THE AMERICAN
MINERAIOGIST,
VOL. 48, JWY-AUGUST,
1963
CLEAVAGE IN QUARTZ
F. Doxarl
Bross aNt Gnnero V. Grnls, Deportment of
Geology, S outhern lllinois U niaersity.
Assrnlct
A new method for studying cleavage in optically uniaxial materials by means of the
universal stage was applied to quartz. Statistical analysis of the results indicates that lorv
quartz, whencrushed, cleavesmost readily parallel to / 1011 or z
{
}
{otTt } and next most
readily para llel to t,11122 l. Lesspronounced cleavagesexist paral lel to c 0001 r r r zr
{
|, {
I,
x f 5 1 6 1 l , r r l 1 0 T 0 l a n d , p e r h a p s , [j ; O B z fa n a a l t t Z O l . T h e d i r e c t i o nd
l 1 0 T z ] ,t h o u g h
reported in the literature, was not observed as a direction for cleavage. The conchoidal
fractures of quartz may represent submicroscopic combinations of cleavage planes
{,
z, r, c, s, r, m and a,
The number of Si-O bonds cut per unit area was determined for a set of rational planes
in the (0001):(1120) zone and a second set in the (0001):(10T0) zone. o{ the first set.of
planes, { cut the fewest bonds; of the second set, r cut the fewest bonds, cutting even
fewer than f.
INrnooucrroN
Various cleavage directions have been reported Ior quartz (Table 1).
However, as previously noted (Bioss, lgST, p. 214_2lS), the existenceof
several of these, including even the most generally accepted r ar'd.z
cleavages,is occasionallyquestioned.Theseconflictsof opinion may possibly arise through lack of a clear-cutdistinction betweenthe terms fracture and cleavage.According to Fairbairn (1939,p. 358),
" . ' . the terms cleavage and fracture have no precise meaning. common usage defines
cleavage as a rupture which is closely controlled by the structure, and fracture as a rupture
in which the structural control is weak.,'
The "perfection" (i.e., degree of structural control) of surfacesof rupture is generallyjudged in a qualitative and subjective manner by their
degreeof planarity, reflectivity, andfor easeof production.
euantitative
studiesare rarely published.rn 1944von Engelhardt introduced a quantitative study of fracture in low quartz. Bloss (1957) independently developed a similar method in comparing the cleavagetendenciesof high
and low quartz. To a limited extent, thesestudies permitted a comparison of the degreeof structural control of breakage for those several crystallographic directions which had already been reported as cleavage
directionsin quartz.
The present study, however, was undertaken since it permits a more
certain and detailed crystallographic identification of the preferred directions of fracture in quartz. The methods used could be applied to the
study of cleavagein any tetragonal or hexagonalcrystal. unfortunately
the method cannot distinguish between the cleavageeffectsdue to correlative forms. consequently, r ll0Il l -uy not be distinguishedfrom
821
822
F. D, BLOSSAND G. V, GIBBS
Ta.nr,r 1. Soun RBponrro OesrnvatroNs op Cr-nav.tcnrN QUARTZ
Symbol
Index
Name
Source
0001
basal pinacoid
Sosman (1927, p. 487); Tsinzerling (7942, p. 556);
Anderson (1945, p 426);Borg and Maxwell (1956,
p. 76); Bloss (1957, p. 221).
rcil2
first-order
positive
rhombohedron
Anderson (1945, p. 426);Borg and Maxwell (1956,
p.76)
second-order
trigonal
pyramid
A n d e r s o n ( 1 9 4 5 ,p . 4 2 6 ) ; B o r g a n d M a x w e l l ( 1 9 . 5 6 ,
p.76)
1011
positive
rhombohedron
Hauy (1801); Lehmann (1886, p. 609); Mallard
(1890, p. 62); Wright and Larsen (1909); Nacken
(1916, p. 80); Ichikawa (1915, p. 472): Sosman
(1927,p.427); Schubnikoffand Zintserling (1932,
p . 2 4 3 ) ; R o g e r s ( 1 9 3 3 ,p . 1 1 1 ) ; W a l k e r ( 1 9 3 5 ,p . 3 1 ) ;
Griggs and Bell (1938, p 1738); Ingerson and
Ramisch (1942, p.597): von Engelhardt (1944, p
49); Anderson (19a5, p. 426); Borg and Maxwell
( 1 9 5 6 ,p . 7 6 ) ; B l o s s ( 1 9 5 7, p . 2 2 1 ) .
0111
negative
rhombohedron
Mallard (1890, p. 62); Sosman (1927, p. 427); Anderson (1945, p.426); Borg and Maxwell (1956, p.
