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Volume 34, pages 142-162, 1949 THE FREQUENCY OF TWIN TYPES IN QUARTZ CRYSTALS1 H. R. GAULT, Lehigh University, Bethlehem, Pa. CONTENTS Abstract 142 ABSTRACT The frequency of twin types and the handedness were determined for 1,179crystals from six localities by the use of etch figures developed withhydrofluoric acid. It is shown that. twinned quartz crystals are much morecommon than untwinned and that the frequencies of twin types and the ratiosbetween twin types vary from locality to locality. It is suggested that crystalstwinned according to both the Dauphiné and Brazil laws should be called"Dauphiné-Brazil" twins rather than by the names that have beenpreviously applied. The local variations of twin ratios are thought to be areflection of geologicenvironment. INTRODUCTION Some years ago while engaged in etch-figure work with the late Dr. A. P. Honess,it became desirable to etch and study a few low-quartz crystals from twolocalities. The crystals from the first locality showed considerably moretwinning than those from the second, although the unetched crystals gave noindication of any twinning. A search through the literature disclosed manyarticles on twinning in quartz but there were few statistical data on thefrequency distribution of twin types and of right- and left-handed crystals.Further studies were made on additional crystals from these two localities andfrom four others in order to determine the frequency of twin types for eachlocality and the frequency of right- and left-handed quartz crystals. Interestin this problem arose more from the geological implications than from the purelymineralogical aspects. The writer is indebted to the late Arthur P. Honess for an introduction to theetch method and for encouragement in this study. Thanks are extended to severalformer associates for gifts of certain crystals and for opportunities to discuss the problem. C. Wroe Wolfe kindly loaned histranslation of Friedel's Lecons de Cristallographie and Siemon Muller certainRussian translations. Appreciation is expressed to J. D. H. Donnay, D. M.Fraser, C. S. Hurlbut, Jr., Earl Ingerson, and R. B. Sosman for constructivecriticism of the original manuscript, and to R. D. Butler for discussions aboutthe phantom crystals. J. C. Wynn very kindly loaned his drawings of phantomcrystals from Brazil. There is a voluminous literature on quartz but it is beyond the scope of thispaper to review all of it. Many of the references are concerned withdescriptions and study of quartz twins and twinning, the nature of the twinboundaries, quartz etch figures, vicinal faces, relations of form and twinningto temperature of formation, as well as geology and occurrence. Among the manyworkers who prior to 1940 contributed to the study of quartz along these linesare Baumhauer, Bendrich, Bomer, Bond, Brauns, Des Cloiseaux, Drugman, Friedel,Gaudefroy, Gill, Goldschmidt, Heide, Hirschwald, Ichikawa, Kalb, Larsen, Leydolt,Martini, Meen, Meyer, Molengraaf, Mügge, Nacken, Niggli, Penfield, Rose, Sosman,Trommsdorf, Von Roth, Websky, Weiss, Wright, and Witteborg. Since 1940, becauseof the great war demand for quartz oscillator-plates in the radio industry,added impetus was given in the United States to the study of quartz and itstwinning by the work of Armstrong, Bond, Frondel, Gordon, Hurlbut, Parrish,Stoiber, Willard, and others. No attempt will be made to cite all of thereferences; some are noted in recent papers by Frondel, Parrish, Hurlbut, Gordonand others. Heide (1928) tabulates data for twenty-eight twin halves of Japanese twins fromSaubach giving three with no twinning, fifteen twinned after the Dauphiné law,of which seven were left-handed and eight were right-handed, two after the Brazillaw and eight after the Dauphiné-Brazil law. Trommsdorf (1937) examined 4,483 crystals from Villa Cristallinanear Tres Capone, Brazil, and reported that 0.91 per cent were twinned according to the Brazil law. He also found that about half of those examined were right-handed and half were left-handed. His results aremarkedly at variance with those of Hurlbut (1946) for Brazilian quartz. Thompson (1937) used the positions and striae on the s {11  1} faces to determine handedness of 52 crystals from ten localities.He found that 24 were right-handed, thirteen were left-handed, and thirteencould not be identified. One Dauphiné twin and one Brazil twin were found. However, Thompson had too few crystals for his data tobe ofstatistical value. His method, while of interest to the mineral collector, isinadequate for a frequency study since only a small proportion