# Hexagonal (hP)#

## Atom arrangement#

Figure 1: Hexagonal lattice structure. X, Y, and Z crystal frame axes are colored red, green, and blue, respectively.

## Slip systems#

 index slip direction plane normal $$1$$ $$[2 \bar 1 \bar 1 0]$$ $$(0 0 0 1)$$ $$2$$ $$[\bar 1 2 \bar 1 0]$$ $$(0 0 0 1)$$ $$3$$ $$[\bar 1 \bar 1 2 0]$$ $$(0 0 0 1)$$
 index slip direction plane normal $$4$$ $$[2 \bar 1 \bar 1 0]$$ $$(0 \bar 1 \bar 1 0)$$ $$5$$ $$[\bar 1 2 \bar 1 0]$$ $$(\bar 1 0 0 1)$$ $$6$$ $$[\bar 1 \bar 1 2 0]$$ $$(1 \bar 1 0 0)$$
 index slip direction plane normal $$7$$ $$[2 \bar 1 \bar 1 0]$$ $$(0 1 \bar 1 1)$$ $$8$$ $$[\bar 1 2 \bar 1 0]$$ $$(\bar 1 0 1 1)$$ $$9$$ $$[\bar 1 \bar 1 2 0]$$ $$(1 \bar 1 0 1)$$ $$10$$ $$[1 1 \bar 2 0]$$ $$(\bar 1 1 0 1)$$ $$11$$ $$[\bar 2 1 1 0]$$ $$(0 \bar 1 1 1)$$ $$12$$ $$[1 \bar 2 1 0]$$ $$(1 0 \bar 1 1)$$
 index slip direction plane normal $$13$$ $$[2 \bar 1 \bar 1 3]$$ $$(\bar 1 1 0 1)$$ $$14$$ $$[\bar 1 2 \bar 1 3]$$ $$(\bar 1 1 0 1)$$ $$15$$ $$[\bar 1 \bar 1 2 3]$$ $$(1 0 \bar 1 1)$$ $$16$$ $$[\bar 2 1 1 3]$$ $$(1 0 \bar 1 1)$$ $$17$$ $$[\bar 1 2 \bar 1 3]$$ $$(0 1 \bar 1 1)$$ $$18$$ $$[1 1 \bar 2 3]$$ $$(0 \bar 1 1 1)$$ $$19$$ $$[2 \bar 1 \bar 1 3]$$ $$(1 \bar 1 0 1)$$ $$20$$ $$[\bar 1 2 \bar 1 3]$$ $$(1 \bar 1 0 1)$$ $$21$$ $$[1 1 \bar 2 3]$$ $$(\bar 1 0 1 1)$$ $$22$$ $$[2 \bar 1 \bar 1 3]$$ $$(\bar 1 0 1 1)$$ $$23$$ $$[1 \bar 2 1 3]$$ $$(0 1 \bar 1 1)$$ $$24$$ $$[\bar 1 \bar 1 2 3]$$ $$(0 1 \bar 1 1)$$
 index slip direction plane normal $$25$$ $$[2 \bar 1 \bar 1 3]$$ $$(\bar 2 1 1 2)$$ $$26$$ $$[\bar 1 2 \bar 1 3]$$ $$(1 \bar 2 1 2)$$ $$27$$ $$[\bar 1 \bar 1 2 3]$$ $$(1 1 \bar 2 2)$$ $$28$$ $$[\bar 2 1 1 3]$$ $$(2 \bar 1 \bar 1 2)$$ $$29$$ $$[1 \bar 2 1 3]$$ $$(\bar 1 2 \bar 1 2)$$ $$30$$ $$[1 1 \bar 2 3]$$ $$(\bar 1 \bar 1 2 2)$$

