DIRECTIONAL GRINDING HARDNESS IN DIAMOND: A FURTHER STUDY* RovNor.os M. DoNNrNc, (Init:ersity of Michigan, Amn Arbor, Michigan.

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1 DIRECTIONAL GRINDING HARDNESS IN DIAMOND: A FURTHER STUDY* RvNr.s M. DNNrNc, (Init:ersity f Michigan, Amn Arbr, Michigan. Assrnacr Additinal results f measurements f directinal relative grinding hardness f single crystal diamnds are given fr selected planes. The dependence f relative grinding hardness f a given directin upn the psitin f the plane being grund is illustrated. The relatin f grinding hardness t class symmetry is discussed. rn a previus paperl the results f the measurement f the relative grinding hardness in riented planes n single crystal diamnds have been cnsidered. The present paper deals with results f further wrk in five additinal planes. The experimental technique f the measurement f relative grinding hardness in single crystals has been briefly described in the abve-mentined paper. Essentially a grinding cnstant, K, the vlume f material remved per unit time per unit thrust n a cnventinal diamnd cutter's wheel' was determined simultaneusly n tw separate crystals fr a reference directin and the directin under investigatin. The relative grinding hardness is the rati f the grinding cnstant f the specified directin with respect t that f the reference directin. rn all cases the reference directin used was [1] in (1). rn the present tests thrusts f tw kilgrams were maintained n the stnes. The areas f the grund facets were between ne-half and tw square millimeters. rn ne [1] measurements n planes 5 and 3g frm the cube plane are given. The er aimuth fr grinding d.irectins in these planes is a directin tward the cube. Fr the plane 5 frm the cube (Fig. 1), the maxima and minima are lcated as in the cube. rt will be nted that the minimum at er degrees represents a very hard directin, but that the minima at " and 18" represent relatively sft directins. rt can be seen frm the great changes in the magnitude f the er degree minimum n this plane as cmpared with the cube that a very small rientatin errr n the cube may prduce a large change in the relative grinding hardness s that unless a cube plane be riented with high accuracy (a few minutes f arc) the characteristic fur-fld symmetry f the hardness vectrs n the cube will nt be bserved. rf it is assumed that the relative grinding hardness variatin with re- * cntributin frm the Department f Mineralgy and petrgraphl,, university f Michigan, N Denning, Reynids M, Directinar grinding hardness in diamnd: Am. Minera.r., 3g, (1953).

2 DIRECTIONAL GRINDING HARDNESS IN A DIAMOND I87 2 <l I 2 a F c Frc. 1. Zne [1] 5'frm cube. when the cube is being grund. Unfrtunately, the difierence lies at abut the limit f accuracy f measurement s that this relatin may nt be 2 lbid., Figure 4. u E i r E >l F A2IMUTH Frc.2. Zne [1] 38' frm cube

3 188 REYNOLDS M. DENNING Frc. 3. Zne [11] 5" frm ddecahedrn. is shifted with respect t ther planes in the ne [1].) rn the plane 38 frm the cube, the hardness minimum is rather brad, cvering tw 45 sectrs. Frm the shape f this curve it can be seen that small rientatin errrs f (11) are nt serius in the determinatin f the hardness curve f the ddecahedrn, prvided that the plane being measured accurately lies in ne [1]. That such is nt the case if the plane measured des nt accurately cntain the [1] directin is illustrated by cnsidering the next plane. If a plane in ne [11], 5' frm the ddecahedrn, be grund in a series f aimuths and the results pltted, a curve such as that f Fig. 3 is btained. The er f aimuth tward the ddecahedrn is cmmn t all f the curves fr the ne [11](including the dd.ecadehrn, Fig. 4, in the previus paper). A very brad maximum f ver 1g is apparent. Experimental difficulties prhibited any reliable measurements in this sectr. Prbably the minimum f.9 at 3 is real, althugh the deviatin frm unit hardness here is f the same rder f magnitude as the uncertainty f the measurements. Frm this curve it can be seen that a plane s d f c U r Fre. 4. Zne [T1] 7+' frm ctahedrn.