of all quartzcrystals have the s and x faces developed. Furthermore, in many cases it is notpossible to determine the presence or absence of twinning from the developmentof these faces.Saparova (1938) reported that, of thirty crystals from Wermsdorf, nineteen weretwinned; eighteen according to the Dauphiné law and one according to the Brazillaw. Hurlbut (1946) gives some excellent data on the volume percentages of Dauphinéand Brazil twinning in quartz crystals from thirteen localities in Brazil, twoin Guatemala, and one in Colombia. His article is based on research to determinewhich localities would yield the best grade of oscillator-plate quartz. Hurlbutexamined 52,000 wafers cut from 3,015 crystals and thus gives a quantitativeviewpoint not ordinarily obtainable by those outside the quartz industry. Sincehe did not report the frequencies of twin types or twinned and untwinnedcrystals, his data cannot be directly compared with those presented below butthere seem to be some relationships. Hurlbut's data (p. 449, Table 3) showsdifferences in the volume percentages of twinning with greater differences amongBrazilian, Colombian, and Guatemalan localities than among just Brazilianlocalities. This is brought out more strikingly by the yield of oscillator-plateblanks per pound than by the percentages of twinning, although, as Hurlbutpoints out, it is unfair in generalizing to say that Colombian and Guatemalanquartz are of lower grade (and thus in one sense more strongly twinned) thanBrazilian quartz because of the limited quantities studied from the formerlocalities. There is also quantitative information on high-quartz crystals. One of the moreinformative studies is Mügge's (1892) on pyrogenic or rock forming quartzincluding a number of euhedral high-quartz crystals from porphyries. QUARTZ ETCH FIGURES Excellent discussions of etch figures of quartz are given by Leydolt, Mügge,Ichikawa, Nacken, Gill, Meyer, Penfield, and Bond. Honess (1927) has discussedthe entire subject of etching very thoroughly. It is relatively easy to distinguish between right- and left-handed quartz by the use of etch figures (Meyer and Penfield, 1889) and,further more, theetch figures for all faces of one form etched with the same solvent are quitedistinctive from those of other forms. The fact that different solvents developdifferent etch figures on the same face is of no significance here. Quartz can be etched by several solvents. Hydrofluoric acid has been the most widelyused, although the quartz industry now uses a water solution of ammoniumbifluoride (Parrish and Gordon, 1945) for safety reasons. Hydrofluoric acid wasused in the present study. The etch figures produced byhydrofluoric acid on the rhombohedral faces r {10 QUARTZ TWIN LAWS There are six known twin laws for low-quartz (Friedel, 1926), namely, Dauphiné,Brazil, Japanese, Esterel, Sardinian, and Breithaupt. In addition, there is acomplex type of twinning which is a combination of the Dauphiné and Brazil lawsand has been variously called. Liebisch twinning, combined twinning, combinedoptical twinning, combined Dauphiné-Brazil twinning, and Dauphiné-Braziltwinning. Dauphiné, Brazil, and Dauphiné-Brazil twins are penetration twins andare the most common types. Although they are the only twin laws considered inthis study, a summary of all the known twin laws of quartz is included. SUMMARY OF TWIN LAWS OF QUARTZ
1 Heide (1928) considers four "laws" for Japanese twins of which thecommon designation (11 Recognition of penetration twins is largely a matter of etching any observingthe type and arrangement of the etch figures (Fig. 2). It is generally acceptedthat untwinned quartz is relatively uncommonand that most crystals are twinned according to the Dauphiné law and theBrazil law (Booth and Sayers, 1939; Gordon, 1945; and others); Booth and Sayersalso indicate that Dauphiné-Brazil ("combined") twinning is verycommon. In Dauphins twinning, the r {10 Brazil twinning, also known as chiral or optical twinning, is the result of anintergrowth of a right- and a left-handed individual as if there had been areflection across a second order prism. Thus a right r {10 Internal twin boundaries of Dauphiné and Brazil twins in sections through thecrystals are well illustrated and described by many workers in recent years byFrondel (1945), Gordon (1945), Johnston and Butler (1946), Parrish and Gordon.