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Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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Bewley Lattice Diagram01:12

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Qualitative Analysis

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For solutions containing mixtures of different cations, the identity of each cation can be determined by qualitative analysis. This technique involves a series of selective precipitations with different chemical reagents, each reaction producing a characteristic precipitate for a specific group of cations. Metal ions within a group are further separated by varying the pH, heating the mixture to redissolve a precipitate, or adding other reagents to form complex ions.
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Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units.
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Related Experiment Video

Updated: Feb 10, 2026

Terahertz Microfluidic Sensing Using a Parallel-plate Waveguide Sensor
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Lattice Slot Waveguide for Terahertz Microfluidics Biomedical Trace Analysis.

Shui Liu1,2, Qi Xie1, Yongye Xia1

  • 1College of Electronic and Optical Engineering & College of Flexible Electronics (Future Technology), Nanjing University of Posts and Telecommunications, Nanjing, China.

Advanced Materials (Deerfield Beach, Fla.)
|February 9, 2026
PubMed
Summary

This study introduces a novel metasurface microfluidic chip for sensitive terahertz analysis of biomedical samples. The design enhances detection sensitivity and accuracy by minimizing signal loss and enabling simultaneous multi-polarization measurements.

Keywords:
biosensorslattice resonancemetasurfacemicrofluidicsterahertz spectroscopy

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Area of Science:

  • Terahertz (THz) spectroscopy
  • Metasurface technology
  • Microfluidics

Background:

  • Conventional metasurface resonators have limited sensitivity and Q-factor due to radiative leakage.
  • Water absorption noise complicates terahertz trace analysis of biomedical samples.
  • Existing platforms struggle with real-time, label-free analysis of volume-limited samples.

Purpose of the Study:

  • To develop a highly sensitive, real-time, label-free terahertz analysis platform for biomedical samples.
  • To overcome the limitations of conventional metasurface resonators by mitigating radiative loss.
  • To achieve enhanced sensitivity and Q-factor through a novel waveguide design.

Main Methods:

  • Design of a metal-insulator-metal (MIM) slot waveguide metasurface to confine terahertz energy.
  • Synergistic excitation of surface lattice resonance and guided mode resonance.
  • Development of an anisotropic detection strategy with a patterned lattice structure for polarization multiplexing.

Main Results:

  • Achieved a significantly enhanced Q-factor and sensitivity by confining energy within the microfluidic channel.
  • Demonstrated simultaneous polarization multiplexed responses with a figure of merit of 135.
  • Experimental validation showed a limit of detection of 625 pmol mL⁻¹ and a Q-factor of 189.

Conclusions:

  • The proposed metasurface microfluidic platform offers a unique approach for enhanced terahertz biomedical trace analysis.
  • The design effectively suppresses water absorption noise and mitigates radiative loss.
  • Multidimensional sensing capabilities provide a pathway for increased accuracy and efficiency in analyzing limited biological samples.