## Twin systems#

 $$η_1$$ $$K_1$$ $$η_2$$ $$K_2$$ $$⟨\bar 1 0 1 1⟩$$ $$\{1 0 \bar 1 2\}$$ $$⟨1 0 \bar 1 1⟩$$ $$\{1 0 \bar 1 \bar 2\}$$
 index slip direction plane normal $$1$$ $$[1 \bar 1 0 1]$$ $$(\bar 1 1 0 2)$$ $$2$$ $$[\bar 1 0 1 1]$$ $$(1 0 \bar 1 2)$$ $$3$$ $$[0 1 \bar 1 1]$$ $$(0 \bar 1 1 2)$$ $$4$$ $$[\bar 1 1 0 1]$$ $$(1 \bar 1 0 2)$$ $$5$$ $$[1 0 \bar 1 1]$$ $$(\bar 1 0 1 2)$$ $$6$$ $$[0 \bar 1 1 1]$$ $$(0 1 \bar 1 2)$$
 $$η_1$$ $$K_1$$ $$η_2$$ $$K_2$$ $$⟨\bar 1 \bar 1 2 6⟩$$ $$\{1 1 \bar 2 1\}$$ $$⟨1 1 2 0⟩$$ $$\{0 0 0 2\}$$
 index slip direction plane normal $$7$$ $$[2 \bar 1 \bar 1 6]$$ $$(\bar 2 1 1 1)$$ $$8$$ $$[\bar 1 2 \bar 1 6]$$ $$(1 1 \bar 2 1)$$ $$9$$ $$[\bar 1 \bar 1 2 6]$$ $$(2 \bar 1 \bar 1 1)$$ $$10$$ $$[\bar 2 1 1 6]$$ $$(\bar 1 2 \bar 1 1)$$ $$11$$ $$[1 \bar 2 1 6]$$ $$(\bar 1 0 1 2)$$ $$12$$ $$[1 1 \bar 2 6]$$ $$(\bar 1 \bar 1 2 1)$$
 $$η_1$$ $$K_1$$ $$η_2$$ $$K_2$$ $$⟨1 0 \bar 1 \bar 2⟩$$ $$\{1 0 \bar 1 1\}$$ $$⟨3 0 \bar 3 2⟩$$ $$\{1 0 \bar 1 \bar 3\}$$
 index slip direction plane normal $$13$$ $$[\bar 1 1 0 \bar 2]$$ $$(\bar 1 1 0 1)$$ $$14$$ $$[1 0 \bar 1 \bar 2]$$ $$(1 0 \bar 1 1)$$ $$15$$ $$[0 \bar 1 1 \bar 2]$$ $$(0 \bar 1 1 1)$$ $$16$$ $$[1 \bar 1 0 \bar 2]$$ $$(1 \bar 1 0 1)$$ $$17$$ $$[\bar 1 0 1 \bar 2]$$ $$(\bar 1 0 1 1)$$ $$18$$ $$[0 1 \bar 1 \bar 2]$$ $$(0 1 \bar 1 1)$$
 $$η_1$$ $$K_1$$ $$η_2$$ $$K_2$$ $$⟨1 1 \bar 2 \bar 3⟩$$ $$\{1 1 \bar 2 2\}$$ $$⟨2 2 \bar 4 3⟩$$ $$\{1 1 \bar 2 \bar 4\}$$
 index slip direction plane normal $$19$$ $$[2 \bar 1 \bar 1 \bar 3]$$ $$(2 \bar 1 \bar 1 2)$$ $$20$$ $$[\bar 1 2 \bar 1 \bar 3]$$ $$(\bar 1 2 \bar 1 2)$$ $$21$$ $$[\bar 1 \bar 1 2 \bar 3]$$ $$(\bar 1 \bar 1 2 2)$$ $$22$$ $$[\bar 2 1 1 \bar 3]$$ $$(\bar 2 1 1 2)$$ $$23$$ $$[1 \bar 2 1 \bar 3]$$ $$(1 \bar 2 1 2)$$ $$24$$ $$[1 1 \bar 2 \bar 3]$$ $$(1 1 \bar 2 2)$$