(1945), Willard (1944) and others. The Dauphiné-Brazil twin has been described for many years but does not seem tohave acquired a name until recently. Leydolt (1855, pl. 4) gives an excellentillustration of this type of twinning in a basal section. Liebisch (1896)mentions it as one possible type of twin but applies no name. Lewis (1899)describes it as a possible composite crystal ("laevo-dextrogyral twinsβ") and refers to amethyst crystals which supposedly show it. This complextwinning is pointed out in both editions of Weiss, Mineralogy (1902, 1929) andby Klockman (1923). Heide (1928) refers to Liebisch's description and shows thesymmetry of the twinned crystals schematically with etch-figure patterns.Heide's discussion is one of the most complete. Gaudefroy (1933) also recognizedthis type of twinning. No mention of twinning of this type is made in Hintze's Handbuch, in the 6th Edition of Dana's System of Mineralogy (1892), Zirkel's Elemente der Mineralogie (1897), nor in Tutton's Crystallography (1922). The first name applied to this twinning was apparently given by Ivanov andShafranovsky (1938) who illustrate types of twinned crystals which they refer toas simple and complex Liebisch twins. Booth and Sayers (1939) describe andfigure this same type of twinning but suggested the name "combinedoptical twinning." Willard (1944) also describes and figures such twinning and calls it "combined twinning." Thomas (1945)suggested "combined twinning" as a shorter form of "combinedoptical twinning." Gordon (1945) and Frondel (1945) have also used the term"combined twinning" as have a few others. According to theillustration of Ivanov and Shafranovsky (1938), a simple Liebisch twin is arigidly defined combination of both Dauphins and Brazil twin-law effects in sucha way that there is first an apparent rotation about the c axis (Dauphinéeffect) and then there is an apparent reflection across a second order prismface (Brazil law effect). Thus in this simple twin a right r and a left z facebecome coincident (see Fig. 2) rather than a right r and a left r as in a Braziltwin or a right r and a right z as in a Dauphins twin. Descriptions and figuresby Heide (1928) and the comments of others agree in principle with the above. 'This combination of the Dauphiné and Brazil laws is perhaps analogous to thecomplex albite-Carlsbad twin in the triclinic feldspars. There is, however, onedifference. Because quartz is enantiomorphous, the twining action cannot beperformed by a single operation as it can for the albite-Carlsbad twin. In thealbite-Carlsbad twin the simplest form has only two parts (1 and 2' of Winchell,1933); part 1 is in the original position and part 2' is in a position that canbe obtained by two rotations, or corresponding to the albite law and one to theCarlsbad law. Similarly in the simple Dauphiné-Brazil twin there are two parts,one in the original position and the second obtained by a rotation combined witha reflection. Such dual Dauphiné-Brazil twins are uncommon in quartz. In mostcrystals twinned according to the complex Dauphiné-Brazil law, as observedin the present study, there are many parts so that any one part will have a Dauphinétwin relation to a second, a Brazil twin relation to a third, a Dauphiné-Brazil relation to a fourth. Typical Dauphiné-Brazil twin-law etch-figure patterns on the rhombohedral facesare shown in Fig. 2, which illustrates possible etch-figure patterns onrhombohedral faces where the Dauphiné effect appears on one face, the Brazileffect on a second face, and the Liebisch effect on a third face. Some of thesevariations have been noted. On the basis of date of publication, Ivanov and Shafranovsky's name "Liebisch" should have precedence over the others. From the standpoint of usage, the term "combined twinning" seems well established and understood in the quartz oscillator-plate industry. Despite precedence and usage, it is suggested that this type of twinning in quartz should be called "Dauphiné-Brazil twinning" just as the complex feldspar twin laws are named after their combinations. As crystals showing only a simple Dauphiné-Brazil twin pattern or "Liebisch" effect are rare, itmay be desirable to drop the term "Liebisch."PROCEDURE All of the crystals used in this study possessed the trigonal symmetry oflow-quartz. Groups of crystals were obtained from each locality without anyselective sampling other than the requirement that each crystal have itsterminal faces completely developed. The crystals were etched with hydrofluoric acid until the etch figures were sufficiently mature forrecognition of outline and orientation. No attempt was made to control the timeof etching or the concentration of the acid. After etching, the crystals wereexamined under a binocular microscope in reflected light and classifiedaccording to the twin laws indicated by the etch figure patterns (see Fig. 2).
