Shah, B S

Vaidya, Nimisha

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Indian J- Phys. 77A (1), 55-58 (2003)U P  Aan international journalA study of absolute hardness of some organic molecular solidsNimisha Vai^ya*' and B S Shah*Solid State Physics andf'Materials Science Laboratories,Department of Physics. Saurashtra University. PO , Rajkot-360 005, Gujarat, India  ^ Christ College. P. B. No. 5. Vwya Niketan, Saurashtra University, PO , Rajkot-360|[)05, Gujarat, IndiaE-mail ' NVjiMDYA^^yahoo.comReceived 18 November 2^00, accepted 23 September 2002Abstract : The absolute hardness is defined as the hardness nitfnber independent of the applied load An evaluation has been made of the absolute or true hardness values for the organic solids anthracene, phenanthrene and carba/ole using both the Knoop and Vickers microhardness vcisiis load data. The results obtained by graphical analysi.s agree very well with the calculated results, within experimental error. The prc.scnt note rcpoifs the results obtained, using the method utilizing the extrapolation functionKeywords . Knoop microhardness, Vickers microhardness, organic molecular solidsPACS Nos. ; 62 20.Mk. 61 72 EfMicrohardness is an important strength property of single crystals. The microhardness anisotropy of various single crystals have been studied 11-41.For organic m aterials, studies have concentrated predominantly on aromatic solids because of their potential as luminescent devices [5, 6], plastic crystals due to their unique mechanical behavior [7] and organic energetic materials because of an interest in the role of dislocations in energetic decomposition processes [81.The microhardness technique is a rapid, low cost, non­destructive method to study the deformation behavior of crystals [9]. The variation of hardness with applied load using the Vickers and Knoop indenters [10-16] has been studied earlier for the organic crystals anthracene, phenanthrene, carbazole and doped anthracene. The results have been explained on the basis of the geometrical arrangement and disposition of the molecules in the crystal structure of these solids. The results obtained from lhe.se studies have been used to derive the absolute hardness of these crystals.Single crystals of organic molecular solids were indented on their cleavage planes using the Vickers and Knoop indenters. A^Corresponding Authorlarge number of indentations were made at each load and the hardness value obtained using the following relation :Vickers hardness = 0.02 x P/Lr (MPa), (I)Knoop hardness //^ = 0 .14 x P/L^ (MPa), (2)where P is the applied load in r and L is the mean diagonal length in micron.The reciprocal indentation length was plotted against hardness and a best fit straight line was drawn from the points using the Harvard graphics .software 117]. This method, which utilizes an extrapolation function to detemiine the true hardness was developed by Tarkanian et al [ 18] and is as follows :lj5lP = applied load,= observed length of indentation,= true length of indentation under applied load,A L -  = length correction of indentation,C = a constant,= observed hardness,//. = true hardness.©20031ACS56 Nhmsha Vaiciya and B S ShahThenP K C  and H, = P I ( CL , ^ ) .Therefore. W„ = H, L,^ . (3)Bui L,=AL-¥t^y,hence, //„ £,,* = H, {AL+ 1,,)*.Therefore. //„ = W, (I + A L /Z^,)^ (4)The precision of ihc hardness measurenienls is not better than \^ 7i so the quadratic term [A L f l^)Y neglected. If {AIJ L^))<0.\ then{ML,,).  (5)Tlie correction term a L >^ccn interpreted a.s being due to either clastic recovery [19] or optical resolution [20]. In either ca.se, if a L Is  ^ constant and if the true hardness isindependent of indentation si/.c, then according to eq. (5), a plot of//^) versus l/L^ j gives a straight line with an ordinate intercept//  ^and a slope (2 AL IIj ).The relation (5) was used to calculate the absolute hardness where = true hardness values obtained from Figures (1-3).AnthraceneTable 1 presents the crystallographic data of the crystalsstudied.PhenanthrenePhenanthreneFigure 2. Rccipiocal inclenialion diagonal length vpisus hardness It phenanthreneCarbazoleCartiazo le3 6 9‘ 12 15Reciprocal indentation length (m m ”')Figure 1. Reciprocal indentation diagonal length versus hardness for anthracene.Figure 3. Reciprocal indentation diagonal length versus hardness fo carbazole.A study o f absolute hardness o f some organic molecular solids Tabic 1. Crystallographic data of the crystals studied57Name of the compoundCrystalsystemCleavageplaneSpacegroupLatticeparumcicrsNumber ol molecules per unit cellAnthracene Monoclinic (001) II = 8 562 A h = 6.038 A 1 - 1 1,184 A fl =r 124,1 1“Phenanthrcncf’uH,.,Monochnic (001:)ii?8 66 A/; = 1 1 .soo A ( 19 240 A ft 98 06‘’2Carbazolc Orthorhombic (0 1 ( |1(1 = 7 772 A h = 19,182 A (• = 5 72,5 Aa ^ P = Y =49()‘>Tabic 2 gives Ihc results of the graphical and inalhemalkal analysis to obtain the absolute hardness.Table 2. The true hardness values obtained from graphical and iiuiiiematical analysis.