7 6 ); B l o s s ( 1 9 5 7 ,p . 2 2 r ) .
second-order
trigonal di-
Ichikawa (1915, p. 472); Anderson (1945, p. 426);
Borg and Maxwell (1956, p. 76); Bloss (1957, p.
222).
, .. ,-^ *:.1
5161
trigonal trapezohedron
Ichikawa(1915,p. 472);Bloss(1957
, p. 222).
1010
unit prism
Ichikawa (1915,p 472); Sosman(1957,p. 427);
Drugman (1939,p 259); von Engelhardt (1944,
p. 50);Anderson(1945,p.429); Borg and Maxwell
(1956,p. 76);Bloss(.1957,
p.221).
second-order
prism
Ichikawa (1915,p. 472); Anderson(1945,p. 426);
Borg and Maxwell (1956,p. 76).
QUARI'Z CLEAVAGE
823
z 1 0 1 1 1 1 , n :l .t Jt 2{ z \ f r o m ' {1 z T t z 1l,tsl 2 t } f r o m, s t 2 l 7 r l , al l j o l
Irom'a (2110},
d {!q12}from,iJllrI2|r j |s0321
ftom,j 10332},
nor
r 1 5 1 6 1i r|o m' r 1 6 1 5 1-1* , l l O 5 t 1o r - , . r l t 5 6 1 l T
. h u ss, y m b o{l ,ss ,
a, d.,j and r are used in the following discussionsto indicate not only a
specificform but also all the correiative forms. For example, the statement that "cleavageexistsparallel.lo x" is to be construedthat cleavage
e x i s t sp a r a l l e lt o r a n d / o r ' * , - , a n d - ' r .
Acr<ITowTBoGMENTS
The writers are particularly indebted to the Council of the Geological
Society of America for researchgrants 729-56and 729-56-S57from the
PenroseBequest which made the study possible.Equipment and laboratory facilitieswerefurnishedby the University of Tennessee
and Iater by
Southern rllinois university. The Graduate council of southern llinois
University kindly provided funds for a calculating machine. The specimens of synthetic qtartz used in the study were graciously supplied by
Dr. Danforth Hale of Clevite ResearchLaboratories and by lllr. J. W.
Neilsenof the Bell TeiephoneLaboratories.Statistical advice was kindly
given by Dr. Harry V. Roberts of the University of Chicago.
nlerenrers .qNl NIBrnons
Clear crystalsof synthetic qttartz,assuredlyfree of strain, were coarsecrushedat room temperature.Fragmentslacking crystal faceswere then
further crushedin a hammermill. The resultant 80-100 mesh fragments
were next strongly irradiated with ultraviolet light to eliminate the possibility of static chargesresidualfrom the crushing process.Ultimately,
the grains were dusted onto glassslidesand cementedin their rest positions with hot, highly fluid, xylol solutionsof Canada balsam (c/. Bloss,
1957, p. 216).
The slide mounts thus prepared were studied under magnificationsof
240X on a 4-axisLeitz universalstage.As describedin the previousstudy
( B l o s s ,1 9 5 7 ,p . 2 1 6 ) , m e a s u r e m e n t w
s e r e m a d e o f d , t h e a n g l eb e t w e e n
the grain's c-axisand the pole to its plane of rest. fn this study, however,
the periphery of each grain was additionally examined (by proper tilting
and rotation of the stage)for possession
of planar fractures at anglesto
the plane of rest, thesebeing herecalled"peripheral planes." Suchperipheral planes were more common in hammermill-crushedqtartz than had
been anticipated; of the first 2269 grainsexamined,32.47o appeareddevoid of peripheral planes, 39.4Yapossessed
one peripheral plane, 22.5%
possessedtwo peripheral planes, and 5.7/s possessedthree or more
1 These two correlative forms are symbolized
as r and'r
by Frondel (1962).
824
F, D, BLOSS AND G. V. GIBBS
peripheralplanes.Occasionallytheseperipheral planeswere observedto
pass into the curved fracture surlacestypicaily associatedwith quartz;
occasionallythey showeda step effect.
The angular relationship of these peripheral planes to both the c-axis
and the grain's plane of rest was next determined by standard universal
one peripheralplane thereforeyielded
stagemethods.A grain possessing
the following angular values (Fig. 1):
(1) A, as already defined
(2) i, herc defined as the interfacial angle between the peripheral plane and the
(generalized) fracture surface of rest.
(3) tr, here defined as the angle between the fragment's c-axis and the zone-axis (line of
intersection) between the peripheral plane and surface of rest.
For a given grain, eachadditional peripheralplane observedwill add a
new set of values for i and tr, whereasthe value of d will not change.A
grain possessingthree peripheral planes would thereforeyield three sets
of data as f ollows: (a) 0, fi,Ir ; (b) 0, i2,\21and(c) 0, i3,13.
