GEOLOGY Module: Twinning and Twin Laws

GEOLOGY

Paper: Crystallography and Mineralogy

Module: Twinning and Twin Laws

Subject Geology

Paper No and Title Crystallography and Mineralogy

Module No and Title Twinning and Twin Laws

Module Tag Min IIb

Principal Investigator Co-Principal Investigator Co-Principal Investigator

Prof. Talat Ahmad

Vice-Chancellor

Jamia Millia Islamia

Delhi

Prof. Devesh K Sinha

Department of Geology

University of Delhi

Delhi

Prof. P. P. Chakraborty


University of Delhi

Delhi

Paper Coordinator Content Writer Reviewer

Prof. Naresh C. Pant


University of Delhi

Delhi

Prof. Naresh C. Pant


University of Delhi

Delhi

Prof. Santosh Kumar


Kumaun University

Nainital

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Table of Content

1. Learning outcomes

2. Introduction

3. Type of twins

3.1. Growth of twins

3.2. Annealing or Transformations twins

3.3. Deformation or Gliding twins

4. Twin Classification

4.1. Contact Twins

4.2. Penetration Twins

4.3. Repeated, or multiple Twins

4.4. Polysynthetic Twin

4.5. Cyclic Twin

5. Twin Laws

5.1. Triclinic System

5.2. Monoclinic System

5.3. Orthorhombic System

5.4. Tetragonal System

5.5. Hexagonal System

5.6. Isometric System

6. Summary

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1. Learning outcomes

After studying this module, you shall be able to:

Learn about the intergrowths of crystals.

Understand the twin classification.

Understand the common twin laws in different crystallographic system.

2. Introduction

A crystal is by definition has a regular internal atomic arrangement of constituent

atoms/molecules/ions in such a way that the regular internal arrangement can be

produced by 'infinite' repetition of a small unit or unit cell. Crystal growth occurs as it

represents a lower energy state then the preceding disordered state. The growth of a

crystal consists of addition of new atoms or ions into the characteristic arrangement of

a crystalline lattice. During the growth of a mineral, offsets may occur in the atomic

arrangement leading to the development of intergrowth patterns of well-formed

crystals. After a nucleus has reached a critical size, generally on account of rapid

deposition of layers of ions on the nucleated crystal, it has higher chances of survival

and growth. However, it is important to note that the growth rate is non-uniform in

crystals and is a function of density of lattice points. The Law of Bravais states that

those crystal faces are most likely to form which are parallel to lattice planes having

high density of lattice points. The larger the number of modes a given face intersects

more is the frequency of that face in the crystal. Twinning refers to the offsets of the

atomic arrangements in the crystal structure, which are non-random.

A type of non-random, crystallographically oriented growth of one crystalline

substance on another of different composition is known as epitaxis. The plane of

contact of two different crystalline substance which are having different internal

structures are known as boundaries and the similarity in substrate reduces the energy

required for nucleation, resulting the preferential overgrowth. For example, the

overgrowth of kyanite over staurolite with the (010) plane of staurolite parallel to the

(100) plane of kyanite. This occurs because the atomic spacing of the (010) plane in

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staurolite is similar to that of the (100) plane in kyanite. In this case, staurolite is a

monoclinic crystal while kyanite crystallizes in the triclinic system.

Twins and twinned crystals and parallel growths refer to the non-random growth of

same composition substance. Twinning is a crystallographically controlled

intergrowth (of the same composition) which is in form of a rational and

symmetrical intergrowth. The term rational and symmetrical, imply that lattice

direction of one crystal bear a definite crystallographic relation to the lattice

direction of the other crystals in twin relation with it. Twinning can be considered as

a type of planar defect.

Fig. 1 Examples of epitaxis. Parallel growth of staurolite and kyanite. (From Kern,

R., and R. Gindt. 1958. Bulletin Societe Francaise Min. Cryst., 81:264.).