## Interaction Matrices#

### Slip-Slip#

 index label description $$1$$ $$S1$$ basal self-interaction $$2$$ $$1$$ basal/basal coplanar $$3$$ $$3$$ basal/prismatic collinear $$4$$ $$4$$ basal/prismatic non-collinear $$5$$ $$S2$$ prismatic self-interaction $$6$$ $$2$$ prismatic/prismatic $$7$$ $$5$$ prismatic/basal collinear $$8$$ $$6$$ prismatic/basal non-collinear $$9$$ $$-$$ basal/pyramidal $$\langle a \rangle$$ non-collinear $$10$$ $$-$$ basal/pyramidal $$\langle a \rangle$$ collinear $$11$$ $$-$$ prismatic/pyramidal $$\langle a \rangle$$ non-collinear $$12$$ $$-$$ prismatic/pyramidal $$\langle a \rangle$$ collinear $$13$$ $$-$$ pyramidal $$\langle a \rangle$$ self-interaction $$14$$ $$-$$ pyramidal $$\langle a \rangle$$ non-collinear $$15$$ $$-$$ pyramidal $$\langle a \rangle$$ collinear $$16$$ $$-$$ pyramidal $$\langle a \rangle$$/prismatic non-collinear $$17$$ $$-$$ pyramidal $$\langle a \rangle$$/prismatic collinear $$18$$ $$-$$ pyramidal $$\langle a \rangle$$/basal non-collinear $$19$$ $$-$$ pyramidal $$\langle a \rangle$$/basal collinear $$20$$ $$-$$ basal/1. order pyramidal $$\langle c+a \rangle$$ semi-collinear $$21$$ $$-$$ basal/1. order pyramidal $$\langle c+a \rangle$$ $$22$$ $$-$$ basal/1. order pyramidal $$\langle c+a \rangle$$ $$23$$ $$-$$ prismatic/1. order pyramidal $$\langle c+a \rangle$$ semi-collinear $$24$$ $$-$$ prismatic/1. order pyramidal $$\langle c+a \rangle$$ $$25$$ $$-$$ prismatic/1. order pyramidal $$\langle c+a \rangle$$ semi-coplanar? $$26$$ $$-$$ pyramidal /1. order pyramidal $$\langle c+a \rangle$$ coplanar $$27$$ $$-$$ pyramidal /1. order pyramidal $$\langle c+a \rangle$$ $$28$$ $$-$$ pyramidal /1. order pyramidal $$\langle c+a \rangle$$ semi-collinear $$29$$ $$-$$ pyramidal /1. order pyramidal $$\langle c+a \rangle$$ semi-coplanar $$30$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$ self-interaction $$31$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$ coplanar $$32$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$ $$33$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$ $$34$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$ semi-coplanar $$35$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$ semi-coplanar $$36$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$ collinear $$37$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$/pyramidal coplanar $$38$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$/pyramidal semi-collinear $$39$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$/pyramidal $$40$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$/pyramidal semi-coplanar $$41$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$/prismatic semi-collinear $$42$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$/prismatic semi-coplanar $$43$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$/prismatic $$44$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$/basal semi-collinear $$45$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$/basal $$46$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$/basal $$47$$ $$8$$ basal/2. order pyramidal $$\langle c+a \rangle$$ non-collinear $$48$$ $$7$$ basal/2. order pyramidal $$\langle c+a \rangle$$ semi-collinear $$49$$ $$10$$ prismatic/2. order pyramidal $$\langle c+a \rangle$$ $$50$$ $$9$$ prismatic/2. order pyramidal $$\langle c+a \rangle$$ semi-collinear $$51$$ $$-$$ pyramidal /2. order pyramidal $$\langle c+a \rangle$$ $$52$$ $$-$$ pyramidal /2. order pyramidal $$\langle c+a \rangle$$ semi collinear $$53$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$/2. order pyramidal $$\langle c+a \rangle$$ $$54$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$/2. order pyramidal $$\langle c+a \rangle$$ $$55$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$/2. order pyramidal $$\langle c+a \rangle$$ $$56$$ $$-$$ 1. order pyramidal $$\langle c+a \rangle$$/2. order pyramidal $$\langle c+a \rangle$$ collinear $$57$$ $$S3$$ 2. order pyramidal $$\langle c+a \rangle$$ self-interaction $$58$$ $$16$$ 2. order pyramidal $$\langle c+a \rangle$$ non-collinear $$59$$ $$15$$ 2. order pyramidal $$\langle c+a \rangle$$ semi-collinear $$60$$ $$-$$ 2. order pyramidal $$\langle c+a \rangle$$/1. order pyramidal $$\langle c+a \rangle$$ $$61$$ $$-$$ 2. order pyramidal $$\langle c+a \rangle$$/1. order pyramidal $$\langle c+a \rangle$$ collinear $$62$$ $$-$$ 2. order pyramidal $$\langle c+a \rangle$$/1. order pyramidal $$\langle c+a \rangle$$ $$63$$ $$-$$ 2. order pyramidal $$\langle c+a \rangle$$/1. order pyramidal $$\langle c+a \rangle$$ $$64$$ $$-$$ 2. order pyramidal $$\langle c+a \rangle$$/pyramidal non-collinear $$65$$ $$-$$ 2. order pyramidal $$\langle c+a \rangle$$/pyramidal semi-collinear $$66$$ $$14$$ 2. order pyramidal $$\langle c+a \rangle$$/prismatic non-collinear $$67$$ $$13$$ 2. order pyramidal $$\langle c+a \rangle$$/prismatic semi-collinear $$68$$ $$12$$ 2. order pyramidal $$\langle c+a \rangle$$/basal non-collinear $$69$$ $$11$$ 2. order pyramidal $$\langle c+a \rangle$$/basal semi-collinear
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