Those grains which lacked observableperipheral planes-and hence
yielded only a d value could not be presentedby the method next to be
Ld
z
{r
o-fr
6tr
-t-
5o
o
o_
,a{?
Y
6
Frc. 1. Highly enlarged quartz fragment. The zone axis common to a peripheral piane
(heavily shaded) and the plane of rest is oriented N-S. The significance of angles d, tr, and
d is illustrated-z'being
the interfacial angle between the peripheral plane and the plane
of rest.
QUARTZCLEAVAGE
825
described.Hence, after establishingthat 32.47oof a random sample of
2269 grainslacked observableperipheral planes,subsequentgrains were
measuredonly if observedto possesssuch planes.Thus only 67.6/6 oI thc
first 2269 grains (plus the grains subsequentlymeasured)hgure in the
data next discussed.
DrscussroN ol RESurrs
Methodof presentation.'fheobserveddata were grouped into five classes
accordingto whether a, the interfacial angle,fell betrveen32 46o,46 57",
57 68o, or 79-90". The 7573 observationswere, as a result, distributed
among these classesas follows: (a) 32-16'-720 observations;(b) 4657"-t020; (c) 57-68"-1a12; (d) 68-79'-1891; and (e) 79 90" 2530.
The greaterfrequency of higher interfacial anglesma1'be due, at least in
part, to the greater iikelihood of observationof such peripheral planes.
Peripheral planes making an interfacial angle of less than 32" with the
plane of rest were not measurabieat all becauseof the limits of excursion
on the horizontal axesof the universalstage.
The individual observationsoccurringwithin eachof the above classes
were plotted in one quadrant of a stereonetas illustrated in Fig. 2. Thus
plotted, the observedangles,dr and X1,define a point (".g. P in Fig. 2)
which denotes the cyclographic projection of the grain's c-axis if the
grain is locatedso that (1) its plane of rest parallelsthe plane of projection
of the stereogramand (2) the zone axis for this plane of rest and the
peripheralplane coincideswith the N-S radius of the stereogram.
For comparisonwith the observeddata, points have been plotted in a
like manner to representidealizedgrains resting upon and peripherally
boundedby perfectly cleavedfacesof the d, [, r, z, s, fi, m, a, andj forms,
ta
><
bJ
z
o
N
Frc. 2. The use of the stereonet for plotting (from the measured values of I and I) the
location of the grain's c axis, if the grain is in "standard position," that is, with its plane
of rest parallel to the plane of projection and the zone axis (common to both this plane of
rest and the peripheral plane) oriented N-S.
F. D. BLOSS AND G. V. GIBBS
all butT 3032) representingpreviously reported directionsfor cleavage.
The resultant theoreticai points are symbolized on the ensuing stereograms by a large ietter (indicating the form of the plane of rest) rvith a
letter subscript (indicating the form of the peripheral plane). Thus a
point labelled r- denotesthe cyclographicprojection of the c-axisfor a
grain lying on a perfectly developed r (1011) face and peripherally
bounded by a perfectly developedm (1010)face,the r:?n zone axis being
oriented N-S.
The observed data and the theoretical points just described were
plotted on quadrants of a stereonet(Figs. 3 6) for four of the five classes
of interfacial angies,the plot for the 32-46" classbeing here omitted since
this classlater proved to contain too few observationsto permit the statistical analysisnext to be described.
Statisl'icalanalysi,s.To facilitate statistical analysis of the data, each
stereonetquadrant in Figs. 3-6 was divided into 200 cells, all such cells
representingequal areasof the fundamental sphereof projection. Next,
the accumulation of points (i..e.,O,;) in each of the 200 cells of, for
example,Fig. 3, was compared with E, the expectedcell content under
the null hypothesis of isotropic fracture (wherein the data would be
e q u a l l y d i s t r i b u t e d a m o n g t h e 2 0 0 c e l l s .) F o r t h e d a t a o f F i g . 3 , c h i squarewas calculatedfrom the formuia
*,: f
'o'- u"
(rr
The value for chi-squarethus rbr"r".U was found to exceedX2 ooo,the
value of chi-squarefor a .999 probability and 199 degreesof freedom as
c a i c u l a t e df r o m t h e f o r m u l a g i v e n b y D i x o n a n d N l [ a s s e(y1 9 5 7 ,p . 3 8 5 ) .
The valuesfor chi-square,using equation (1), werealso calculatedfor the
data of Figs. 4-6 and in eachcaseexceeded12.eee.
Thus the null hypothesisthat qrartz lacks any preferred directionsfor cleavagewas rejected
with considerableconfidence.
