) Martensitic transformation com-in the heated material occurs as theresult of quenching at a known rate of heat extraction, highest at the surface,causing a volumetric increase in the superficial layer When the carbon con-tent in martensite is 1%, volume increase of martensite relative to austenite isapproximately 4% In the slower cooled core, martensitic transformation isretarded The core is subjected to stretching, causing compressive stresses atthe surface Next, the onset of martensitic transformation in the core causesthe stretching of the outer layers which were hardened earlier and, in conse-quence, the compression of the core Changes in specific volume which aredue to structural transformations are greater than those brought about by

thermal expansion Stresses caused by these factors are termed structural residual stresses.

Other examples of external forces causing the formation of residualstresses with varied value and range of action may be, besides pressure(mechanical stresses) and temperature (thermal and structural stresses),chemical interaction (e.g., formation of chemical compounds by atomsintroduced through diffusion and substrate atoms) and physico-chemi-cal (e.g., implantation with the formation of chemical compounds).Through the change of chemical composition, such interaction causeschanges in the specific volume of the material or in the coefficient ofthermal expansion As an example, the saturation of iron and its alloyswith nitrogen increases volume and decreases the thermal expansioncoefficient of the saturated layer relative to that of the core which causescompressive stresses to be set up in the layer and tensile stresses in thecore

Usually, residual stresses are formed as the result of joint interaction ofseveral forces (causes) and their separation is usually difficult For ex-ample, during hardening, when the effects of thermal and structural stressformation overlap, structural stresses tend to either raise or diminish ther-mal stresses, depending on the size and shape of the element’s cross-section plane, rate of heat extraction and steel hardenability Tying in the

above to point U in Fig 5.21 [40] the following can be stated:

– structural stresses raise thermal stresses if they are formed in the core

before and in the superficial layer after reaching point U and vice versa;

– structural stresses across the entire cross-section or after passing

through point U counteract thermal stresses;

– greatest compressive stresses in the superficial layer and tensile inthe core are formed when transformation in the core occurs before and in

the superficial layer after passing through point U.

When, after removing the external forces, residual stresses prove to beonly slightly less than the material’s strength, the material may deform, warp,suffer delamination or exfoliation If they prove to be greater, the materialwill crack.

Residual stresses are superimposed on operating stresses, induced byexternal forces (see Fig 5.44)

– They can be added to them, resulting in the material being destroyedalready under operating stresses, lower than material strength, sometimesunder quite small loads Residual stresses can also cause the material tocrack spontaneously [37]; it is said that residual stresses reduce materialstrength In the superficial layer, these are usually tensile stresses

– They may be subtracted from operating stresses, resulting in tion of the material only when operating stresses exceed the material’sstrength; it is then said that residual stresses raise material strength Inthe superficial layer these are usually compressive stresses

destruc-Residual stresses are formed in the superficial layer and in the core.Usually, the value of residual stresses is greatest in the superficial layer and,the greatest stress gradients are located there, especially at the interface be-tween the superficial layer and core (Fig 5.22)

Residual stresses in the superficial layer usually occur in zones of ture, plastic deformation, and elastic deformation, but it is in the texturedzone that they assume their highest values Their distribution and valuedepend on the type of material and its three-dimensional and metallo-graphic structure, on strength and thermal characteristics, on externalfactors (e.g., rate of heat extraction) and on the associated strain-hardening ofthe superficial layer, as well as on wear resistance

tex-General functional expression of residual stresses In the broadest

sense, residual stresses σw may be expressed by an implicit function of themost important, mutually interacting parameters in the form below:

σw = f (m, t, k, o) (5.16)

where: m = f 1 (c, w, f, ch, s) - is the function of the primary material (core, superficial layer, coating), described mainly by its properties: c - thermal (especially: thermal conductivity, thermal expansion, specific heat); w - me- chanical (especially strength: Young’s modulus, Poisson ratio); f - physi- cal (e.g., ion implantation); ch - chemical (especially: chemical composition, formation of chemical compounds of diffusing atoms with substrate atoms); s

- structural (especially: roughness and valley bottom radius) and

metallo-graphic (especially grain type, size and orientation, defects); t - technology of

formation of superficial layer or coating (type, number, sequence and eters of treatment operations; temperature, temperature variation rate, tem-perature gradient, pressure, loading, feed rate, energy, element concentration,

param-etc.); k - shape and size of component in which residual stresses are sured; o - interaction of core with superficial layer or coating.

mea-Fig 5.23 Distribution of residual stresses, resulting from: a) diffusion chromizing of

D2 grade steel; b) TiC coating of D2 steel; c boriding of 1045 steel; designations: B boriding; Cr - chromizing; Ti - TiC treatment; H - hardening; T - tempering (From Janowski, S [41] With permission.)