All observations were confined to the rhombohedral faces of crystals except inthe case of those from Herkimer County, N. Y. This was necessary in most casesbecause of the lack of development of prism faces or because the prism faceswere too striated or otherwise roughened for etching. In some cases,particularly with the Arkansas crystals, it was possible to trace twinboundaries from the rhombohedral faces to the adjacent prism faces. RESULTS AND DESCRIPTION OF MATERIAL A total of 1,179 crystals from six widely separated geographic locations anddistinct geologic occurrences were examined. The statistical data are presentedin Table 2. No distinction is made in the table between simple and complex Dauphiné-Brazil twinning. In classifying Brazil and Dauphiné-Brazil twins thereis always the problem of whether they should be placed with right-handed orleft-handed crystals. Only in few instances was any difficulty experienced indetermining which type of quartz was dominant in a crystal. It is generallyobvious from visual inspection that one or the other is dominant. As others have pointed out, right- and left-handed quartz occur in about equalproportions in "untwinned" crystals as well as in Dauphiné twins.Brazil twins and Dauphiné-Brazil twins, with respect to to dominant handednessin each crystal, also show right- and left-handed quartz in about equalproportions. The relative frequency of untwinned and twinned crystals varies from place toplace, and the relative frequency of the interpenetration laws also variesconsiderably. Accordingly, there is a determinable ratio between twin types forindividual localities. For the total number of crystals studied, Dauphiné-Braziltwins are slightly more common than Dauphiné twins. Brazil twins are relativelyuncommon. However, in the breakdown by localities, the relative frequencies, atany one occurrence show more variation. Actually, Dauphiné twins are more abundant in fourof the six occurrences (Arkansas, Utah, Maryland, Alaska) than Dauphiné-Braziltwins. Brazil twins are more abundant than Dauphiné twins and nearly equal to Dauphiné-Brazil twins at one locality (New York).Dauphiné twins are present atall localities but Brazil twins are lacking at three localities (Pennsylvania,Maryland, Alaska). Dauphiné-Brazil twins were not recognized at two localities(Utah and Maryland). An apparent correlation was noted, particularly for the Arkansas crystals,between the frequency and amount of twinning and the shape of the crystal. Themore tapered crystals (candle-like habit) tend to show less twinning. Hurlbut(1946) shows this quantitatively in graphic form for Brazilian quartz. There isalso a suggestion that individual crystals bearing the less common faces s {11 Arkansas crystals - Quartz crystals from Arkansas are well known and. theiroccurrence and geology have been well described by Miser (1943) and Engel(1946). The material used in this study came from the Fisher mines about sevenmiles southeast of Mount Ida, Montgomery County, near the southwest end of themain district in western Arkansas (Engel Fig. 1, 1946). The crystals are singlyterminated and range from 3/8 inch to one inch in diameter and one inch to twoinches in length. They belong to Engel's simple type (p. 606, 1946). Most ofthem have clear terminations with milky lower portions. None of the crystals reported in Table 1showed any s or x faces. Typical twin boundaries on the rhombohedral faces ofthe Arkansas crystals are shown in Fig. 3. In addition to the Arkansas crystals reported in the table, a second group of160 singly terminated crystals representing a number of Arkansas localities werealso examined. It is a pleasure to thank Mr. Hugh D. Miser, U. S. GeologicalSurvey, for the gift of these crystals. The crystals in this group aredistinctive in that they all show the development of at least one x {51 TABLE 1. FREQUENCY OF TWIN LAWS IN ARKANSAS QUARTZ CRYSTALS
Ratio (d:b:db) 10:7.5:3 *R=right; L=left; nt=no twinning; d=Dauphiné; b=Brazil; db=Dauphiné-Brazil.
This assemblage of crystals shows a greater proportion of untwinned crystalsthan do those lacking the x and s faces. This difference is largely at theexpense of the Dauphiné twins. There is also a slight decrease in the totalfrequency of intergrowths of right- and left-handed individuals with the Dauphiné-Brazil twinning giving way to Brazil twinning. Pennsylvania crystals. -- There are a number of localities in Pennsylvania andMaryland where quartz crystals occur in soil overlying limestones. Presumablythey are residual from the weathering of the limestones. The material describedhere came from a field underlain by Trenton limestone (Butts and Moore, 1936)just east of Lemont, Centre County. Quartz crystals were found also in thelimestone and in calcite veins cutting the limestone. None of them, however, wasas large as the largest crystals found in the soil. TABLE 2. FREQUENCY OF TWIN LAWS IN QUARTZ CRYSTALS
Total right-handedd or right-handed dominant 518 or 51.6% * R=right; L=left; nt=no twinning; d=Dauphiné; b=Brazil; db=Dauphiné-Brazil. 112 additional crystals showed Rb at one end and Lb at the other. 3 additional crystals showed Rnt at one end and Lnt at the other end. 2 1addition at crystal showed Rnt at one end and Lnt at the other end.