Criteria were next set up to determine (at the 95 per cent confidence
Ievel) whether the content of any lth cell (i..e.O;) is significantlyabove or
below the interval about E to be expectedfrom merely chancevariations
from the null hypothesis.In an approximatemanner this was determined
for each cell since
-:E
p ( - t s a -. o i
< 1 . e 6 \: o . e s
\
/
\/E
holds to the extent that the O,- E/ \/E valuesare normally distributed
and mutually independent.Such is approximately the case;hence,computation oI Or E/lE for eachcell permits recognition(with an expected
QUARTZ CLEAVAGE
6
x
bJ
z
o
N
L-
o
z
o
F
U
IJ
E,
6
8
I
!
t
ir i it isf iiiBEk:ig;h
! s B
.g
.$;
io'6
I i h
t.c t l!rbE's l'N'p'e
E ANGLE
Frc. 3. Plotted data for 2530 observations in which i, the interfacial angle between the
peripheral plane and plane of rest, was between 79 and 90". For comparisons, the plotted
positions of combinations of previously reported cleavages are indicated by r", saretc. whete
the letter subscript refers to occurrence as a peripheral plane whereas the larger letter refers to occurrence as a plane of rest. If a grain were to have cleaved precisely parallel to two
of the previously reported directions for cleavage, it would plot at one of these black circles.
The stereonet quadrant has been divided into 200 cells, each of which represents an equal
area on the sphere of projection. The number of observations falling in each cell is indicated
near the cell's center whenever possible. Cells containing statistically beiow-average, average or above-average numbers of observations (at the 95le confidence level) are respectively unshaded, gray-shaded, or horizontally ruled.
828
F. D. BLOSSAND G. V. GIBBS
ratio of one wrong decisionin twenty) of those cells which contain, with
respectto the null hypothesis,significantly above-averagefrequencies
/O;-E
\
> 1 e6),
\ vu__
averagefrequencies
( -t.ru -.L---u -. ,
\
\
'u)'
vE
or below-average
/O;-I:
\;u
<-reb)
\
of data. Tn Figs. 3 to 6 the "above-averageceils,, thus determined arc
horizontally ruled, the "averagecells" are shadedlightly, and the ,,belowaveragecells" are unshaded.For compactnessin the tables and discussions to follow, these three cell types will be referred to as (*), (0), and
( - ) c e l l s r. e s p e c t i v e l y .
Inlerpretalionof d,ata.The (*) cellsof Figs. 3 6 generallycontain a preponderanceof observations.Of the 200 celisin Fig. 3, for example,the 37
(f ) cells contain 1282 oI the 2530 observationsupon which Fig. 3 is
based.Conversely,the 72 (-) cellsin Fig. 3 contain a total of only 176
observations.The situation for Figs. 4-6 is similar. Even allowing for the
one in twenty probability that (*) and (-) cells may actually be (0)
t y p e s ,t h e d i s p e r s ao
l f ( + ) a n d ( - ) c e l l si n F i g s . 3 - 6 i n d i c a t e s ,r e s p e c tively, the existenceof regionsalong which qu.artzis most likely and least
likeiy to rupture.
Table 2 summarizesthe extent to which the theoretical points (r.g.r^,
r , . . . e t c . ) o c c u r w i t h i n ( + ) , ( 0 ) , o r ( - ) c e l l si n F i g s . 3 - 6 . S t u d y o f
Table 2 indicates d {01121 to be unlikely as a cleavagedirection even
though it has been previously reported as such. of 35 theoreticalpoints
involving d as either a plane of rest or as a peripheral plane, oniy one is
Iocated in a (f) cell whereas20 were located in (0) cells and 14 in 1-7
c e l l s .r n t h e f a c eo f 1 a ( - ) o c c u r r e n c e st h
, e o n e i n s t a n c eo f a d c o m b i n a tion in a (*) cell doesnot seemsignificantsince,on the 9516 confidence
I e v e l u s e d , I i n 2 0 c o u l d b y c h a n c eo c c u r i n a ( * ) c e l l . S i n c ed i s t h u s
highly unlikely as a possiblecleavagedirection, the theoreticaipoints representingits combinationswith other suspectedcleavageforms were disregardedin compiling the remainder of Table 2.
Evidence is rather strong for the existenceoI the r and e cleavagesin
quartz. The distribution of 32.51theoreticalpoints involving r or z either
1 Half values were assigned if tivo theoretical
points occurred in the same (*) cell,
each combination then "being given half the credit" for the iarger frequency of observations within this cell.
QUARTZ CLEAVAGE
829
--ti^-
*l-
l*
-^ll
+
!
Q
p
o
a
z
L
2",
Il
.6
H1;
bo
N
E
xz
?6
2
z)
^e
HO
14
Ft^
E
o
OI
- v
I
t4&
'a
a
o
t4V
o
U
Z
E
o
N
d
\
,
F
da
4..
