# The Unit Cell Essay

Custom Student Mr. Teacher ENG 1001-04 11 September 2016

## The Unit Cell

In the case of protein structures, the length of the lattice constants may be 100 A or higher. A crystal structure is generally described using the types, as well as locations of all the constituent atoms in the unit cell. Generally, one crystal structure may be comprised of at least 1 to 1,000 atoms. Figure 1. Lattice parameters a, b and c characterize a unit cell Parameters of an atom Atoms are generally described in terms of their positions in a lattice. The positions are featured with three crystallographic axes, namely a, b and c.

The lattice constants are employed as units, while the positions of the atoms are provided with fractional coordinates that are designated as x, y or z, which in turn are described by fractions of these lattice constants of a, b and c. The crystal structures All solid matter is comprised of a crystalline lattice, with is described as an orderly configuration of particles that are situated in three-dimensional space. The particles constituting the crystal lattice may be composed of atoms, or in some cases, molecules or ions. The unit cell thus pertains to the smallest segment of a lattice that is representative of the whole array.

The repetition of each unit cell in all three axes of the three-dimensional space thus creates the structure of a crystal lattice. Each unit cell is featured with crevices that have varying dimensions, depending on the type of the unit cell. The organization of the atoms of each unit cell is technically referred to as packing. The assumption that the shape of atom is usually spherical would generally result in a packaging configuration that contains spaces between each atom. The volume of each unit cell and the volume of the spherical atom are generally employed to calculate for the amount of space within a cube.

The total volume of the spherical structure is expected to account of the total number of atoms that are present in the unit cell. Packing of a crystal structure During the crystallization process of a solid matter, the constituent atoms or the ions of the structure are tightly placed together, leaving minimal space between each atom or ion. As ions are known to be charged particles, then it is possible for similarly charged ions to repel each other. On the other hand, oppositely charged ions may attract each other, resulting in a maximal degree of packing.

It is possible to generate different packing schemes for atoms and ions, especially when these structures are envisioned as spherical structures. It is thus possible to describe a packing scheme as to be comprised of multiple layers, with each layer designated as A, B and so forth. The resulting configuration is therefore a cube that is composed of eight spheres, with each cube being repeated several times. This configuration thus generated a cubic lattice, which is characterized by a significant amount of space around each sphere. Experimental methods 1.

Diffraction equipment X-ray diffraction was performed in this study using the Bruker D8 diffractometer system (Bruker AXS, Madison, WI, USA), which operates on a Debye-Scherrer geometry. The diffraction data was recovered using a 0. 15o angular resolution using a rotating anode CuK? radiation (? = 1. 5428 A) and set at a voltage of 40kV and running of 40mA current. Optimization of the equipment was initially performed using smaller structural materials, which generated diffraction data within the range of 10° < 2? < 120° (ca. 9 to 1 A d-spacing range).

The step size of approximately 0. 01–0. 02° was chosen for the collection of the data and the count time of s/step. The generated image was collected on a plate, or a charged coupled device (CCD) detection with a resolution pre-established from sample dimensions, as well as sample-detector distances. A liguid nitrogen cryostat Cryostream, equipped with a controller (Oxford Cryostreams Ltd. Hanborough Oxford OX29 8LN), a rotary vacuum pump, sample holder assembly and an impedance analyzer were also interface with a computer for data collection and subsequent analysis.

The appropriate measurement step was performed within the temperature range of 100 to 500 Kelvin, resulting in the collection of lattice parameters that would best estimate the thermal expansion values. The initial data that was collection from the study was performed using 100 K, followed by 110 K and subsequent increments of 10 K, until the temperature reached 500 K. Approximately 20 minutes was required in order to collect the data for each temperature point. Parameters were followed in order to ensure that the geometrical features of the crystal structure were reliable.

More importantly, the geometrical features were determined to be reproducible, as well as interpretable in term of line shapes. Power samples are usually delicate to handle and may require high levels of resolution. X-ray crystallization is also advantageous when dealing with minute quantities of matter, especially those that could only be handled through capillaries. In order to employ an external standard for the study, silicon was included in the experiment. The quantity of the sample was regulated at a small amount so that any sample size complications, as well as effects would be avoided.

In addition, larger samples may require larger time delays, especially during equilibration, thus slowing the entire process of heat diffusion. The XPRD data patterns were subjected to further analysis using the Bruker EVA software. Sample preparation Copper. The objective of this study was to understand the principles behind heat diffusion and thermal equilibrium, as well as to measure the parameters associated with the expansion of copper during heating. The study also aims to calculate for the coefficient values associated with the expansion of the volume of copper during heating.

The sample studied in this experiment was pure copper powder (99. 99% Cu), which was loaded onto a 0. 3 mm diameter thin-walled quartz capillary tube. The parameters of the lattice were determined through the collected measurements of the reflections generated from the Bragg angle region. The capillary glass was then sealed in order to prevent transformation into gas. The tube was then attached to the goniometry head of the diffractometer for viewing in the x, y and z axes. The detector would read the beam released by the diffractometer, resulting in a high-resolution data of the unit cell.

Paracetamol form I. Paracetamol form I was melted on a LTS 350 Linkman Hot Stage Unit, set at 180? and then drawn into the capillary tube of 0. 7 mm thickness. This was then left cool to a temperature of 160? for subsequent crystallization. The sample was then placed in the XRPD Bruker D8 diffractometer system (Bruker AXS, Madison, WI, USA) for diffraction. Paracetamol Form II. Paracetamol form II was prepared by melting on a LTS 350 Linkman Hot Stage Unit and then drawing this into the capillary tube of 0. 7 mm thickness. This was left to cool and crystallize.

For both paracetamol forms I and II were subjected to XRPD pattern analysis using a Bruker D8 diffractometer system (Bruker AXS, Madison, WI, USA). This system operated in a Debye-Scherrer geometry with a wavelength (? ) of 1. 54059A and running of 40kV voltage, and a current of 40mA. The sample was heated using a Cryostream plus controller (Oxford Cryostreams Ltd. Hanborough Oxford OX29 8LN) from temperatures 100K to 540K and subsequently subjected for pattern collection at each temperature step, with a scan speed of 0. 02 second.

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• University/College: University of Chicago

• Type of paper: Thesis/Dissertation Chapter

• Date: 11 September 2016

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