3. Type of twins

3.1. Growth twins are the result of an emplacement of atoms, or ions (or groups

of atoms or ions) on the outside of a growing crystal in such a way that the

regular arrangement of the original crystal structure is interrupted. The two

or more individual crystals of the twinned aggregate are related by a

symmetry element that is absent in the original (untwined) crystal. Twinning

in the lower symmetry groups generally produces a resulting aggregate

symmetry higher than that of each individual because the twin planes, or

twin axis, are added symmetry elements. The operations that relate a crystal

to its twinned counterpart are symmetry operations:(1) reflection by a mirror

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plane, twin plane; (2) rotation about a crystal direction, common to both,

twin axis, with angular rotation normally 180˚; and (3) inversion about a

point, twin center.

3.2. Annealing or Transformation twins results when crystal structures become

unstable during cooling and reorganize or transform into more stable forms

by generation of crystallographically related forms or twins.

3.3. Deformation or Gliding twins form due to the stress a crystal experiences

after its formation. These are common in metamorphic rocks.

4. Twin Classification

4.1. Contact Twins: They have a regular composition surface separating the two

individuals.

Fig. 2 (a) Octahedron with possible twin plane b-b(̄1̄11). This is one of four

octahedral directions in the form {111}. (b) Octahedral twinning (111) as shown

by spinel. (c) Right-and left-handed quartz crystals twinned according to the

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Japan twin law; (d) Two interpenetrating cubes of fluorite twinned on [111] as

the twin axis; (e) Two pyritohedral crystals forming an iron cross, with twin axis

[001]; (f) Orthoclase exhibiting the Carlsbad twin law in which two

interpenetrating crystals are twinned by 180˚ rotation about the c-axis, [001]

direction. The schematic cross section, parallel to (010), reveals the presence of

the two-fold twin axis along [001]. (Source: Klein, C., Dutrow, B.D. and James

Dwight, K., 2008. The 23rd edition of the manual of mineral science (after

James D. Dana)).

4.2. Penetration Twins: These are made up of interpenetrating individuals

having an irregular composition surface, and the twin law is usually defined

by a twin axis direction.

4.3. Repeated, or multiple Twins: It consists of three or more individual

crystals twinned according to the same law.

4.4. Polysynthetic Twin: If all the composition surfaces are parallel, the

resulting group is a polysynthetic twin. When a large numbers of individuals

in a polysynthetic twin are closely spaced, crystal faces or cleavages crossing

the composition planes show striations because of the reversed positions of

adjacent individuals.

4.5. Cyclic Twin: In a multiple twin, if successive composition planes are not

parallel, then it results in cyclic twin. It is common in aragonite and rutile.

Fig. 3 (a) Albite polysynthetically twinned on {010}. (b) Cyclic twin in

chrysoberyl with the twin planes parallel to faces of the form {031}. (c)

Cyclic twin in rutile with the twin planes parallel to faces of the form {011}.

(Source: Klein, C., Dutrow, B.D. and James Dwight, K., 2008. The 23rd

edition of the manual of mineral science (after James D. Dana)).

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5. Twin Laws

5.1. Triclinic System: Example: Feldspars and microcline.

Albite Law: The feldspars are twinned according to the albite law, along the

{010} plane. It is so common that it acts as a diagnostic property for

identification of feldspars. (See figure 3(a))

Perciline Law: When the triclinic feldspars twin along [010], the twin axis.

When albite and pericline twins are closely interwoven, as frequently occurs

in microcline, a typical crosshatched or “tartan” pattern is seen. Pericline

twinning generally occurs in combination with the albite twinning in

microcline.

5.2. Monoclinic System: Example: K-feldspars and sanidine.

Manebach Law: Contact twin occurring at {001} in alkali feldspar. Acts as

a diagnostic property.

Swallow-tail twin law: The twin plane is at {100} and commonly found in

gypsum.

Baveno twin law: The twin plane is at {021} and commonly occurs in K-

feldspars.

Carlsbad twin law: Twinning in K-feldspars in which the c-axis, [001] is

the twin element. It acts as a diagnostic property under polarizing

microscope for K feldspars.

Fig. 4 Twin laws of Monoclinic system. (Source: Klein, C., Dutrow, B.D.

and James Dwight, K., 2008. The 23rd edition of the manual of mineral

science (after James D. Dana)).

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5.3. Orthorhombic System: The twin plane is commonly parallel to a prism

face. The most common is a {100} twin that results in many orthorhombic

minerals having cyclical twins.