9o
-6
n*
o
O
F. D. BI.OSS AND G. V. GIBBS
l l a n ei n F i g s .3 - 6 w a s : ( f ) , 1 6 . 5 ;( 0 ) '
a s a p l a n eo f r e s t o r a s a p e r i p h e r a p
16;and (-), none. The absenceof theoreticalpoints involving r ot zlrom
(-) ceilsprovides further evidencefor the existenceof cleavageparallel
to thesedirections.Furthermore the theoreticalpoint indicating cleavage
combinations rr, rz,zr or zzfallsin the cell of greatestdata concentrationof
all the cellsin Figs. 3 to 6.
The f { ll22l direction is also corroboratedas a plane of cleavage.As
Table 2 illustrates,theoreticalpoints involving f were distributed among
t h e c e l l so f F i g s .3 6 a s f o l l o w s :( { ) 1 3 . 5 ;( 0 ) , 1 7; a n d ( - ) , n o n e .L o c a l
a
x
bJ
z
o
N
l!
o
z
o
F
(J
IJ
E
6
b
o
o
!
:i I b p;
'e'r
itsBEli!;s;
i! S ii
t
:'H i'c'9's's's b's b I'p t : i L 3
E ANGLE
Fro.4. Plotted data for 1891 observations in which i, the interfacial angle between the
peripheral plane and plane of rest, was between 68 and 79o. The conventions observed are
the sameas in Fie.3.
QUARTZ CLEAVAGE
831
mm,qo
L
x
hJ
z
o
N
l!
o
z
o
F
IE
d
d-a,-d a
dr -d
ir i i iliE ! i!; B; ir r ! s'E
i'sglggEEbIF'e:t
bp
E ANGLE
Frc. 5. Plotted data for 1412 observations in which i, the interfacial angle between the
peripheral plane and plane of rest, was between 57 and 68'. The conventions observed are
the sameas in Fig. 3.
highs in the accumulations of data sometimes occur near theoretical
points involving {, particularly when { is in combination with r or e (Fig.
5). However, comparedto the r and z directions,{ seemssomewhatinferior as a direction for cleavage.
Concentrationsof data were observedin Figs. 3-6 which seemedbest
explained by assuming that qtartz has a tendency to cleave parallel to
j 130321.This cleavage,not previously reported in the literature (to the
writers' knowledge),forms theoreticalpoints distributed among the cells
o f F i g s .3 - 6 a s f o l l o w s :( * ) , 1 0 ; ( 0 ) , 1 9 ; a n d ( - ) , n o n e .i l h u s T i s a p o s sible cleavagedirection for quartz sincethe ten occurrencesin (f) cells
seemsignificantlyabove the number expected.
Evidencein Figs. 3-6 for the existenceof s, r, m, and o cleavagesis less
conclusivethan that lor r, z, and {. Theoretical points involving the s
F. D. BLOSS AND G. V. GIBBS
cleavage,however, occur more frequently in (*) cells than may be
attributed to chance (Table 2). The single occurrenceof the theoretical
point s- in a (-) cell in Fig. 3, is possiblyattributable to chance.Of 41.5
theoreticaipoints involving the * cleavage,4.5 occur in (*) cells (Table
2) whereasonly 2 would have been expectedon the basisof chancevaritions from the null hypothesisof no preferreddirectionsof cleavage.The
m cleavagealso shows two more occurrencesi" (*) cells (Table 2) than
can be attributed to chance.The singleoccurrenceof a theoreticalpoint
involving m in a ( - ) celi is the s- point previously attributed to chance.
Theoreticalpoints involving the a cleavageoccurin (*) cellsonly slightly
tJj
x
t-rl
z
o
N
L
o
z
o
F
O
ld
E,
6
o
o
!
i
5 g i?:iBBBERhsb
o
o
b
b
.o
b ' - ' o ' o! t' o ' e
o
I
t
60
b'o
o
o
*$
b'o'N'o'.'G
o
F
F
F
o
! s E
1
a
?. b
o
o
E ANGLE
Frc. 6. Plotted data for 1020 observations in which i, the interfacial angle between the
peripheral plane and the plane of rest, was between 46 and 57". l'he conventions observed
are the sameas in Fig. 3.
833
QUARTZCLEAVAGE
more frequently than is attributable to chance.Thus, although s, r, and
rn appear to be cleavagedirections for qttartz, the evidence for cleavage
parallel to o is slightly lessconvincing.