All of the crystals studied are doubly terminated with roughened striatedprism faces. Inclusions of dark materials, cavities, irregular growth habitsand internal flaws are common to all crystals. They are not clear like theHerkimer County, New York, crystals. The crystals examined are one-quarterinch to one inch in diameter and one-half inch to one and one-half inches long.Typical twin boundaries on the rhombohedral faces are shown in Fig. 4a. Figure 4b shows internal twinned parts. Utah crystals -- The crystals were taken from a small drusy specimen collected in the Tintic district. Barite crystals were associated with the quartz crystals. The latter are small singly terminated crystals with a diameter of about one-eighth inch and a length of about three-eighth inch. New York Crystals --- The material used in this study is typical of the well-known Herkimer County, New York, product. The crystals range fromone-quarter inch to three-quarters inch in diameter and one-half inch to one andone-half inches in length. On all of these crystals it was possible to trace theexternal twin boundaries on the prism faces. The exact locality is unknown, butall are from the same general location. Maryland crystals -- These crystals came from a small quartz vein in theWissahickon formation near Baltimore. The crystals are about the same size as the Tintic, Utah, material and are singly terminated with only the rhombohedral faces developed.Alaska crystals - The Alaska crystals are from Glacier Basin, near Wrangell,Alaska. They occurred as drusy deposits with a comb-like structure in vugs oralong the walls of quartz-fluorite breccia veins cutting a series of metamorphicrocks in the Coast Ranges. The geology and veins are described by Gault, Rossuran and Flint (1944a & b). The crystalsare singly terminated with only the rhombohedral faces developed. The bases ofthe terminations are one-eighth inch to one-half inch in diameter. Typical twinpatterns are shown in Fig. 4c. The etch figures on these crystals indicate an unusual development of the r {10 No crystals were noted twinned only according to the Brazil law. In thecrystals twinned according to the Dauphiné-Brazil complex law, the secondenantiomorphous individual always made its appearance near the base of therhombohedral faces and in practically all cases it was indicated by thecoincidence of right- and left-handed r faces. DISCUSSION Some discussion of the procedure seems warranted to avoid criticism with regardto confining observations to the rhombohedral faces. It is obvious, of course,that where no prism faces were developed, no etch figures could be obtained forstudying twin boundaries on the exterior of the crystals. Some twinning may havebeen overlooked by not studying the prism faces as thoroughly as therhombohedral faces. However, further observations were made, where possible, onthose crystals which showed no twinning on the rhombohedral faces to see ifthere were twin boundaries on the prism faces not extending to the rhombohedralfaces. In some instances such boundaries were observed but not in enough casesto change noticeably the actual numbers of crystals and, even less, to changethe ratios among twin types. Another comment which may be made is that this study has dealt thus far onlywith the exterior of the crystal and no consideration has been given to theinterior. An approach to this question of interior twinning was made by taking20 Arkansas crystals which showed no twin boundaries on the rhombohedral faces,cutting a basal section from each one slightly below the base of thetermination, and etching the basal sections. Of the 20 sections, 12 showed notwinning at all. The other 8 crystals showed quite small irregular patches of twinning which were restrictedto the very edges of the crystals but were not always recognizable on the prismfaces. Four of these eight crystals each carried one small twinned part near thecenter of the section. Because these did not appear on the rhombohedral faces,it is suggested that some twinned parts were wholly internal, i.e. entirelysurrounded by other quartz. Heide (1928) also suggested that material appearingas untwinned quartz in poorly developed crystals might actually be twinned elsewhere in the crystal.This suggestion is further substantiated by Hurlbut, 4 who, from his extensiveexperience in the quartz industry, says it is quite possible, and frequentlyhappens that twinned parts are entirely enclosed by other quartz and do notappear on the exterior of the crystal. Hurlbut's work with so many thousands ofwafers should be conclusive.