Cyclical Twin law: This is commonly found in aragonite, chrysoberyl and

cerrusite. The pseudo hexagonal appearance is due to twinning on {110}

plane. Staurolite law: Although staurolite is a monoclinic mineral, the β-

angle closeness to 90˚ gives it a look of that of an orthorhombic mineral and

hence it is also called pseudo- orthorhombic. It commonly displays two types

of penetration twins, in one, the {031} is the twin plane, resulting in a 90˚

cross, while in other the twin plane is {231}, resulting in a 60˚ cross.

Fig. 5 (a) Contact or cyclic twinning in aragonite, (b) Staurolite twinned on

{031} and {231}. (Source: Klein, C., Dutrow, B.D. and James Dwight, K.,

2008. The 23rd edition of the manual of mineral science (after James D.

Dana)).

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5.4. Tetragonal System: The common type of twin in the tetragonal system at the

{011} as twin plane. Crystals of cassiterite and rutile follow this twin law.

Fig. 6 Examples of common twin in tetragonal crystals.

5.5. Hexagonal System: Examples: Calcite and Quartz.

Calcite Twins: The twin planes are at {0001} and {01̄12}. Both are contact

twins.

Brazil Law: {11̄20} is a penetration twin that results from transformation.

Mostly observed in quartz.

Dauphine Law: [0001] is also a penetration twin and occurs due to

transformation.

Japan Law: {11̄22} is a contact twin, which is the result from accidents

during growth.

Fig. 7 Examples of twin laws from Hexagonal system. (Source: Klein, C.,

Dutrow, B.D. and James Dwight, K., 2008. The 23rd edition of the manual of

mineral science (after James D. Dana)).

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5.6. Isometric System: The twin plane is parallel to a face of the octahedron.

Spinel Law: {̄1̄11} it is a twin plane parallel to an octahedron. Commonly

occurs in spinel. [111] twin axis is perpendicular to an octahedral face and

adds three fold symmetry.

Iron Cross Law: It is often shown by pyrite in which a cross forms due to

interpenetration of two pyritohedrons at the twin axis [001].

Fig. 8 Examples of twin laws from Hexagonal system. (Source: Klein, C.,

Dutrow, B.D. and James Dwight, K., 2008. The 23rd edition of the manual of

mineral science (after James D. Dana)).

6. Summary

Thus, we see that twinning is a crystallographically related intergrowth of same

composition minerals and is generally a crystal growth phenomenon though it can

also occur during cooling as annealing or transformation twins or post formation as

deformation twins. In growth, twinning it represents an accident in growth. There

are several types of twins such as contact twins, penetration twins, multiple twins or

polysynthetic twins. Different crystal systems have different types of twins and these

are represented in form of twin laws. Many of the twins are useful as a diagnostic

property of the mineral under microscope.

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Frequently Asked Questions-

Q1. What is twinning?

Q2. Differentiate between cyclic twins and penetration twins?

Q3. Explain the different types of twin laws of Isometric system?

Q4. How iron cross twin is formed?

Multiple Choice Questions-

1. Penetration twinning is shown by

(a) Spinel

(b) Fluorite

(c) Quartz

(d) Gypsum

Ans: b

2. Twinning is a type of defect

(a) Point defect

(b) Line defect

(c) Planar defect

(d) Other defect

Ans: c

3. Which mineral follows twin law of tetragonal system

(a) Rutile

(b) Quartz

(c) Spinel

(d) None of the above

Ans: a

4. Cyclic twin is shown by

(a) Quartz

(b) Spinel

(c) Pyrite

(d) Chrysoberyl

Ans: d

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5. Which is not a twin law of Monoclinic System

(a) Manebach law

(b) Japan law

(c) Baveno law

(d) Carlsbad law

Ans: b

Suggested Readings:

1. Klien, Cornelis and Dutrow, Barbara, (2008). Manual of Mineral Sciences

(Manual of Mineralogy), 23rd Edn. John Wiley & Sons, New York. ISBN:

0471721573, 978-0471721574.

2. Putnis Andrew (1992), An Introduction to Mineral Sciences, 1st Edn.,

Cambridge University Press, UK. ISBN: 0521429471, 978-0521429474.

GEOLOGY Module: Twinning and Twin Laws

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