In Figs.3-6 the (*) cells tend to be concentratedin particular areas
rather than being spottily distributed throughout; this is particularly
true for Figs.3 and 4 wherein the (f) cells are distributed in the areas
linking certain theoreticalpoints-for example,between Et,tu, 8,, zt, rE,rz,
zr, sE,xz,x, and m6in Fig. 3-in a manner that suggeststhat the data represent measurementson quartz fragments which rest on slightly conchoidal surfacesor on surfacesconsistingof cooperativebreakagealong
two or more cleavagedirections.The well known conchoidalfractures of
quartz seemmost likely to representcooperativebreakagealong two or
more cleavagedirections (on such an intimate scale that curved rather
than visibly steppedsurfacesresult). The distribution of the (*) ceilsbetween the theoretical points in Figs. 3-6 probably indicates the broad
iimits within which the conchoidalfracture of quartz undergoesstructural
control.
2
IL
F
z
trj
U
t
UJ
(l
tt
z<
E
'rrZ
D
IJ
x
(,4
L
nlr9
Js
d
"a
z
\))
't
ITl
-
Tl]|
Hl
oloa)304r
5060108090
ANGLE E
Frc. 7. (A) Histogram indicating the frequency of observation of particular values of 0
for 735 grains in which peripheral cleavage planes were not observed. The dashed lines indicate where data from grains resting on particular cleavages would plot. The isotropic distribution curve previousiy discussed by Bloss (1957) is shown by a dotted line.
(B) Histogram indicating the frequency of observation of particular values of 0 for
5804 grains, most of which possessedperipheral planes.
F. D. BLOSSAND G. V. GIBBS
The basal cleavage,c {0001}, embracesonly one direction in its form.
Consequentlyit forms too few "theoretical points" (in combination with
other cleavages)to permit an adequate study by the zonal method embodied in Figs. 3 to 6. Fortunately, the existenceof a basal cleavagecan
be unequivocably demonstratedby histogramswhich show the relative
frequencyof observationof 0 in grains of crushed quartz. Two such histograms were prepared,one for crushedgrains on which peripheral planes
were not observed(Fig. 7A), a secondfor grainsin which they were (Fig.
7B). The dotted line in each indicatesthe classheights to be expectedif
quartz possessed
no cleavageat ail, the sine-curvenature of this distribution having been previousiy discussedby Bloss (1957). In both histograms the 0-2o classprojects above the sine curve and thus indicatesthe
presenceof the basal cleavagec. This is more pronouncedin Fig. 7A than
in Fig. 78, afact which suggeststhat a basal cleavageis developedon a
grain only when it is orientedcrystallographicallyat an angleto the stress
such that this stress can be resoived almost entirely along the (0001)
plane. This was further corroboratedby subdividing the data of Fig. 78
into different histograms, one histogram for grains in which only one
Tenr-B3. BoNn DnNsrrrrislon SunracnsrN rHE (0001):(1120)
ZoNn
Polefc-axis
Bonds per A2
of surface
0tr
to
1)l
8" 27,
1,2"25',
76" 27',
20" 8'
23" 45',
27010'
30" 24',
33" 25',
36015',
38058',
4lo 2t'
43038',
45" 45',
47" 43',2
49" 33',
51" 16',
1 Corresponds
to c (0001).
2 Correspondsto
t 0122).
3 Correspondsto a (1120).
.0961
.0958
.0951
0938
.0922
.0902
.0879
0855
.0829
.0802
. o 7 75
.0747
.0721
.0695
0670
.0646
.0665
.0681
PoleIc-axis
52" 57',
54" 20',
56'11',
58007',
60008'
620 14',
6+" 26',
66" 42',
69. 03'
7l" 29',
73" 59',
76031',
79" 10',
81" 50',
84" 32',
87" 1.6',
9003
Bondsper A2
of surface
.0696
0709
.0726
.0742
. o 75 7
.0773
.0788
.0802
.0816
.0828
.0839
.0849
.0858
.0865
.0869
.0872
.0873
QUARTZ CLEAVAGE
Tasln 4. BoNo DnNsrrmsron SunrlcEs rN rHE (0001):(1010)ZoNe
PoleAc-Axis
0ot
50 1l',
70027'
15074'
79" 57',
24024'
28" 34'
32025',
35" 5g'
39" 74',
42013'
Mo 56',
47026'
49042'
51"47'2
53" 47',
55" 26'
Bonds per A2
of surface
.0961
.0957
.0945
.0926
.0903
.0875
.0844
.0811
.0777
.0744
.0711
.0680
.0650
.0621
.0594
.0609
.0623
PoleIc-Axis
570 03'
58" 31',
590 52',
6 1 01 l '
63" 33',
65030'
67" 29',
69033',
77" 39',
73049'
76002'
78" 77',
80035',
82055',
85" 18',
87039',
9003
Bonds/perAz
.0635
.0645
.0654
.0666
.0677
.0688
.0699
.0709
.0718
.0726
.0734
.0741
.0746
0751
.0754
.0756
. (r/.)o
1 Corresponds
to c (0001).
2 Corresponds
to r (10T1)
or z (0111).