4 DIRECTIONAL GRINDING EARDNESS IN A DIAMOND 189 accurately riented in ne ltot] Uut therwise differing frm the ddecahedrn by a small angle will prduce a large errr f hardness measurements with respect t thse btained n a true ddecadehrn. This errr chiefly ccurs in aimuths frm t 27". Figure 4 represents the relative grinding hardness n a plane in ne tfofl, Z+'frm the ctahedrn (27f; fum ddecahedrn)' The directin i*ard th. ddecahedrn is mst readily cut. The directin tward the ctahedrn is very hard. The maximum hardness seems t lie at an aimuth f 135, aithugh satisfactry measurements were nt btained in the sectr frm 1 t 26. Frm this curve it can be seen that a d I q Frc. 5. Zne UTO] 15'frm cube. plane accurately riented, lcated in ne [tot] Uut therwise nt accurately lcated n the ctahedrn, wuld shw a hardness minimum tward the nearest ddecahedrn. In the remaining imprtant ne, [1I], a plane 15 frm the cube was studied. The resulting curve is pltted in Fig. 5 with the et aimuth taken as a directin tward (111). The maximum at is quite lw' This An attempt was made t btain a curve n a plane 48 frm the cube (8!" frm ttre ctahedrn), but the results were nt cnsistent enugh t warrant pltting a curve. This plane pssesses a very high grinding hardness in a directin tward the ctahedrn and a lwer hardness tward the cube. S far the variatin f hardness alng a series f aimuths fr each

5 1 REYNOLDS M. DENNING T,lsrn 1. DBpeNrNcr r GntmrNc H.q.nnNnss rn CrnrarN Drnrcrtxs upl,r rgr OnrrNtarrN r.trre GnrNnrxc pr,axn Preliminary Data Grinding Directin Plane Being Grund Relative Grinding Hardness.) Z 38 5.) (assumed) 1.2 I. 1. (?) t x. plane has been cnsidered. rt can be seen frm the data presented that fr a given linear directin f grinding, the relative grinding hardness is dependent upn the rientatin f the plane being grund. 3 Bergheimer, H., Die Schleifhiirte des Diamanten und seine struktur: Neues ahrb. Min., Gel. und, Pa1.,74, (193$. Kraus, E. H., and Slawsn, c.8., variatins f the hardness f the diamnd: lr. Mineral., 24, (1939). Slawsn, c. B ', and chn [sic],. A., Maximum hardness vectrs in the diamnd : Id. Diamnd Rea., lo, (195). wilks, Eileen M., An interfermetric investigatin f the abrasin hardness prperties f diamnd: Phi.lsphi.cal Magaine, Ser. 7, 43, 114, Nvember,1952.

6 DIRECTIONAL GRINDING HARDNESS IN A DIAMOND 191 tive grinding hardness value btained is dependent upn the psitin f the "(h}l)" surface n which the hardness measurements are made' The dependence f the psitin f the grund surface alng a linear directin is much mre striking in mre generally lcated linear directins. Table 1 illustrates, by way f preliminary data, this interdependence. The linear grinding directin is expressed in S and p values. AIs the sense f the grinding is defined by these crdinates. It is assumed that the upper prtin f the crystai is being grund. The plane in which the grinding directin lies is indicated by the cnventinal d and p f twcircle gnimetry. Thus a grinding directin f 6:, p:95, indicates that the grinding is tward the frnt f the crystal, while 6:27, p:85, indicates that the grinding is tward the rear f the crystal. Only ne directin f a kind is specified, inasmuch as the duplicatin f these accrding t the hexctahedral symmetry wuld unnecessarily lengthen the table. rn grinding directin 6:, p:, i'e' [1], it will be nted that there is a small gradual increase in hardness as the plane is changed frm (1) t (11). The lw value fr the plane f p:38 seems rather ut f place' Mre detailed wrk is planned fr this easy grinding directin' Fr a grinding d'irectin 6--, p:95, the plane (1) shws a smewhat greater hardness ver the (/l) plane. Hwever, here an interplatin between " and 1 is invlved, and the effect may nt be significant. Fr grinding directin 6:27, p:85, the relative grinding hardness is much greater n the,,(hal),,than n (1). Similar relatins hld fr the last fur grinding directins in the table. Thus it can be seen that the psitin f a plane being grund may pr- Iundly affect the grinding hardness f a given grinding directin, especially in the mre general directins, i.e., thse that d nt bear special relatins t the symmetry directins f the crystal. cnsequently, bnd strength cmpnents in the grinding directin can nt by themselves explain all f the bserved variatins f directinal relative grinding hardness. It will be nted that grinding hardness curves n diamnd are indicative f the crystal symmetry. Surfaces accurately lcated nrmal t planes f symmetry shw in the curves a line f reflectin symmetry paratlel t the trace f the symmetry plane. If a rtatin symmetry axis is nrmal t the surface being grund, then a pint f rtatinal symmetry is bserved in the hardness curve. In the case f diamnd, hardness measurements indicate hexctahedral symmetry. This investigatin was carried ut as a part f the Crystal Hardness prgram spnsred by the ffice f Naval Research. The diamnds used were cntributed by Industrial Distributrs (1946) Ltd. f hannesburg' ManustriPt receitted Mar' 1, 1954'