('umpounds H, (Knoop) graphical (MPa)(Knoop)calculated(MPa)H, (Vickers) graphical (MPa)(Vickers)calculated(MPa)Aiiihiacene 50 10 49 55 49 0 48 74Phenanthrene 76 40 76 16 71 50 62 61Caiba/olc 45 50 46 25 45 04 45 25b’lgurcs (1-3) depict the plots of reciprocal indentation length versus hardness for the crystals studied.It is seen from the plots that the slopes of the lines using the Vickers hardness versus load data arc opptisite to that using the Kiu)op hardness versus load data. This sort of behavior could be due to change in the mode of deformation as seen from the load versus hardness curve where the peaks in the Vickers curve arc due to the operation of the slip systems whereas in the case of Knoop indentations, it is due to splitting of a dislocation into partials. These different stress criteria can give rise to opposite anisotropies.The absolute hardness values Ht obtained from the graphs (Figures 1-3) are used to find the length correction terms A L . Ihe calculated true hardness values arc found using the relations:H, (Vickers) =  0.02 x  P I {AL+ (M Pa), H, (Knoop) = 0.14 x  P I {AL + L o f  (M P a).(6)(7)seen from Table 2. It is seen from Tabic 1 that both anthracene and phenanthrcnc have the same chemical formula and the monoclinic crystal structure with space group 2Pj^  ^ and two molecules per unit cell. The packing coefficient is given by :K ^ Z x V J V  . (S )These values compare well with the absolute hardness values obtained graphically, irrespective of the mode of indentation, aswhere V is the cell volume, Z is the number t»f molecules per unit cell and is the molecular volume. Hie packing coelficienls of anthracene and phenanthrcnc are 0.722 and 0.684 respectively. Table 2 shows that the absolute hardness values of anthracene and phenanthrcnc arc same within experimental error, both experimentally and theoretically using Knoop and Vickers indentation techniques. The absolute Vickers hardness value of anthracene is 49.00 MPa and that of phenanthrcnc is 71.50 MPa respectively as seen from the graphs 1 and 2. The higher hardness value of phenanlhrene is due to the shape and molecular disposition of the molecules in the unit cell as the packing coefficients arc not the same.Carbazolc crystallizes m the orthorhombic crystal structure with four molecules per unit cell and space group Though the carbazolc molecular shape is similar to that of the anthracene molecule, the ab.solute hardness value (45.04 MPa) is less than that of anthracene due to the way the molecules arc dispositioned in the unit cell.[i] It is .seen from the plots that the slopes of the lines using the Vickers hardness versus load data arc opposite to that using the Knoop hardness versus load data. This sort of behavior is attributed to change in the mode of deformation as different stress criteria can give rise to opposite anisotropies.[iil ITie calculated true hardness values are found to compare well with the absolute hardness values obtained graphically, irrespective of the mode of indentation.|iii| The absolute Vickers hardne.ss value of anthracene is 49.00 MPa and that of phenanthrcnc is 71.50 MPa respectively58 Nimisha Vaidm and B S Shahas seen from the graphs 1 and 2. The higher hardness value of phcnanthrene is due to the shape and molecular disposition of the molecules in the unit cell as the packing coefficients are not the same.|iv | Though the carhaxolc molecular shape is similar to that o f the anthracene molecule, the absolute hardness value (45.04 MPa) is less than that of anthracene due to the way the molecules are dispositioned in the unit cell.R efe re n c e sII) Y H Han. Hong Li. T Y Wong and R C Bradt J Am Ceram Sac. 74 3129 (1991)(2J T Y Wong and R C Bradi Main. Chem. Phy.s. (Switzerland) 30 261 (1992)(31 Y Fang. .S Danyluk, Z Li and D Lam J Mater. Sa U tt 12 1070 (1993)14 1 T Thirmal Rao. K Krishna Rao and 0  B Sirdeshmukh C’/r.vf. Res. Techiwt. 26 K 189 (1991)[5] J M Thomas and J 0  Williams Proi> Saliil Stale Client 6 271 (1971)(6] N T Corke and J N Sherwood J Mater. Sd  6 68 (1971)[7] J N Sherwood The Plastkally Crystalline State (New York : Wilcyi p, 39 (1979)[8] R W Armstrong, C S Coffey and W L Elban Ada. Metal. 30 2111 (1982)[9] B W Mott Microindentatiim Hardness Testing, (London Butterworths) (1956)flOl R K Marwaha and B S Shah Cryst. Res. Technol. 23 K63 (1988i[11] R K Marwaha and B S Shah Cryst. Res. Technol. 26 491 (1991)[12] R K Marwaha and B S Shah Indian J. Pure Appl. Phys. 34 550 (1996)[13] Nimisha Vaidya. B S Shah and D R Joshi Indian J. Phy.<, 70A 641 (1996)[14] Nimisha Vaidya and B S Shah Indian J. Pure Appl. Phys. 34 9IS (1996)[15] Nimisha Vaidya, M J Joshi, B S Shah and D R Joshi Bull. Mum Su  20 333 (1997)[16] Nimisha Vaidya, J H Yagnik and B S Shah Indian J. Phys 72A 295 (1998)[17] Harvard Graphics, Ver. 4.0. for Windows 95[18] ML Tarkanian, J P Neumann and L Raymond The Science nj Hardness Testing and its Research Applications (eds) J H Westbrook and Conrad (Ohio : ASM) p 187 (1973)[19] DR Tate Tran.s. ASM 35 374 (1945)[20] L P Tara.sov and N W Thibaull Trans ASM 38 331 (1947)

A Study of Absolute Hardness of some Organic Molecular Solids

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A Study of Absolute Hardness of some Organic Molecular Solids

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