3 Corresponds
to z (1010).
pedpheralplane was observed,a secondfor grainsin which two peripheral
planes were observed,and a third for grains possessingthree or more
peripheral planes.The height of the 0-2o classwas observedto decrease
steadily in the histogramsas the number of observedperipheral planes
increased.
Fig. 7A (735 observations)does not readily illustrate the influenceof
the s and tr cleavages,whereas Fig. 78 (5804 observations)does. The
fewer observationson which Fig. 7A is basedis probably the reason.Evidently a rather large number of observationsis required before the effect
of minor cleavagessuch as s and r becomesapparentin thesehistograms.
Srnucrun,qr Cor.rsroBnerroxS
From a projection of the quartz structure on a plane perpendicularto
the (0001):(1120)zoneaxis, the number of Si O bonds cut per unit area
was determinedfor a seriesof rational planesin the (0001):(ll2}) zorre
(Table 3 and Fig. 8, curve A). Of these planes,t 0l2D cuts the fewest
bonds per unit area and thus marks the minimum in Curve A. From a
second structural projection on a plane perpendicular to the (0001):
(1010)zone axis,the Si-O bonds cut by a series6f rational planesin this
F, D. BLOSS AND G, V. GIBBS
zonewas also determined (Table 4 and Fig. 8, Curve B). Of theseplanes,
r (1011) cuts fewest bonds per unit area and marks the minimum for
Curve B, cutting even fewer bonds than the previouslydiscussed€. Consequently,on the basisof bond density, cleavagesr (or z) and { would be
anticipated from the quartz structure, r being superior to {. This is, in
fact, in agreementwith the observations.
Factors other than the number of Si-O bonds cut per unit area also
affect the easeof rupture along a particular plane in qtattz. To illustrate,
the observeddata (Fig. 7) indicatec {0001} to be more frequent as a piane
of rupture than planesfor which d lies between2o and I|"-yet, as Fig. 8
illustrates,c {0001} cuts more bonds per unit area. Thus it seemslikely
that a factor such as the angle of the Si-O bond to the prospectivesurface of rupture may also be operative.
Von Engelhardt (1944)and Hofier (1961)have consideredthe efiect of
bond directions.Hoffer (1961,p. 85) definesa "cohesiveforce field" and
then assumesthat (1) the twelve difierent Si O bonds coincide with
directions for maxima in this field whereas(2) the normals to 24 (irrational) planes defined by two intersecting bonds-that is, by trios of
neighboringnuclei such as O-Si-O or Si O-Si-represent minima in
LrJ
U
r
E.
l
a
LL
s<
E.
LiJ
A--.
o-
q
O
z
o
co
o
FRACTURES LYING IN
zoNE (il20),(ooot)
IJ
B - o o o F R A C T U R E SL Y I N GI N
ZONE (t0lO):(0OOl)
a
z9i
76
30'
80'
ANGLE BETWEENPOLE TO FRACTURESURFACE
AND C-AXIS
Frc. 8. The density of Si--O bonds broken per square angstrom oI fracture surface as
calculated from the structure of quartz for (A) a family of fractures lying in the (1120)
: (0001) zone but at various angles of tilt to the c-axis and (B) a family of fractures lying in
the (1010): (0001) zone and at various angles of tilt to the c-axis. The minimum for curve I
corresponds to cleavage parallel to {; the minimum for curve B corresponds to cleavage
uarallel to r or z.
QUARTZCLEAVAGE
837
this field. From the atomic parametersfor Si and O in the low quartz
structure, Hoffer computed (1) the directionsof the Si-O bonds, (25 the
indicesof the 24 irrational planesand (3) the sinesof the anglesof intersectionbetweeneachSi-O bond and, successiveiy,
eachirrational plane.
He acceptsthe 21 irrational planes (whoseg vaiues are 29" Ig,,47o 38,,
51" 46',61o 38' and 78o 56') to be potential fracture planes,and usesthe
"absoiute sum of sinesof anglesof intersectionwith bonds,' to determine
which would perhapsbe better. For one irrational plane,d equals Sl" 46,,
a value like that to be expectedfor cleavageaiong r | 1011 I ; however,
plotted on a stereogram,the two planesdiffer in @angle by 30.. Hoffer
suggeststhat in histogramslike thosein Fig. 7, peaks near 52"may be the
expressionof the irrational plane rather than the r {l0Tl } cleavage.However, this present study provides more data than the histogram method
and corroboratesthe existenceof cleavageparallel to r 11011|. Further
evidencein support of cleavageparailel to r ot z, rather than to the irrational plane suggestedby Hofier, may be found in: (1) the numerousreports of r cleavagein the literature (cf. Table 1) and (2) broken, handspecimen-sized,
single crystals of quartz in which interrupted cleavage
surfacesreflect light simultaneouslywith (and are thereforeparallel to)
the r and a crystal facespresenton the specimen.