-In the absolute sense, a given value of residual stresses when all otherparameters are equal depends heavily on the method of measurement.Numerical values of residual stresses, obtained by different measurementmethods, may differ by several to several tens percent In certain cases

differences exceeding 100% and even results with opposite signs may beobtained [41, 42].

Residual stresses in a superficial layer directly affect the layer’s sion but their action may also be of an indirect nature - by forcing themigration of atoms with small diameters (e.g., hydrogen, carbon, nitrogen,boron) through the crystal lattice of the host material The force exerted

cohe-by stress gradient on an atom in an interstitial position is, admittedly, notbig in comparison with the force exerted by a concentration or tempera-ture gradient However, local stresses may cause migrations of interstitialatoms to sites preferred by geometry or thermodynamics (vacancy clus-ters, dislocation lines, grain boundaries and stacking faults) causing sig-nificant local stresses, favoring the initiation of cracks [38]

When knowingly shaping the properties of the superficial layer, it isendeavored to obtain, as the final result, compressive residual stresses inthe superficial layer, while in the core - tensile residual stresses with asmall gradient Compressive stresses in the superficial layer may evenattain a value equal to approximately 50% of the material’s ultimate strength[37]

The value of compressive residual stresses obtained as the result of face diffusion treatments may even reach 2400 MPa (Fig 5.23) [41] As anexample, the value of compressive stresses in nitrided layers on low alloynitriding steels and on high alloy structural steels may reach 900 MPa [38]

sur-In the case of mechanical strain hardening, the depth of penetration ofstresses is usually greater than the depth of hardening even by severaltens percent With a rise of stress value at the surface, the depth of theirpenetration diminishes [37] The value of residual stresses rises when me-chanical strain hardening is coupled with heat treatment of thermo-chemi-cal treatment (Fig 5.24)

Generally, with a rise in the strength of the mechanically ened material and in the strain-hardening parameters (mainly, the loadingforce), residual stresses in the superficial layer increase Their value, depth ofpenetration and character of distribution may all be controlled by treatmentoperation parameters In almost all cases the formation of compressive stresses

strain-hard-in the superficial layer causes a rise of fatigue strength (with tensile stressesthe effect is opposite) and hardness, wear resistance and corrosion resis-tance A greater degree of plastic deformation causes an increase in residualstresses and in fatigue strength

Regardless of the root cause of formation of residual stresses, their valueand distribution affect strength properties, especially fatigue strength, resis-tance to dynamic loading and to brittle cracking (see Section 5.8.1), as well

as tribological properties, especially contact fatigue (see Section 5.8.2) [42]

A particularly significant effect of residual stresses on mechanical erties, especially fatigue, is revealed in the case of superficial layers con-taining technological or structural flaws, surrounded by stress concentra-tions

prop-In surface shaping treatment processes the following types of cal residual stresses are formed:

technologi-– quenching stresses, caused by volumetric changes due to predominantly

phase transformations but also to heating and cooling,

– casting stresses, caused by solidification and cooling,

– welding stresses, caused by phase transformations and thermal

ex-pansion

In all superficial layer shaping treatment operations, the character andvalue of technological residual stresses change during the technologicalprocess (see Fig 5.10) and from process to process [13] in the followingmanner:

– at first, the superficial layer contains only primary (initial) residualstresses, created during the previous treatment operation (in the steel-making process, forging, casting, cold forming or heat treatment) andbeing the net result of a superimposition of effects which had occurredprior to the considered operation;

– under the influence of the treatment operation considered, logical residual stresses are created which, when added to initial stresses,become resultant stresses;

techno-– resultant stresses of the considered treatment operation constitute, atthe same time, the initial stresses for subsequent treatment operation.Technological residual stresses do not constitute a value which is con-stant in time or for any location Under the influence of external forcesoccurring during storage or service, technological stresses become servicestresses and their value and distribution change, due to processes of relax-ation and redistribution (Fig 5.25)

Fig 5.25 Redistribution and relaxation of residual stresses during service: a) in 1045

steel, induction hardened and subjected to fatigue testing (From Janowski S [42] With permission.); and b) structural steel, subjected to wear testing (From Svecev, V.D [43] With permission.); 1 - before test; 2 - after test.

