Introduction to Crystallography and Mineral Crystal Systems
by Mike and Darcy Howard

Part 5: The Orthorhombic System

Now we are ready to consider the Orthorhombic system. We again will start by examining the axial cross for this system. If you remember in Article 4, the tetragonal system, we held the a and b axes the same length (a1 and a2) and varied the length of the c axis. Well, in the orthorhombic system, we will continue the 90 degree angular relationships between all 3 axes, but will vary the length of each individual axis. Note that THE 3 AXES MUST BE UNEQUAL IN LENGTH. If any two are equal, then, by convention, we are discussing the tetragonal system.

In Figure 5.1, by current practice we orient any crystal in this system so that the length of c is greater than the length of a, which, in turn, is greater than the length of b. You will commonly find this in textbooks as "c<a<b".

There may also be 3 mirror symmetry planes, which must be at right angles to each other. But guess what! In the past, mineralogists have not always observed the axial length practice given here, and presently, the consensus is to conform when possible to the existing literature. This reason is why we will encounter some special orientation situations when dealing with certain common orthorhombic minerals.

When examining an orthorhombic crystal, we find that the highest obtainable symmetry is 2-fold. In a simple form, like the combination of the 3 pinacoids (open form), the crystal takes on an elongate, and often tabular appearance. These are typical forms to see expressed on barite and celestine.

The 3 pinacoids are at right angles to each other and usually the orientation of a given crystal to the axes is accomplished by an examination of the habit and any apparent cleavage. In topaz, the prominent pinacoidal cleavage is in the plane of the 2 shortest axes and perpendicular to the longest axis, so by convention, it is considered perpendicular to the c axis.

However, you will often encounter the situation where a given crystal displays a very prominent pinacoid and the crystal is tabular in form. In such a case, we then consider the c axis at right angle to the prominent pinacoid and the crystal is oriented as in Figure 5.2. This is a much different appearance than the example of topaz, noted in the paragraph above.

The orthorhombic system has 3 general symmetry classes, each expressed by its own Hermann-Mauguin notation.

Let's look at the forms designated by the symmetry 2/m2/m2/m. There are 3 of these (have you noticed that almost everything mentioned in this article is in 3's!): the pinacoid (also called the parallelohedron); the rhombic prism; and the rhombic dipyramid.

The pinacoid consists of 2 parallel faces, and can occur in the 3 different crystallographic orientations. These are the pair that intercept the c axis and are parallel to the a and b axes {001}; the pair that intercept the b axis and are parallel to the a and c axes {010}; and the pair that intercept the a axis and are parallel to the b and c axes {100}. They are called the c pinacoid, the b pinacoid, and the a pinacoid, respectively (fig. 5.3).

The rhombic prism, an open form, consists of 4 faces which are parallel to 1 axis and intersect the other two. There are 3 of these rhombic prisms and they are given by the general notational forms: {hk0}, which is parallel to the c axis; {h0l}, which is parallel to the b axis; and {0kl}, which is parallel to the a axis. Figure 5.4 a,b,c present the 3 rhombic prisms, each in combination with a corresponding pinacoidal form. Only the positive face of the rhombic prism is labeled in these examples.

5.4a Prism {110} and
pinacoid {001}
5.4b Prism {101} and
pinacoid {010}
5.4c Rhombic prism {011}
and pinacoid {100}

However, we may discover after examining a large number of different orthorhombic minerals that we see a large number of prism forms expressed on a single crystal, and these forms cannot be expressed with unity in their numbers because their intersects upon the horizontal axes are not proportionate to their unit lengths. This is where our general symbol notation comes in handy. In the old days of crystallography, these forms were designated as either macroprisms or bracyprisms, depending on whether h > k or k > h. A macroprism has the general symbol of {h0l} and a bracyprism has the general symbol of {hk0}.

5.5a Macro- Brachy- and
Basal Pinacoids
5.5b Prism and Basal Pinacoid 5.5c

With Figure 5.5, we have 3 sets of prisms expressed by the letter designations of m, l, and n, and a pinacoid face letter-designated as a.

The rhombic dipyramid is the last form to consider of this symmetry class. It is designated by the general form {hkl} and consists of 8 triangular faces, each of which intersects all 3 crystallographic axes. This pyramid may have several different appearances due to the variability of the axial lengths (figs. 5.6 a,b,c).

5.6a Rhombic dipyramid 5.6b 5.6c Sulfur crystal

A relatively large number of orthorhombic minerals are encountered with combinations of the various forms presented so far. These include andalusite, the members of the aragonite and barite group, brookite, chrysoberyl, the orthopyroxenes, goethite, marcasite, olivine, sillimanite, stibnite, sulfur, and topaz.

Next to consider are the few forms having the symmetry mm2 (termed the rhombic pyramidal). The two-fold rotational axis corresponds to the c crystallographic axis and the 2 mirror planes (at right angles to each other) intersect this axis. Due to the fact that no horizontal mirror plane exists, forms at the top and bottom of the crystal are different. Look at Figure 5.7a. Also, due to the lack of the horizontal mirror plane, there exists no prisms, but instead we have 2 domes in place of each of the prisms (do you remember that a dome consists of 2 faces that intersect each other, but have no corresponding parallel faces on the other end of the crystal?). Think of the minerals hemimorphite (fig. 5.7b), struvite (fig. 5.7c) or bertrandite when you think of this symmetry class.

5.7a Rhombic pyramid 5.7b Hemimorphite 5.7c Struvite

And now to the last (and the lowest) symmetry class of the orthorhombic system, the rhombic disphenoid.

The form has also been called the rhombic tetrahedron. It has the symmetry notation of 222, that is 3 axes of 2-fold rotation which correspond with the 3 crystallographic axes.

I'm sorry, but there is just no other symmetry here! The forms are, however, enantiomorphic, that is to say present as right and left images (fig. 5.8). These closed forms consist of 2 upper triangular faces which alternate with 2 lower triangular faces, the pair of upper faces being offset by 90 degrees in relation to the pair of lower faces.

Figure 5.9

Pinacoids and prisms may also exist in this class. The most common mineral in this crystal class is epsomite (fig. 5.9). Note that in Figure 5.9 the rhombic disphenoid is designated by the letter z and the unit prism by m.

Well, well. Now we have completed the orthorhombic system and we have looked at 3 (again a 3) of the 6 crystal systems! What do you think? I hope it has been interesting to read and consider the geometry of these crystal systems. It has been interesting for me to write about them. I think the artist began to get a little bored drawing all these figures, so started to use some color to liven things up a bit! I do like it.

This is the "hump" article as we have completed 5 of the 9 in the series. In fact, you might even consider it the 'center of symmetry' of the series and our journey. But so much for looking in the rearview mirror at where we've been, better to look and see where we are going - to that land where symmetry becomes less and less a factor! But before we go begin to lose more of our symmetry, I want to take a side road to the Hexagonal world, where we can look at all manner of items from either 3 or 6 directions in the next installment, Article 6.

Part 6: The Hexagonal System

Index to Crystallography and Mineral Crystal Systems

Table of Contents

Bob Keller