Of the 20 crystals mentioned above, 40 per cent of those tested showed twinnedparts which were not recognized on the rhombohedral faces. Although this is aconsiderable percentage of the so-called untwinned crystals, actually thedistribution of these twins did not change the ratio of twin types. Thus, ifthere is any hesitancy in accepting the untwinned group as truly untwinnedcrystals, it can be disregarded and only the ratios of twin types accepted. Onthis basis, the approximate ratios of twin types for each locality are given belowas derived from the relative frequencies in Table 2 (see also Fig. 5). Practically, of course, the study of twin boundaries in quartz only at thesurface of the crystals does not tell much about the extent of the twinnedmaterial within the crystal. Confining the observations to the rhombohedralfaces limits this still more. However, it can be shown from the geometry of mostof the crystals that the principal direction of growth was parallel to the caxis and probably on the rhombohedral faces. It is readily apparent that if, asa seed crystal grows, the rhomb faces are the areas of greatest deposition thecrystal will become elongate parallel to the c axis. In order to produce broadshort crystals the rate of growth on the prism faces must be greater than on therhomb faces. One indication of direction of growth is phantom crystals. Johnstonand Butler (1946) figure a number of phantom crystals from Brazil and state (p,639): The prismatic habit of quartz is reflected by the phantom relations - growth wasusually pronounced along the c axis after formation of the phantom even thoughthe center of gravity in the basal planes conspicuously shifted. Their figures as well as other unpublished figures 5 of phantom crystals fromBrazil all show the rhomb faces as having a greater thickness of quartz in eachphantom than do the corresponding prism faces.6In a general way, similar conditions of growth are inferred for the crystalsdescribed herein, all of which have their long dimension parallel to the c axis.Therefore, observations on the rhombohedral faces of these crystals shouldreflect the frequency and nature of twinning at the places ofgreatest deposition, at least during the last stage of growth of the crystals.The groups of so-called untwinned crystals should now take on more significancebecause they would indicate there was no twinning developing at that time. Unless there were radical changes in conditionsof growth from early to late stages, the observations should perhaps be anindication of what would be found within the crystal. Even if there wereradical changes from early to late stages, it seems reasonable to believe thatthey would have been in degree of controlling factors rather than in type. Whereno twinning or only isolated patches of twinned quartz are exposed at thesurface of the crystal, it does not seem probable that the interior of thecrystal should show strong twinning with many parts. RATIOS OF TWIN TYPES
Because internal twinned parts are not taken into account, these data are notrigidly quantitative but rather they express a relative frequency of and ratiobetween twin types. If the materials described herein were studied along thelines applied by Hurlbut (1946), there might be no groups of untwinned crystalsbut such groups according to the present classification might show only very small volume percentages of twinned quartz.The ratios between twin types for each locality may be characteristic ofdifferent types of geologic occurrence. Frondel (1945) has stated that therelative development of Dauphiné and Brazil twinning varies widely as does theindividual percentage of the twin types and that the type of occurrence seems tobe a controlling factor in the relative development of twins. Hurlbut's (1946)data, although given as volume percentages indicate a difference in the amountof twinning from place to place. As Hurlbut points out, the correlation betweenpercentage of twinning and yield of oscillator blanks per pound is far fromperfect, but study of his data shows the yield from Brazilian localities tofall within certain limits which are higher than the limits of the yield fromother than Brazilian localities. The correlation of volume percentages of Dauphinéand Brazil twinned parts with locality is less obvious than for yieldof blanks, but again all of the Brazilian localities fall within certain limitsoutside of which the volume percentages of the other localities lie. There is also a suggestion, albeit weak, that for a group of localities ofsimilar origin there may be upper and lower limits for the volume percentage oftwinning as compared with other types of occurrences. Unfortunately, Hurlbutcould not list specific localities for security reasons, and so it is notpossible to compare his Brazilian localities with the four major quartz belts inBrazil (Stoiber, Tolman, and Butler, 1945). Possibly a closer correlation andnarrower limits for each belt might be forthcoming. On the other hand, Campbell(1946) includes