CoNcrusroNs
1 . L o w q r a r t z c l e a v e sm o s t r e a d i l y p a r a l l e tl o r { 1 0 1 1 f o r z [ 1 0 1 1 ]a n d
n e x t m o s t r e a d i l yp a r a l l e it o { { I L 2 2 l .
2. Thesedirectionsbreak the leastnumber of Si-O bonds of all olanes
i n t h e ( 0 0 0 1 ) : ( 1 0 1 0a)n d ( 0 0 0 1 ) : ( 1 t 2 Ozl o n e sr,e s p e c r i v e l y .
3 . L e s sp r o n o u n c e dc l e a v a g ees x i s rp a r a l l e lt o c { 0 0 0 1 f ,s { 1 1 7 1 } ,x
[ 5 1 6 1t , m l 1 0 I 0 l , a n d ,p e r h a p sj , t , S O 3 Za1n d o { I t 2 0 l .
4. The direction d II01,2l is unlikely as a cleavageunlessdirection of
stressis closely controlled.
5. The conchoidalfracture ol quartz is, to a degree,structurally controiled. The curved surfacesmay representsubmicroscopiccombinations
of cleavageplanes{, z, r, c, s, r, rn, and a.
Rnrrnnxcss
AxntnsoN, J L. (1945) Deformation planes and crystallographic directions in quarrz
Geol, Soc. Am. BulL 56, 409-430.
Br.oss, F. D. (1957) Anisotropy of fracture in quartz. Arn. Iour. Sci.2SS,2l+-225.
Bonc, Inrs lNo J. C Mexwnr.r. (1956) Interpretation of fabrics of experimentally def o r m e d s a n d s .A m . f o w . 1 c i . 2 5 4 , 7 1 - 8 1 .
Dtxox, W. J. axr F. J. Messnv. (1957), Introducti:n tc Stotisticol Anal,ysis. McGrarvHill, New York,
Dnucuex, J. (1939) Prismatic cleavage and steep rhombohedral form in a qtaftz Minerol.
Mog 25,259-263.
838
F. D. BLOSSAND G, V. GIBBS
FernnnnN, H. W. (1939) Correlation of quartz deformation with its crystal structure.
Am. Mineral. 24t 351-368.
Horlen, A. (1961) Low-quartz, on the geometry of its structure framework in terms of the
directed bond Zeil Krisl. 116, 83-100.
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deformed rocks. Geol.Soc. Am. Bull.49' 1723-1746.
Hruv, R. J. (1801) Trait| ile Mi.neralogie.Paris.
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Icurrrwa, S (1915) Studies on the etched figures of Japanese quartz Am. Iour. Sci.189,
455473.
InornsoN,'E. aNr J. L. ILnnrscn (1942) Origin of shapes of quartz sand grains.,4zz.
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Lnuu.nNN, J. (1886) Contractionsrissean Krystallen. Zeit. Kryst. ll' 608-612.
MAT.LAR.D,E. (1890) Sur les clivages du quartz. Soc. Mi'n. France BuII. 13,61-62.
Necxlr, R. (1916) Atzversuche anKugeln aus Quartz und a-Quartz. Neues Jahrb. Minuatr.
1,71-82.
Rocnns, A. (1933) Cleavageand parting in qtartz. Am. Minual. 18' 111.
(1932) Percussion and pressure-figures, and mechaniA. ANDK. Znrtsrnlrxc
Scnunrrnoll,
cal twinning in quartz. Zeit. Krist.83,243-264.
SosueN, R. (1927), The Properties oJ Silica. Chem. Catalogue Co., Nelv York, p. 487.
Tsrnzrnr-rNo, E. V. (1942) Cleavage oI quartz along the basis plane in an electric field'
f ow. Teeh.P/zys. (U.S.S.R.) 12, 552-556 (Chem.Abst. l9M).
voN ENGELHARDT,W. (19a4) Die Anisotropie der Teilbarkeit des Quarzes' Nachr. Ahad'.
Wiss. Gdtti,ngm.Math. Phys. Klasse,43-56.
W A r - K E R , T .( 1 9 3 5 )A n u n u s u a l t y p e o f q u a r t z . U n i r . T o r o n t o S t u d i e s , G e o l S e r . 3 8 , 3 7 - 3 2 .
Wnrcnr, F. E. ano E. S. Lansnn (1909) Quartz as a geologicthermometer. Am. Jour. Sci'
27,441-M7.
ZrNsnnr-rNc, K. nNo A. V. SnueNrrov (1933) On the plasticity of qtartz Lomonosof Inst.
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Manuscriptreceited,Nolember 15, 1962;accepledJorpublicotion, Moy 3, 1963.