5.7.3.6 Absorption

Absorption (from Latin: absorptio - imbibition) is a physico-chemical

pro-cess of permeation of mass, consisting of the taking up of a constituent,

usually a gas mixture called absorbate, by a liquid or a solid (called bent) and uniform dissolution of the former in the entire mass of the latter This is a volumetric process, i.e the entire volume of the absorbent uni-

absor-formly takes up the absorbate The effect of volumetric absorption is oftenaccompanied by diffusion of the absorbate In a simplified manner, absorp-tion is treated as dissolution in a liquid (for that reason, the amount ofequilibrium absorption is described by solubility) or - in a more generalway - as the permeation of one phase into another in a diffusion process.Absorption is often accompanied by chemical reactions, e.g., in pack car-burizing of steel, carbon from the carburizing powder pack reacts withoxygen contained in pores of the carburizing mixture, forming carbon mon-oxide CO which breaks down at the steel surface, due to its catalytic action:2CO ♦ CO2 + C, giving off atoms of nascent carbon, capable of diffusinginto the steel In gaseous carburizing, some atoms are obtained from thebreakdown of hydrocarbons [39] The effect of absorption is widely used inthe chemical and related industries in order to separate a harmful or avaluable component out of a gas mixture or to combine the gas with anabsorbent to obtain a compound, an extraction of a substance dissolved in

a liquid (e.g., in water) by another liquid which does not mix with thesolvent, etc In surface engineering, absorption of gases by metals and al-loys is utilized chiefly in order to saturate the superficial layer by the dif-fusing element The course of absorption is, in this case, dependent on thedifference of chemical potentials in metals and alloys on the one hand, andthe surrounding environment (gas atmosphere, salt bath, powder pack, paste)

on the other Absorption also plays an important role in tribology

5.7.3.7 Adsorption

Adsorption (from Latin: ad - at, sorbe - to absorb) is the process of attraction of

substances (gases, vapors, solids in solution, ions and liquids) and theircollection at the surface of solids and liquids, at the interface between solidand gas or liquid and gas Adsorption is manifest in changes of concentra-tion of a substance in the boundary layer between two neighboring phasesand depends both on the properties of the adsorbing body (adsorbent), aswell as the adsorbed body (adsorbate) Greater adsorption is exhibited bybodies with a developed surface (e.g., rough and porous) than by bodies with

smooth surfaces [9, 40-43] Often, adsorption is treated as surface tion.

adsorp-Adsorption may occur in static conditions - from a fixed volume phase(static adsorption) and in dynamic conditions - from a flux of gas orsolution (dynamic adsorption)

A molecule from the volume phase, e.g., gas, having reached the surface ofthe solid or liquid adsorbent is maintained there (or adsorbed) by

Fig 5.26 Adsorption at solid/gas; solid line - profile of substance concentration (i) vs.

distance from physically pure solid surface; dashed line - profile of substance tration vs distance from solid surface in reference system; surface concentration

concen-excess n i is represented by the shaded area (From Oœcik, J [45] With permission.)

surface forces for a certain time, dependent on the character of the bate and adsorbent, on temperature and pressure, and finally leaves thatsurface or is desorbed Commensurate with the saturation of the surface,the rate of adsorption decreases while the rate of desorption increases.When both rates are equal, desorption equilibrium is set

adsor-Molecules of the adsorbate at the surface of the adsorbent form sorption layers.

ad-We distinguish positive adsorption when the concentration of the stance is greater in the superficial layer than in the deeper phase, and nega-tive adsorption when the concentration in the superficial layer is less than inthe deeper phase

In most cases, positive adsorption of gases, vapors and dissolved stances occurs at solid surfaces The molecules of a very volatile phase(adsorbate) are then subjected to spontaneous densification in the thinlayer at the surface of the very condensed phase (adsorbent)

sub-Fig 5.26 shows the profile of gas concentration at the interface with a solid,

vs distance z from the physically pure surface The area covered between points BC and E expresses the surface excess (in concentration) of the adsorbed

gas substance, relative to the reference concentration of the gas phase

The surface excess n i of the adsorbed gas substance i (or volumetric

ex-cess), which is the surface (or volumetric) concentration, expresses the excess

in the number of moles of that substance in comparison with the number ofmoles which would be present in a reference system without adsorption,given the same equilibrium pressure

(5.17)adsorption surface adsorbent

where n i a - number of moles of substance i in field FBDH; n i g - number of

moles of substance i in field FEDH; n i p - number of moles of substance in

field ABF; C i a - local concentration of substance i in the adsorption space;

C i g - local concentration of substance i in the gas phase; C i p - local

concen-tration of substance i in the superficial layer of the adsorbent; V 1 - local

volume of adsorption space; V 2 - local volume of superficial layer ofadsorbent

Due to the very small depth of permeation of the adsorbate into the

adsorbent, the quantity n i p (or C i p ) is sufficiently small to be neglected in

expression (5.17) With this assumption, the quantity n i corresponds to

the total amount of substance i (adsorbate) remaining within the field of

adsorbent forces

Fig 5.27 Types of adsorption isotherms of gases and vapors, according to Brunauer;

n i - total amount of adsorbed substance i; p - pressure; p o - pressure of saturated gas Type I - typical curve for chemical adsorption, less frequent for physical adsorption; types II to V - various curves for physical adsorption; the most frequent is type II, least frequent - type V.

The amount of a substance adsorbed by the superficial layer depends

on its pressure and on temperature For a gas mixture, the partial pressure