two of the quartz belts described by Stoiber in one type ofgeologic occurrence. It would appear that very broadly speaking all Brazilianlocalities are similar in origin and geologic occurrence and belong to a singlegenetic period (Kerr and Ericksen, 1942; Johnston and Butler, 1946, and others). Where the frequencies of twin types for a number of localities fallwithin certain limits, these limits may be distinctive for deposits which havesimilar conditions of origin and geologic environment, but which aregeographically distinct. Further study is needed to verify or refute this. Engelstates (p. 608, 1946) that, although all correlation of occurrence and nature ofoptical twinning is speculative, it is known that the ratio of highly twinned torelatively untwinned quartz is fairly constant for a single deposit or group ofrelated deposits. It varies considerably between localities in dissimilarcountry rock. The problem of the geological significance of variations of the frequency oftwins and of the ratios between twin types is of considerable interest, but manyadditional observations and some experimental data are needed before anysatisfactory conclusions can be drawn. The frequencies of twins and the ratiosbetween twin types seem to be a reflection of the mode of occurrence which willrequire the consideration of many environmental factors, in fact, more than canbe resolved at present. Thus it is not possible to relate twin ratios andfrequencies at this time to geological occurrence. Factors which probably exertan important influence are temperature, concentration, impurities, nature of thewall rock, rate of cooling and pressure. Temperature studies have been made to (1) determine whether the quartzcrystallized as the high or low form (Mügge, 1907, 1921; Wright and Larsen,1909) and (2) to distinguish temperature stages in types of low-quartz crystals(Maucher, 1914; Mügge, 1921; Kalb, 1933, 1935; Virovlyanski, 1938a, 1938b). Thecriteria of the nature of twin boundaries and their patterns for determininghigh- or low-quartz crystallization are becoming less and less applicable as aresult of recent work (Frondel, 1945; Armstrong, 1946). Virovlyanski (1938a andb) and Engel (1946) found Kalb's scheme (based on vicinal faces) unreliable. The influence of impurities on twinning in quartz has been pointed out recentlyby Zinserling (1941), Johnston and Butler (1946), and Armstrong (1946). Twotypes of impurities are important; those incorporated in the crystals during itsgrowth and those which settled out of suspension onto earlier growth planes. SUMMARY AND CONCLUSIONS There is a great need for further observation and experimentation before thegeological significance of the frequency of twins and the ratios between twintypes in quartz can be fully understood. Temperature measurements on inclusionssimilar to those reported by Newhouse (1933), Ingerson (1947), and Twenhofel(1947) would be very valuable. Further studies along that line are in progressfor the crystals described herein. Study of growth patterns and twinning in the various parts of phantomcrystals may contribute much to the problem. There are, however, several well established points with respect to quartztwinning which can serve as a basis for future work. 1 Twinned quartz crystals are much more common than untwinned crystals - in fact,untwinned crystals may be considered a rarity. 2. Penetration twins are the most common type. Contact twins are rare. 3. Crystals twinned according to both the Dauphiné and the Brazil laws should hecalled "Dauphiné-Brazil" twins rather than "combined" twins. 4. Of the three types of penetration twins, those twinned according to the Dauphinéand Dauphiné-Brazil laws are as a rule more abundant than Brazil twins,particularly the Dauphiné-Brazil. The excess is sometimes slight, sometimesoverwhelming. The common occurrence of Dauphiné-Brazil twins has not been fullyrecognized. 5. Right- and left-handed quartz crystals are found to occur in equalproportions when a sufficient quantity of material is examined. Even in Braziland Dauphiné-Brazil twins, though one handedness is dominant over the other ineach crystal, those with right dominant are equal to those with left dominant. 6. Dauphiné twin boundaries are irregular, whereas Brazil boundaries are morelikely to be parallel to crystallographic planes. 7. Crystals on which the less common faces of general forms are developed showless twinning than other crystals from the same locality. 8. The relative frequency of the twin types varies considerably from locality tolocality. These variations must surely be a reflection of the conditions ofgrowth and geologic environment. REFERENCES 1. ARMSTRONG, ELIZABETH, (1946), Relation between secondary Dauphiné twinningand. irradiation-coloring in quartz: Am. Mineral., 31, 456-462. 2. BANDY, .MARK C. (1942), Direction of flow of mineralizing solutions: Ec.Geol., 37,330- 333. 3. BOOTH, C. F., AND SAYERS, C. F., (1939), The production of quartz resonatorsfor the London-Birmingham coaxial cable system: P. O. Elec. Eng. Jour., 31,245-253. 4. BUTTS, CHARLES, AND MOORE, ELWOOD S., (1936), Geology and mineral resourcesof the Bellefonte quadrangle, Pa.: U. S. Geol. Surv., Bull. 855. 5. CAMPBELL, D. F., (1946), Quartz crystal deposits in the state of Goiaz,Brazil: Ec. Geol., 41, 773-800. 6. ENGEL, A. E. J., (1946), The quartz crystals of western Arkansas: Ec. Geol.,41, 598- 619. 7. FRIEDEL, GEORGES, (1926), Leçons de cristallographie: Berger-Levrault, Paris,602pp. 8. FRONDEL, CLIFFORD, (1945), SecondaryDauphiné twinning in quartz: Am.Min 30, 447-461. 9. GAULT, H.. R., (1944a), Zinc deposits of Groundhog Basin, Wrangell district,southeastern, Alaska; mimeographed report. U. S. Geol. Surv., (March). 10. _____ ROSSMAN, D. L., AND FLINT, G. M., JR., (1944b), Geology and mineral deposits of Glacier Basin and vicinity, Wrangell district, southeastern, Alaska: mimeographed report, U. S. Geol. Surv., (May). 11. GAUDEFROY, M. C. (1933), Sur les groupements de cristaux de quartz ä axesparalleles Bull. Soc. Min. (France), 56, 5-63. 12. GORDON S. G., (1945), The inspection and grading of quartz: Am. Mineral., 30,269- 119 13. HEIDE, F., (1928), Die Japaner Zwillinge des Quarzes und ihr Auftreten inQuarz porphyr vom Saubach i. V.: Zeit. Krist., 66, 239-282. 14. HONESS, A. P., (1927), The nature, origin, and interpretation of the etchfigure: John Wiley and Sons, New York. 15. HURLBUT, CORNELIUS S., JR., (1946), Influence of twinning on the usabilityof quartz: Am. Mineral., 31, 443-455. 16. INGERSON, EARL, (1947), Liquid inclusions in geologic thermometry, Am.Mineral., 32, 375-388. 17. IVANOV, N. A., AND SHAFRANOVSKY, I. I., (1938), Outward indications of theimportant twins of quartz: Soc. Russe Miner., Mem. 67, Iv. 3, 435-445. 18. JOHNSTON, W. D., JR., AND BUTLER, R. D., (1946), Quartz crystal in Brazil:Bull. Geol. Soc. Am., 57, 601-650. 19. KALB, G., (1933, 1935), Beiträge zur Kristallmorphologie des Quarzes: Zeit.Krist. 86, 439-465; 90, 163-186. 20. KERR, P. F., AND ERICHSEN, A. I., (1943), Origin of the quartz deposits atFazenda Pacú, Brazil: Am. Mineral., 27, 487-499. 21. KLOCKMAN, F., (1923), Lehrbuch der Mineralogie: Stuttgart. 22. LEWIS, W. J., (1899), A Treatise on Crystallography: Cambridge Univ. Press. 23. 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R., (1937), How to tell right-handed from left-handed quartzcrystals: Rocks and Minerals, 12, 38-43. 39. TROMMSDORF, WOLF, (1937), Das Verhältnis der Anzahl der Linksquarze zu der Rechtsquarze in einer grösseren Menge von Quarzkristallen: Neues. Jahrb. f. M.,P., P., ß. B., Abt. A, 462 495. 40. TUTTON, A. E. H., (1922), Crystallography and Practical Crystal Measurement,vol. 1, Form and Structure, MacMillan. 41. TWENHOFEL, W. S., (1947), The temperature of crystallization of a fluoritecrystal from Luna County, New Mexico: Ec. Geol., 42, 78-82. 42. VIROVLVANSKY, G. M., (1938a), Quartz as a geologic thermometer: Soc. RusseMiner, Mem. 67, Iv. 2, 236-246. 43. (1938b), On the question about the mirogenetic importance of vicinalfigures on the edges of quartz: Soc. Russe Miner., Mem.,., 67, Iv. 2, 446-450. 44. WILLARD, G. W., (1944), Use of the etch technique for determiningorientation and twinning in quartz crystals: Bell Sys. Tech. Jour., 23, 11-51. 45. WINCHELL, A. N., (1933), Elements of Optical Mineralogy, part II, John Wileyand and Sons, New York. 46. WRIGHT, F. E., AND LARSEN, E. S., (1909), Quartz as a geologic thermometer:Ana, Jour. Sci., 4th ser., 27, 421-447. 47. ZINSERLING, E. V., (1941), Quartz twinning control under alpha-betainversion; Quartz coloring as dependent on its twinning capacity underalpha-beta conversion; (and Laemmlein, G. G.) Conversion of a negative quartzrhombohedron into a positive one as a result: of alpha-beta transformation:Comple Rendu, Acad. Sci., U.S.S.R., 33, 365 368, 419. 48. ZIRKEL, F., (1897), Elemente der Mineralogie (Naumann), Leipzig. NOTES 1 Published by permission of the Director, U. S. Geological Survey. 2 The term low-quartz refers, in this paper, to low-temperature quartz, thatmodification of ten called alpha and occasionally called beta which is stable below573° C. 3 Symposium on quartz oscillator-plates, Am. Mineral., 30, 205-468, nos. 5 and 6(1945);also other numbers of the Am. Mineral.; see also Bell System Tech. Jour.;reports and information circulars from the Office of the Chief Signal Officer,War Department; bulletins of the Fort Monmouth (Long Branch) CrystalLaboratories. 4 Personal communication 5The writer is indebted to Mr. J. C. Wynn for the opportunity to study a set of100 unpublished drawings of phantom crystals from Brazil. Johnston's andButler's (1946) illustrations of phantoms are from this set. 6 The problem of asymmetry of apices and direction of flow of solutions does notenter into this discussion (Newhouse, 1941; Bandy, 1942; Engel, 1946). TheBrazilian. crystals apparently have retained the asymmetry of the"seed" crystal of the phantoms throughout the growth of the phantoms.
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